{"text": "We present the Dark-ages Reionization and Galaxy-formation Observables from Numerical Simulations (DRAGONS) program and Tiamat, the collisionless N-body simulation program upon which DRAGONS is built. The primary trait distinguishing Tiamat from other large simulation programs is its density of outputs at high redshift (100 from z=35 to z=5; roughly one every 10 Myrs) enabling the construction of very accurate merger trees at an epoch when galaxy formation is rapid and mergers extremely frequent. We find that the friends-of-friends halo mass function agrees well with the prediction of [Watson:2013p2555] at high masses, but deviates at low masses, perhaps due to our use of a different halo finder or perhaps indicating a break from universal behaviour. We then analyse the dynamical evolution of galaxies during the Epoch of Reionization finding that only a small fraction (~20%) of galactic halos are relaxed."}
{"text": "We illustrate this using standard relaxation metrics to establish two dynamical recovery time-scales: i) halos need ~1.5 dynamical times following formation, and ii) ~2 dynamical times following a major (3:1) or minor (10:1) merger to be relaxed. This is remarkably consistent across a wide mass range. Lastly, we use a phase-space halo finder to illustrate that major mergers drive long-lived massive phase-space structures which take many dynamical times to dissipate. This can yield significant differences in the inferred mass build-up of galactic halos and we suggest that care must be taken to ensure a physically meaningful match between the galaxy-formation physics of semi-analytic models and the halo finders supplying their input."}
{"text": "Following cosmological recombination the baryonic gas filling the Universe became predominantly neutral. The fact that this gas is known to be mostly ionized today [Gunn:1965p2569] implies that the intergalactic medium (IGM) under went a significant reionization event at some early point in its history. This fact is responsible for some of the major questions in extragalactic astronomy including: when did this process occur and what were the responsible ionizing sources? Recent observations have begun to provide preliminary answers to this question [Fan:2006p2573, Ouchi:2010p2575, PlanckCollaboration:2015p2562]. Soon measurements of highly redshifted 21-cm radio emission [Furlanetto:2006p2567, Morales:2010p2568] will open an important new observational window for study of the first galaxies, providing the first direct probe of the neutral hydrogen content in the early Universe."}
{"text": "The development of theoretical models that self-consistently include the physics of galaxy formation and intergalactic hydrogen will play a key role in understanding the nature of the first galaxies and in interpreting these observations. This paper is the first in a series describing the Dark-ages Reionization and Galaxy-formation Observables from Numerical Simulations (DRAGONS) project which aims to integrate detailed semi-analytic models constructed specifically to study galaxy formation at high redshift, with semi-numerical models of the galaxy–IGM interaction [Zahn:2007p2570, Mesinger:2007p2571, Geil:2008p2572]. The galaxy-formation modelling for DRAGONS is implemented using a set of large N-body simulations which we refer to as the Tiamat simulation suite. Tiamat provides a framework within which to implement a semi-analytic model for reionization and to study the formation histories, structure and properties of the dark matter halos that dictate the formation sites and assembly histories of the first galaxies."}
{"text": "Over the past decade the requirements for simulations aiming to address the structure of reionization and galaxy formation in the Epoch of Reionization (EoR) have been studied extensively. The consensus from previous N-body studies [Iliev:2007p2581, Zahn:2007p2570, McQuinn:2007p2582, Shin:2008p2583, Lee:2008p2584, Croft:2008p2585] and analytic models [Furlanetto:2004p2578, Wyithe:2007p2579, Barkana:2009p2580] is that large-scale over-dense regions near bright sources ionize first with clustered neighbouring sources contributing to increase the size of ionised regions. Simulations on the scale of 100 Mpc are found to be large enough to correctly capture the structure and duration of reionization, although volumes up to 500^3 Mpc are required to capture all large scale power due to clustering of HII regions [Iliev:2014p2577]. The challenge is to model galaxy formation in volumes of this size with sufficient resolution."}
{"text": "In the cold neutral IGM prior to reionization, molecular cooling may proceed within minihalos with masses ~10^6 solar masses. However, the processes principally responsible for regulating galaxy formation are expected to be active in halos with virial temperatures greater than T_min ~ 10^4 K, above which atomic hydrogen cooling becomes efficient. On the other hand, the growth of HII regions during reionization is also expected to be influenced by radiative feedback due to suppression of galaxy formation below the cosmological Jeans mass within a heated IGM [Dijkstra:2004p2576]. Together these constraints indicate that sufficient resolution is required to identify halo masses down to ~5x10^7 solar masses within a volume of ~100 Mpc. In addition to this dynamic range of scales, for the DRAGONS program we aim to accurately resolve the relevant time-scales of high-redshift galaxy formation putting an additional constraint on the cadence with which simulation outputs must be generated."}
{"text": "At z~6 the dynamical time of a galactic disc falls below the lifetime of the least massive Type-II supernova progenitor (~4x10^7 yr). As a result, snapshots with a cadence of ~10^7 years are required to follow galaxy formation correctly during the EoR with a semi-analytic model. This interval is an order of magnitude shorter than needed to describe galaxy formation at redshifts z~0. In this paper we present the Tiamat suite of collisionless N-body simulations which we have run to satisfy these requirements and upon which the DRAGONS program will be constructed. Given its critical importance as the foundation of the program, we take this opportunity to present the methodology of constructing this set of simulations and to characterise the populations of galactic halos obtained. In particular, we shall carefully examine the dynamical evolution of galactic halos during the reionization era."}
{"text": "We seek this understanding because of its potential impact on the structure of galactic halos, which is of fundamental importance to the physics of galaxy formation at any epoch, including the EoR. In particular, halo concentrations and angular momenta are generally believed to dictate the size and surface density of the disc-like structures in which the majority of star formation occurs. Dynamical disturbances can additionally drive starbursts or affect the stability of these disc-like structures, strongly affecting star formation and forcing morphological transformations which contribute to the assembly of galactic spheroids. This can in turn affect observable galaxy sizes or alter UV fluxes and escape fractions with important effects on the reionization history of the Universe. At low redshift, it has been shown that a halo's dynamical state can systematically affect the structure and gravitational potential of galactic halos [Thomas:1998p2559, Neto:2007p2556, Power:2012p2560, Ludlow:2014p2558]."}
{"text": "These studies have collectively established a set of criteria (which we refer to henceforth as standard relaxation criteria) capable (at low redshifts at least) of separating halos with disturbed structure from those with relaxed structure. These standard criteria consist of cuts on three metrics for each halo: the separation of its dense centre from its centre of mass (x_off), its pseudo-virial ratio constructed from its velocity dispersion and gravitational binding energy (T/|U|), and its substructure fraction (f_sub). When low-redshift halos are separated into relaxed and unrelaxed samples in this way, substantial effects on halo concentration and (to a lesser extent) spin have been demonstrated. This is of particular importance to studies which aim to understand the processes which establish the universal density profiles of halos extracted from collisionless N-body simulations [Navarro:1997p2543]. While there is broad agreement at low redshift as to the dependance of halo structure on mass, redshift and dynamical state, recent studies which have attempted to push this understanding to the EoR [Prada:2012p2538, Diemer:2015p2657, Dutton:2014p2658, Hellwing:2015p2659] have found less consensus."}
{"text": "At high redshifts where simulations predict that merger rates are very high, halos significantly less concentrated, and merger orbital properties quite different, the influence of dynamical state on halo structure may differ from local trends. It is unclear to what degree dynamical disturbance may play a role in the differences in high-redshift halo structure reported in the literature since these studies have not been consistent in their treatment of this issue. Unfortunately, the details of how the standard relaxation metrics evolve following dynamical disturbances has not been properly explored at any redshift, nor has their efficacy at separating relaxed systems from unrelaxed systems been demonstrated at high redshift. Before presenting a detailed analysis of halo structure at high redshift to understand the discrepancies present in the literature, we aim first to address both of these issues here. Given its fine snapshot temporal resolution, Tiamat represents a unique resource for exploring these issues across the full range of masses most relevant to galaxy formation in the early Universe."}
{"text": "We will find that the standard relaxation criteria are effective at identifying systems that are recovering from their formation or from recent significant mergers. With this methodology properly validated at high redshift, we will subsequently perform a detailed analysis of the structure of both relaxed and unrelaxed high redshift dark matter halos -- including spin parameter and concentration-mass relations -- in a companion paper (Angel et al. 2015; PAPER-II). The Tiamat N-body simulation hosts a semi-analytic model of galaxy formation named Meraxes, which has been integrated within a semi-numerical model for ionization structure. In subsequent papers we will present this model (Mutch et al. 2015; Paper-III) and use it in a range of studies including high redshift galaxy luminosity functions (Liu et al. 2015, PAPER-IV) and the ionization structure of the intergalactic medium (Geil et al 2015, PAPER-V)."}
{"text": "Complementary high resolution hydrodynamics simulations called Smaug [already presented in][]{Duffy:2014p2561} will characterise the basic scaling relationships of early galaxy formation. There will then be a detailed comparison of Meraxes to the results of Smaug with suggested constraints of the semi-analytic model based on hydrodynamics (Qin et al, in prep). This section examines the time-scales by which galactic halos at high redshift relax following formation and mergers. We relate these time-scales to their dynamical age and to intervals between merger events and will find that only towards the end of the epoch of reionization do significant numbers of halos exist in relaxed states. Lastly, we will also present some preliminary results about their phase-space structure that may be of consequence for the application of semi-analytic models at high redshift. It has long since been shown that the structure of halos extracted from collisionless N-body simulations has a significant dependance on the dynamical state of the system [Thomas:1998p2559, Neto:2007p2556, Power:2012p2560, Ludlow:2014p2558]."}
{"text": "At low redshifts at least, cuts on three metrics for quantifying the dynamical state of halos have found success at separating systems with disturbed structure from those with relaxed structure: the offset parameter (x_off), given by the displacement of the densest centre of a halo from its centre of mass; the virial ratio (T/|U|), given by 2K/|U|, where K is the kinetic energy and U is the halo's gravitational binding energy [see Section 5.1 of][and references therein, for a detailed description of virialisation]Poole:2006p41; and the substructure fraction (f_sub), which we take here to be the ratio of the particle count of all but the most massive of a FoF halo's substructures to its total particle count. Each have simple physical interpretations as measures of dynamical state. Elevated values of f_sub naturally arise during the earliest stages of a merger when a halo is naturally split between multiple similarly sized substructures."}
{"text": "Elevated values of the virial ratio are found prior to the dissipation of orbital energy following a merger. Lastly, elevated values of x_off are a natural result of the movement of a halo's dense core as it orbits the centre of mass of its system following even minor disturbances. The standard values for relaxed systems which we adopt are those proposed originally by [Neto:2007p2556] and recently confirmed to be successful in the study of halo density profiles [Ludlow:2014p2558]; specifically, x_off < 0.07, T/|U| < 1.35 and f_sub < 0.1. To date, a careful examination of how these metrics evolve following dynamical disturbances has not been performed however, leaving the physical nature of these cuts unclear. Additionally, it is unclear how appropriate they are for high-redshift studies. In what follows we shall study the evolution of these relaxation metrics following three sorts of mass accretion event capable of driving dynamical disturbances: halo formation (defined as the point at which a halo last reached 50% of its present mass), mergers between a primary halo and a secondary halo at least one third its mass (so-called `major', or 3:1 mergers) or mergers between a primary halo and a secondary halo at least one tenth its mass (so-called `minor', or 10:1 mergers)."}
{"text": "Throughout our analysis we will measure intervals of time for a halo at redshift z in units of its dynamical time, which we take to be 10% of the Hubble time at that redshift. Times in this dimensionless system of units will be denoted by tau. At all redshifts, the Hubble time is tau=10 in this system. The three times since a halo last experienced each of these events will be referred to as dynamical ages. The dynamical ages required for our relaxation criteria (x_off, T/|U| and f_sub) to return to and maintain standard values for relaxed halos following these events are used to motivate two recovery times: a formation recovery time and a merger recovery time. We find that x_off starts with high values of ~0.2 at the time of halo formation, declining to our relaxed level of 0.07 at a formation age of ~1.5 and then to baseline levels of x_off~0.04 afterwards."}
{"text": "Following 3:1 and 10:1 mergers, peak levels occur roughly one dynamical time after a merger begins with relaxed levels obtained at a merger age of ~2. Peak values of 0.2 and roughly 0.07 are reached following 3:1 and 10:1 mergers, suggesting that mergers are progressively less likely to excite the system above our x_off~0.07 relaxation criterion as mass ratios drop below 10%. Interestingly, the virial ratio shows significantly less evolution following both formation and merger events. In all cases, the distribution peak sits at levels similar to our virial ratio ~1.35 relaxation criteria at times when x_off lies above its relaxation criteria. Once x_off is found to drop below relaxation levels (or shortly before) the virial ratio can be seen to decline somewhat from values of ~1.35 to ~1. Generally however, the virial ratio exhibits much less sensitivity to dynamical disturbances and relaxes to baseline levels quicker than x_off, suggesting that it is a much less robust discriminator of dynamical state."}
{"text": "Lastly, the substructure fraction shows a very simple and well defined behaviour following dynamical events. At formation, a wide range of values are seen about a distribution peak of ~0.2. A slow decline to baseline values follows. After merger events, the substructure fraction increases by expected amounts: 30% for 3:1 mergers and 10% for 10:1 mergers. The subsequent decline in the substructure fraction is more rapid than what is seen following formation, with levels dropping at a rate of approximately 20% per dynamical time. We also find that substructure fractions return to standard relaxed values 30 to 50% faster than core offsets following dynamical disturbances. Despite this, because the substructure fraction is most sensitive to dynamical disturbance in the earliest stages of mergers, it is an effective compliment to the x_off statistic which exhibits a slight delay in reacting during merger events."}
{"text": "We conclude then that, of the three metrics we study here, the x_off statistic is the most effective single measure of dynamical state. It is sensitive to disturbances from mergers greater than approximately 10:1 and retains this sensitivity for approximately 2 dynamical times afterwards. The virial ratio is significantly less discriminating than these statistics but evolves in ways consistent with the relaxation of x_off and f_sub. With the exception of f_sub, all metrics are essentially independent of mass throughout the period of relaxation following halo formation or mergers larger than 10:1. The differing trends of f_sub with mass for each simulation is a numerical effect arising from their differing resolutions as a function of mass and is an expected result. Despite this one numerical effect, this clearly illustrates that high-redshift halos recover from formation and merger events within a time which is highly insensitive to their mass."}
{"text": "These results suggest that following formation or mergers greater than 10:1, a small and fixed number of pericentric passages of the material disturbed at large radius in the merger remnant are required for relaxation. If this is the case, the mass independence of relaxation could be seen as a product of the fact that halo crossing times depend only on their mean density, which is defined in terms of a fixed overdensity, and independent of mass. Secondary factors which could influence halo relaxation include halo concentrations, shapes and merger orbital properties. From these results, we define two mass-independent recovery times separating relaxed and unrelaxed systems at high redshift: a formation age of 1.5 and a merger age of 2. Our expectation is that high-redshift halos which have doubled their mass within one and a half dynamical times or which have experienced mergers larger than 10:1 within two dynamical times are likely to be disturbed."}
{"text": "How then do the fractions of halos meeting these recovery criteria evolve with redshift? The distribution of all three dynamical ages evolves very little from z=15 to z=5. Over this redshift range, the distribution of formation ages is very narrow and peaked very close to our formation recovery timescale of 1.5. The near constant value of the formation age during this epoch is consistent with early mass accretion histories which are exponential, as found previously by several other authors [Wechsler:2002p1783, McBride:2009p1230, Correa:2015p2654]. The distribution of times since 3:1 mergers is much broader and is also peaked near our merger recovery timescale of 2. This tells us that typical halos at high redshifts across all galactic masses are doubling their mass on timeframes that only barely permit relaxation while simultaneously, major mergers are occurring at rates which only barely permit recovery between events."}
{"text": "The situation is importantly different for minor mergers. In this case we find that halos experience minor mergers at rates which are much too rapid (on average) to permit dynamical relaxation between events. The narrow distribution of formation ages, broad distribution of merger ages and short times between 10:1 mergers persists almost unchanged until approximately z~2. At this time, we find that 10^12 solar mass halos begin to become progressively older, as typical formation ages and times since major mergers increase and times since minor mergers creep above merger recovery times of 2 by z=0. The increase of formation age at lower redshifts corresponds to a transition in these halos' mass accretion histories from an exponential form to a linear form, as discussed already in the literature [McBride:2009p1230, Correa:2015p2654]."}
{"text": "The fractions of halos which meet these recovery criteria as a function of redshift is presented explicitly. Here we see the disappearance of halos with formation times less than 1.5 and the sustained low levels of halos having had sufficient time to recover from their most recent mergers. We have added to these plots the fraction of halos that simultaneously satisfy our standard x_off, T/|U|,and f_sub relaxation criteria. Remarkably, the fraction of relaxed halos and the fraction having had sufficient time to recover from their last 10:1 (or larger) merger are very similar across a wide range of masses and redshifts. We conclude from this that the standardised relaxation criteria of [Neto:2007p2556] are effectively identifying systems that have been disturbed by 10:1 (or larger) mergers. It should be noted however that our recovery criteria of 1.5 and 2 have been calibrated at high redshift and may need adjustment at low redshift, where halos are substantially more concentrated and the orbital properties of merging systems are significantly different."}
{"text": "This is likely the reason why our estimates of the recovered fraction exceeds the relaxed population at z<2. Taken together, we see that at high redshifts (z>5), the fraction of relaxed halos drops to levels of ~20% at all galactic masses. Combined with the rapid decline in the number density of halos with redshift at this time, we conclude that the abundance of relaxed galactic halos prior to the epoch of reionization drops to very low levels. This should make it very challenging to assemble large populations of relaxed halos at z>10, which is of particular concern for studies seeking to understand the processes acting to establish universal density profiles for collisionless systems at high redshift. As an exercise during the development phase of the Tiamat simulations, we analysed one of our simulations (TinyTiamatW) with the ROCKSTAR halo finder, allowing us to study the effect of halo finding on our semi-analytic modelling campaign."}
{"text": "Doing so has yielded an interesting new insight into the dynamical lives of high-redshift galactic halos. There is a stark difference between the results from ROCKSTAR and SUBFIND. We can see clearly that while the halo appears relatively undisturbed with unremarkable substructure, it in fact consists primarily of two very massive subhalos which are distinct in phase space. Phase-space halo finders such as ROCKSTAR are of course designed to separate halo substructures in this way, but it is not entirely clear that this is a desired result for applications in galaxy formation modelling. While approaches differ in detail, the central premise of all semi-analytic galaxy formation models is that the total matter assembly provided by their merger tree inputs can be reliably mapped to a faithful description of the baryonic assembly of galactic halos. Problems may arise if the collisional fluids (particularly the hot halos) associated with multiple collisionless systems oscillating through each other for >3 dynamical times can not follow the collisionless material of their initial hosts."}
{"text": "Substantial amounts of this gas will be stripped or rapidly coalesce into one hot halo, loosing its association with its original collisionless component while that material continues to orbit. This is the case with the Bullet Cluster for instance, albeit at a different mass scale and redshift. It is also the situation modelled by [McCarthy:2008p2661] who find that the stripping of a galaxy's hot halo (due to tides, ram pressure stripping, and hydrodynamic instabilities) is extremely efficient up to and during its first pericentric passage. The amount of material removed varies with halo mass, concentration and orbit, but is substantial and typically in the range of 60 to 80% for the broad range of cases they examine. If such structures were short lived, the impact on our galaxy formation model would likely be insignificant. However, they are in fact long lived in dynamical terms."}
{"text": "A comparison of the evolving substructure fractions of FoF halos extracted from TinyTiamatW using Subfind to those obtained from ROCKSTAR as functions of the dynamical ages shows that while we see the familiar decline of f_sub following formation and mergers in the Subfind trees, the ROCKSTAR trees exhibit a much slower decline, reaching constant levels only after approximately 5 dynamical times, sustaining levels well above our standard relaxation criteria even after that. On the other hand, if these substructures were rare, their impact on galaxy formation modelling would again be minimal. They are in fact very common. The FoF halo mass functions for the two catalogs are virtually identical (except at the highest masses where the larger linking length used by ROCKSTAR unsurprisingly yields more systems, presumably due to overlinking), the substructure fractions at the highest (and most resolved) masses of the two catalogs are very different."}
{"text": "Substructure fractions are 50 to 60% at the highest masses in ROCKSTAR indicating that only around half of the mass in these systems is assigned to the most massive component of the system. This is a consequence of a very different splitting of the top level of the FoF group's substructure hierarchy. Suggestions of this effect can be seen in the recent work of [Behroozi:2015p2660]. While these authors find that substructure properties like position and velocity generally agree between configuration and phase-space halo finders, they find that substantial differences in masses can occur. They also find strong disagreements in the frequency and duration of major mergers, particularly at redshifts z>1. We emphasise that we make no attempt here to advocate for one halo finding approach over another. Rather, we seek to make the point that care should be taken to ensure that each semi-analytic model is matched, in a physically meaningful way, to the nature of the substructure hierarchy supplied by the halo finder contributing to its input."}
{"text": "Such differences may lead to significant systematics with mass in the evolution of merger trees which could masquerade as physical processes as diverse as mass dependancies in dust properties, photon escape fractions, feedback and cooling. A detailed account of how the cooling and feedback modelling of DRAGONS compares to the Smaug hydrodynamic simulations of [Duffy:2014p2561] will be presented in Qin et al (2015, PAPER-VII), where a direct halo-by-halo comparison of the two methodologies will be presented. We take this opportunity to point out one other possible important astrophysical consequence of large bulk phase-space structures such as this. Recent studies have begun to investigate the possibility that heating from dark matter annihilation may be observable in the redshifted 21-cm background from z>30 [Furlanetto:2006p2566, Evoli:2014p2655, Mack:2014p2655, Schon:2014p2564]. If phase-space structures such as these prove to be common at this epoch, important changes to inferred annihilation cross sections may result."}
{"text": "We have introduced the Dark-ages Reionization and Galaxy-formation Observables from Numerical Simulations (DRAGONS) program and presented the Tiamat collisionless N-body simulation suite upon which it is constructed. The abundance of friends-of-friends (FoF) structures populating Tiamat is a good match to the universal model proposed by [Watson:2013p2555] at high masses, but we find a supression of low-mass systems, possibly due to differences in our halo finding procedure or perhaps indicating a deviation from universal behaviour, at least at large redshifts. Using Tiamat we have also illustrated the dynamically violent conditions experienced by galactic halos at large redshift. We find that across a wide range of galactic mass (10^8 to 10^11 solar masses) above z=5, halos relax from their formation and from mergers in essentially the same way and in the same amount of time: within one and a half dynamical times in the case of their formation and within two dynamical times following mergers involving a primary and a secondary larger than 10% of its mass."}
{"text": "The distribution of formation times and times since major mergers maintain approximately these time-scales across all redshifts above z=5 while the time between minor mergers is typically significantly less. Relaxed fractions maintain levels of less than 20% at z>5 as a result. Using the GiggleZHR simulation we find that this remains true for 10^12 solar mass halos until z~2. It appears that the rate of minor mergers principally regulate a halo population's relaxed fraction, as measured by standard metrics. Combined with the rapid decline of the halo mass function at redshifts z>10, the abundance of relaxed halos prior to the epoch of reionization must be extremely low. Using the phase-space halo finder ROCKSTAR, we also demonstrate that high-redshift halos host large and long-lived substructures that go undetected to halo finders such as Subfind which utilise configuration-space information only."}
{"text": "This results in substructure fractions that are much higher for ROCKSTAR than for Subfind, with probable implications for semi-analytic models of galaxy formation at high redshift. Taken together, these results illustrate the dynamically violent circumstances under which galaxy formation proceeds in the early Universe. The consequences are many and significant, including implications for photon escape fractions, efficiencies of feedback from winds (both stellar and AGN) and the efficiency of spheroid assembly. These in turn can have important consequences for the reionization history of the Universe during the EoR and observed galaxy sizes."}
{"text": "We use high resolution N-Body simulations to study the concentration and spin parameters of dark matter haloes in the mass range between 10 to the power of 8 and 10 to the power of 11 solar masses per h and redshifts between 5 and 10, corresponding to the haloes of galaxies thought to be responsible for reionization. We build a sub-sample of equilibrium haloes and contrast their properties to the full population that also includes unrelaxed systems. Concentrations are calculated by fitting both NFW and Einasto profiles to the spherically-averaged density profiles of individual haloes. After removing haloes that are out-of-equilibrium, we find a concentration-mass (c(M)) relation at redshifts greater than 5 that is almost flat and well described by a simple power-law for both NFW and Einasto fits. The intrinsic scatter around the mean relation is approximately a delta c_vir of 1 (or 20 per cent) at redshift z=5. We also find that the analytic model proposed by [2014MNRAS.441..378L] reproduces the mass and redshift-dependence of halo concentrations."}
{"text": "Our best-fit Einasto shape parameter, alpha, depends on peak height, nu, in a manner that is accurately described by the equation alpha equals 0.0070 times nu squared plus 0.1839. The distribution of the spin parameter, lambda, has a weak dependence on equilibrium state; lambda peaks at roughly 0.033 for our relaxed sample, and at approximately 0.04 for the full population. The spin-virial mass relation has a mild negative correlation at high redshift. In the current cosmological paradigm cold dark matter (CDM) collapses to form gravitationally bound structures within an expanding background universe. Known as dark matter (DM) haloes, these objects are initially small but undergo repeated merging to form ever larger systems. Galaxies form within these haloes as in-falling gas cools and converts to stars [1978MNRAS.183..341W]. Their evolution and structural properties therefore underpin those of the embedded galaxies. These ideas have evolved into the field of semi-analytic modelling in which galaxies are grown within an evolving population of dark-matter haloes extracted from purely N-Body simulations [2006RPPh...69.3101B, 2006MNRAS.365...11C, 2008MNRAS.391..481S, 2008MNRAS.388..587L]."}
{"text": "The characteristics of DM haloes have been the subject of extensive research. Mass determines the overall size of the halo, but several other important parameters have also been identified. For example, using N-Body simulations [1997ApJ...490..493N] found that the density profiles of virialised haloes can be well described by rescaling a simple formula (hereafter known as the NFW profile), which states that the density rho at radius r over the critical density rho_c equals the characteristic density delta_c divided by (r/r_s) times (1+r/r_s) squared. Here r_s is the characteristic scale radius at which the logarithmic density slope is equal to -2; delta_c is the characteristic density contrast, and rho_c is the critical background density at redshift z. These parameters can be expressed in a variety of forms. One common approach is to use a virial mass and concentration, c_vir, defined as the ratio of the halo's virial radius to its scale radius, R_vir/r_s. The virial mass of a halo is defined as that enclosed by the radius R_vir within which the density is a specific factor times the background density [1998ApJ...495...80B]."}
{"text": "While the NFW profile is a common description, several recent studies [2004MNRAS.349.1039N, 2008MNRAS.388....2H, 2010MNRAS.402...21N] have shown that the density profiles of simulated haloes exhibit small but systematic deviations from the NFW equation. The Einasto profile [1965TrAlm...5...87E], provides a better approximation to the radial density profile [2004MNRAS.349.1039N, 2013MNRAS.432.1103L]. Its equation is defined by the natural logarithm of rho(r) over rho_-2 equals -2/alpha times [(r/r_-2) to the power of alpha minus 1]. Like the NFW profile, the Einasto equation has two scaling parameters, r_-2 and rho_-2, and an additional shape parameter, alpha. Note that r_-2 and r_s are equivalent. At low redshift the concentration parameter decreases with increasing halo mass. NFW interpreted this finding as a result of hierarchical clustering: smaller haloes form earlier than more massive objects, when the universe was denser [1997ApJ...490..493N]. They suggested that concentration reflects the background density of the Universe at the halo's formation time. The same negative trend was also seen in subsequent N-Body simulations [2001ApJ...554..114E, 2002ApJ...568...52W, 2008MNRAS.390L..64D]."}
{"text": "One approach relates the characteristic density to the past accretion history of the halo's main progenitor. [2002ApJ...568...52W], for example, calculated the mass assembly histories (MAHs) of simulated haloes and used a proportionality constant to relate the concentration to background density at the halo's time of formation. The redshift dependence of the c(M) relation was later studied by [2003ApJ...597L...9Z], who found a weakening of the relation for the highest mass haloes at any redshift. By redshift of approximately 3-4 the negative trend is no longer present in the simulations of [2008MNRAS.387..536G], who focus on masses greater than 10 to the power of 11 solar masses per h. The flattening of the c(M) relation was also reported by [2009ApJ...707..354Z] who connected halo concentrations to the period at which halo growth transitions from a rapid to a slow phase. These models provide a clear interpretation of why concentration depends only weakly on mass for the most massive systems: because these haloes are forming today, they share the same formation time, and therefore concentration."}
{"text": "[2007MNRAS.381.1450N] studied the z=0 c(M) relation in the Millennium simulation [2005Natur.435..629S], while [2011ApJ...740..102K] and [2012MNRAS.423.3018P] extended the analysis to z=6 using both the Millennium and Bolshoi simulations. In agreement with previous work, these authors each find a decline of concentration with mass. However, both [2012MNRAS.423.3018P] and [2011ApJ...740..102K] have also reported an upturn of the c(M) relation at the high mass end. On the other hand, Ludlow et al. (2012) demonstrated that there is no upturn amongst relaxed haloes, and showed how the transient dynamical states of merging systems can result in a non-monotonic c(M) relation. While the details continue to be debated, it is clear overall that the diversity of halo formation histories play a critical role in establishing the shape and evolution of the c(M) relation [2014MNRAS.441..378L, 2015arXiv150200391C]. While the low redshift mass-concentration relation is well studied, at high z the relation is poorly constrained."}
{"text": "For example, [2012MNRAS.423.3018P] and [2014arXiv1407.4730D] find a high-mass upturn (above a few times 10 to the power of 10 solar masses per h) at z=5 amongst the full halo population. At similar masses, [2014arXiv1402.7073D], find a relation with a slightly positive slope, whereas [2015arXiv150506436H] report a weak negative slope that flattens by z=9. These authors, however, imposed different equilibrium cuts on their halo samples, which hampers a direct comparison with their results. Given this unsettled state of affairs it is clear that there is some debate on the precise nature of the high redshift c(M) relation and the role played by unrelaxed haloes. For example, a halo suffering a merger is unlikely to have a simple, smooth density profile, and will take time to settle back into equilibrium. This situation becomes increasingly important at high redshift due to the elevated merger rates of potentially star-forming haloes. These sorts of concerns led [2007MNRAS.381.1450N] to introduce three physically-motivated parameters to identify systems far from equilibrium: 1) the mass-fraction in substructure f_sub; 2) the offset between the halo's center of mass and its most-bound particle, x_off, and 3) the pseudo-virial-ratio of kinetic and potential energies, phi."}
{"text": "The effectiveness of these parameters in isolating relaxed DM haloes is further discussed in [2008MNRAS.387..536G] and [2012MNRAS.427.1322L]. A detailed study of these parameters with regard to dynamical relaxation at high redshift is provided by the first paper of the DRAGONS series, Poole et al. (2015b) (hereafter referred to as Paper I). Their results suggest that, across the mass range of our simulations, and for z>5, standard relaxation values for f_sub, x_off and phi obtained from low redshift studies are very effective at identifying systems relaxing from halo formation or recent mergers at high redshift. Concentration is not the only relevant halo property for galaxy formation. Halo spin also plays an important role in semi-analytic models, since angular momentum conservation determines the size of galactic disks [1998MNRAS.295..319M, 2011MNRAS.413..101G], which in turn determine their star formation rates [1959ApJ...129..243S, 1998ApJ...498..541K]. A halo's angular momentum is often expressed as a dimensionless spin parameter, lambda, defined as J_vir divided by sqrt(2) * M_vir * V_vir * R_vir, where J_vir is the total angular momentum within R_vir."}
{"text": "Most studies of the spin parameter have focused on the distribution of spins and its dependence on halo mass [2007MNRAS.376..215B, 2007MNRAS.381.1450N, 2008ApJ...678..621K, 2010crf..work...16M]. At any redshift, halo spins are distributed approximately log-normally, and peak at a lambda of approximately 0.03-0.04. At low redshift, spins are approximately independent of mass but gain a slight negative correlation at higher redshifts [2008ApJ...678..621K, 2010crf..work...16M]. Recently, [2014arXiv1402.7073D] measured the redshift evolution of the lambda - M_vir relation, reporting a weak negative correlation at z=5. In this work we use the Tiamat simulation suite to extend the study of concentration and spin to redshifts z>5. Our simulations were designed to resolve halo masses relevant for galaxy formation during this high-redshift epoch. The purpose of our study is to measure the structural and dynamical properties of haloes that are necessary for forthcoming semi-analytic models of reionization. We organise the paper as follows. In Section 2 we describe the numerical simulations, including halo finding, analysis techniques, and our parametrization of concentration and spin."}
{"text": "In Section 3 we present our concentration--mass relation and its redshift dependence, and in Section 4 the spin distribution, and its mass and redshift dependence. Finally, in Section 5 we summarise our main results. Our analysis focuses on DM haloes identified in three cosmological N-body simulations. These include a 2160-cubed-particle, 67.8 Mpc/h cubed box (the Tiamat simulation) and two smaller but higher resolution volumes of 10 and 22.6 (Mpc/h)-cubed. Each run was carried out with GADGET-2 [2001NewA....6...79S, 2005MNRAS.364.1105S] with RAM (random-access memory) consumption changes in accordance with those detailed in [2015MNRAS.449.1454P]. For each run, the Plummer-equivalent softening length was 1/50th of the mean Lagrangian inter-particle spacing, and the integration accuracy parameter, eta, is set to 0.025, as motivated by the convergence study presented in [2015MNRAS.449.1454P]. Initial conditions were generated using 2nd order perturbation theory using the code 2LPTIC at z=99 and each simulation was run down to z=5; 100 snapshots of particle data were taken equally spaced in time from z=35 to z=5 (one every 11 Myr)."}
{"text": "Cosmological parameters for each box were chosen to be consistent with the Planck 2015 data release [2015arXiv150201589P] (h, Omega_m, Omega_b, Omega_Lambda, sigma_8, n_s) = (0.678, 0.308, 0.0484, 0.692, 0.815, 0.968). The relevant numerical parameters are summarised in Table 1. A more detailed discussion of these simulations can be found in Paper I. Summary of simulation parameters. N_p is the total number of particles, L is the length of the box, m_p is the mass of each particle and epsilon is the gravitational force softening length. The ratio between the minimum bin size of the halo profile in dark blue and the size of the virial radius, plotted as a function of particle number for the Tiamat simulation. The solid line is the median while the shaded area is the scatter (68 per cent confidence interval). The largest bin size of 0.09 R_vir indicates our bins begin well inside the halo scale radius for the halo masses considered here."}
{"text": "Haloes were identified in each simulation snapshot using Subfind [2001MNRAS.328..726S]. This produces two outputs: the first contains structures found by a friends-of-friends (FoF) algorithm (we adopt a linking length of 0.2 times the mean inter particle spacing); the second is obtained by dissecting each FoF group into its self-bound 'substructure'. This results is a central 'main halo', typically containing >90 per cent of its virial mass, and a group of lower-mass subhaloes which trace the undigested cores of previous merger events. Each main halo and its substructures were further analyzed to catalog their basic properties and to build their spherically averaged profiles. A (FoF or substructure) halo was required to have a at least 32 particles to be included, resulting in a minimum halo mass of 8.4x10^7 solar masses/h in Tiamat, 2.5x10^7 solar masses/h in MediTiamat and 2.2x10^6 solar masses/h in TinyTiamat. However, when estimating concentrations, a stricter limit of n_p > 5000 within the bound structure was imposed to ensure that the halo's inner regions are well-resolved. For the purpose of estimating spin parameters, this limit is relaxed to 600 particles."}
{"text": "For each main halo, spherically-averaged density profiles were constructed in bins containing an equal number of particles. Only particles considered by Subfind to be bound to the central haloes were used. The number of bins was increased along with the number of halo particles. We imposed a minimum of 5 bins for the smallest haloes, and a maximum of 1000 bins for the largest (reached as particle number tends to 10^6). For example, haloes with 5000 particles have 25 bins, rising to approximately 125 bins for haloes containing 10^5 particles. Best-fit NFW and Einasto profiles were obtained by minimizing a function psi, which is 1/N times the sum of (delta r_i / r_i) * (log rho_i - log rho_model)^2. The factor delta r_i / r_i appropriately weights bins of differing size. Note that only bins in the radial range 0.05 R_vir < r_i < 0.8 R_vir were used. We have verified that the minimum bin radius is always larger than the convergence radius defined in [2003MNRAS.338...14P]."}
{"text": "In defining our sample of equilibrium DM haloes we impose both dynamical and resolution criteria following the procedure established by [2007MNRAS.381.1450N], [2008MNRAS.387..536G] and [2012MNRAS.427.1322L]. The behaviour of these equilibrium diagnostics over the mass and redshift range probed by the Tiamat simulation suite is discussed further in Paper I. The criteria defining relaxed haloes include upper limits on the following three quantities: I) The fraction of mass found in satellite subhaloes, f_sub, must be less than 0.1. A high fraction of mass in substructure may be indicative of a recent merger [2007MNRAS.381.1450N]. II) The offset between the position of the most-bound-particle and center-of-mass, x_off, must be less than 0.07. This is complementary to f_sub as it includes mass from unresolved subhaloes. III) The pseudo-virial ratio of kinetic and potential energies, phi = 2K/|U|, must be less than 1.35. This criterion tends to be sensitive to haloes at the pericenter of a merger."}
{"text": "[2007MNRAS.381.1450N] find that these restrictions provide a simple and physically motivated method to exclude haloes that are not well described by an NFW profile. In Paper I these parameters were also shown to be discriminate between haloes that have either recently doubled in mass, or suffered a major or minor merger, within the last 1-2 dynamical times. We therefore adopt them as our standard equilibrium criteria. A further criterion is imposed to select only well-resolved haloes. For the halo concentration analysis a lower limit on particle number of greater than 5000 is imposed. This is derived from work studying convergence of NFW and Einasto profile fits in [2007MNRAS.381.1450N] and [2008MNRAS.387..536G]. This ensures that the inner portion of the halo is well enough resolved to measure the scale radius r_s. We impose a restriction of greater than 600 particles for the spin parameter measurement following [2008ApJ...678..621K]. The dynamics of hierarchical growth means that at the high redshifts studied here, many of our haloes will be far from equilibrium and thus have ill-defined values for concentration and spin."}
{"text": "These sample cuts are designed to remove such systems and to keep transients out of our analysis as much as possible. For example, a halo which has just undergone a major merger may be comprised of two large, high density clumps, and consequently have a high x_off and poorly defined center. The density profile of such a system cannot be captured by simple spherical averages. We stress, however, that there is a continuum of values for x_off, f_sub and phi; the particular values chosen to separate relaxed haloes from unrelaxed are the result of extensive past investigations [2007MNRAS.381.1450N, 2012MNRAS.427.1322L]. To quantify the effects of our sample selection, we note that in Tiamat there are 14391 haloes with more than 5000 particles at redshift z~5, but only 4433 (or ~30 per cent) of these satisfy our relaxation criteria; this reduces to ~15 per cent by z~10. These numbers underline the importance of the dynamical state of haloes at high redshift. Nevertheless parametrised fits to the entire population are useful for many semi-analytic calculations [2014MNRAS.439.2728M, 2015MNRAS.451.2840S] and for this reason we report fits to both our full halo sample as well as the relaxed sub-sample."}
{"text": "Caption: Concentration--mass relation of relaxed central haloes at z=5. Left and Right panels are the NFW and Einasto concentrations respectively. Inner shaded region denotes the bootstrapped 90 per cent confidence interval on the median. The outer shaded region shows the 68 per cent scatter. The line of best fit is fit to the median using the Monte Carlo Markov Chain method implemented in the Python package emcee [2013PASP..125..306F]. This produces c_vir equals 3.8 (+/-0.4) times (M/10^10 solar masses per h) to the power of -0.035 (+/-0.005) at z=5 for NFW fits and c_vir equals 3.8 (+/-0.4) times (M/10^10 solar masses per h) to the power of -0.039 (+/-0.005) for Einasto fits. The fits from [2014arXiv1402.7073D] are also shown with thick solid lines. The Tiamat simulation is designed to study reionization and explores a mass range below previous studies. The dashed black line at c_vir=4 is added for a point of reference. Solid black points represent the [2014MNRAS.441..378L] model where halo concentrations are calculated from the median accretion history in the mass bin."}
{"text": "Caption: The same concentration mass relations for relaxed central haloes as shown in the previous figure, but now at z=7. Inner shaded region denotes the bootstrapped 90 per cent confidence interval on the median. The outer shaded region shows the 68 per cent scatter. The line is fit to the median and gives c_vir = 3.4 (+/-0.6) times (M/10^10 solar masses per h) to the power of -0.019 (+/-0.008) at z=7 for NFW and 3.3 (+/-0.6) times (M/10^10 solar masses per h) to the power of -0.018 (+/-0.008) for Einasto profiles. The dashed black line at c_vir=4 is added for a point of reference. Solid black points represent the [2014MNRAS.441..378L] model where halo concentrations are calculated from the median accretion history in the mass bin. Error bars are derived from the 68 per cent scatter of the accretion histories. The c(M) relations for our equilibrium haloes at z=5 and z=7 are shown in the figures. Both NFW and Einasto concentrations are plotted."}
{"text": "The inner shaded region shows the bootstrapped 90 per cent confidence interval on the median for mass bins containing at least 20 haloes. The outer shaded area fills the 68 per cent scatter in individual concentration estimates. We find a weak trend of decreasing concentration with mass at z=5 for both NFW and Einasto fits. This trend becomes shallower as redshift increases. By redshift 9 there is no trend apparent for either set of fits. The c(M) relations obtained from both NFW and Einasto fits are similar over this mass range. We note that the systematic difference between NFW and Einasto concentrations is less than 0.1, which is smaller than the change in concentration from the lowest to highest masses studied here. Best-fitting power laws at z=5 are 3.8 (+/-0.4) times (M/10^10 solar masses per h) to the power of -0.039 (+/-0.005) for NFW fits and 3.8 (+/-0.4) times (M/10^10 solar masses per h) to the power of -0.039 (+/-0.005) for Einasto fits. Best-fit parameters are obtained using the Monte Carlo Markov Chain (MCMC) method implemented with the emcee package [2013PASP..125..306F]."}
{"text": "The quoted errors are the 68 per cent confidence interval derived from the posterior distribution. We find intrinsic scatter in the c(M) relation of delta c_vir ~ 1.0 (or 20 per cent) for fits to both NFW and Einasto profiles. Best-fit power-law relations are provided in Table 2 for a range of redshifts. In addition to the two scaling variables, the Einasto profile has a shape parameter, alpha. Previous studies have found that alpha depends in a complex way on both halo mass and redshift, but follows a simple relation when expressed in terms of the dimensionless 'peak height' mass parameter, nu = delta_sc / sigma(M,z). Here delta_sc=1.686 is the density threshold for the collapse of a spherical top-hat density perturbation, and sigma(M,z) is the rms density fluctuation in spheres enclosing mass M. We find a similar alpha-nu relation to the previous authors - the fit from [2008MNRAS.387..536G] is shown as a dashed line. Our best fit for the alpha-nu relation is alpha = 0.007 * nu squared + 0.1839."}
{"text": "In order to check for any subtle bias in our fits we have also constructed c(M) and alpha(nu) relations using the median density profiles obtained by stacking haloes in narrow mass bins. This smooths out any unique features of individual systems and allows for a robust estimate of the median structural properties of haloes of a given mass. For our relaxed population we recover the c(M) to within delta c ~ 0.1, for both NFW and Einasto fits. We choose to use the individual fits when computing the best fit c(M) relation. The weak trend in concentration with mass found in our simulation is in qualitative agreement with previous work that found a negative trend at low redshift that becomes progressively shallower with increasing z. For example, both the shallow negative slope and the magnitude of our Einasto concentrations are in good agreement with [2015arXiv150506436H]. In Figure 2 we also plot the c(M) relations from [2014arXiv1402.7073D] (hereafter DM14), also obtained from both NFW and Einasto fits. As DM14 employ different relaxation and resolution criteria, the differences we observe, although slight, are unsurprising."}
{"text": "However, the shape of our trend at redshift 5 is in qualitative disagreement with DM14, who find that a positive trend emerges at z=5 for both Einasto and NFW concentrations. We also find a higher normalization (about 25 per cent) than DM14 at ~10^10 solar masses per h. We do not speculate on the exact combination of these differences that effects the c(M) relation but note that: firstly, halo profiles in DM14 are fit out to 1.2 R_vir while Tiamat profiles are only fit out to 0.8 R_vir, and second, different resolution and relaxation criteria were used. DM14 adopt a minimum halo mass corresponding to 500 particles, and define relaxed haloes as those satisfying x_off < 0.07 and rho_rms < 0.5, where rho_rms is the rms deviation between the haloes density profile and the best-NFW fit. However, we do find good agreement between our c(M) relation results and the model proposed by [2014MNRAS.441..378L], as indicated by the black dots in Figures 2 and 3. We emphasise there is no fit to the halo density profiles here, only the accretion histories are required."}
{"text": "Caption: Best fit values from the relaxed population for NFW-derived and Einasto-derived c(M) relations. N_sample denotes the number of haloes in the sample for Tiamat, MediTiamat, TinyTiamat. Fits and errors are the median and 68 per cent confidence interval using the MCMC package quoted previously. Caption: The Einasto profile alpha-nu relation. At each redshift the median alpha is plotted for bins containing >20 haloes, with the errors derived from the bootstrapped 90 per cent confidence interval on the median. Each symbol denotes a different redshift. We find a similar alpha-nu relation to the low redshift results of previous authors despite the redshift range of our simulations being z>5. Caption: The dependence of concentration on x_off for central subgroups in several mass ranges. Blue lines represent the median. The dashed red line denotes the relaxation criteria cut above which a halo is considered to be out of equilibrium [2007MNRAS.381.1450N, 2008MNRAS.387..536G, 2012MNRAS.427.1322L]. It can be seen that lower x_off parameters (i.e. more relaxed haloes) correlate with higher c_vir for all mass ranges."}
{"text": "Caption: Concentration-mass relation for relaxed haloes at z=5, but now with haloes containing >500 particles. The inner shaded region represents the bootstrapped median value and the outer region the 68 per cent scatter. The inclusion of haloes with particle number <5000 introduces more haloes with lower concentrations at the low mass end of each simulation. Einasto shape parameters, alpha, for haloes with <500 particles are also higher. Caption: The same as Figure 2 but now the case in which no non-equilibrium cuts are enforced and the full sample of haloes with >5000 particles is analysed. The median magnitude of the concentrations has decreased by delta c_vir ~ 1 over all masses in our simulations. To investigate the effect of our equilibrium selection criteria we plot in Figure 5 the variation of concentration with x_off. There is a clear trend that haloes with higher x_off have lower concentrations, representing a delta c_vir ~ 2 decrease for haloes with the largest offsets. The trend is similar at all three of the mass ranges considered. This figure illustrates how important it is to understand the dynamical state of the haloes included in the sample."}
{"text": "In Figures 6 and 7 we again present the c(M) relation but now relax the strict resolution and equilibrium criteria. Firstly, in Figure 6 we show the relation that results from lowering the minimum particle limit for a halo to 500 particles, while maintaining the relaxation criteria. Whereas our n_p > 5000 relation agreed where simulations overlapped, we find a significant discrepancy between the simulations for masses corresponding to haloes with 5000 > n_p > 500. In particular, lower particle numbers result in lower values of c_vir. For Einasto profiles the alpha-nu relation also changes slightly. Many of the 500 < n_p < 5000 haloes have alpha ~ 0.25 and do not follow the previous quadratic alpha-nu relation. We thus caution against over-interpreting Einasto fit parameters at low particle number. In Figure 7 the c(M) relation is plotted for the entire halo sample. At all masses, the median concentrations decrease relative to those of our relaxed haloes. We also note that inclusion of unrelaxed haloes alters the alpha-nu relation slightly. Our best-fit to the full population is alpha = 0.0091 * nu squared + 0.1447."}
{"text": "Table 3 shows the best fit parameters for the full population of resolved haloes with n_p > 500 particles. In the left hand panel of Figure 7 we also plot the models of [2014arXiv1407.4730D] and [2012MNRAS.423.3018P]. [2014arXiv1407.4730D] use the phase space halo finder ROCKSTAR [2013ApJ...762..109B], and do not enforce any relaxation criteria. The mass range covered in [2014arXiv1407.4730D] is equivalent to the mass range covered by Tiamat with halo particle numbers of n_p > 1200. In this mass range we see slight evidence for an upturn in the Tiamat c(M) relation, which is consistent with their findings. Note that this upturn is a feature exclusive to our full halo sample, suggesting its connection to departures from equilibrium. Caption: The Einasto alpha-nu relation but including haloes above n_p > 500 particles. Each symbols denotes a different redshift. These low particle number haloes introduce high alpha parameters which are not in accord with the best fit quadratics found for more resolved haloes in this and previous works."}
{"text": "Our concentrations at these masses and redshifts are lower than those found by [2012MNRAS.423.3018P]. The delta c_vir ~ 1 difference likely originates from a combination of: a) the use of M_200 and c_200 in their definitions, b) the use of maximum circular velocity as a measure of concentration, which is shown in [2013arXiv1303.6158M] to reconcile differences in the c(M) relation, c) a different halo finder (Bound-Density-Maxima), and/or d) a lower particle limit of 500. We also note a similar comparison with [2014arXiv1411.4001K]. When we relax our halo equilibrium criteria we obtain concentrations which are in better agreement with DM14 and [2014arXiv1407.4730D]. Our simulations do not show an upturn after unrelaxed haloes are removed, as pointed out in [2015arXiv150200391C]. In the case of both the relaxed population and the full population we find the weak trend in the M_vir - c_vir to be steady across this mass range. The redshift dependence of the relaxed population of NFW concentrations can be described by an equation. The trend for both NFW and Einasto fits are consistent with being mass-independent at z>8."}
{"text": "In Figure 8 we show the distribution of spin parameters for relaxed haloes in the Tiamat simulation for z=5. The mass range covered is now increased so that particle number n_p > 600 [2008ApJ...678..621K]. Rather than a log-normal, the solid black lines show the best-fitting function of [2007MNRAS.376..215B], which has been shown to better describe the low spin tail. Also shown are log-normal fits by [2008ApJ...678..621K] and [2010crf..work...16M]. Although evaluated at different redshifts from Tiamat, these authors report minimal redshift-evolution in the halo spins. Our results support this, with the distribution being well fit by the Bett et al. equation with a small dependence on redshift. At z=5 we have (lambda_0, alpha) = (0.033 +/- 0.0002, 2.25 +/- 0.04) changing to (lambda_0, alpha) = (0.029 +/- 0.0004, 2.36 +/- 0.1) at z=10. Best fit parameters and errors are again derived using the MCMC method. Parameters for all redshifts are shown in Table 4 along with the numbers of haloes in each sample."}
{"text": "Both [2010crf..work...16M] and [2008ApJ...678..621K] fit a log-normal to their spin distribution, with best-fit parameters given by sigma_0= 0.57 (variance) and lambda_0 = 0.031 (mean), and sigma_0 = 0.53 and lambda_0 =0.035, respectively. Both have slightly higher spins overall. As found by [2007MNRAS.376..215B], the Bett et al. equation provides a better fit to our low spin distribution than does the log-normal. We find that unrelaxed haloes have a noticeable impact on our spin distribution, which is shown in Figure 9. Without removing these haloes we find the best-fit parameters to be (lambda_0, alpha) =( 0.042 +/- 0.0002, 2.70 +/- 0.04). Figure 10 shows the relation between spin and virial mass at z=5, with a power-law best-fit. A slight negative slope of B = -0.01 +/- 0.006 at redshift z=5 decreases to -0.023 +/- 0.016 by z=10. Fits from previous work that study the Bullock spin parameter at high redshift are also shown. We find the scatter in the spin to be roughly constant in each mass bin."}
{"text": "The existence of a small negative trend of spin parameter with mass at these redshifts is in qualitative agreement with [2008ApJ...678..621K], who find no trend at z=0-1 but an emerging trend at z=10. As noted, the virialised halo cut has an affect on our results. However, we find a small negative trend in both the full and relaxed population. For example, the lambda - M_vir relation for the full sample at redshift 5 is shown in Figure 11. Without making cuts we find a relation with slope A=-0.009 at z=5, changing to B=-0.029 at redshift 10. Our spin mass relation with sample cuts is in agreement with the result of B = -0.06 +/- 0.17 from [2008ApJ...678..621K]. Caption: The distribution of Bullock spin parameters for relaxed haloes at redshift 5 in Tiamat. Caption: The distribution of Bullock spin parameters for the full sample of haloes in Tiamat at redshift 5, without cutting unrelaxed haloes. Caption: The spin-virial mass relation for relaxed haloes at z=5. For comparison results for relaxed haloes from [2011MNRAS.411..584M] are also shown."}
{"text": "Caption: The spin-virial mass relation for the full population of haloes at z=5. For comparison fiducial results for relaxed haloes from [2011MNRAS.411..584M] are also shown. We used N-Body simulations to study concentrations and spins of DM haloes at z=5-10 and across the mass range 10^8 to 10^11 solar masses per h; the regime relevant for studies of structure formation during the epoch of reionization. The dependence of these parameters on equilibrium state was investigated by splitting our halo sample into two populations which include i) only relaxed haloes and ii) the full population. We find qualitatively similar results to previous studies. However, we find quantitative differences between our derived c(M) relations and spin-mass relations and those of previous studies, which we attribute to each author's use of different halo finders, to our higher simulation resolution, and to the different relaxation criteria used for our sample. We find the model proposed by [2014MNRAS.441..378L] reproduces both the slope and redshift evolution of our c(M) relation. Our key results are as follows:"}
{"text": "Our best-fit concentration-mass relations at z=5 have a slightly negative slope that becomes more shallow towards z=9. Limiting our analysis to equilibrium haloes has a strong impact on the derived c(M) relation due to unrelaxed haloes having lower concentrations at all masses and redshifts. Haloes with larger center-of-mass offset (x_off) typically have lower concentrations. The slope of the c(M) relation becomes shallower at higher redshift, although concentrations decrease at all masses. However, at high redshifts the number of haloes passing the equilibrium criteria is low: only ~30 per cent of haloes in the 67.8 Mpc/h box pass our resolution and relaxation cuts at z=5. Such a high proportion of unrelaxed haloes at the mass scales studied here is a distinct property of the high redshift universe, as discussed in Paper I. We find concentrations of relaxed haloes at z>5 to be well described by specific relations for NFW and Einasto fits. The intrinsic scatter around the c(M) relations is delta c_vir ~ 1 (or 20 per cent). We find the shape parameter of the Einasto profiles to depend on the peak height mass parameter."}
{"text": "Without imposing equilibrium cuts on our sample, the concentrations found in Tiamat have similar values to those reported by [2014arXiv1402.7073D], [2014arXiv1407.4730D] and [2015arXiv150506436H]. Concentrations of haloes in Tiamat are a factor of delta c_vir ~ 0.5-1 lower than reported by [2012MNRAS.423.3018P] and [2014arXiv1411.4001K]. The shallow negative trend in the c(M) relation that flattens from z=5 to z=10, and the overall decrease in the magnitude of our Einasto concentrations agree well with [2015arXiv150506436H]. The distribution of Bullock spin parameters for relaxed haloes at z >= 5 is found to be well fit by the Bett et al. equation with little evolution with redshift. Including unrelaxed haloes results in a spin distribution with a higher mean of lambda_0=0.042. As in previous studies, we find a spin-virial mass relation with a slight negative correlation at high redshift. The trend found here has a slope of approximately -0.02 at z=10. The exclusion of unrelaxed haloes also has the effect of increasing the peak of the spin distribution while the slope of the lambda-M_vir relation remains slightly negative."}
{"text": "Our best-fit power-law relation for relaxed haloes at z=5 is given, as is the relation for the full halo population. The growth of dark matter haloes drives high-z galaxy formation [2013ApJ...768L..37T], while the concentration and spin of haloes are key ingredients for semi-analytic models of galaxy formation [2006MNRAS.365...11C]. This study of these properties for haloes corresponding to the galaxies responsible for reionization will provide a valuable resource for understanding the framework of early galaxy formation. This research was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant ref. UOM0005, on its Peak Computing Facility hosted at the University of Melbourne, an initiative of the Victorian Government, Australia. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne and the Australian Government’s Education Investment Fund. This research program is funded by the Australian Research Council through the ARC Laureate Fellowship FL110100072 awarded to JSBW. ADL is financed by a COFUND Junior Research Fellowship. We thank Volker Springel for making the GADGET2 and SUBFIND codes available. We also thank N.Gnedin for useful comments on our manuscript."}
{"text": "Correlations between black holes and their host galaxies provide insight into what drives black hole--host co-evolution. We use the Meraxes semi-analytic model to investigate the growth of black holes and their host galaxies from high redshift to the present day. Our modelling finds no significant evolution in the black hole--bulge and black hole--total stellar mass relations out to a redshift of 8. The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. In our modelling the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. We find that black hole growth is dominated by instability-driven or secular quasar-mode growth and not by merger-driven growth at all redshifts. Our model also predicts that disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation, in agreement with recent observations and hydrodynamical simulations."}
{"text": "Extensive low-redshift studies reveal a complex interplay between galaxies and the supermassive black holes that reside at their centres, with clear correlations observed between black hole mass and host bulge mass, total stellar mass, velocity dispersion and luminosity [Magorrian1998, Gebhardt2000, Merritt2001, Tremaine2002, Marconi2003, Haring2004, Bentz2009, Kormendy2013, Reines2015]; see the review by [Heckman2014]. These tight correlations suggest a co-evolution between galaxies and supermassive black holes, which may be causal, due to feedback from the active galactic nucleus [AGN; e.g.][Silk1998, Matteo2005, Bower2006, Ciotti2010] or the efficiency with which the galaxy can fuel the black hole [e.g.][Hopkins2010, Cen2015, AnglesAlcazar2017], or coincidental, simply due to mergers causing both black hole and galaxy growth [e.g.][Haehnelt2000, Croton2006b, Peng2007, Gaskell2011, Jahnke2011]. To understand what drives black hole--host co-evolution, it is necessary to study how these correlations change with redshift."}
{"text": "Observing high-redshift black hole--host correlations is fraught with difficulties. Host galaxies are hard to detect since they are often completely outshined by the AGN light, particularly in the rest-frame optical where common stellar mass estimators can be used [Zibetti2009, Taylor2011]. Subtracting the quasar light has resulted in host detections out to redshift z is approximately equal to 2 [Jahnke2009, Mechtley2016], but is yet to be successful for detecting the highest redshift quasars at redshift z is approximately equal to 6 [Mechtley2012]. For these quasars, host masses are often estimated using the widths of observed submillimeter and millimeter emission lines, such as the [CII] 158 micron and CO (6--5) lines [Wang2013]. However, dynamical masses determined from emission line widths are highly dependent on the assumptions made, such as the gas-disc geometries and inclination angles [Valiante2014]. In fact, inclination angle assumptions can change the determined black hole mass to bulge mass ratio measurements by roughly 3 orders of magnitude [Wang2013]."}
{"text": "In addition, the emission regions may not trace the spatial distribution of the stellar component of the galaxy, meaning that these dynamical masses may not be representative of the total stellar mass [Narayanan2009]. Determining the black hole masses of high-z quasars is also difficult, with emission-line based estimators relying on calibrations at low redshift. Where these observations are unavailable, Eddington accretion rates are instead often assumed to estimate the black hole mass [as in e.g.][Wang2013, Willott2017], which also leads to large uncertainties. High-redshift studies of the black hole--host mass relations are thus very uncertain. With this in mind, high redshift observations find black holes that are more massive than expected by the local relation, where the canonical black hole--bulge mass ratio is 10 to the power of (-2.31 +/- 0.05) for a bulge mass of 10^11 solar masses [Kormendy2013]."}
{"text": "For example, ALMA observations of five redshift z is approximately equal to 6 quasar hosts show black hole to dynamical mass ratios ranging from 10 to the power of -1.9 to 10 to the power of -1.5 [Wang2013]. Similar studies at redshift z is approximately equal to 4--7 [Maiolino2007, Riechers2008, Venemans2012] also give estimates for individual quasars of a black hole mass to dynamical mass ratio greater than or approximately equal to 10 to the power of -2, which is significantly larger than the local value if dynamical masses and bulge masses are assumed to be roughly equivalent. This suggests a faster evolution of the first supermassive black holes relative to their host galaxies [Valiante2014], which could potentially be a result of super-Eddington accretion [Volonteri2015]. The high observed black hole mass to dynamical mass ratio relation at high redshift could, however, be a result of selection effects [Lauer2007, Schulze2011, Schulze2014, DeGraf2015, Willott2017]."}
{"text": "[Willott2017] suggest that since only the most massive z>6 black holes are observed, if the relation has a wide dispersion then one would expect to see a higher value due to the Lauer bias [Lauer2007]: since the luminosity function falls off rapidly at high masses, the most massive black holes occur more often as outliers in galaxies of smaller masses than as typical black holes in the most massive galaxies. Indeed, [Willott2017] found that black holes with mass less than 10^9 solar masses at redshift z>6 fall below the black hole mass--dynamical mass relation for low redshift galaxies, in contrast to the opposite being true for higher mass black holes. Similarly, [Schulze2014] claim that selection effects are the reason for the observed evolution of the black hole mass--bulge mass relation; on applying a fitting method to correct for selection effects, they find no statistical evidence for a cosmological evolution in the black hole mass--bulge mass relation."}
{"text": "A lack of evolution in the black hole--host relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016], which observes very little evolution in the black hole mass--stellar mass relation from redshift z=0 to 5, and BlueTides [Huang2018], which finds a black hole mass--stellar mass relation at redshift z=8 that is consistent with the local [Kormendy2013] relation. [DeGraf2015], on the other hand, found that the relation evolves slightly for redshift z greater than or equal to 1 for the highest mass black holes, with a steeper slope at the high-mass end at higher redshifts, making selection effects important. The more statistical study of [Schindler2016] found that the ratio of the black hole to stellar mass density is constant within the uncertainties from redshift z=0 to 5, with a slight decrease in the ratio at redshifts between 3 and 5; this is also consistent with no cosmological evolution in the black hole mass--stellar mass relation."}
{"text": "In this work we explore the evolution of the black hole--host relations with the Meraxes semi-analytic model [Mutch2016]. Meraxes is designed specifically to study galaxy formation and evolution at high redshifts, making it ideal for studying the evolution of black holes and their host galaxies. In this work we use Meraxes, a semi-analytic model designed to study galaxy evolution at high redshifts [Mutch2016]. Using the properties of dark matter halos from an N-body simulation, Meraxes analytically models the physics involved in galaxy formation and evolution. We run Meraxes on the collisionless N-body simulations Tiamat and Tiamat-125-HR [Poole2016, Poole2017]. Tiamat is ideal for studying high redshifts, with a high mass and temporal resolution. Tiamat runs from redshift z=35 to z=1.8, with a box size of (67.8 per h Mpc)^3, 2160^3 particles of mass 2.64x10^6 per h solar masses, and a high cadence of 11.1 Myr per output snapshot at redshift z>5."}
{"text": "Tiamat-125-HR is a low-redshift counterpart to Tiamat, running from redshift z=35 to z=0 with the same temporal resolution, but with a lower mass resolution (1080^3 particles of mass 1.33x10^8 per h solar masses) and larger box size of (125 per h Mpc)^3, more suited for low-redshift studies. Throughout this work, we use the higher resolution Tiamat at high-redshifts, and Tiamat-125-HR for redshift z<2, unless otherwise specified. Meraxes assumes that galaxies reside in the centre of dark matter haloes produced by the N-body simulation. Using the properties of these haloes, Meraxes analytically models the baryonic physics involved in galaxy formation and evolution, such as gas cooling, star formation, black hole growth, and supernova and black hole feedback. These analytical prescriptions involve a range of free parameters, which must be calibrated using observations such as the stellar mass function."}
{"text": "In Meraxes, stars in galaxies reside in three components: an exponential disc, a spheroidal merger-driven bulge and a disc-like instability-driven bulge. Bulges grow through both galaxy-galaxy mergers and disc-instabilities. In Meraxes, we assume that galaxy mergers with merger ratio greater than 0.01 trigger a burst of star formation, by causing shocks and turbulence in the cold gas of the parent galaxy. The galaxy will also accumulate the mass of the secondary galaxy. We assume that the dominant mass component of the primary galaxy will regulate where these stars produced by the burst and the secondary's mass will be deposited. If the primary is dominated by a discy component, the mass is added to the instability-driven bulge. Otherwise, we assume that the new stars will accumulate in shells around the spheroidal merger-driven bulge. In major mergers, where the merger ratio is greater than 0.1 or 0.3, we assume that the stellar disc and instability-driven bulges are destroyed, with all stars placed into the merger-driven bulge."}
{"text": "In our model we assume that the galaxy discs are thin, with an exponential surface density and flat rotation curve. Such discs become unstable if the disc mass is greater than the disc velocity squared times the scale radius divided by the gravitational constant, which equals the critical mass [Efstathiou1982, Mo1998]. Here, we take the disc mass as the combined mass of both gas and stars in the disc, and the disc velocity and scale radius as the mass-weighted velocity and scale radius of the stellar and gas discs. If such a disc instability occurs, Meraxes returns the disc to stability by transferring the unstable mass of stars from the disc to the instability-driven bulge. The Meraxes black hole model was introduced in Q17, and updated to include instability-driven growth in M19. In Meraxes, black holes are seeded in every newly-formed galaxy, with a seed mass of 10^4 solar masses. Black holes then grow by accretion of both hot and cold gas, through the radio- and quasar modes, respectively."}
{"text": "We also assume that black holes grow in galaxy mergers, with the black holes in each galaxy merging together. Black holes accrete hot gas from the static hot gas reservoir around the galaxy, at a fraction of the Bondi-Hoyle accretion rate. We consider this fraction a free parameter, which adjusts the efficiency of radio-mode black hole growth [Croton2016]. This accretion is limited by the amount of hot gas in the reservoir and the Eddington limit. A fraction of this accretion mass is radiated away and so during one snapshot, black holes grow through the radio-mode by the remaining mass. We include the effects of radio-mode AGN feedback by assuming that a fraction of the radiated energy is coupled to the surrounding gas, adiabatically heating a mass which is subtracted from the cooling flow, regulating the accretion of new gas onto the black hole [Croton2006a, Croton2016]. This AGN feedback has no significant effect on the results of Tiamat at redshift z greater than or equal to 2."}
{"text": "Black holes accrete cold gas from the galaxy, when triggered by either a galaxy-galaxy merger or a disc instability. During such an event, the black hole mass grows by a certain amount, where the virial velocity and a free parameter adjust the growth efficiency. For merger-triggered growth, we take the efficiency parameter to be proportional to the merger ratio. For instability driven growth, we consider two separate free parameters. During the quasar mode, black holes are assumed to accrete at the Eddington rate, and thus the mass accreted by the black hole during one simulation snapshot is limited. This can result in the mass being accreted over multiple simulation snapshots. We incorporate quasar-mode AGN feedback by considering the energy injected into the gas during a simulation time-step. We assume that this energy generates a wind that heats the cold disc gas and transfers it to the hot gas reservoir, depleting the supply of cold gas available for the black hole to accrete. If sufficient energy is injected by the quasar, this wind can also eject the hot gas."}
{"text": "We calculate the bolometric luminosities of each black hole in the model following the Q17 method, which assumes Eddington luminosity for all accreting black holes, and self-consistently calculates the duty cycle. We consider the luminosities from both the quasar- and radio-modes of accretion. At high-redshifts the contribution from the radio-mode is negligible. At the lowest redshifts (redshift z less than or equal to 2), the radio-mode becomes a more significant growth mechanism for the most massive black holes, and so their luminosities are enhanced slightly by the addition of the radio-mode luminosity. We convert from bolometric to B-band luminosities using the [Hopkins2007] bolometric correction, and then assume a continuum slope of 0.44 to convert to UV luminosities. We also account for obscuration due to quasar orientation, by scaling the UV luminosity function by a factor related to the opening angle of quasar radiation. In our model we assume a constant opening angle, for simplicity, which is a free parameter in our model."}
{"text": "In M19 we calibrated the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8, and the black hole--bulge mass relation at redshift z=0. Using this model, we find that the black hole mass function and quasar luminosity functions are much larger than predicted by the observations. In addition, we note that [Shankar2016] find significant selection biases in the black hole--bulge mass relation---a topic of recent debate [see e.g.][Kormendy2019]. Due to the M19 predictions and this potential bias, we assume that the [Shankar2009] redshift z=0 black hole mass function is a less biased indicator of the local black hole population, and retune the model here to better reproduce the black hole observations. Note that we use the same parameter values for Tiamat and Tiamat-125-HR, and use both simulations to tune the model: Tiamat for matching redshift z greater than or equal to 2 observations and Tiamat-125-HR for redshift z<2."}
{"text": "We find that our results from the two simulations are generally consistent at redshift z is approximately equal to 2, with broad qualitative agreement at higher redshifts. We calibrate the free parameters in the model to match the observed stellar mass functions at redshift z=0--8, the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0, and the quasar X-ray luminosity functions from redshift z=5 to 2. Since [Shankar2016] find that the observed black hole--bulge mass relation is biased to high black hole masses, we also require our model to not over-predict this relation, however we do not otherwise tune to it. We note that our best models produce black hole--host mass relations lower than the observations, consistent with the expectations of [Shankar2009], and have steeper slopes. We find that these criteria are met by a range of free parameter values for the merger-driven black hole growth efficiency, and the definition of a major merger."}
{"text": "We note that all of these parameter sets produce very similar results. As a further check of the black hole population, we plot the black hole accretion rate density as a function of redshift for models with these different merger-driven black hole growth efficiencies. We find that the models with lower efficiencies give black hole accretion histories in approximate agreement with the observations. The larger efficiencies overproduce measurements of the black hole accretion rate density [e.g.][Delvecchio2014]. The opening angle of AGN radiation, theta, adjusts the normalization of the UV luminosity function. We tune this to match the observations, finding a preferred theta of 70 degrees, corresponding to an observable fraction of UV quasars of 18 per cent. We show the quasar X-ray luminosity functions at redshift z=5--0, with X-ray luminosities calculated using the [Hopkins2007] bolometric to X-ray correction."}
{"text": "At redshift z=2 the model and the observations agree remarkably well. At redshift z>2 the model over-predicts the observed quasar X-ray luminosity function at intermediate luminosities, by up to ~0.7 dex at redshift z=4, while at redshift z<2 the model under-predicts the luminosity function at these luminosities. Our model shows better agreement with the observations than previous versions of Meraxes. While the observations show a slight increase in the X-ray quasar luminosity functions from redshift z=4 to 2, the model predicts a slight decrease. In fact, we cannot find a combination of black hole parameters that results in a redshift evolution that matches that of the observed X-ray quasar luminosity function at redshift z>2. However, the key quantity of black hole accretion rate density is predicted by the model to peak at redshift z=2 as observed."}
{"text": "In addition to published uncertainties in the observations, it may also be the case that at higher redshifts X-ray AGN are more likely to be obscured, which is consistent with evidence from a range of X-ray observations [Treister2006, Vito2014, Buchner2015]. Thus we argue that the inability of our model to match the redshift evolution of the X-ray quasar luminosity function may not represent a significant concern. We show the quasar UV luminosity functions at redshift z=5--0. We find that, as with the X-ray luminosity function, the UV luminosity function decreases from redshift z=5 to 0, though it agrees well with observations at redshift z>2. At redshift z<2, however, we note that the faint-end of the UV luminosity function becomes flat, and by redshift z<1 there is a significant disagreement with the observations, with the model producing too many luminous quasars."}
{"text": "The black hole accretion rate density becomes significantly higher than the observations at redshift z<1, consistent with the quasar luminosities being overestimated at these redshifts. This excess black hole accretion is most likely a result of the model missing important physics required for modelling low-redshift galaxy evolution, particularly in the quenching of massive galaxies, or due to the simplifications assumed in the model such as a constant black hole accretion efficiency. However, as the overall accretion rate density at these redshifts is low, this will not have a significant impact on the black hole mass, an integrated quantity. Thus, while the redshift z<1 black hole accretion rates are overestimated, the black hole mass function and black hole--host mass relations are reliable at low redshifts. Indeed, we find that assuming a lower Eddington ratio significantly improves the match between the model and observed UV luminosity functions at redshift z<1."}
{"text": "However, this causes the model to no longer match the observations at higher redshifts. Thus, some evolving Eddington ratio is necessary for Meraxes to accurately reproduce the redshift z<1 quasar UV luminosity function. We now use the model described to explore black hole growth. We investigate the redshift evolution of the black hole--host scaling relations. To investigate the redshift evolution of the black hole--bulge and black hole--total stellar mass relations we first perform linear least squares fits to the relations at a range of redshifts. We only include galaxies with mass > 10^9.5 solar masses in our fits, so that they are not biased by the large number of low-mass galaxies. Both relations have a slope and normalization that increase with redshift from redshift z=0 to 2, with much weaker evolution for redshift z>2."}
{"text": "Relative to the scatter in the relations, we see minimal evolution in both the black hole--bulge and black hole--total stellar mass relations from redshift z=0 to 6. This lack of evolution in the black hole--host mass relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016] and BlueTides [Huang2018]. We find that our black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. While the black hole mass has a slightly stronger relationship with the bulge stellar mass, the black hole and total stellar mass are still tightly correlated. The scatter in the relations is slightly larger than the 0.28 dex observed by [Kormendy2013] locally. However, they are very consistent with those from the BlueTides simulation at high redshift."}
{"text": "The scatter decreases with increasing stellar mass. The median black hole mass to total stellar mass ratio as a function of redshift for galaxies with black hole mass > 10^6 solar masses shows no statistically-significant evolution out to redshift z is approximately equal to 8. This is consistent with current high redshift observations; when selection effects are accounted for, the observations at high redshift are consistent with no cosmological evolution in these relations [Schulze2014]. Our model predicts no significant evolution in the black hole--host mass relations, with the scatter in the relations decreasing at the highest redshifts. This indicates that there is a connection between the growth of black holes and their host galaxies. Indeed, our model includes joint triggering of star formation and black hole growth during galaxy mergers, and black hole feedback which regulates star formation, meaning that the co-evolution of black holes and galaxies is implicit in our model."}
{"text": "This is not consistent with the scenario proposed by [Peng2007] and [Jahnke2011], for example, where the black hole and galaxy growth is uncorrelated and the relationships are generated naturally within a merger driven galaxy evolution framework, due to a central-limit-like tendency. The median black hole mass to total stellar mass ratio as a function of redshift with galaxies split into black hole mass bins shows that lower mass black holes have lower mass ratios than higher mass black holes. This will lead to a notable selection bias, since when observing the most massive black holes, the measured ratio will be higher than that of the entire population. This is generally expected for any sample selected by black hole mass or luminosity where the scatter in the relation is large [e.g.][Lauer2007]. Finally, we note an interesting effect of changing the parameter controlling the black hole efficiency for converting mass to energy."}
{"text": "For a higher efficiency, the median black hole--stellar mass ratio decreases at redshifts z greater than or approximately equal to 6, instead of remaining constant with redshift. We investigate the cause of this high-redshift decrease in the black hole--host relation by considering the Eddington limit. Increasing the efficiency from 0.06 to 0.2 decreases the Eddington limit. This results in many black holes having Eddington-limited growth at the highest redshifts (redshift z greater than or approximately equal to 6), which is not the case for the lower efficiency model. This causes black holes to grow slower than their host galaxies at high redshifts, resulting in a decreased black hole--stellar mass ratio. Observing the high-redshift black hole--stellar mass relation may therefore probe the Eddington limit and the efficiency of black holes in converting mass to energy."}
{"text": "We consider the cumulative fraction of black hole mass formed through each of the mechanisms in our model: black hole seeding, merger-driven quasar-mode accretion, instability-driven quasar-mode accretion, radio-mode accretion and black hole--black hole coalescence in galaxy mergers. The merger-driven growth mode becomes more important at low redshifts, at both low- and high-black hole masses. On average, instabilities grow the majority of mass in black holes at all redshifts, except for galaxies with black hole mass > 10^9 solar masses at redshift z is approximately equal to 0, whose black hole growth becomes dominated by galaxy mergers. Radio-mode growth slowly increases in significance with redshift, yet still has only contributed to a small proportion of the total black hole mass by redshift z=0, except at the highest masses. Note that we consider growth from disc instabilities that are triggered by earlier galaxy mergers as growth via the instability-driven mode."}
{"text": "We also consider the instantaneous growth fractions of black hole mass formed through each mechanism as a function of redshift. As discussed, the model produces unreliable black hole accretion rates at redshift z<1, and so we only consider these black hole growth rates at redshift z>1. The instability-driven growth mode is the dominant growth mechanism, on average, at all redshifts, regardless of black hole mass. The merger-driven quasar mode and black hole--black hole coalescence mode are sub-dominant at all redshifts. The radio-mode grows more mass at low redshift and in the most massive galaxies, with the percentage of total instantaneous black hole growth from this mode increasing from only 0.1 per cent at redshift z=5 to almost 5 per cent at redshift z is approximately equal to 1. Our finding that mergers are not the dominant mechanism for growing black holes is in agreement with a range of observations."}
{"text": "For example, [Koss2010] find that only 25 per cent of local, moderate luminosity X-ray AGN show signs of mergers, though the fraction is much higher for luminous AGN [Hong2015]. From redshift z from approximately 0.3 to 1.0, [Cisternas2010] find that the vast majority (>85 per cent) of X-ray selected AGN do not show signs of mergers, suggesting that the bulk of their black hole accretion has been triggered by some other mechanism. This is also consistent with the findings of [Georgakakis2009], [Villforth2018], [Schawinski2012], [Mechtley2016], [DelMoro2015] and [Marian2019] for AGN at various redshifts. Our result that disc instabilities cause the majority of black hole growth is also consistent with predictions from other simulations. In the GALFORM semi-analytic model, [Fanidakis2011] found that the growth of black holes is dominated by accretion due to disc instabilities."}
{"text": "Using an updated GALFORM model, [Griffin2019] found that accretion of hot gas dominates the growth of black holes at redshift z<2, with disc-instabilities dominant at higher redshifts. [Hirschmann2012] found that instability-driven black hole growth was required to reproduce AGN downsizing, and that while major mergers are the dominant trigger for luminous AGN, especially at high redshift, disc instabilities cause the majority of black hole growth in moderately luminous Seyfert galaxies at low redshift. [Menci2014] find that in their semi-analytic model disc instabilities can provide enough black hole accretion to reproduce the observed AGN luminosity functions up to redshift z is approximately equal to 4.5, but are not likely to be dominant for the highest luminosity AGN or at the highest redshifts. In contrast, [Shirakata2018] find that the primary trigger of AGN at redshift z less than or equal to 4 in their semi-analytic model is mergers."}
{"text": "The hydrodynamical simulation Horizon-AGN found that only ~35 per cent of black hole mass in local massive galaxies is directly attributable to merging, with the majority of black hole growth instead growing via secular processes [Martin2018]. The Magneticum Pathfinder Simulation also found that merger events are not the dominant fuelling mechanism for black holes in redshift z=0--2, with merger fractions less than 20 per cent, except for very luminous quasars at redshift z is approximately equal to 2 [Steinborn2018]. Finally, we comment on the effect of the efficiency parameters for merger-driven and instability-driven black hole growth in the model. We find the instability-driven efficiency from tuning the model, whereas the merger-driven efficiency is less constrained, with several values producing reasonable model results."}
{"text": "Having a merger growth efficiency that is twice, six times or even 18 times larger than the instability-driven growth efficiency may have an effect on the conclusions outlined above. We find, as expected, that models with larger merger efficiencies result in more merger-driven growth. For a merger efficiency twice the instability efficiency, the instability-driven mode still dominates at redshift z=2, while for a six times larger efficiency, the merger-driven mode begins to dominate at the highest black hole masses. For the model with an 18 times larger merger efficiency, the merger-driven mode contributes even more black hole growth, but is still not the dominant growth mode for black holes with mass between 10^6 and 10^9 solar masses. Thus, while the efficiency parameter for merger-driven growth has some effect on the relative distributions of the instability-driven and merger-driven growth modes, the instability-driven mode is still dominant for the majority of black holes, even if the merger growth efficiency is as much as 18 times larger than the secular growth efficiency."}
{"text": "A popular explanation for the black hole--host correlations is that major mergers drive the growth of both black holes and bulges [e.g.][Haehnelt2000, Croton2006b]. If this were the case, one would expect that black holes would only correlate with galaxy properties directly related to the merger process, such as bulge mass, and not, for example, total stellar mass. [Simmons2017] consider a sample of 101 disc-dominated AGN hosts from the SDSS, which they assume must have a major merger-free history since redshift z is approximately equal to 2. They found that these galaxies lie on the typical black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation. This indicates that the substantial and ongoing black hole growth in these merger-free disc galaxies must be due to a process other than major mergers, and that major mergers cannot be the primary mechanism behind the black hole--host correlations."}
{"text": "We plot the black hole mass--total stellar mass and black hole mass--bulge mass relation for disc-dominated and bulge-dominated galaxies at redshift z=0. Our simulated disc galaxies lie on the black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation, as they have small bulges relative to their black hole mass. This is consistent with the [Simmons2017] observations, and the results from the Horizon-AGN hydrodynamical simulation [Martin2018]. However, we see a less significant offset, which occurs at lower black hole masses than [Simmons2017] and [Martin2018], since the black holes in our disc-dominated galaxies are less massive in comparison. [Mutlu-Pakdil2017] also find no dependence of the black hole mass--total stellar mass relation on galaxy type in the Illustris hydrodynamical simulation. [Martin2018] suggest that major mergers therefore cannot be primarily responsible for feeding black holes."}
{"text": "This is consistent with our finding that the instability-driven mode is the dominant growth mechanism for black holes. We use the Meraxes semi-analytic model to investigate the evolution of black holes and their relations to their host galaxies. We find the following key predictions of our model: There is minimal statistically-significant evolution in the black hole--bulge and black hole--total stellar mass relations out to high redshifts (redshift z is approximately equal to 8). The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. This indicates that the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. Higher mass black holes have higher black hole--total stellar mass ratios, leading to a significant selection effect in measurements of this ratio when observing only the most massive black holes."}
{"text": "The instability-driven or secular quasar-mode growth is the dominant growth mechanism for black holes at all redshifts. The contribution from merger-driven quasar-mode growth only becomes significant at low redshift for black holes with mass greater than or approximately equal to 10^9 solar masses. Disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation. Our simulation is limited in making predictions for the highest redshift quasars at redshift z=6--7 due to the simulation box size and resolution. In future work we will run Meraxes on larger N-body simulations in order to make predictions for these objects. We calibrate the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8 and the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0. The black hole mass functions produced by Tiamat and Tiamat-125-HR are converged at redshift z=2 for black holes with mass > 10^7.1 solar masses [see Marshall2019]."}
{"text": "We therefore focus on matching the observed black hole mass functions at masses > 10^7.1 solar masses. While the [Shankar2009] and [Davis2014] relations are different, particularly at black hole mass ~ 10^8.5 solar masses, they are similar relative to the freedom we have in adjusting our model black hole mass function, and so when calibrating we found the most reasonable fit to both. In the model stellar mass function, we also plot the Meraxes stellar mass function produced when AGN feedback is switched off. This shows that AGN feedback has no effect on galaxies in Tiamat at redshift z greater than or equal to 2, but suppresses the growth of the most massive galaxies at lower redshifts as seen in Tiamat-125-HR. Throughout this work, we use the higher resolution Tiamat simulation at redshift z greater than or equal to 2, and Tiamat-125-HR for redshift z<2, where Tiamat is unavailable."}
{"text": "We find that the results discussed in this paper are generally consistent between the two simulations at redshift z is approximately equal to 2. However, one notable result is that the best-fitting black hole--stellar mass relations change rapidly between redshift z=2 (using Tiamat) and z=1 (using Tiamat-125-HR). To verify that this jump is not purely a result of the simulation change, we show the best-fitting relations from redshift z=6--0 using Tiamat-125-HR. The Tiamat-125-HR simulation shows similar results to those found using Tiamat at redshift z greater than or equal to 2, with a slightly milder but still relatively rapid evolution from redshift z=2 to z=1. The qualitative result of the evolution being insignificant relative to the scatter in the relation still holds. Thus, while the change in simulation slightly amplifies the rapid change in the black hole--stellar mass relations from redshift z=2 to z=1, this does not change our conclusions."}
{"text": "We also note that where the black hole mass functions are converged, the black hole--stellar mass relations are in good agreement between the two simulations."}
{"text": "We directly compare predictions of dwarf galaxy properties in a semi-analytic model (SAM) with those extracted from a high-resolution hydrodynamic simulation. We focus on galaxies with halo masses of 10^9 < virial mass / solar mass less than or approximately equal to 10^11 at high redshift (redshift z >= 5). We find that, with the modifications previously proposed in [qin2018], including to suppress the halo mass and baryon fraction, as well as to modulate gas cooling and star formation efficiencies, the SAM can reproduce the cosmic evolution of galaxy properties predicted by the hydrodynamic simulation. These include the galaxy stellar mass function, total baryonic mass, star-forming gas mass and star formation rate at redshift z~5-11. However, this agreement is only possible by reducing the star formation threshold relative to that suggested by local observations. Otherwise, too much star-forming gas is trapped in quenched dwarf galaxies."}
{"text": "We further find that dwarf galaxies rapidly build up their star-forming reservoirs in the early universe (redshift z>10), with the relevant time-scale becoming significantly longer towards lower redshifts. This indicates efficient accretion in cold mode in these low-mass objects at high redshift. Note that the improved SAM, which has been calibrated against hydrodynamic simulations, can provide more accurate predictions of high-redshift dwarf galaxy properties that are essential for reionization study. Reionization refers to an important process after the Big Bang, during which the intergalactic medium (IGM) was transiting from neutral hydrogen to its ionized state [Wyithe:2004kb]. According to the observed galaxy sample at high redshift [Bouwens2014, Bouwens2015, Stefanon2016arXiv161109354S, Oesch2016ApJ...819..129O], this process can only happen with ionizing photons from much fainter galaxies taken into account [Robertson2013ApJ...768...71R, duffy2014low, Bouwens:2015hk, Liu2016]."}
{"text": "Although there are still some debates on other possible sources that can dominate the high-redshift photon budget such as active galactic nuclei (AGN; [Giallongo2015A&A...578A..83G, Madau2015ApJ...813L...8M, Qin2017c, Hassan2018MNRAS.473..227H]), dwarf galaxies that are beyond our observational capabilities are generally thought to have driven the Epoch of Reionization (EoR). In this context, understanding the formation of these unobserved objects is crucial to studying the EoR and can only be probed at this stage with theoretical simulations. Hydrodynamic simulations evolve dark matter and baryonic particles simultaneously and provide direct insights into the relevant astrophysical process [Vogelsberger2014, Schaye2014, Hopkins2014MNRAS.445..581H, feng2015bluetides]. However, resolving dwarf galaxies within a cosmological volume for reionization studies usually involves more than a few billions of particles, which remains computationally challenging at this stage. A more efficient method is to apply semi-analytic models (SAMs; [croton2006many, Somerville2008, guo2011dwarf, Henriques2015]) to N-body simulations that only consider collisionless particles."}
{"text": "Using the halo properties inherited from the parent simulation, SAMs approximate baryonic physics such as gas accretion, star formation and feedback using simplified scaling relations. These relations are motivated directly from physical processes, or empirically from observational results and more complicated numerical techniques such as hydrodynamic simulations and radiative transfer calculations. The semi-analytic prescriptions that indirectly model galaxy formation introduce free parameters to describe efficiencies which are inevitably accompanied by parameter degeneracies [Mutch2013, Henriques2013]. This can make their predictions sometimes controversial, and potentially disconnected from the true behaviour in the universe. An alternative to validate SAMs in the absence of observations at high redshift is to compare their results against hydrodynamic calculations that start from identical cosmological initial conditions. The goal of this work is to capture emergent behaviours from the hydrodynamic simulations and to improve the parametrised modelling in SAMs as so to replicate these processes."}
{"text": "Under the assumption that hydrodynamic simulations are a more natural description of the astrophysical phenomenon and hence more representative of real galaxies, we can explore the semi-analytic prescriptions for quantities that are, in practice, unobservables and potentially reveal improper assumptions or missing physics in SAMs. [Guo2016] compared the L-galaxies [Cole2000, Bower2006] and GALFORM [Springel2005, Henriques2015] SAMs with the EAGLE hydrodynamic simulations [Schaye2014], and concluded that the models can reproduce the stellar mass function predicted by EAGLE. However, discrepancies were also found in the efficiencies of stellar and AGN feedback as well as the prediction of stellar mass-metallicity and size relations. [Mitchell:2017je] also used EAGLE to assess GALFORM and found the angular momentum as well as the baryon cycling might not be properly traced in the SAM, leading to inaccurate predictions of galaxy sizes."}
{"text": "[Stevens:2017fi], on the other hand, investigated cooling of Milk Way-like galaxies in EAGLE and addressed the necessity of updating the cooling prescription employed in most SAMs (see recent updates of the cooling model in [Hou2018mnras.475..543h, Hou2018arxiv180301923h]). We, in the previous paper [qin2018], also found that the cooling prescription needs revision for more accurate modelling of low-mass galaxies at high redshift and proposed an alternative modification to the current prescription, avoiding the introduction of a new model. [Cote:2017uh] recently extended the comparison from cosmological simulations of smoothed particles to zoom-in simulations of a system with a total mass of approximately 10^9 solar masses, and investigated the difference in dwarf galaxy formation between a SAM and hydrodynamic simulation. They found their SAM was successful in reproducing the hydrodynamic calculation of star formation history but with a prediction of a much narrower distribution of metallicity compared to the hydrodynamic result."}
{"text": "This is the second paper following the work of [qin2018], where we investigated the performance of SAMs when applied to high-redshift dwarf galaxies. We used the Meraxes SAM [Mutch2016a] as an example and focused on gas accretion, cooling and star formation with reionization and supernova feedback isolated. We compared the stellar and gas masses with a high-resolution hydrodynamic simulation from the Smaug suite, and found that, in the SAM, 1) due to the lack of hydrostatic pressure in parent N-body simulations, inheriting halo properties directly from the dark matter halo merger trees overestimates the total mass of haloes hosting dwarf galaxies; 2) the assumption that, in the absence of feedback, haloes consists of a baryonic reservoir with a mass of the cosmic baryon fraction of their total mass is not accurate for dwarf galaxy formation modelling; 3) star formation modelled by consuming the total gas disc in a few dynamical times of that disc cannot capture the evolutionary path of star formation implemented in hydrodynamic simulations; and 4) gas accreted by dwarf galaxies is cold."}
{"text": "Accordingly, we proposed modifications to SAMs, seeking for consistency with hydrodynamic simulations in calculations of the evolution of stellar and gas components of dwarf galaxies. In this work, we include these modifications as well as feedback from reionization and supernovae, and investigate whether the updated SAM can broadly agree with the hydrodynamic calculation of dwarf galaxies in the presence of feedback. We start with a brief review of the Meraxes SAM as well as the modifications proposed in [qin2018] and the Smaug hydrodynamic simulation suite in Section 2. We then present and discuss our comparison results in Section 3. Conclusions are given in Section 4. In this work, we adopt the Chabrier initial mass function (IMF) in the mass range of 0.1-120 solar masses and cosmological parameters from WMAP7."}
{"text": "The Dark-ages Reionization And Galaxy Formation Observable from Numerical Simulation (DRAGONS) project employs N-body simulations, hydrodynamic simulations and SAMs to study reionization and galaxy formation at high redshift (redshift z >= 5). In the previous publication of this series, we used the Meraxes SAM as an example and investigated the semi-analytic modelling prescriptions adopted in the literature. We focussed on comparisons of dwarf galaxy properties calculated by Meraxes with a simplified model that ignores feedback from the Smaug hydrodynamic simulation suite. Based on the comparison, we proposed modifications to the halo properties as well as the cooling and star formation prescriptions. In this work, we include reionization and supernova feedback, and extend the comparison of high-redshift dwarf galaxies modelling with a molecular-hydrogen-based star formation law in the SAM."}
{"text": "We briefly introduce the Meraxes SAM and Smaug hydrodynamic simulation in this section with emphasis on reionization and supernova feedback. Meraxes evolves galaxies with scaling relations capturing baryonic processes. These include gas infall, cooling, star formation, supernova feedback, metal enrichment, stellar mass recycling, reionization, supermassive black hole growth, AGN feedback and mergers. It also calculates the ionization state of the IGM using the 21cmFAST semi-numerical algorithm. Note that, in order to take hydrostatic pressure into account in this work, halo masses inherited from the merger trees that are constructed from collisionless N-body simulations as well as total baryonic masses are updated using the halo mass and baryon fraction modifiers provided in [Qin2017a]."}
{"text": "Gas falls into a halo from the IGM and cools through thermal radiation. Within a transition time-scale, this process leads to the formation of a star-forming disc, which is assumed to follow an exponential surface density profile. In previous DRAGONS publications, we follow [croton2006many], form stars by consuming the total star-forming gas, and calculate the star formation rate (SFR) by a formula where the depletion time-scale of total star-forming gas on the disc is proportional to the dynamical time-scale of the host halo. However, this was found to be inconsistent with the implementation in hydrodynamic simulations. In this work, we instead adopt a different equation and use free parameters to directly adjust the evolutionary path of the depletion time-scale. A second star formation prescription will be explored in this work, the detail of which will be presented in Mutch et al. (in prep.)."}
{"text": "Note that this prescription is based on the depletion of molecular hydrogen (see [Lagos2011] and references therein) and is considered as a more physically plausible model compared to the total-gas-based star formation prescription. First, we assume stars follow the same distribution as the interstellar medium (ISM) and they are considered as a stellar disc with an exponential surface density profile. We then calculate the pressure of the ISM accounting for both stars and hydrogen through the [Elmegreen1993] approximation. In order to split the disc into molecules and atoms, the observed relation between the ISM pressure and the surface density ratio of neutral to molecular hydrogen is implemented. [Blitz2006] investigated the neutral hydrogen, CO and stellar densities of 14 nearby galaxies and found a power-law relation between the ratio of neutral to molecular hydrogen surface densities and the ISM pressure. With this, we estimate the molecular hydrogen mass and calculate the SFR."}
{"text": "Inferred from the stellar lifetime-mass relation and the assumed IMF, we calculate the fraction of the newly formed stars which will have reached the supernova stage at the end of the current time step. These stars recycle their masses to the ISM, and the metals and energy produced by the supernovae provide feedback to the environment. In particular, the metals enhance the cooling rate through the metallicity dependent cooling function while the supernova energy leads to transition of gas between different reservoirs. In practice, supernova energy converts star-forming gas to hot (i.e. non-star-forming gas) and, in the case of strong supernova feedback, further ejects hot gas from the galaxy. In this work, we adopt the [guo2011dwarf] prescriptions to calculate the energy coupled to the surrounding gas. We consider two supernova feedback regimes: 1) contemporaneous feedback; and 2) delayed feedback where long-lived stars formed at earlier times are taken into account."}
{"text": "Therefore, the total energy released in the current snapshot is the sum of the supernova energy from stars formed in the current and previous 4 snapshots. On the other hand, the expected mass of gas that is heated by supernovae depends on the mass loading factor, which is assumed to follow the same form as the coupling efficiency. We first calculate the maximum reheated mass with an upper limit set to be 10 following [Mutch2016a], which is a typical value for high-redshift dwarf starburst galaxies [uhlig2012]. Note that, since the total supernova energy is finite, a galaxy might not be able to heat all the mass estimated from the loading factor. Therefore, we calculate the mass of actually reheated gas. While in the case of an intense supernova event, the energy released by supernovae further unbinds the hot gas which is removed from the galaxy and stored in a reservoir termed the ejected gas. We assume the ejected gas does not contribute to star formation."}
{"text": "In order to model the feedback from reionization, we further inhibit the local baryon fraction of haloes by a factor of f_mod which is defined as 2 to the power of (-M_crit / M_vir), where M_vir is the halo mass and M_crit represents a filtering mass below which haloes are not able to efficiently accrete baryons from the IGM. We calculate the critical mass for each halo following [Sobacchi2013a], where it depends on the local UV background intensity and the redshift at which the surrounding IGM was first ionized, which is determined using the 21cmFAST algorithm. Smaug, a high-resolution hydrodynamic simulation suite, was performed using a modified version of the GADGET-2 N-body/hydrodynamics code, following the same parameter configuration of the OverWhelmingly Large Simulations project (OWLS; [Schaye2010]). The simulations presented in this work start from the same initial conditions generated with the grafic package at redshift z=199 using the Zel'dovich approximation."}
{"text": "Each simulation evolves (2x)512^3 particles including dark matter (and baryons) within a periodic cube of comoving side of 10 per h Mpc. The Plummer-equivalent comoving softening length is 0.2 per h kpc and the particle resolution is 4.7 and 0.9 x 10^5 per h solar masses for dark matter and baryons or 5.7 x 10^5 per h solar masses if only dark matter particles are considered. We summarize the adopted subgrid physics prescriptions in this section. Cooling [Wiersma2009a] consists of both primordial elements and metal emission lines from carbon, nitrogen, oxygen, neon, magnesium, silicon, sulphur, calcium and iron. Star formation [Schaye2008] occurs in the ISM that is assumed to be multiphase. Supernova feedback can be simulated kinetically [DallaVecchia2008] or thermally [DallaVecchia2012]. In order to compare galaxy properties between Meraxes and Smaug, we focus on the hydrodynamic simulation with thermal supernova feedback implemented."}
{"text": "Reionization feedback is implemented as a UV/X-ray background with all gas particles being instantaneously heated to 10^4 K at a given redshift. Although this prescription is numerically achievable and is considered appropriate in the 10 per h Mpc volume of Smaug simulations, it is not an accurate calculation of reionization feedback. Therefore, the semi-analytic prescription of reionization feedback will be compared to two hydrodynamic simulations with reionization redshifts of 9 and 6.5, which bracket the observed CMB and Lyman-alpha forest boundaries of the EoR, and represent the strongest and weakest feedback scenarios, respectively. Simulations utilized in this study is summarized below: (1) DMONLY, a collisionless N-body simulation; (2) NOSN_NOZCOOL, NOSN_NOZCOOL_LateRe and NOSN_NOZCOOL_NoRe, three toy models with cooling in the absence of metal line emission and ignoring supernova feedback; and (3) WTHERM, a complete hydrodynamic simulation including radiative cooling from primordial elements and metals, as well as stellar evolution, thermal supernova feedback and instantaneous photoionization heating from a reionization background at redshift z=9."}
{"text": "In this work, with algorithms described in [qin2018], we 1) include the aforementioned modifications of the semi-analytic properties or prescriptions; 2) build halo merger trees using the DMONLY simulation; 3) match each individual galaxies between Meraxes and Smaug outputs; and 4) identify star-forming and hot gas in Smaug. We present the comparison result between dwarf galaxy properties predicted by the hydrodynamic simulation and SAM in this section. Reionization feedback in the SAM is incorporated by inhibiting the local baryon fraction of haloes using a filtering mass. In this work, we adopt the average filtering mass, which ignores the spatial distribution of the IGM ionization state and depends only on redshift. In order to assess the validity of this feedback prescription, we compare with two Smaug hydrodynamic simulations in which gas particles are instantaneously heated to 10^4 K at different redshifts."}
{"text": "Note that the suppression due to the ionizing background is quantified in the SAM using a baryon fraction modifier, which, in hydrodynamic simulations, can be informed by comparing the baryonic components of galaxies matched between the different reionization feedback runs. We see that, through photoionization heating, reionization plays a significant role in reducing the fraction of baryons, and that the baryon fraction modifier adopted in the SAM is in general agreement with the hydrodynamic result -- the modifier decreases in less massive haloes and towards lower redshifts. In a 10 per h Mpc volume, the UV/X-ray ionizing background adopted in the two hydrodynamic simulations represents the strongest and weakest feedback scenarios that are consistent with the CMB and Lyman-alpha observations. However, since reionization does not affect the gas component before the reionization redshift in these simulations, its feedback on the baryonic reservoirs cannot be captured by the simulations at higher redshifts."}
{"text": "Therefore, the time when reionization feedback becomes important is relatively late compared to the SAM where the onset of reionization is more gradual and realistic on large scales. As a result, the baryon fraction is overestimated in the hydrodynamic simulations at earlier times, which can potentially lead to an overproduction of stellar mass in dwarf galaxies. We next investigate the stellar evolution and feedback in Meraxes and Smaug, starting with a discussion of involved free parameters in the SAM. Cosmological SAMs are usually calibrated against the observed galaxy stellar mass functions where a sufficient sample is available. By doing this, the stellar component is assured to be well modelled in a statistical context, and with more upcoming observations, the parameter space becomes better constrained and missing physics in the SAM might be revealed. However, one of the issues about this calibration strategy is that it cannot guarantee the modelled galaxies are also representative of real galaxies in terms of their unobservable properties."}
{"text": "Taking the gas component as an example, although a handful of radio telescopes are capable of observing the gas component of distant galaxies, the current sample remains small, limiting our understanding of how galaxies accrete baryons and convert their hydrogen into stars in the early universe. In order to illustrate this, we use the total-gas-based star formation model with parameters adopted in [Mutch2016a] as an example. With a short depletion time-scale of the total star-forming gas, the dynamical time-scale for gas transition, and strong supernova feedback, Meraxes was able to reproduce the observed stellar mass function at redshift z=5-7 in [Mutch2016a]. We see that the semi-analytic prediction is in agreement with Smaug above the resolution limit. We next show more detailed galaxy property evolution, including the total baryonic mass, star-forming gas mass and SFR, from the two numerical experiments in two mass ranges."}
{"text": "We see that, although the SAM is in agreement with the hydrodynamic simulation on the stellar mass function at a large range of redshifts, they disagree on the evolutionary path of the gas component. We find that the baryonic mass is about 2-5 times smaller in the SAM compared to the hydrodynamic simulation, suggesting that too much supernova energy has been coupled to the ISM. In addition, the hydrodynamic simulation shows an increasing amount of star-forming gas towards higher redshifts for a given halo mass. This suggests that cooling (or cold-mode accretion) might be more efficient in the early universe. On the other hand, the SAM underestimates the star-forming gas reservoir at higher redshift but predicts a similar SFR. This suggests that the depletion time-scale might be set shorter in the SAM, which happens to result in an agreement with the hydrodynamic result on the stellar mass function."}
{"text": "We recalibrate our chosen parameters in order to simultaneously reproduce the evolutions of the stellar mass function of the hydrodynamic simulation, as well as the following three quantities: total baryonic mass, star-forming gas mass, and SFR. After exploring the parameter space, we identify a set of parameters that lead to a better agreement on the property evolution of galaxies with virial mass > 10^10 solar masses. This model is referred to as SAM_KS_limited. However, in the low-mass range where the virial mass is between 10^9 and 10^10 solar masses, this model fails to reproduce the evolutionary path of the star-forming gas reservoir calculated by the hydrodynamic simulation. During the experiment, we find that the star-forming gas mass at low redshift does not change by incorporating a larger mass loading factor, which is expected to further suppress the star-forming gas mass through supernova heating."}
{"text": "This suggests that the bulk of star-forming gas is stored in quenched galaxies where the star-forming gas mass is less than the critical mass for star formation. According to the total-gas-based star formation prescription, galaxies can only form stars when their gas reservoirs are adequate. This reservoir mass threshold is calculated based on observations at the local Universe. In the current DRAGONS series, we instead have adopted a lower critical mass. This is supported by [Henriques2015], which proposes to reduce the mass threshold of star-forming galaxies to reconcile the issue that previous SAMs have overpredicted the number of quenched galaxies in the low-mass range while these galaxies still possess a significant amount of star-forming gas reservoir. This might explain the evolution of star-forming gas mass of dwarf galaxies predicted by SAM_KS_limited and suggests that the threshold of star formation needs to be further reduced in these low-mass galaxies."}
{"text": "We next focus on the dwarf galaxies and recalibrate the model without any thresholds of star formation. The result of this model, SAM_KS_unlimited, shows that while SAM_KS_limited with a critical mass of approximately 10^8 solar masses is better at reproducing the hydrodynamically simulated high-mass galaxies, the updated model with no threshold is more consistent with the hydrodynamic result at the low mass range. This indicates high-redshift less massive galaxies, in general, possess lower thresholds of star formation as well. Note that in SAM_KS_unlimited, a rapidly evolving gas transition time-scale is crucial to reproducing the evolution of the star-forming gas mass calculated by the hydrodynamic simulation. However, it also leads to unrealistically rapid changes of the gas transition efficiency in the SAM. We note that, with more intense supernova heating to offset it, additional gas can be allowed to transition from hot to star-forming."}
{"text": "Therefore, incorporating a larger mass loading factor at lower redshifts will decrease the transition time-scale accordingly and allow moderate changes of the transition rate. However, as we will see, supernova heating only plays a secondary role in changing the evolution of star-forming gas of high-redshift dwarf galaxies. In these two SAM_KS models, stars form by consuming the total star-forming gas reservoir. However, due to the unknown time-scale of depleting the total gas, the degeneracy between the processes of cooling and heating exists. [Duffy2017] investigated the molecular hydrogen component of dwarf galaxies using the Smaug simulations and found the depletion time-scale of molecular hydrogen is approximately 0.3 Gyr, independent of the feedback regime. They also discussed the mass and redshift dependencies when applying SAMs with molecular hydrogen-based star formation laws and proposed a redshift-dependent depletion time-scale, the extrapolation of which agrees with the previous findings at the local Universe."}
{"text": "We note that the scaling index of the depletion time-scale was motivated from the KS law with an assumption that galactic discs are self-gravitating and follow exponential surface profiles. The latter might need revising for high-redshift dwarf galaxies. In the early universe, galaxies tend to possess larger velocity dispersions and both mergers and cold-mode accretion are significant. These all indicate that high-redshift galaxies might have thickened discs. In this section, we adopt a less steeply evolving redshift dependency due to thicker discs at high redshift, and then calibrate cooling and supernova feedback efficiencies to reproduce the dwarf galaxy properties from Smaug. We will further discuss the semi-analytic prediction when varying the depletion time-scale. We see that without any degeneracies, the molecular hydrogen-based model can still reproduce the hydrodynamic calculation of the properties of dwarf galaxies as well as the cosmic evolution of the stellar mass function."}
{"text": "Compared to the SAM_KS_unlimited result, SAM_H2 agrees better with Smaug on the evolution of the total baryonic mass of dwarf galaxies, and the calculation of massive galaxies. However, it still overestimates the total baryonic mass and underestimates the mass of star-forming gas and SFR of massive galaxies, suggesting that these galaxies might possess different cooling and supernova feedback efficiencies or shorter depletion time-scale of molecular hydrogen compared to less massive galaxies. The success of our SAM with the molecular hydrogen-based star formation prescription and a fixed molecular hydrogen depletion time-scale is encouraging. It indicates that the accretion-cooling-depletion-heating-and-ejection pathway of gas is still representative for dwarf galaxy formation at high redshift in terms of predicting the gas and stellar properties of the hydrodynamic simulation. We next use the molecular hydrogen-based SAM as an example and illustrate the impact of changing the relevant parameters with comparisons to the fiducial SAM_H2 model."}
{"text": "The gas transition time-scale of the fiducial SAM_H2 model results in a significantly larger value at low redshift. We show this scaling, as well as the result of assigning the transition time-scale with the free-fall time-scale (a common assumption adopted in the literature for the rapid cooling regime), and a time-scale that evolves slower towards higher redshifts compared to the fiducial model. We see that adopting a shorter transition time-scale results in the star-forming gas reservoir receiving more efficient replenishment. In the case of unchanged gas depletion time-scale, SFR increases. Consequently, more energy gets ejected from supernova explosions, leading to more suppressed total baryonic masses given that the energy coupling efficiency and mass loading factor for heating do not change. We see that without changing other parameters, a significantly evolving transition time-scale is required to reproduce the rapidly decreasing star-forming gas mass at lower redshifts as predicted by the hydrodynamic simulation."}
{"text": "We note again that varying the transition time-scale from the dynamical time-scale was proposed to compensate for the overestimated collapse rate attained by assuming SIS profiles for hot gas and the underestimation due to large transition radii between hot and star-forming gas. In the presence of feedback, the star-forming disc shrinks, in particular at lower redshifts. Correspondingly, the overestimation of the transition time-scale becomes insignificant -- gas indeed needs to collapse into the central region to become star-forming gas. Therefore, we need a much longer transition time-scale at low redshift to take into account that hot gas is less dense at the inner regions compared to the SIS profile -- only a small amount of gas can collapse into the centre within the dynamical time-scale. We will investigate below whether the other free parameters can have a significant impact to the star-forming gas reservoir evolution, so that the steep gradient of star-forming gas mass with redshift can be reproduced without the implementation of a rapidly-evolving redshift dependency in the transition time-scale."}
{"text": "The molecular hydrogen depletion time-scale is better constrained than that of the total gas. However, observational results still possess large variance even in the local Universe, from a half to a few Gyr. Therefore, we use the redshift-dependent molecular hydrogen depletion time-scale proposed in [Duffy2017]. For the fiducial model, we use a less steeply evolving redshift dependency due to thicker discs at high redshift. We show the property evolution of using the time-scales proposed by [Duffy2017] as well as a constant value, which is commonly adopted for SAMs in the literature. We see that by increasing the time-scale of converting hydrogen into stars, star formation quenches, leading to weaker supernova ejection and heating. With the current configuration of parameters, we see that a constant 2 Gyr depletion time-scale significantly underestimates star formation at high redshift in agreement with [Duffy2017] and the star-forming gas evolution gradient is not expected to change significantly by varying the redshift dependency."}
{"text": "Supernova explosions increase the thermal energy of the ISM and expel baryons in dwarf galaxies. However, since the relevant region cannot be resolved in cosmological simulations, subgrid physics with free parameters are adopted by both hydrodynamic and semi-analytic modelling approaches. The fraction of supernova energy that contributes to feedback is f_th and epsilon_energy in Smaug and Meraxes, respectively. Since f_th is chosen to be unity, with all the supernova energy being coupled to the ISM, one might expect epsilon_energy=1 as well. However, because SAMs ignore the thermal energy of the star-forming gas and assume the temperature of hot gas does not change during one time step, some energy terms are zero. This means that, despite all supernova energy being coupled to the ISM in the hydrodynamic simulation, only a fraction of it contributes to feedback in the SAM."}
{"text": "How much of the supernova energy is coupled to the ISM and used to heat gas is governed by free parameters describing the mass loading factor in the SAM while in the hydrodynamic simulation, it is the increment of gas temperature that determines the number of gas particles that are affected. This indicates that, in the hydrodynamic simulation, the mean number of instantaneously heated nearby gas particles per stellar baryon is approximately 1.34 [DallaVecchia2012]. This small mass loading factor places the heated gas in the Bremsstrahlung cooling regime, achieving an efficient supernova feedback mechanism through heating. Moreover, due to the increased pressure from the thermal feedback, gas particles within high overdensities tend to move outwards in a wind. As the wind particles travel, they further increase the thermal energy of the nearby gas particles along the path, leading to a much larger effective mass loading factor over a long period of time."}
{"text": "Since the SAM captures the average property over 11Myr, one might expect the SAM mass loading factor to be much larger than 1.34 as well. However, we have also shown that in hydrodynamically simulated dwarf galaxies, gas particles need not be fully virialized to become non-star-forming gas while on the other hand, SAMs ignore the thermal energy of the star-forming gas and assume the non-star-forming hot gas shares the virial temperature of host halo. Without properly tracking the thermal energy of varied gas reservoirs in the SAM, it is challenging to determine the energy-ISM coupling efficiency and mass loading factor. In this work, against the hydrodynamic result of WTHERM, we have calibrated our fiducial SAM. We see that when the mass loading factor is fixed, more coupled energy to the ISM leads to stronger suppression of the total baryonic mass, which subsequently decreases the mass of the star-forming disc and quenches star formation."}
{"text": "From the MaximumSNCoupling model, we see that with all supernova energy used to convert star-forming gas to hot and eject hot gas from the galaxy, the total baryonic mass and star-forming gas become significantly suppressed. On the other hand, when the supernova energy coupling efficiency is fixed, less heating leads to a larger reservoir of star-forming gas and enhanced star formation. Consequently, more supernova energy is coupled to the ISM. With less energy used for heating, more mass in the hot gas reservoir gets ejected. Depending on the increased amount of star-forming gas and stellar mass as well as the decreased hot gas mass, the total baryonic mass varies slightly. In addition, the property evolution does not change significantly between these three models. Therefore, we do not expect that, by changing the heating efficiency of supernovae, the issue of incorporating a rapidly evolving gas transition time-scale can be resolved."}
{"text": "Following [qin2018], we further investigate the semi-analytic modelling prescriptions of galaxy formation that are commonly adopted in the literature. In this work, we include supernova feedback and homogeneous reionization background in both the Meraxes SAM and Smaug high-resolution hydrodynamic simulation, and make comparisons between the stellar and gas reservoirs predicted by these two methods. We focus on galaxies with virial mass between 10^9 and 10^11 solar masses. With the modifications previously proposed in [qin2018] including adjustments to halo masses from the merger trees, suppression of baryon fractions accounting for hydrostatic pressures, and the modulation of time-scales for the transition of gas from hot to star-forming and from star-forming to stars, we find that the current SAM is able to reproduce the hydrodynamic calculation of the cosmic evolution of galaxies with virial mass > 10^10 solar masses at high redshift."}
{"text": "This includes the stellar mass function, total baryonic mass, star-forming gas mass and SFR between redshift z=5-11. However, in less massive galaxies with SFR calculated using the total star-forming gas, we identify a significant amount of star-forming gas stored in quenched galaxies due to the imposed mass threshold of star formation. After reducing the threshold, the SAM successfully mimics the evolution of dwarf galaxies in the hydrodynamic simulation. We also investigate a second star formation prescription, which splits the star-forming gas disc into molecular and atomic hydrogen and forms stars from molecules [Lagos2011]. Fixing the depletion time-scale of molecular hydrogen inferred from a previous study of the Smaug hydrodynamic simulation [Duffy2017], we find that, with only calibrations of the gas transition rate and supernova efficiencies, the SAM can also reproduce the dwarf galaxy properties calculated by the hydrodynamic simulation."}
{"text": "In addition, we find that when reionization and supernova feedback are included, dwarf galaxies tend to accrete a significant amount of star-forming gas at early times (redshift z>10), which quickly becomes suppressed towards lower redshifts. Future work needs to take this into account and incorporate modelling of cold-mode accretion to study dwarf galaxies in the early universe. We show the impact to the semi-analytic calculation, in the presence of reionization and supernova feedback, of incorporating the halo mass and baryon fraction modifiers, which correspond to the slower evolution of haloes and less efficient gas accretion due to hydrostatic pressure. We apply Meraxes with the total-gas-based star formation law and the same parameters adopted in [Mutch2016a] but without the baryon fraction modifier and without any modifiers."}
{"text": "We see that without the halo mass modifier, the halo mass function is overestimated compared to the hydrodynamic result at high redshift, which consequently increases the mass function of gas and stars. In addition, further excluding the baryon fraction modifier increases the amount of gas accreted by the host halo and subsequently causes more stars to form. However, we see that the modifications have an insignificant impact to the stellar mass function in the current observable range, which requires deeper surveys with upcoming space programs such as JWST. [qin2018] shows that in the absence of feedback, the majority of dwarf galaxies in the hydrodynamic simulation accrete gas particles with temperatures around a few of 10^4 K, which is much lower than their halo virial temperatures. This represents a cold-mode accretion of the infalling gas [Keres2005, Keres2009], which in the SAM is currently modelled through the cooling prescription of the rapid cooling regime proposed by [white1991]."}
{"text": "The infalling hot gas is also assumed to follow the singular isothermal sphere (SIS) profile. To ease demonstration in this paper, we term the time-scale of gas being transited from hot reservoir to the star-forming disc as a transition time-scale. Most massive haloes are able to create shocks and heat the infalling gas, resulting in hydrostatic equilibrium. In this case, which is termed the hot halo regime, the time-scale of hot gas transitioning to star-forming is determined by the thermal cooling time-scale. However, it is difficult to generate shock heating in less massive systems, leaving little support to prevent gas from infalling onto the central disc, and cooling becomes rapid. In this rapid cooling regime, the prescription assumes the star-forming gas disc is relatively small and such a process happens as free-fall. In making comparisons of the gas reservoir calculated by the SAM and hydrodynamic simulation in [qin2018], we found the transition time-scale equals the dynamical time-scale becomes less accurate when applying the rapid cooling prescription to high-redshift dwarf galaxy modelling."}
{"text": "This is due to the aforementioned two assumptions which lead to over- and under-estimations of the gas transited from hot to star-forming, respectively. 1) Assuming the SIS profile of the accreted mass overestimates the gas density in the inner regions. 2) star-forming gas particles of dwarf galaxies (in the hydrodynamic simulation) possess larger extensions and can be found as far as the virial radius. This means that assuming gas can only transfer from non-star-forming hot gas to star-forming when it reaches the galaxy centre introduces a longer inflow path and hence leads to an overestimated transition time-scale. In this case, the mass of hot gas transitioning to star-forming is underestimated instead. We note that when feedback is included, semi-analytic modelling of dwarf galaxies still suffers from these two factors. First, in order to demonstrate that most high-redshift dwarf galaxies in the SAM are still identified as in the rapid cooling regime when reionization and supernova feedback are included, we calculate the cooling radius, at which the time-scale of thermal cooling is equal to the halo dynamical time in the SAM."}
{"text": "Note that gas within the cooling radius is considered to have reached hydrostatic equilibrium and cool thermally if the cooling radius is less than the virial radius. However, in the case of a large cooling radius, the infalling gas will not be able to form stable shocks or remain in hydrostatic equilibrium. Accordingly, all of the accreted gas directly collapses into the central regions as free-fall. We see that most low-mass galaxies discussed in this work are considered to be in the rapid cooling regime. Next we show the evolution, in terms of the density--temperature phase and spatial distributions of star-forming and non-star-forming gas particles, of the most massive halo in the WTHERM Smaug simulation identified at redshift z=5 as an example, and discuss the gas density profile of galaxies with stellar mass of approximately 10^7 solar masses. We see that, compared to the NOSN_NOZCOOL_NoRe simulation where heating from supernova (and reionization) is not included, galaxies within the same stellar mass range are hosted by larger haloes with more gas particles identified as non-star-forming when the feedback is considered."}
{"text": "However, the total gas mass does not change significantly, indicating suppressions of baryonic mass and self-regulation of star formation. Moreover, although the star-forming regions become relatively smaller in WTHERM, they still possess a large dispersion at high redshift. This can also be observed from the large radius of the maximum rotation of the most massive halo, which suggests the necessity of an enhanced inflow rate between the circum-galactic medium and ISM at earlier times. More accurate semi-analytic modelling of gas accretion should not only distinguish the hot- and cold-mode inflows with gas reaching the star-forming disc on different time-scales, but also account for the larger disc size at higher redshifts. We consider these as a future project with a more complete cooling function implemented. For the purpose of accurately capturing the gas transition time-scale using the current rapid cooling prescription, in [qin2018], we proposed to change the cooling efficiency when galaxies are identified in this regime."}
{"text": "We introduced a maximum cooling factor, which was used to modulate the gas transition time-scale based on the time-scale of free-fall. In this work, we adopt this modification by incorporating a form of the transition time-scale as a function of redshift. However, considering the transition radius between star-forming and non-star-forming gas changes due to feedback, the normalization and scaling index are not expected to possess the same values as adopted in [qin2018]. Therefore, we leave them as free parameters and explore the transition time-scale in this work."}
{"text": "We use the Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) framework to investigate the effect of galaxy-formation physics on the morphology and statistical signatures of ionized hydrogen (HII) regions during the Epoch of Reioinization (EoR). DRAGONS self-consistently couples a semi-analytic galaxy-formation model with the inhomogeneous ionizing UV background, and can therefore be used to study the dependence of morphology and statistics of reionization on feedback phenomena of the ionizing source galaxy population. Changes in galaxy-formation physics modify the sizes of HII regions and the amplitude and shape of 21-cm power spectra. Of the galaxy physics investigated, we find that supernova feedback plays the most important role in reionization, with HII regions up to approximately 20 per cent smaller and a fractional difference in the amplitude of power spectra of up to approximately 17 per cent at fixed ionized fraction in the absence of this feedback. We compare our galaxy-formation-based reionization models with past calculations that assume constant stellar-to-halo mass ratios and find that with the correct choice of minimum halo mass, such models can mimic the predicted reionization morphology."}
{"text": "Reionization morphology at fixed neutral fraction is therefore not uniquely determined by the details of galaxy formation, but is sensitive to the mass of the haloes hosting the bulk of the ionizing sources. Simple EoR parametrizations are therefore accurate predictors of reionization statistics. However, a complete understanding of reionization using future 21-cm observations will require interpretation with realistic galaxy-formation models, in combination with other observations. Many fundamental questions about the first galaxies remain unanswered despite recent progress in both observations and theoretical studies. Future indirect observations of the first sources of light, through their impact on the surrounding intergalactic medium (IGM), promise to shed new light on some of the important processes involved in their formation and evolution. For this reason, the period during which galaxies reionized the Universe -- the Epoch of Reionization (EoR) -- has become a focus of both theory and observation [see][for reviews][FCK2006, FOB2006, MW2010]."}
{"text": "Observations of the cosmic microwave background (CMB) and high-redshift sources (such as quasars, Lyman-break galaxies, Lyman-alpha emitters and gamma-ray bursts) have allowed some constraints to be placed on the timing and duration of the EoR. Without further measurements of the degree of reionization throughout this period, however, its detailed history will remain unknown. Furthermore, the constraints provided by these observations are confined to the global ionization state of the IGM, with limited information on the sources and environmentally-dependent astrophysics at play. The new observational window provided by low-frequency radio experiments will be the first direct probe of neutral hydrogen during reionization. Together, instruments such as LOFAR, MWA, PAPER and GMRT promise to yield statistical measurements of the state and morphology of cosmic hydrogen throughout the EoR through fluctuations in the redshifted 21-cm emission line intensity."}
{"text": "The next generation of instruments, including SKA and HERA, will allow high-resolution tomographic images of the ionized structure around individual regions of ionized hydrogen (HII) to be made [see, e.g.,][MELLEMA2015, WGK2015]. Combined with detailed simulations, these observations should pave the way to a better understanding of the connection between galaxies and reionization. Numerous theoretical methods have been used to study reionization. Analytic modelling [e.g.][SHAPIRO1994, WL2003, FZH2004] can provide insight into some of the processes involved, but cannot include many of the most important physical effects, and do not generate spatial realizations. N-body simulations, post-processed using radiative transfer methods based on ionizing sources placed within dark matter haloes, provide a description of the structure, but not a self-consistent calculation of source properties [see, e.g.,][ILIEV2005, MLZD2007]."}
{"text": "Hydrodynamical simulations that include radiative transfer [see, e.g.,][GNEDIN2000a, PETKOVA2011, PAARD2013, BAUERetal2015] include the effects of feedback and follow structure formation and cosmic reionization self-consistently but do so at great computational expense when performed with the temporal cadence, cosmic volume and resolution required to capture the evolution and relevant spatial scales of reionization. As a compromise, semi-numerical simulations [ZAHN2005, MF2007, GW2008, ALV2009, CHR2009, THOMAS2009, MFC2011] are computationally inexpensive and provide an efficient means of exploring high-dimenisional parameter spaces and very large volumes (and hence rare objects). However, these simulations have not previously included realistic galaxy formation in their formulation. Previous theoretical work constraining properties of the ionizing sources throughout the EoR with 21-cm observations has been carried out using a number of approaches."}
{"text": "[BARKANA2009] fitted properties of the galaxy population during reionization (such as mean halo mass of the ionizing sources) to simulated 21-cm power spectra using analytical modelling. Extensive investigation using radiative transfer simulations run on top of suites of N-body simulations has been performed by [MLZD2007] and [ILIEV2012]. This work investigated whether or not observations will be able to distinguish reionization due to sources within populations of atomically-cooled haloes of different mass ranges, as well as the effects of ionizing source efficiencies and self-regulation. Other work has explored the effect and relative dominance of supernova feedback during reionization [see, e.g.,][KIM2013a], and the ability of observations to constrain galaxy formation through the effect of variation in the mass- and redshift-dependent escape fraction of ionizing photons [KIM2013b]."}
{"text": "Using a Markov chain Monte Carlo analysis tool, [GREIG2015] made estimates of astrophysical parameter contraints from simulated observations, including the ionizing efficiency and mean free path of ionizing photons, as well as lower limits on the virial temperature of star-forming haloes. The Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) project takes a hybrid approach by integrating a semi-numerical calculation of reionization within a semi-analytic model (SAM) of galaxy formation built upon an N-body simulation specifically designed for EoR studies. DRAGONS aims to answer the following questions about galaxy formation and cosmic reionization. What was the nature of the ionizing sources and the processes involved in reionization? What was the relative impact of these processes on cosmic reionization and subsequent galaxy formation? Was reionization a self-regulatory process? Will future observations enable us to distinguish these processes, quantify them, or rule out certain reionization scenarios?"}
{"text": "This paper focusses on the morphology and statistical signature of cosmological reionization and is the fifth in a series describing the DRAGONS project. The first paper in the series [[DRAGONS1]] introduces the collisionless N-body simluation, Tiamat, which is used as the basis of this work. The structure of the high-redshift dark matter haloes contained within Tiamat is described in the second paper [[DRAGONS2]]. The third paper [[DRAGONS3]] presents Meraxes, the semi-analytic model of galaxy formation and evolution developed for DRAGONS, while the fourth [[DRAGONS4]] discusses the resulting galaxy luminosity functions. This paper is structured as follows. We begin by describing our simulation and modelling methodologies in Section 2. In particular, Section 2.4 provides a description of the model runs we perform in order to explore the effect of key astrophysical mechanisms included in our simulations."}
{"text": "We then present our results in Section 3, where we compare our model runs using various statistics. We discuss aspects of these results in Section 4 before presenting a summary in Section 5. We include an appendix containing supporting material demonstrating the spatial convergence of our results. All globally-averaged quantities (e.g. neutral fraction) are volume weighted, and distances given in comoving units unless stated otherwise. Our choice of cosmology throughout is the standard spatially-flat Planck LambdaCDM cosmology [PLANCK2015] (h, Omega_m, Omega_b, Omega_Lambda, sigma_8, n_s) = (0.678, 0.308, 0.0484, 0.692, 0.815, 0.968). In this section we summarize our simulation and modelling methodologies, beginning with our collisionless N-body simulation (Tiamat), then our semi-analytic model (Meraxes) and finally how we integrate these with the semi-numerical reionization code 21cmfast [MFC2011]."}
{"text": "The collisionless N-body simluation used as the basis of this work is called Tiamat. It consists of 2160^3 particles in a 100~Mpc, periodic, cubed box evolved using GADGET-2 [GADGET22005]. Initial conditions were generated at redshift z = 99 and the simulation was run down to redshift z = 5 providing 100 snapshots of particle data equally spaced in time between redshifts 5--35 (roughly one every 11 Myr). Halo finding was performed using SUBFIND [SUBFIND2001] and merger trees from the resulting halo catalogues were created using the methodology to be presented in Poole~et~al.~(in preparation). A triangular-shaped cloud mass assignment scheme [see, e.g.,][CUI2008] was used to create density grids used by Meraxes/21cmfast. A complete description of Tiamat, resulting halo mass functions and analysis is given in Paper-I."}
{"text": "Semi-analytic models parametrize the physics of galaxy formation to enable fast and accurate realizations of galaxy properties within cosmic volumes. The semi-analytic model of galaxy formation used in this work is called Meraxes, and includes baryonic infall, cooling, star formation, reionization and supernova feedback, metal enrichment, stellar mass recycling, mergers, and ionizing flux from galaxies hosted by dark matter haloes temporarily unresolved in our input merger trees. Calibration was performed so as to agree with observations of the CMB optical depth to electron scattering, and to replicate the observed evolution of the galaxy stellar mass function between redshifts 5--7. A complete description of Meraxes is given in Paper-III. A feature of Meraxes that is important for its application to reionization is that it is run on `horizontal' merger trees, which enable calculation of the evolution of all galaxies at each time-step, so that feedback processes from neighbouring sources can be incorporated self-consistently."}
{"text": "We simulate cosmic reionization by applying the 21cmfast algorithm [details of 21cmfast are described in][MFC2011] within the Meraxes semi-analytic model including the effect of a local/inhomogeneous ionizing UV background (UVB) as described by [SM2013a]. Coupling the galaxy properties modelled by Meraxes with the UVB calculated by 21cmfast provides a self-consistent, UVB-regulated realization of reionization. This is implemented in the following manner: 1. At the end of each snapshot, Meraxes constructs halo mass, stellar mass and star-formation rate grids; 2. 21cmfast's excursion-set filtering algorithm calculates the corresponding ionization state and inhomogeneous UVB-intensity grids; 3. Meraxes keeps track of the redshift at which each voxel was first ionized, and calculates a baryon fraction modifier of each halo which is then used to calculate the effect of the local UVB on the amount of infalling bayonic matter; 4. Meraxes evolves all of the galaxies in the simulated volume forward to the next time-step, and then the process is repeated."}
{"text": "Reionization was simulated on a 512^3 grid, which we find sufficiently resolves behaviour for analysis in this paper (see Appendix A which discusses the spatial convergence of our results). The basic methodology of the 21cmfast algorithm is to utilize an excursion-set approach to identify HII regions and provide a neutral hydrogen fraction grid of the simulation volume. Starting at scales comparable to the mean free path of ionizing photons in an ionized IGM at redshift z ~ 6 and incrementing toward smaller scales, voxels are flagged as being ionized if, in a sphere of radius R, the integrated number of ionizing photons is greater than the number of hydrogen and neutral helium atoms plus the mean number of recombinations. In our prescription this ionization condition can be written in terms of an ionization efficiency factor, xi, and the collapsed fraction of mass, f_coll, in the form of stars within R: xi times f_coll is greater than or equal to 1."}
{"text": "The collapsed fraction is defined as f_coll equals the stellar mass M_star divided by the total mass M_tot. We set the unresolved, sub-cell neutral hydrogen fraction corresponding to the last smoothing scale in our simulations to xi times f_coll, where R_voxel is of the order of the grid resolution of 21cmfast. The ionization efficiency factor depends on the baryon fraction, f_b, mean number of ionizing photons per stellar nucleon, N_gamma_bar, and their escape fraction, f_esc. We set the baryon fraction to its universal value, f_b = Omega_b / Omega_m. The (1-3Y_He/4) factor, where Y_He = 0.24 is the mass fraction of helium, accounts for helium in the ionization budget. Both f_b and Y_He are well constrained, while N_gamma_bar is set by an assumed initial mass function of stars. The value of f_esc is less well constrained for galaxies at high redshift."}
{"text": "We account for recombinations by commencing the reionization excursion-set filtering at a scale comparable to the mean free path of ionizing photons in an ionized IGM. This effectively acts as a `global reionization horizon' [see][for a discussion of this in terms of the framework of 21cmfast][GREIG2015] and slows reionization during its late phase. Alternatively, it is possible to account for homogeneous recombinations by appropriately including a factor of (1 + N_rec_bar) in the equation for the ionization efficiency factor, where N_rec_bar is the globally-averaged number of recombinations. Homogeneous recombinations are, however, degenerate with the ionizing efficiency. The effect of inhomogeneous recombinations has been investigated by a number of authors [see, e.g.,][CHR2009, SM2014, WMPS2015] and is left for future work. In order to simulate the effect of feedback from a UV background on star formation, the 21cmfast algorithm calculates a grid of the local average UVB intensity within a given ionized region."}
{"text": "Following [SM2013a], this is given by the average intensity at 21cm, <J_21>_HII, equals ((1+z)^2 / 4pi) times lambda_mfp times h_P times alpha times f_bias times epsilon, where lambda_mfp is the comoving mean free path of ionizing photons (assumed within the excursion-set algorithm to be equal to the filtering radius, R), h_P is the Planck constant, alpha is the spectral index of the UVB, f_bias is an ionizing emissivity bias factor and epsilon is the ionizing emissivity. We model the background spectrum using a power law with spectral index alpha = 5 [TW1996], which leads to a steep spectrum corresponding to a stellar-driven UVB, effectively ignoring the contribution from harder spectral sources such as quasars. We expect using a much harder spectrum would cause feedback to be more effective [see, e.g.,][TW1996], hence changing our results. We leave this investigation to future work."}
{"text": "The bias factor in the UV background equation accounts for the higher than average ionizing emissivity at halo locations due to their clustering. We use a value of f_bias = 2 based on discussion in [MD2008]. The ionizing emissivity is the number of ionizing photons emitted into the IGM per unit time, per unit comoving volume. This is calculated for each voxel using the grid of gross stellar mass, M_star,gross, through epsilon equals f_esc times N_gamma_bar times (M_star,gross / m_b_bar) times (1 / t_H(z)) times (1 / V_R), where the gross stellar mass has been averaged over a sphere of radius R with volume V_R, t_H(z) is the Hubble time which acts as the average star-formation time-scale, and m_b_bar is the mean mass of each baryon. A UV background can lead to negative feedback on cosmic reionization in various ways. Its presence reduces baryonic infall by way of heating the IGM, therefore affecting its gas cooling properties."}
{"text": "It can also photo-evaporate gas from shallow potential wells surrounding small galaxies. Both of these mechanisms lead to the quenching of star formation. We parametrize this effect in Meraxes using a spatially- and temporally-dependent baryon fraction modifier, 0 <= f_mod <= 1, which acts to reduce the mass fraction of baryons contained in freshly accreted matter from its universal value, f_b, to f_mod times f_b. Following the work of [SM2013b], we calculate f_mod using f_mod = 2^(-M_filt / M_vir), where M_vir is the halo mass and M_filt is a `filtering' mass, defined to be the total halo mass at which the baryon fraction is half the universal value. Together with the snapshot redshift, z, and the redshift at which the voxel was first ionized, z_ion, the local average UVB intensity within a given ionized region is used to calculate the filtering mass. The free parameters were fit by [SM2013b] to one-dimensional collapse simulations."}
{"text": "The ionizing efficiency of very high-redshift galaxies is poorly constrained by observations of galaxy UV luminosity functions and our knowledge of the escape fraction of ionizing photons and the abundance of faint galaxies is poor. Furthermore, simulations show a strong mass dependency and anisotropy of the escape fraction [e.g.][PAAR2015], both of which can strongly impact the topology of reionization. This lack of observational constraint and expected complexity allows for a wide variety of plausible reionization scenarios [examples of recent work in this area include studies by, e.g.,][KFG2012, KIM2013b, PAAR2015]. As shown in Paper-III, while we are able to match high-redshift galaxy stellar mass functions and satisfy constraints imposed by CMB measurements using an escape fraction which does not evolve with redshift, we are unable to also match the normalisation and slope of the observed ionizing emissivity at redshift z <= 6 without using a redshift-dependent escape fraction."}
{"text": "Furthermore, Lyman-alpha emitter studies suggest that reionization ends at redshift z ~ 6 [see, e.g.,][DIJKSTRA2014, CPHB2015]. An evolving escape fraction prolongs reionization and delays its completion, hence simultaneously satisfying these constraints. Similarly, inhomogeneous recombinations [a la][SM2014] are expected to prolong the late stages of reionization. However, for the purpose of comparing models presented in this work, we have kept our prescription for the escape fraction as simple as possible by assuming it to be spatially and temporally invariant. This section describes the set of models used in this work. Models that ignore the effects of supernova feeback have been recalibrated so as to provide the same total redshift z = 5 stellar mass density as the fiducial model. This has been achieved by using a lower star-formation efficiency parameter, alpha_SF."}
{"text": "In order to facilitate direct comparison between our models, we `tune' the ionization efficiency factor of each by varying the escape fraction of ionizing photons so as to match the globally-averaged neutral fraction of our fiducial model at redshift z is approximately equal to 8.4 (the mean neutral hydrogen fraction is approximately 0.68). This results in the models having very similar reionization histories. Therefore, with each model having a similar global neutral fraction and the same underlying density field at each snapshot/redshift, we can sensibly compare models by way of their 21-cm power spectra (which are sensitive to both neutral fraction and density). We choose to match at a mean neutral hydrogen fraction of approximately 0.7 as our cosmic volumes at this stage of reionization provide a fair sample of different HII region sizes and forms. Fiducial model (F): We couple both the spatial and temporal evolution of the reionization structure and ionizing field to the growth of the source galaxy population through the incorporation of feedback by an inhomogeneous UVB."}
{"text": "Supernova feedback is included and a spatially-homogeneous, redshift-independent escape fraction of ionizing photons of f_esc = 0.2 is used. This model is identical to the fiducial model in Paper-III and is discussed at length in that paper and Paper-IV. No SN feedback (NoSNeFB): This is a recalibrated version of the fiducial model which ignores the effect of feedback from supernovae. A constant f_esc = 0.239 is used. No feedback (NoFB): This is a recalibrated version of the fiducial model which ignores the effect of feedback from both reionization and supernovae. A constant f_esc = 0.2328 is used. Constant stellar-to-halo mass ratio (CSHR): This model ignores the galaxy properties calculated by Meraxes and is therefore decoupled from the effects of any form of feedback. Stellar mass is calculated assuming a constant ratio between stellar mass and the virial mass of each Friends-of-Friends (FoF) halo group using M_star / M_vir = 0.055."}
{"text": "This is based on the value we find in the high-mass regime of a simulation with no feedback from either reionization or supernovae. This model (along with the following mass-cut models) is included so as to facilitate comparison of our fiducial model simulation with previously published semi-numerical simulations and models that do not include realistic galaxy formation and feedback effects. A constant f_esc = 0.01547 is used. Constant stellar-to-halo mass ratio with 10^9 M_sun mass cut (CSHR.Mcut.9): This is the same as the CSHR model but only includes galaxies whose FoF virial mass is M_vir >= 10^9 M_sun. A constant f_esc = 0.0312 is used. Constant stellar-to-halo mass ratio with 10^10 M_sun mass cut (CSHR.Mcut.10): This is the same as the CSHR model but only includes galaxies whose FoF virial mass is M_vir >= 10^10 M_sun. A constant f_esc = 0.1302 is used."}
{"text": "Figure 1 shows the evolution of the globally-averaged neutral fraction, of each model (top panel) and their difference with respect to the fiducial model (middle panel) as a function of redshift. Reionization for our fiducial model occurs over a period of 411~Myr (period between the simulation volume being 1--99~per~cent ionized) and is 99~per~cent ionized at redshift z is approximately equal to 6.9. The data point in Figure 1 indicates the neutral fraction at which the models have been matched. This figure provides a comparison between the duration and rates of reionization for each model. Each model follows a similar reionization profile, the greatest difference being for the NoFB model. The CSHR model reionizes least rapidly, owing to the more complete distribution of ionizing source masses for this model. The bottom panel in Figure 1 shows the cumulative CMB optical depth to Thomson scattering as a function of integrated redshift for our reionization model simulations."}
{"text": "These results have been calculated in the same manner as in Paper-III. The horizontal dashed line and surrounding shaded region mark the latest Planck observations and +/-1-sigma uncertainty [PLANCK2015]. The total CMB optical depth to electron scattering of our fiducial model falls within this observational constraint. While the other models have had their reionization histories matched to the fiducial model, small differences in their reionization profiles result in a small variation in their optical depths. All results, however, fall well within the constraints provided. The spatial progression of reionization can be seen in Figure 2 which shows slices of the neutral gas density for our fiducial model at selected redshifts. The underlying dark matter density contrast is shown in fully ionized regions (`bubbles'). In this section we focus on the morphology of reionization, and compare the effect of different ionizing source populations and feedback mechanisms."}
{"text": "The corresponding results for 21-cm power-spectra statistics are discussed in Section 3.3. Reionization on intergalactic scales is expected to proceed in an `inside-out' manner whereby more-over-dense regions (e.g. sites of the first-formed galaxies) reionize before less-over-dense regions [see, e.g.,][ILIEV2006, MLZD2007, MFC2011, BAUERetal2015]. The spatial correlation between the higher-density cosmic web and regions of ionized hydrogen is clear in the neutral gas density slices of our fiducial model shown in Figure 2. The effect of feedback and different ionizing source populations can be seen in Figure 3, which shows slices through the ionization field of our models at three different global neutral fractions. In order to help explain differences and similarities between the ionization fields of our models, we refer to the plots in Figure 4 which show the following ionization properties of their source populations. In the top panel we have calculated the median fraction of mass in the form of stars at redshift z is approximately equal to 8.4 as a function of FoF virial mass, weighted by the escape fraction of each model."}
{"text": "This quantity acts as a proxy for the average ionizing luminosity of sources as a function of their host halo virial mass but includes no information about the size of their populations. In the bottom panel we show the probability distributions of the integrated ionizing photon contribution up to redshift z is approximately equal to 8.4 as a function of FoF virial mass for each model. As these histograms have been weighted by the gross stellar mass in each halo mass bin, the distributions include the effect of source population. The ionization field for the NoSNeFB model has a slightly larger population of small (1--3~Mpc) ionized regions and its overlapping regions tend to be smaller than those of the fiducial model. As evident from the top panel of Figure 4, including the star-formation suppressing effect of SNe feedback and tuning the escape fraction so as to match the models' reionization states effectively lowers the specific luminosity of sources hosted by medium-mass haloes, but increases it for the very lowest- and highest-mass sources."}
{"text": "Due to their relative populations, these medium-mass sources are the dominant drivers of reionization in the NoSNeFB model up to this period of reionization. As these haloes are less biased than more-massive haloes, they tend to populate the less-dense regions of the simulation volume away from the clustered sources central to the overlapping ionized regions. Therefore, without the feedback effects of supernovae, more small isolated ionized regions will exist and the overlapping regions will be smaller at fixed ionized fraction. This is in agreement with previous work investigating SNe feedback [see, e.g.,][KIM2013a], although the effects are significantly weaker in our results. We attribute this difference to Tiamat having an order of magnitude higher temporal resolution than the simulation used by [KIM2013a]. This resolution is required to resolve the dynamical time at redshift z > 6. The ionization field for the NoFB model is almost identical to that of the NoSNeFB model."}
{"text": "This is due to the dominance of supernova feedback over reionization feedback in suppressing star formation as discussed in Paper-III. The ionization field for the CSHR model has a larger population of small ionized regions, including very small (< 1~Mpc) regions, and its overlapping regions tend to be smaller than those of the fiducial model. Galaxies with low-mass FoF hosts in the Meraxes models contain, on average, less stellar mass than that expected using a constant stellar-to-halo mass ratio prescription. This is due to both the galaxy-formation modelling, and star-formation suppressing effects of reionization and (predominantly) supernova feedback. As evident in the bottom panel of Figure 4, sources hosted by these low-mass haloes in the CSHR model dominate reionization. This leads to a larger population of small isolated ionized regions, with a greater number of very small regions. Despite the relatively large shift in the host halo mass scale of sources which dominate reionization between the Meraxes-based models and the CSHR model, the resulting ionization fields are remarkably similar."}
{"text": "The ionization field of the CSHR.Mcut.9 model bears a striking resemblence to those of the no-feedback and CSHR models, but contains fewer very small isolated ionized regions. The mass cut imposed on this model removes the ionizing contribution of sources hosted by the lowest-mass haloes present in the fully-populated CSHR model but, as evident in the bottom panel of Figure 4, leaves reionization to be dominated by sources hosted by haloes in the same medium-mass range as the no-feedback models (hence their similarity). Ionized regions in the CSHR.Mcut.10 model are larger, more clustered and more spherical than those of the other models. On average, ionizing sources of the CSHR.Mcut.10 model are more luminous than those in all of our other models. Since only high-mass ionizing sources have been included in this model and these sources are more biased, they tend to cluster within the densest environments, forming large overlapping ionized regions."}
{"text": "In order to quantify these differences in the real-space morphology of reionization we calculate the ionized region (or `bubble') size distributions for each snapshot using the Monte Carlo method described in [MF2007]. In this method, an ionized voxel is randomly selected and its distance from an ionization phase transition in a randomly chosen direction is recorded. This is repeated 10^7 times to form a probability distribution function of region size. This methodology provides an approximate measure of the mean free path of ionizing photons inside ionized regions and has been extensively used as a proxy for bubble radius in other work [e.g.][FO2005, MLZD2007, MF2007]. The top panel of Figure 5 shows the mean size of ionized regions, as a function of global neutral fraction for each model. The bottom panel shows the ratio of the resulting mean scale of ionized regions relative to the fiducial model. This figure quantitatively supports the qualitative results illustrated in Figure 3."}
{"text": "We show the probability distribution of ionized region size for our models at a globally-averaged neutral fraction of approximately 0.68 in Figure 6. Relative to the fiducial model, we find the following comparisons of average `bubble' size: i) without SNe feedback, regions are approximately 19 per cent smaller; ii) without SNe or reionization feedback, regions are approximately 18 per cent smaller; iii) using a constant stellar-to-halo mass relationship results in regions that are approximately 22 per cent smaller, iv) using a constant stellar-to-halo mass relationship, but including only sources with haloes of mass greater than 10^9 M_sun, regions are approximately 17 per cent smaller, and; v) using a constant stellar-to-halo mass relationship but including only sources with haloes of mass greater than 10^10 M_sun leads to regions that are approximately 19 per cent larger."}
{"text": "We calculate the spatially-dependent 21-cm differential brightness temperature, delta T_b, between hydrogen gas and the CMB along the line of sight. For redshift z >> 1, the evolution of delta T_b can be written as delta T_b is approximately equal to 27 * x_HI * (1 + delta) * ((1+z)/10 * 0.15 / (Omega_m * h^2))^0.5 * (Omega_b * h^2 / 0.023) mK, where delta is the local dark matter overdensity and x_HI is the local neutral fraction of the gas. By using this formulation we ignore redshift-space distortions and assume the spin temperature of the cosmic gas, T_s, to be much higher than the CMB temperature, T_gamma. As a result, this signal is seen in emission. The latter assumption is valid in the post-heating regime where X-ray heating and the Lyman-alpha background act to decouple the 21-cm transition from the CMB [see, e.g., the discussion by][FOB2006]."}
{"text": "Caution must be taken, however, if claiming the spin temperature can be neglected during the early stages of reionization since the effect of X-rays on the 21-cm signal depends on the timing of the X-ray heating epoch. As discussed in [MFS2013], an overlap of these epochs can lead to 10--100 times more power at wavenumber k is approximately equal to 0.1 Mpc^-1 at a mean neutral fraction >~ 0.9 than predicted assuming T_s >> T_gamma. At a mean neutral fraction of approximately 0.7, this assumption is found to overpredict 21-cm power by a factor of 1--2. Therefore, while we show results for redshift z <~ 15 only in this work, these effects must be kept in mind. They should, however, not affect our model-relative results as we compare the power spectra of our models in terms of their power ratio at the single global neutral fraction of approximately 0.68."}
{"text": "The spherically-averaged dimensionless 21-cm power spectrum is a measure of the relative power of fluctuations in the 21-cm brightness temperature field as a function of scale: the dimensionless power spectrum Delta^2_21(k,z) equals (k^3 / (2*pi^2*V)) times the angle-averaged power of the Fourier transform of the brightness temperature contrast field. Here V is the volume of the simulation and the brightness temperature contrast field is calculated using delta_21 = (delta T_b / mean delta T_b) - 1. A dimensional form of the 21-cm power spectrum (with units of mK^2) can be obtained through the mean brightness temperature squared times the dimensionless power spectrum. Both can be calculated from observational data but the dimensional power spectrum has the advantage of including the effect of the global ionization state on the overall power. Simulations show that the variance of the brightness temperature field reaches a maximum approximately midway through the reionization process [see, e.g.,][LIDZ2008, ICHIKAWA2010, WP2014]."}
{"text": "These maxima are also present in the dimensional 21-cm power spectra but not in the dimensionless power spectra. This feature may enable the observational determination of the redshift at which the IGM is approximately half ionized. The evolution in the dimensional 21-cm power spectra for our fiducial model is shown in Figure 7. The redshifts and global neutral fractions shown correspond to those of the maps in Figure 2. At early times, when the simulation volume is fully neutral, the 21-cm power spectrum reflects that of the underlying density field. Soon after the first regions ionize, the 21-cm power spectrum drops briefly. This is due to what [LIDZ2008] describe as an `equilibration phase', when over-dense and under-dense regions have similar brightness temperatures due to the `inside-out' nature of reionization."}
{"text": "As reionization progresses, ionized regions grow resulting in an increase in large-scale power (small k) and a supression of small-scale power. Power on scales corresponding to wavenumber k ~ 0.1--1 Mpc^-1 tends to a maximum and the slope of the power spectrum flattens when reionization approaches its midpoint at a mean neutral fraction of approximately 0.5 (which occurs at redshift z is approximately equal to 8 for our fiducial model). Past this point power on all scales falls until there is no signal. The shaded region in Figure 7 corresponds to wavenumbers k > 0.7 k_Ny, where k_Ny is the Nyquist frequency of our simulation. Due to aliasing effects in our simulation, power for modes in this region are unreliable [see, e.g.,][CUI2008]. However, based on fiducial instrumental specifications, current- and future-generation radio interferometers will be most sensitive to modes with k ~ 0.1--1 Mpc^-1 [see, e.g.,][LIU2014, PRITCHARD2015], therefore these aliasing effects do not affect our predictions for observable differentiation between models."}
{"text": "Figure 8 shows the dimensional 21-cm power spectra for our models at redshift z is approximately equal to 8.4 where they have been matched, together with their ratios with respect to the fiducial model. The metric we use to compare the power spectra of our models is the maximum fractional difference in dimensional 21-cm power with respect to the fiducial model in the wavenumber interval k = 0.2--1 Mpc^-1. Using this metric, our results show there is a difference of up to: i) approximately 17 per cent without SNe feedback; ii) approximately 15 per cent without SNe or reionization feedback; iii) approximately 18 per cent using a constant stellar-to-halo mass relationship; iv) approximately 15 per cent using a constant stellar-to-halo mass relationship including only sources with haloes of mass greater than 10^9 M_sun, and; v) approximately 69 per cent using a constant stellar-to-halo mass relationship including only sources with haloes of mass greater than 10^10 M_sun."}
{"text": "The evolution of spatial fluctuations in the 21-cm signal has been shown to be sensitive to the nature of the sources driving reionization and to the size of their populations [see, e.g.,][MLZD2007]. Observing how the 21-cm power spectrum evolves may therefore be used to probe the clustering characteristics and bias of the sources responsible for reionization. In order to explore this we show the evolution of our models' dimensional power spectra for specific wavenumbers in Figure 9. It can be seen that while each model exhibits similar evolutionary behaviour on large scales, there are noticable differences on smaller scales. In particular, not all models' 21-cm power spectra pass through a local minimum during the first half of reionization. These minima are a feature of models with relatively weakly biased ionizing sources. The CSHR and CSHR.Mcut.10 models provide useful examples to help explain this."}
{"text": "The CSHR model includes ionization due to sources associated with haloes of any mass resolved by Tiamat, in contrast with the CSHR.Mcut.10 model which has fewer sources hosted by smaller-to-medium-mass haloes. During the early stages of reionization, ionized regions form around these `low-mass sources' in the CSHR model, reducing 21-cm power on scales comparable to the source separation. This leads to persistant minima for wavenumber k <~ 1 Mpc^-1. However, when only `high-mass sources' are included in the CSHR.Mcut.10 mass-cut model, ionized regions only form about the most clustered, highly biased haloes, leaving 21-cm power on other scales. This leads to the absence of a local minimum in the power spectrum evolution for this model on scales k >~ 0.4 Mpc^-1. This behaviour has been investigated previously [see, e.g.,][MLZD2007, LIDZ2008] using models that assume ionizing source luminosities that are proportional to their host halo mass and implementing different source-luminosity relationships."}
{"text": "However, these models do not capture the complex interplay between galaxies and the ionization state of the IGM through the effects of feedback. We find that on smaller scales, semi-analytic modelling of galaxies and feedback reduces the signature of the equilibration phase that is seen in constant stellar-to-halo mass ratio models. In addition to the 21-cm power spectrum amplitude, the evolutionary behaviour of its slope also serves as a diagnostic of reionization. Since the global neutral fraction is not directly measurable, we follow the work of [LIDZ2008] and [KIM2013a, KIM2013b] by exploring the joint evolution of the 21-cm power spectrum amplitude and its slope at selected scales. Figure 10 shows loci of the power spectrum gradient versus amplitude for our models. As was shown in Figure 9 for the amplitude, we find that the models exhibit similar evolutionary behaviour during the first half of the reionization process. As before, the main exception is the CSHR.Mcut.10 model."}
{"text": "We find a smaller level of difference between models with and without supernova feedback than described in [KIM2013a, KIM2013b]. This is most likely due to the high temporal resolution of our simulation as mentioned in Section 3.2. As mentioned in Section 3.2, there is a remarkable similarity between the ionization fields of the no-feedback and CSHR models despite the relatively large difference in the host halo mass scale of sources which dominate their reionization. This motivated the implementation of the CSHR mass-cut models, of which, CSHR.Mcut.9 is the most similar to the no-feedback models. As explained, this follows from the fact that their dominant ionizing sources are hosted by haloes in the same mass range. This is in contrast to the CSHR.Mcut.10 model which has a significantly different ionization field owing to the bias of its ionizing sources."}
{"text": "While this may not be surprising, since none of these models include feedback effects, what is surprising is the similarity between either the CSHR or CSHR.Mcut.9 model and the fiducial model (which does include feedback effects). This suggests the existance of a mass cut for the CSHR model which best replicates the morphology and 21-cm power spectra results of the fiducial model. Considering the added complexity of implementing a SAM-based prescription to simulate reionization, such `simple' semi-numerical prescriptions have their utility. While reionization morphology at fixed neutral fraction is not very sensitive to the details of galaxy formation, it is sensitive to the mass of the haloes which host the bulk of the ionizing sources. Simple EoR parametrizations may therefore be used to predict reionization morphology, and from that infer the dominant ionizing source population. This utility, however, has its limitations."}
{"text": "By not including realistic galaxy-formation physics in their formultion, these models cannot be used to investigate the effect of reionization on galaxy formation. Therefore, unlocking the details of galaxy formation requires interpretation with SAMs, in combination with other observations. This work has investigated the dependence of the morphology and statistics of HII regions on galaxy-formation physics during the Epoch of Reioinization using the Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS). DRAGONS includes the galaxy properties modelled by the semi-analytic model Meraxes and includes calculation of the inhomogeneous ionizing UV background using the 21cmfast algorithm, providing a self-consistent realization of reionization. This allows us to explore the effect of environment on galaxy formation, subsequent reionization of the IGM, and its observable signatures."}
{"text": "We use this coupled model to make updated cosmic 21-cm signal simulations, and predictions for low-frequency 21-cm experiments. We have presented results for a range of models that capture important physical mechanisms such as reionization and supernova feedback. We have demonstrated that the morphology and statistics of reionization are sensitive to both the ionizing source population and to feedback effects. We have shown how galaxy formation can modify the observable morphology of reionization by looking at the sizes of ionized regions and 21-cm power spectra. Of the galaxy physics we have investigated, we find that supernova feedback plays the most important role in reionzation, and that in the absence of this feedback, HII regions are up to approximately 20 per cent smaller, while the fractional difference in amplitude of power spectra is up to approximately 17 per cent at fixed ionized fraction. We have compared our SAM-based reionization models with past calculations that assume constant halo mass-to-luminosity ratios."}
{"text": "We find that the correct choice of minimum halo mass in these models leads to a reionization morphology that mimics that of a realistic galaxy-formation model. Therefore, reionization morphology at fixed neutral fraction is not uniquely predicted by the details of galaxy-formation physics. However, morphology is sensitive to the mass of the haloes which host the bulk of the reionizing sources. Simple EoR parametrizations therefore have utility for predicting the cosmic 21-cm signal, however, a better understanding of galaxy-formation physics using future 21-cm observations requires interpretation including a model of galaxy formation, in combination with other observations. In future work we will include a number of improvements to our modelling, including redshift and mass dependency of the escape fraction of ionizing photons, the effect of gas temperature and X-rays, a Markov chain Monte Carlo exploration of the model parameter space, and inhomogenous recombinations."}
{"text": "In this appendix we demonstrate the spatial convergence of our simulations through refinement of the grids used by 21cmfast. This is done for both the reionization history and 21-cm power spectra of our fiducial model. Figure A1 shows the globally-averaged neutral fraction, as a function of redshift, z, for our fiducial model using a 128^3, 256^3 and 512^3 21cmfast grid and the differences between them. We find that our final refinement results in convergence to within +/- 0.01 neutral fraction at all redshifts. In order to show spatial convergence of the power spectrum, Figure A2 shows the dimensional 21-cm power spectra for our fiducial model at a mean neutral fraction of approximately 0.68 using a 128^3, 256^3 and 512^3 21cmfast grid and their ratios with respect to the 512^3 simulation. The vertical dotted line shows the scale at which current- and future-generation radio interferometers are most sensitive. We find that successive refinement results in convergence to within 3 per cent on this scale."}
{"text": "Using Hubble data, including new grism spectra, Oesch et al. recently identified GN-z11, an M_UV=-21.1 galaxy at z=11.1 (just 400 Myr after the big bang). With an estimated stellar mass of ~10^9 solar masses, this galaxy is surprisingly bright and massive, raising questions as to how such an extreme object could form so early in the Universe. Using Meraxes, a semi-analytic galaxy-formation model developed as part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) programme, we investigate the potential formation mechanisms and eventual fate of GN-z11. The volume of our simulation is comparable to that of the discovery observations and possesses two analogue galaxies of similar luminosity to this remarkably bright system. Existing in the two most massive subhaloes at z=11.1 (M_vir=1.4x10^11 solar masses and 6.7x10^10 solar masses), our model analogues show excellent agreement with all available observationally derived properties of GN-z11. Although they are relatively rare outliers from the full galaxy population at high-z, they are no longer the most massive or brightest systems by z=5."}
{"text": "Furthermore, we find that both objects possess relatively smooth, but extremely rapid mass growth histories with consistently high star formation rates and UV luminosities at z>11, indicating that their brightness is not a transient, merger-driven feature. Our model results suggest that future wide-field surveys with the James Webb Space Telescope may be able to detect the progenitors of GN-z11 analogues out to z~13-14, pushing the frontiers of galaxy-formation observations to the early phases of cosmic reionization and providing a valuable glimpse of the first galaxies to reionize the Universe on large scales."}
{"text": "Using Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) grism spectroscopy, [Oesch2016] recently identified the most distant galaxy known to date (GN-z11). The spectrum, combined with photometric data from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) survey, placed the system at z=11.09 (+0.08 / -0.12), with lower redshift spectral energy distribution (SED) solutions excluded with high confidence. At M_UV = -22.1 +/- 0.2, GN-z11 is approximately three times more luminous than L* at z=7-8, and is therefore extremely bright for such a high-z object. Extrapolations of the z=4-8 ultraviolet luminosity function (UV LF) suggest that such objects should be rare with fewer than ~0.06 such systems expected in the total volume surveyed (~1.2x10^6 Mpc^3; [e.g.][Bouwens2015, Finkelstein2015])."}
{"text": "LF evolution models based on hierarchical assembly ([e.g.][Trenti2010, Mason2015]), the extrapolation of abundance matching results to higher luminosities/redshifts ([e.g.][Trac2015, Mashian2016]), and cosmological hydrodynamic simulations such as BlueTides ([Waters2016, Waters2016b]), all similarly point to GN-z11 being an exceptional and rare system. This begs the question of what the formation mechanisms might be for such a galaxy, as well as what its descendants are at lower redshifts? In this work we use the semi-analytic galaxy-formation model Meraxes [Mutch2015], developed for the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) programme ([Angel2016, Geil2015, Liu2015]), in order to investigate whether galaxy-formation models of this type predict the existence of such extreme systems as GN-z11 and, if so, what their properties, origins and potential fates are."}
{"text": "The DRAGONS parent N-body simulation (Tiamat; [Poole2016]) possesses a comparable volume to that of the discovery observations, yet Meraxes predicts two z=11.1 galaxies of comparable UV magnitude to GN-z11, suggesting that such luminous galaxies may be a more common outcome of early galaxy formation than previously thought. This paper is laid out as follows. In Section 2, we give a brief overview of the DRAGONS framework, including both the Tiamat N-body simulation and Meraxes semi-analytic model. In Section 3, we discuss the presence and properties of luminous GN-z11 analogues in our model galaxy population before going on to investigate the origin and fate of these objects from z=5-20. In Section 4, we discuss the prospects for detecting the progenitors of GN-z11 analogues with the forthcoming James Webb Space Telescope (JWST) and provide forecasts for the maximum redshift out to which these may be observed. We close with a summary of our findings in Section 5. The Tiamat simulation was run with a standard, spatially flat LambdaCDM cosmology, utilizing the latest [Planck-Collaboration2015] parameters. However, for consistency with [Oesch2016] we present all results with h=0.7 throughout."}
{"text": "The DRAGONS programme was designed specifically to study the Epoch of Reionization (EoR) and the growth of the first galaxies. It consists of two main parts: the Tiamat suite of high resolution N-body simulations, and the Meraxes semi-analytic galaxy formation model. The main Tiamat simulation consists of a (96.9 Mpc)^3 volume with enough mass resolution to resolve dark matter haloes down to approximately three times the atomic cooling mass threshold at z=5. It also possesses a high temporal resolution of ~11 Myr per output snapshot, allowing us to capture the stochastic nature of star formation and quenching during the EoR. Only trees constructed from the main Tiamat N-body simulation are utilized in this work. For more details, including information on the other simulations in the Tiamat suite, please see [Poole2016] and [Angel2016]."}
{"text": "The Meraxes semi-analytic model runs atop the merger trees extracted from Tiamat and includes the dominant physical process thought to shape the evolution of high-redshift galaxies, including cooling, star formation, metal enrichment, satellite infall and merger events. The model also features a novel delayed supernova feedback and enrichment scheme and self-consistently incorporates the semi-numerical reionization scheme, 21CMFAST ([Mesinger2007, Mesinger2011]), in order to model reionization and its effects on galaxy evolution both temporally and spatially [Geil2015]. A detailed description of Meraxes and its design can be found in [Mutch2015]. The fiducial Meraxes model calibration (used in this work) was constructed to reproduce the observed evolution of the galaxy stellar mass function from z=5-7 ([Gonzalez2011, Duncan2014, Grazian2014, Song2015]) and to provide a reionization history consistent with the latest Planck optical depth measurements [Planck-Collaboration2015]. The model has also been shown to accurately reproduce the evolution of the observed UV LF from z=5-10 [Liu2015]."}
{"text": "The bright end of the z=11.1 UV LF predicted by Meraxes (grey line) along with associated Poisson uncertainties (shaded region). The luminosities of our two analogue galaxies, DR-1 and DR-2, are shown as a green circle and orange square, respectively. No dust extinction has been applied to the model results. The red data point indicates observational estimated value and 1-sigma uncertainty derived from the GN-z11 detection. Also shown are the z=6 and z=8 LFs predicted by the model, along with observational results from [Bouwens2015] which have been dust corrected using the inverse of the methodology outlined in [Liu2015]. The agreement between the model and observations demonstrates the success of our model at reproducing the normalization and evolution of high-z UV LFs. In Fig. 1 we present the bright end of the z=11.1 UV LF predicted by Meraxes (grey line and with shaded Poisson uncertainties). The effects of dust extinction are not included. The orange square and green circle indicate the magnitudes of the two most UV-luminous galaxies in our model whilst the red data point indicates the observationally estimated phi and 1-sigma uncertainty derived from the GN-z11 detection."}
{"text": "As can be seen, these two most luminous Meraxes systems are comparable in luminosity to GN-z11. The properties of the GN-z11 analogues, DR-1 and DR-2, at both z=11.1 and 5. For comparison, the observationally determined values for GN-z11 itself are also shown [Oesch2016]. For reference, we also show in Fig. 1 the z=6 and 8 UV LFs predicted by Meraxes as well as the observational results of [Bouwens2015]. The observations have been corrected for dust extinction using the inverse of the methodology described in [Liu2015]. The agreement between the observational data and our model results indicates that Meraxes correctly predicts both the normalization and evolution of the bright end of the UV LF at lower redshifts, giving us confidence in the z=11.1 result."}
{"text": "Due to the limited volume of the parent Tiamat N-body simulation, the bright end of the LF is poorly constrained for number densities <~10^-5 Mag^-1 Mpc^-3. This precludes us from making any quantitative statements regarding the probability of detecting a galaxy as bright as GN-z11 other than to simply state that we find at least one such system in our ~1x10^6 Mpc^3 volume. However, we note that this is approximately equal to the volume surveyed during the detection of GN-z11 (~1.2x10^6 Mpc^3) and therefore the presence of any galaxies as bright as this observed object in our model is significant. Given the success of Meraxes in reproducing the evolution of the galaxy stellar mass functions [Mutch2015] and observed UV LFs [Liu2015] at z=5-8, the presence of any systems as luminous as GN-z11 in our model is remarkable, opening up the possibility that such galaxies may not be as rare as extrapolations of the observed z~4-8 LFs to higher redshifts may suggest ([see][and references therein]Oesch2016)."}
{"text": "Having established that galaxies as UV-luminous as GN-z11 exist in the output of DRAGONS, we selected the two brightest UV magnitude galaxies at redshift z=11.1 for detailed study. The properties of these objects, hence forth referred to as DR-1 and DR-2, show good agreement with the best observational measurements of GN-z11 [Oesch2016], as can be seen in Table 1. This suggests that we can use these model galaxies as analogues with which to investigate the potential formation, evolution and fate of GN-z11."}
{"text": "The observed frame SED of DR-1 (green) and DR-2 (orange) in units of flux density. Lyman-alpha absorption has been included, however, no dust extinction model has been applied. Red points show the observed GN-z11 HST photometric measurements and upper limits. The black thin line indicates the best-fitting SED for GN-z11 [Oesch2016]. Both model analogue galaxies have a spectral shape in good agreement with the GN-z11 measurements. The normalization of both model spectra further show reasonable agreement with GN-z11 photometric measurements due to their comparable UV luminosities. As well as those properties listed in Table 1, DR-1 and DR-2 also possess similar SEDs to GN-z11. In Fig. 2 we plot the observed frame SEDs of DR-1 (green) and DR-2 (orange) in terms of their flux density between 0.2 and 6 micrometers. The red data points show the GN-z11 HST photometric measurements and upper limits, whilst the black thin line indicates the best-fitting SED presented in [Oesch2016]."}
{"text": "Lyman-alpha absorption has been included in the model spectra and is manifested as the sharp drop in flux at wavelength <~1.1 micrometers; however, no dust extinction model has been applied. For more details on the methodology used to construct the model SEDs, see [Liu2015]. Both analogue galaxies possess spectra and UV slopes (beta) in close agreement with the GN-z11 observations, supporting the claim that this observed system is relatively dust free [Oesch2016]. The normalization of both model spectra further show reasonable agreement with GN-z11 photometric measurements due to their comparable UV luminosities (cf. Table 1)."}
{"text": "The UV magnitude versus stellar mass distribution of Meraxes galaxies at z~11. The thick black line and shaded region indicate the median and 95 pc confidence intervals of the distribution as a function of stellar mass. The top (right) panels indicate the marginalized log-probability distribution of stellar mass (UV magnitude) values. The red point with error bars indicates the position of GN-z11 in this plane, whilst the grey squares show the model analogue galaxies, DR-1 and DR-2. Both analogue galaxies (as well as GN-z11) are rare outliers from the main distribution, but are approximately consistent with an extrapolation of the median relation from lower masses. DR-1 and DR-2 are the two most massive galaxies in the simulation at the redshift at which they were selected (z=11.1) and are hosted by the two most massive subhaloes. They are also rare outliers from the majority of the model galaxy population in terms of their stellar masses, star formation rates and UV luminosities. However, they remain broadly consistent with the mean trends displayed by galaxies at lower luminosities/masses, suggesting that their history is not particularly special or unique."}
{"text": "As an example, in Fig. 3 we present the distribution of all Meraxes z=11.1 galaxies in the UV magnitude versus stellar mass plane. The positions of DR-1 and DR-2 are shown as grey squares, whilst GN-z11 is indicated by the red point with error bars. Although these three objects lie out with the bulk of the main distribution, they are roughly consistent with the median M_1600-M_* trend extrapolated from lower masses."}
{"text": "The detection of such a massive and luminous galaxy at z~11 raises a number of interesting questions. How do such massive systems form so rapidly? Is their extreme brightness merely a transient feature of their evolution brought on by a merger or other significant event? If not, then how can the level of star formation required to produce new, UV luminous stars be maintained? In this section we address these questions using our model analogue galaxies and further explore what the eventual fate of such objects is at lower redshifts."}
{"text": "Property histories for the model analogue galaxies, DR-1 (green) and DR-2 (orange): (a) rest frame intrinsic absolute UV magnitude (1600 Angstrom); (b) star formation rate; (c) stellar mass; (d) subhalo mass; (e) cold gas fraction; (f) half light radius assuming a pure-exponential disc; (g) merger baryonic mass ratios for all galaxy merger events with ratios >0.01 (mergers of lower mass ratio are indicated by tick marks on the x-axis). The red dots with error bars show the best estimates of the properties of GN-z11 [Oesch2016], whilst the vertical dashed line indicates z=11. For comparison, thin grey lines and dots show the histories of the ten next-most-luminous galaxies selected at the same redshift as our analogues (z~11). Fig. 4 shows the full formation histories of DR-1 (green) and DR-2 (orange) for a number of properties from z=18 to 5. The corresponding measured values for GN-z11 are shown as red points with error bars where available."}
{"text": "As with the UV luminosity and stellar masses discussed above, we see close agreement between our model analogues and GN-z11 in terms of star formations rates (panel b) and disc sizes (panel f). The UV luminosities of both DR-1 and DR-2 continually, but extremely rapidly, increase from high redshift (panel a). The formation (or half-mass) redshift of each z=11.1 analogue's dark matter subhalo is z~11.4 and 11.9, respectively. For comparison, theoretical expectations using extended Press-Schechter theory [Bond1991] are for these two haloes to have formed far earlier, at z~12.1, and hence to have grown at a much slower pace [Tacchella2013, Trenti2015]. In our simulation, the host subhalo of DR-1 grows by a factor of approximately 5 in just 65 Myr (panel c) immediately preceding z=11.1, resulting in a growth in stellar mass of a factor of 9 during the same period."}
{"text": "A visual inspection of the evolution of the local environment of DR-1 indicates that this period of rapid growth coincides with infall into a filamentary like structure. During this time, the host subhalo is subjected to multiple minor mergers (of haloes with no stellar mass), as well as significant smooth accretion below the resolution limit of the simulation. It is also immediately apparent from Fig. 4, however, that the extreme UV brightness of DR-1 and DR-2 are not transient features of their evolution; the star formation rates and UV luminosities of both analogue systems remain high or increasing throughout their evolution. For comparison, thin grey lines show the evolution of the 10 next-most-luminous galaxies selected at the same redshift (z=11.1). These luminous counterpart galaxies all possess similar growth histories, with high star formation rates (panel b) driven by continual growth of their host haloes (panel d) and associated accretion of fresh gas. However, their star formation is less sustained than that of DR-1 and 2, with more numerous periods of inactivity."}
{"text": "The distribution of model galaxy UV magnitudes (M_1600) as a function of subhalo mass M_vir at z~11 (top row). The right-hand panel shows a zoom in scatter plot of the highest M_vir (/M_1600) region. Again, both GN-z11 analogue galaxies are outliers of the main population. However, by z=5 (bottom row), this is no longer the case. Whilst these galaxies remain some of the most UV luminous and massive, they have regressed towards the mean trend and there now exists a small number of other, more extreme systems."}
{"text": "So how can DR-1 and 2 achieve and sustain such a rapid stellar mass growth? High star formation rates should result in large amounts of supernova energy being deposited into the interstellar medium, heating and ejecting cold gas and thus curtailing star formation until this material is replenished. Indeed, this is the dominant mechanism by which star formation is regulated in Meraxes [Mutch2015]. In panel (e) of Fig. 4 we show the cold gas fraction, M_cold / (m_cold + M_*), of our ten luminous comparison galaxies in grey. Many show the expected large drops in cold gas fraction caused by star formation events which deplete gas, both by converting it to stars and ejecting it from the galaxy through supernova feedback. Occasionally these low gas fractions remain for tens of millions of years, but more often gas reserves are quickly replenished by accretion from the IGM. By comparison, our GN-z11 analogues, DR-1 and DR-2, show typically fewer major depletion events."}
{"text": "This is due to the large amounts of cold gas available to these galaxies which results in any one star formation episode removing only a small fraction of the available material. In panel (g) we show the baryonic merger ratios (m_baryon_satellite / m_baryon_central) of all merger events with mass ratios greater than 0.01 for both DR-1 and DR-2, as well as our ten comparison objects. The horizontal grey line indicates a ratio of 1/3, above which we deem the merger to be a major event. The ticks on the lower x-axis indicate merger events with ratios below the range of the plot. Interestingly, we see that neither DR-1 nor DR-2 has experienced a merger with a baryonic mass ratio greater than ~0.1. We further find that none of the luminous comparison galaxies has experienced a major merger prior to z~11."}
{"text": "Although these results refer to galaxy merger events (as opposed to mergers between haloes which may potentially be devoid of stars), we confirm that >90% of the z<11.1 halo mass growth of all plotted objects is driven by smooth accretion of systems below the halo mass resolution limit of our input N-body simulation (~1.4x10^8 h^-1 M_sun). Such quiescent merger histories are an important aspect of the successful growth of GN-z11 analogues in Meraxes. Within our model, and as suggested by hydrodynamical simulations ([e.g.][Cox2008, Powell2013, Kannan2015]), major merger events induce shocks and instabilities which in turn result in efficient star formation events. Such events consume large fractions of the cold gas of both progenitors with the resulting supernova feedback ejecting even more material from the system."}
{"text": "Although both DR-1 and 2 have plentiful and continuous replenishment of cold gas from the IGM, it is likely that numerous major merger events would have curtailed the eventual z~11 stellar mass and would certainly have introduced more variability into the star formation histories of these objects, reducing their duty cycles and limiting their probability of detection."}
{"text": "As well as using the DRAGONS framework to explore the origins of GN-z11 analogues, we can also exploit the realistic galaxy populations it provides to explore the eventual fate of these rare objects. From Fig. 4, we can see that the haloes which DR-1 and 2 occupy continue to grow steadily to z=5. This steady growth brings with it fresh gas, allowing for a slowly increasing star formation rate and UV luminosity. As such, these galaxies remain the most luminous and massive of the twelve objects shown in the figure (selected to be the twelve most UV-luminous objects at z=11.1). However, when compared to the full galaxy population at z=5, our two GN-z11 analogues are no longer the brightest or most massive in the simulation volume. Such a regression of extreme objects towards the mean at later times is an expected feature of structure formation [Trenti2008]."}
{"text": "In Fig. 5 we show the absolute UV magnitude versus subhalo mass distribution for the full galaxy population at z=11.1 (top) and z=5 (bottom). The panels on the right-hand side show a zoom in scatter plot of the highest M_vir (/M_1600) regions. As with Fig. 3 above, the thick black line indicates the median of the distribution, with the shaded region showing the 95 pc confidence intervals. Grey squares indicate the positions of DR-1 and DR-2. At z~11 both galaxies lie in the most massive subhaloes and are clear outliers from the bulk of the galaxy population. At z=5, this is no longer the case. Not only have both systems rejoined the tail of the main distribution, but there are several systems which are both more massive and luminous. Our model therefore predicts that although GN-z11 may be a highly biased, rare galaxy in the redshift z~11 Universe, it is likely the progenitor of more common massive galaxies in the post-reionization epoch. For reference, we present the full z=5 properties of DR-1 and DR-2 in Table 1."}
{"text": "The rest-frame intrinsic UV apparent magnitude history of DR-1 (green) and DR-2 (orange) along with the 8-sigma detection threshold (grey horizontal line) corresponding to the example future wide-field JWST/NIRCAM survey presented in [Mason2015]. This survey design corresponds to an 800 hour total exposure time split amongst multiple pointings and bands, covering a total survey area of 4000 arcmin^2. See Section 4 for more details. Our model predicts that future JWST surveys such as this may be able to detect the progenitors of GN-z11 analogues out to z~13-14, corresponding to the early stages of reionization. GN-z11 represents the highest redshift galaxy found to date, and pushes the boundaries of what is technically achievable using HST. JWST will possess the capability to go approximately two magnitudes deeper in the rest frame UV at high redshift, opening up the possibility of detecting more GN-z11 type systems at z~11 [Waters2016], as well as their progenitors at higher redshifts."}
{"text": "In Fig. 6 we present the rest-frame apparent UV magnitude histories of DR-1 and DR-2 from z=5-20 (green and orange lines, respectively). No dust extinction has been included, in agreement with the observed blue UV continuum slope of GN-z11 [Oesch2016]. The grey horizontal line indicates the 8-sigma detection limit for the example wide-field JWST/NIRCAM survey presented in [Mason2015]. This survey design corresponds to a total of 800 hours of exposure time divided up amongst 400 pointings in 5 bands, and covering a total area of ~4000 arcmin^2. Further details can be found in [Mason2015]. The total comoving volume of this example survey is (178.4 Mpc)^3 at z=11.1. This is approximately 6 times the volume of our Tiamat simulation, and ~90% of that of the much larger BlueTides simulation [Feng2015], within which it has been recently shown that approximately 30 systems of similar or brighter luminosity than GN-z11 are found [Waters2016]."}
{"text": "Such a survey should therefore provide both a volume and sensitivity to easily detect multiple GN-z11 analogue systems at z~11. Our model further suggests that the progenitors of such systems may remain luminous enough to be detected out to z~13-14, corresponding to the early stages of Reionization when the Universe was less than ~10% ionized ([e.g.][]Greig & Mesinger in prep.[Kuhlen2012, Mutch2015])."}
{"text": "In this work, we identify two GN-z11 analogue systems from the results of the semi-analytic model, Meraxes, created as part of the DRAGONS programme. The presence of these two analogues in a simulated volume approximately equal to that of the observational survey volume supports claims by other authors [Waters2016] that galaxies as luminous as GN-z11 are more common than extrapolations of z~4-8 UV LFs would suggest [Oesch2016]. Using the detailed properties and full formation histories afforded to us by Meraxes, we have investigated the formation, evolution and fate of our two model analogue systems (DR-1 and 2). Our results can be summarized as follows."}
{"text": "Both DR-1 and 2 possess stellar masses, UV luminosities, star formation rates, sizes and SEDs, which are in close agreement with the measured values of GN-z11. These analogues are the most UV-luminous and massive systems in our simulated volume at z=11 and are rare outliers from the bulk of the galaxy population. However, despite their extreme nature, their properties are broadly consistent with extrapolations of the mean trends at lower masses. The extreme UV brightness of our analogues at z=11 is not a transient feature of their histories. Instead both their luminosities and stellar masses increase relatively smoothly, but extremely rapidly, from higher redshifts and continue to increase for the remainder of their evolution to z=5."}
{"text": "The sustained and increasing SFRs of DR-1 and DR-2 are due to rapid growth of their host dark matter haloes, driven predominantly by smooth accretion of objects below the mass resolution limit of our simulation and bringing with it an ample supply of fresh cold gas to fuel star formation. Another important feature of these growth histories is a notable lack of major mergers which would have caused a significant star burst, ejecting a large amount of cold gas and temporarily stalling star formation. Despite being the most extreme and rare outliers of the full galaxy population at z~11, by z=5 neither analogue is the most massive nor UV-luminous system in the simulation. Future, wide-field surveys with JWST will likely be able to identify the progenitors of GN-z11 type galaxies out to z~13-14. The potential ability of JWST to detect GN-z11 progenitors all the way out to z~14 will push the frontiers of galaxy-formation observations to the early phases of cosmic reionization and provide a valuable glimpse of the first galaxies to reionize the Universe on large scales."}
{"text": "This research was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant ref. UOM0005, on its Peak Computing Facility hosted at the University of Melbourne, an initiative of the Victorian Government, Australia. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne and the Australian Governments Education Investment Fund. AM acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 638809 AIDA). PO and GDI acknowledge the support of NASA grant HST-GO-1387 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. The DRAGONS research programme is funded by the Australian Research Council through the ARC Laureate Fellowship FL110100072 awarded to JSBW."}
{"text": "We investigate high-redshift galaxy sizes using a semi-analytic model constructed for the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation project. Our fiducial model, including strong feedback from supernovae and photoionization background, accurately reproduces the evolution of the stellar mass function and UV luminosity function. Using this model, we study the size--luminosity relation of galaxies and find that the effective radius scales with UV luminosity as the effective radius is proportional to UV luminosity to the power of 0.25 at redshift of approximately 5 to 9. We show that recently discovered very luminous galaxies at redshift of approximately 7 [2016arXiv160505325B] and redshift of approximately 11 [2016ApJ...819..129O] lie on our predicted size--luminosity relations. We find that a significant fraction of galaxies at redshift greater than 8 will not be resolved by JWST, but GMT will have the ability to resolve all galaxies in haloes above the atomic cooling limit. We show that our fiducial model successfully reproduces the redshift evolution of average galaxy sizes at redshift greater than 5. We also explore galaxy sizes in models without supernova feedback."}
{"text": "The no-supernova feedback models produce galaxy sizes that are smaller than observations. We therefore confirm that supernova feedback plays an important role in determining the size--luminosity relation of galaxies and its redshift evolution during reionization. The evolution of galaxy size during the Epoch of Reionization (EoR) provides an additional probe for understanding galaxy formation in the early Universe. In the hierarchical structure formation scenario [1978MNRAS.183..341W], dark matter haloes form first, then baryonic gas cools and falls into their potential wells of to form galaxies. Within this scheme, [1980MNRAS.193..189F] studied the formation of galaxy discs. In this model, the spin of a rotationally supported galaxy disc originates from the conservation of angular momentum during the collapse of cooling gas. Further analytic modelling by [1998MNRAS.295..319M] provided a relation between the disc scale length of a galaxy, R_d, and the virial radius of its dark matter halo, R_vir for infinitesimally thin discs with exponential surface density profiles."}
{"text": "The disc size can be written as: The disc scale length, R_d, is given by the halo spin parameter lambda divided by the square root of 2, multiplied by the ratio of the disc's angular momentum fraction (j_d) to its mass fraction (m_d), all multiplied by the halo's virial radius, R_vir. Here, m_d and j_d are the fraction of mass and angular momentum in the disc relative to the halo and lambda is the spin parameter of the halo. The virial radius of a dark matter halo scales with redshift and virial velocity, V_vir, or virial mass, M_vir, as: The virial radius, R_vir, scales with the virial mass, M_vir, and the Hubble parameter, H(z), or can be expressed as the virial velocity, V_vir, divided by 10 times the Hubble parameter., where H(z) is the Hubble parameter, and the Hubble parameter, H(z), is proportional to (1+z) to the power of 3/2 at high redshifts [1992ARA&A..30..499C]. Therefore, from the first equation, the proportionality of R_d with R_vir predicts that the sizes of discs scale with redshift as (1+z) to the power of -3/2 at fixed circular velocity, or (1+z) to the power of -1 at fixed halo mass."}
{"text": "Caption for Table 1: Observed evolution of galaxy sizes, R_e is proportional to (1+z) to the power of m from literature, where L*_z=3 corresponds to UV magnitude M_UV=-21.0. Observations of Lyman break galaxies (LBGs) show that galaxies are more compact at higher redshift, and that average sizes evolve with redshift as (1+z) to the power of -m with m of approximately 1 to 1.5 [e.g.][2004ApJ...600L.107F, 2004ApJ...611L...1B, 2010ApJ...709L..21O, 2012A&A...547A..51G, 2013ApJ...777..155O, 2015ApJ...804..103K, 2015ApJ...808....6H, 2015ApJS..219...15S]. Semi-analytic models have had considerable success studying the formation and evolution of galaxies in the past two decades [e.g.][1991ApJ...379...52W, 1993MNRAS.264..201K, 2000MNRAS.319..168C, 2006MNRAS.365...11C, 2006MNRAS.370..645B, 2011MNRAS.412.1828L, 2015arXiv150908473L]. Galaxy sizes are important for semi-analytic models since the cold gas is assumed to settle in discs where star formation occurs at a rate depending on the surface density [e.g.][2006MNRAS.365...11C]. Reproducing the evolution of galaxy sizes in the early and dense Universe is therefore important for semi-analytic models of reionization."}
{"text": "On the other hand, feedback mechanisms are already known to play an important role in suppressing star formation in galaxies. Using the observed size evolution and the luminosity function of galaxies, [2011MNRAS.413L..38W] presented a simple model to constrain the feedback mechanism using galaxy sizes: The effective radius, R_e, is proportional to luminosity L raised to the power of 1 divided by 3 times (1+a), and also proportional to (1+z) to the power of -m. Here L is the galaxy luminosity, and a and m are free parameters which can be constrained using both the slope of the galaxy luminosity function and galaxy size evolution. Feedback arising from energy release and momentum outflow could affect the luminosity at fixed disc sizes. Based on the observed relation between size, luminosity and redshift, [2011MNRAS.413L..38W] ruled out the no-supernova feedback model with high confidence, and suggested a supernova feedback model through the transfer of momentum. Here we improve on this analysis using a more realistic semi-analytic model."}
{"text": "Investigation of galaxy sizes using semi-analytic models have previously been made using galaxies in both the local and high redshift Universe [e.g.][2000MNRAS.319..168C, 2009MNRAS.397.1254G, 2010MNRAS.405..948S, 2015MNRAS.447..636X, 2016MNRAS.461..859S, 2016MNRAS.459.4109T]. Our purpose-designed semi-analytic model provides a tool to study galaxy sizes during the EoR. The semi-analytic model, MERAXES [described in][hereafter Paper-III]{2016MNRAS.462..250M}, is a new purpose-built galaxy formation model designed for studying galaxy evolution during the EoR. The MERAXES model is a part of the Dark-ages Reionization And Galaxy-formation Observables from Numerical Simulation (DRAGONS) project. MERAXES includes a temporally and spatially coupled treatment of reionization, and is built upon the high resolution and high snapshot-cadence N-body simulation Tiamat [hereafter Paper-I]{2016MNRAS.459.3025P}. MERAXES successfully reproduces a series of high-redshift galaxy observables including the stellar mass function (Paper-III) and UV luminosity function [hereafter Paper-IV]{2016MNRAS.462..235L}. In this paper, we run simulations to investigate the size--luminosity relation, the size--stellar mass relation and the redshift evolution of galaxy sizes at redshifts between 5 and 10. We aim to use the evolution of galaxy sizes to probe the physics of galaxy formation during the EoR."}
{"text": "The galaxy formation model used in this work is MERAXES (Paper-III). MERAXES is implemented upon dark matter halo merger trees generated from the cosmological N-body simulation Tiamat (Paper-I). Tiamat and MERAXES have special features designed for the study of reionization. The collisionless N-body simulation, Tiamat, was run using a modified version of GADGET-2 [2005MNRAS.364.1105S] and the Planck 2015 cosmology [2015arXiv150201589P]. It includes 2160 cubed particles in a comoving 100 Mpc cube box. The mass of each particle is 2.64 times 10 to the power of 6 h inverse solar masses, which allows us to identify the low mass dark matter haloes close to the hydrogen cooling limit across the redshifts relevant to reionization. Dark matter halo finding was carried out using SUBFIND code [2001MNRAS.328..726S]. This code first identifies dark matter collapsed regions by a friends-of-friends (FoF) algorithm using a link length criterion of 0.2 times of the mean inter-particle separation."}
{"text": "A FoF group typically contains a central halo holding most of the virial mass and a group of lower-mass subhaloes which trace the undigested parts of merger events. Tiamat outputs include 100 snapshots from z=35 to z=5 with a temporal resolution of 11 Myr per snapshot. This high cadence resolves the dynamical time of galaxy discs at high redshift, and is comparable to the lifetime of massive stars. Dark matter halo merger trees constructed from Tiamat are stored and processed in a horizontal form. This allows the semi-analytic model to implement a self-consistent calculation of feedback from reionization on low mass galaxy formation. This is achieved by incorporating the semi-numerical reionization algorithm 21cmFAST [2011MNRAS.411..955M] at each snapshot. MERAXES is a new semi-analytic model based on [2006MNRAS.365...11C] with updated physics for application to redshift greater than 6. It consists of baryonic infall, gas cooling, star formation, stellar mass recycling, metal enrichment, galaxy mergers, gas stripping, and feedback from both supernova and reionization."}
{"text": "To model the formation and evolution of galaxies during the EoR, MERAXES incorporates several improvements in the feedback scheme. Firstly, it considers a delayed supernova feedback mechanism. In an instantaneous feedback scheme, a massive star instantly produces a supernova and so releases energy and mass within the same snapshot that the progenitor star formed. This is appropriate at low redshift, where the stellar lifetime is short compared to the galaxy dynamical time. However, our Tiamat merger trees have a much higher time resolution of approximately 11 Myr, which is shorter than the lifetime of the least massive Type II supernova progenitor stars (e.g., approximately 40 Myr for 8 solar mass stars). Therefore, MERAXES implements a delayed supernova feedback scheme, where a supernova may explode several snapshots after the progenitor star formed. MERAXES also includes feedback from a spatially and temporarily variable ultraviolet background (UVB). The UVB radiation heats the intergalactic medium and reduces baryonic infall within small dark matter haloes suppressing both gas cooling and star formation."}
{"text": "To achieve this, MERAXES integrates the semi-numerical code 21cmFAST [2011MNRAS.411..955M] to construct the reionization structure. We assume a standard [1955ApJ...121..161S] initial mass function (IMF) with stellar mass in the range of stellar mass in the range of 0.1 to 120 solar masses: The initial mass function phi(m_*) is proportional to stellar mass m_* to the power of -2.35. The free parameters in MERAXES were calibrated to replicate the observed stellar mass functions at redshift of approximately 5--7 [2011ApJ...735L..34G, 2014MNRAS.444.2960D, 2015A&A...575A..96G, 2016ApJ...825....5S] and the Planck optical depth to electron scatting measurements [2015arXiv150201589P]. For a more detailed description of MERAXES, see Paper-III. In our semi-analytic model, we adopt the disc scale radius from [1998MNRAS.295..319M] and the standard assumption that the specific angular momentum of the material forming the disc is the same as that of the host halo [1980MNRAS.193..189F]."}
{"text": "The spin parameter, lambda, is calculated from the N-body simulation using the definition from [2001MNRAS.321..559B]: The spin parameter lambda is defined as the halo's angular momentum, J_vir, divided by the product of the square root of 2, the virial mass M_vir, the virial velocity V_vir, and the virial radius R_vir., where M_vir and J_vir are the mass and angular momentum enclosed within the virial radius, and V_vir is the circular velocity at R_vir [see][for a discussion of spin parameters for haloes in Tiamat]{2016MNRAS.459.2106A}. The disc scale equation was obtained assuming a simple model in which dark matter haloes have singular spherical isothermal density profiles and the gravitational effects of baryonic discs are neglected. It is therefore important to note that inclusion of gravity from the disc may alter the size and rotation curve of galaxies and modify the dark matter concentration in the inner region of the halo. However, [1998MNRAS.295..319M] showed that a more realistic model with NFW halo profiles [1997ApJ...490..493N] and self-gravitating discs results in only minor modifications to the equation."}
{"text": "Simulations also show that inclusion of the self-gravity of discs will lead to instabilities of gas and stars, which drives disc material towards the centre of galaxies and results in instability-driven star bursts and bulge growth in galaxies. This will have an impact on the distribution of disc sizes [e.g.][2000MNRAS.319..168C, 2006MNRAS.370..645B, 2016MNRAS.461..859S, 2016MNRAS.459.4109T]. Another significant assumption in the model is that the specific angular momentum fraction is 1, since lost angular momentum in the gas component during galaxy assembly would lead to a smaller disc. On the other hand, strong feedback mechanisms which release the energy and angular momentum to the interstellar medium will suppress the formation of small discs. To quantify these effects in semi-analytic models, [2016MNRAS.461.3457G] compared galaxy sizes from semi-analytic models L-galaxies and Galform at redshift less than 2. Galform includes the self-gravity of discs while L-galaxies ignores it."}
{"text": "[2016MNRAS.461.3457G] showed that self-gravity does not significantly affect the sizes of galaxies with stellar mass less than 10 to the power of 9.5 solar masses. However, for galaxies with stellar mass greater than 10 to the power of 9.5 solar masses, self-gravity of discs in Galform reduces galaxy sizes and results in a decreasing size--mass relation. In this work, which considers the small galaxies that drive reionization, we do not have a large number of galaxies with stellar mass greater than 10 to the power of 9.5 solar masses at redshift greater than 6. Thus, we utilize the simple model of [1998MNRAS.295..319M] in this study, as has been common in semi-analytic models [e.g.][2006MNRAS.365...11C, 2007MNRAS.375....2D]. We see that the disc sizes of galaxies are determined by the properties of dark matter haloes. We assume star formation and feedback processes do not directly modify the disc sizes. On the other hand, the size of the disc does play a fundamental role in the build up of stellar mass."}
{"text": "Based on the observational work of [1998ApJ...498..541K], the global star formation rate of spiral galaxies can be related to the surface density of cold gas above a given threshold. In our model, we adopt a critical surface density for the disc, above which gas cannot maintain stability and will start forming stars. The critical density at a radius r is adopted from [1996MNRAS.281..475K]: The critical surface density Sigma_crit at a radius r is proportional to the virial velocity and inversely proportional to the radius, with units of solar masses per square parsec. where Sigma_norm = 0.2 is a free parameter in MERAXES. Stars are assumed to form within a maximum radius set to 3 times the disc scale length, based on the properties of the Milky Way [2000glg..book.....V]. By integrating the critical density, we obtain the critical mass of the disc. If the mass of cold gas in the disc exceeds this threshold mass the stars will form with a star formation rate given by: The star formation rate is given by the star formation efficiency alpha_SF, multiplied by the difference between the cold gas mass and the critical mass, all divided by the disc's dynamical time."}
{"text": "Galaxy mergers can also trigger a strong burst of star formation. We assume a fraction of the total cold gas of the newly formed system is consumed during such a burst [2001MNRAS.320..504S]. The fraction of cold gas consumed is determined by: The fraction of cold gas consumed in a merger-driven burst, e_burst, is determined by the mass ratio of the merging galaxies raised to the power of gamma_burst, and multiplied by an efficiency factor alpha_burst., where the mass ratio of merging galaxies, and alpha_burst = 0.56 and gamma_burst = 0.7 are chosen to fit the numerical results of [2004ApJ...607L..87C] and [1994ApJ...431L...9M, 1996ApJ...464..641M] for merger mass ratio in the range 0.1 to 1.0 [2006MNRAS.365...11C]. For simplicity, we assume the merger-driven burst occurs within a single snapshot, which is comparable to the disc dynamical time of the majority of galaxies. We do not consider irregular morphologies during galaxy mergers and the sizes of remnants are calculated using the standard disc size equation."}
{"text": "Through the star formation process, disc size affects a number of galaxy properties, including UV luminosities. The size--luminosity relation therefore becomes an important predictor from galaxy formation models. We note that the star forming process is rather complicated. It is not only determined by the galaxy sizes but also by other effects including cooling, mergers and feedback. To study the role of supernova feedback in the build up of the size-luminosity (stellar mass) relation, we also run a simulation with the supernova feedback switched off. This no supernova model cannot reproduce the stellar mass function in detail, but is recalibrated to provide the observed stellar mass density at z = 5 (see Paper-III). In this paper, to compare with observations we present the sizes of model galaxies using the physical effective radius (i.e. half-light radius), R_e, within which half of the galaxy's luminosity originates. Here R_e is estimated using R_e is equal to 1.678 times R_d, where the constant originates from the assumed exponential surface density profile and constant mass-to-light ratio."}
{"text": "Luminosity is the most direct observable of high-redshift galaxies. We calculate the UV luminosities using stellar population synthesis. For each galaxy we obtain the stellar population components by tracking its star formation and merger history. We integrate the stellar populations with model spectral energy distributions (SEDs) calculated using STARBURST99 [1999ApJS..123....3L, 2005ApJ...621..695V, 2010ApJS..189..309L, 2014ApJS..212...14L] with a constant metallicity of Z = 0.05 solar metallicity. We do not include nebular components as they would not affect the UV luminosities of our model galaxies at these redshifts. To obtain the observed luminosities we apply a dust extinction model to each galaxy. We adopt a luminosity dependent dust model [e.g.][2012ApJ...756...14S, 2015ApJ...803...34B] which is based on the IRX-beta relation from [1999ApJ...521...64M] and the observed luminosity-beta relation from [2014ApJ...793..115B]. This dust model is empirical and is calibrated to reproduce the observed properties of galaxies. For more details about the galaxy photometric modeling see Paper-IV."}
{"text": "We first investigate the relationship between the physical size and UV luminosity of model galaxies. Figure 1 caption: Effective radius of galaxies as a function of UV luminosity at redshift of approximately 5 to 10. The colour profile shows the logarithm density of the distribution. The black squares and error bars represent the median and 16th to 84th percentiles of the R_e distribution. The black solid lines are the linear best-fits for galaxies with M_1600 less than -14.5. The pink and orange lines show the observed relations from [2013ApJ...765...68H] and [2015ApJS..219...15S]. The blue and yellow diamonds show the observations at z~7 from [2016arXiv160505325B]. The blue star shows luminous galaxy GN-z11 found by [2016ApJ...819..129O]. For model comparison, the red circles and error bars show the size--luminosity from the model with supernova feedback turned off. The dash-dotted lines represent the minimum measurable effective radii of HST, JWST and GMT."}
{"text": "The figure shows the relation between the effective radius and UV magnitude M_UV for model galaxies at redshift of approximately 5 to 10. We see that at UV magnitudes less than or equal to -14, galaxies with brighter UV luminosity tend to have larger sizes. The effective radius does not significantly change with luminosity for galaxies with luminosities M_UV greater than -14. This is because galaxies fainter than M_UV of approximately -14 are located in the dark matter haloes of the minimum gas cooling mass. This is similar to the turnover at M_UV of approximately -14 in the relation between UV luminosity and the mass of dark haloes found in Paper-IV. We see that at fixed luminosity, the size of galaxies grows from z~10 to 5. For comparison, we show the observed R_e--M_UV relations from [2013ApJ...765...68H] at z~5 and [2015ApJS..219...15S] at z~5 to 8. Our results are in close agreement with the observations."}
{"text": "Recently, [2016ApJ...819..129O] found an unexpectedly luminous galaxy (GN-z11) at z~11, which has M_UV= -22.1 and R_e=0.6 kpc. In [2016MNRAS.463.3556M] we demonstrated that the properties of GN-z11 are in good agreement with the results of our model in terms of stellar mass, star formation rate and UV luminosities. We show the measured size of GN-z11 in the figure and find that it is in agreement with our fitted size--luminosity relation at z~10. The relation between the galaxy size and luminosity is commonly fitted by: The effective radius R_e is equal to a reference radius R_0, multiplied by the ratio of the UV luminosity to a reference luminosity, raised to the power of beta. We set the reference luminosity L_0 = L*_z=3 which corresponds to M_0 = -21 [1999ApJ...519....1S]. This equation can be rewritten as: The logarithm of the effective radius, log10(R_e), is linearly related to the UV magnitude, M_UV, with a slope of -0.4 times beta. We linearly fit this relation for galaxies brighter than M_UV=-14.5 at each redshift."}
{"text": "Caption for Table 2: The best-fitting parameters R_0 and beta for the model galaxies with UV magnitudes M_UV less than -14 at z~5 to 10. We see that the slope of the size-luminosity relation, beta, does not significantly change at z~5 to 9 and has a median value of beta of approximately 0.25 for galaxies with UV luminosity brighter than M_UV of approximately -14. This value agrees with observational studies for both local and high-redshift galaxies. For example, [2000ApJ...545..781D] found beta = 0.253 for local spiral galaxies. [2003MNRAS.343..978S] derived a slope of beta of approximately 0.26 for the late-type galaxies from SDSS. [2007ApJ...671..203C] obtained beta=0.321 from local field and cluster spiral galaxies. [2012A&A...547A..51G] found beta=0.3 to 0.5 for LBGs at z~7, while [2015ApJ...808....6H] derived beta=0.24 using the [2012A&A...547A..51G] data."}
{"text": "In addition, [2013ApJ...765...68H] found beta=0.22 and 0.25 for the galaxies in GOODS and HUDF fields at z~4 and z~5 respectively. Finally [2015ApJS..219...15S] investigated the galaxy effective radius from a large Hubble Space Telescope (HST) sample and obtained beta = 0.27 at z~0 to 8. They also showed that beta does not significantly evolve over this redshift range. Due to limitations in sample volumes and selection biases, observed values of beta often have large uncertainties and vary between studies. For example, observations are generally biased towards galaxies with high surface brightness and are not sensitive to measured properties of fainter, more spatially extended galaxies. Because a model does not suffer from these selection effects and can have a large sample of both bright and faint galaxies, we are able to investigate the true scatter of the size--luminosity relation. The size-luminosity relation fitted to the model predictions is also consistent with the analytic prediction of [2011MNRAS.413L..38W]."}
{"text": "In that work they considered a supernova feedback model where supernova-driven winds conserve momentum in the interaction with the galactic gas. The model results in a luminosity scaling of a=1/3 which corresponds to R_e is proportional to L to the power of 0.25. While the model without supernova feedback yields a=0 which corresponds to R_e is proportional to L to the power of 0.33. To study the role of supernova feedback on the build up of galaxy sizes, we show the size-luminosity relation for the no supernova feedback model. The size-luminosity relation for the no supernova feedback model is also flat at M_UV greater than -14. This is because the minimum size is set by the mass scale of efficient cooling in both models. There is no clear difference between the fiducial and no supernova feedback model at M_UV greater than -17, where the accumulated effect from supernova feedback on star formation histories is not significant enough to be observed."}
{"text": "However, at M_UV less than -17, the median size of galaxies from the no supernova feedback model is notably smaller than the fiducial model. In other words, for the same size galaxy, the no supernova feedback model results in a much brighter luminosity. We note that removing supernova feedback allows more stars to form, and so the model has been recalibrated to produce the correct stellar mass density at z=5. The luminosity difference is approximately 2 to 3 mag at z=5 to 7, which is larger than the approximately 1 mag difference at z = 8 to 10. This is also due to the correct galaxy mass only being achieved at z=5 in this recalibrated model. The different size-luminosity relations from these two models arise because the supernova feedback in the fiducial model suppresses star formation resulting in a more gradual star-formation history. In contrast, galaxies without supernova feedback have much burstier star-formation histories and contain more young stellar populations which are UV bright."}
{"text": "The spatial resolution of a telescope with effective diameter D_tel is given by: The spatial resolution, delta l, is given by the Rayleigh criterion, which is 1.22 times the observed wavelength lambda, divided by the telescope diameter D_tel, all multiplied by the angular diameter distance d_A. where delta_theta is the angular resolution determined by the Rayleigh criterion, lambda=1600(1+z) Angstroms is the observed wavelength of UV photons and d_A is the angular diameter distance. In this equation, the observed wavelength is scaled by a factor of (1+z) at fixed intrinsic wavelength, while the angular diameter distance decreases at a similar rate at redshift greater than or equal to 1. Thus the spatial resolution does not rapidly change with redshift. Galaxy sizes are usually measured through light profile fitting [e.g.][2002AJ....124..266P]. As a result, one can trace the galaxy outskirt light, and obtain an effective radius bellow the spatial resolution of the telescope."}
{"text": "The comparison between the observed R_e and the spatial resolution limits of the Hubble Space Telescope (HST) indicates that values of R_e can be measured which are smaller than the resolution limit of the telescope by roughly a factor of ~ 2 [e.g.][2013ApJ...777..155O, 2015ApJS..219...15S]. In Fig. 1 we show the minimum observable disc size R_min of HST, James Webb Space Telescope (JWST), and the Giant Magellan Telescope (GMT), where we adopt the relation R_min is approximately delta l/2 as discussed above. We see that HST (D_tel=2.4 m) can resolve the R_min of observed galaxies at z~5 to 7, and the structures of typical z>8 galaxies can not be resolved. The larger diameter JWST (D_tel=6.5 m) will resolve the R_min for galaxies brighter than M_UV=(-14, -16, -18) at z=(6, 8, 10). However, with an exposure time of 1 million seconds, JWST will observe galaxies to M_UV=(-15.0, -15.8, -16.3) with signal-to-noise ratio S/N=10 at these redshifts, hence a significant fraction of z>8 galaxies will be still unresolved."}
{"text": "Due to the large mirror size, GMT (D_tel=25 m) will have the ability to resolve all galaxies in haloes above the atomic cooling limit. Figure 2 caption: Size-mass relation of model galaxies at z=5, 6, 8, 10. The colour profile shows the logarithm density of the distribution. The black squares and red circles show the median relation in bins. The error bars represent the median and 16th to 84th percentiles of the intrinsic scatter. The orange diamonds show the observations from [2012ApJ...756L..12M]. The figure shows the relation between the effective radius and stellar mass of galaxies at z~5, 6, 8 and 10 for both fiducial and no supernova feedback models. Observed data from [2012ApJ...756L..12M] are also shown. The model size-mass relation is in good agreement with these observations. We see that for galaxies with stellar masses above 10^6.5 solar masses, more massive galaxies tend to have larger sizes."}
{"text": "The galaxies from the fiducial model have larger sizes than the galaxies from no supernova feedback model at fixed stellar mass. However, the difference in the size-mass relation between the fiducial and no supernova feedback model is much smaller than in the size--luminosity relation. This is expected because we have tuned both models to produce the galaxy stellar mass density. However, star formation histories including supernovae lead to less variable UV luminosities resulting in larger difference seen in the size-luminosity figure. For galaxies with stellar mass less than 10^6.5 solar masses, our two models show similar galaxy sizes due to the inefficient star formation in the minimum cooling mass, as was the case in the size--luminosity relation."}
{"text": "Figure 3 caption: The redshift evolution of the mean effective radius for galaxies in two luminosity ranges. The blue line shows the mean effective radius from the fiducial model and the green line shows the mean effective radius from the model without supernova feedback. The shaded regions show the associated 1-sigma uncertainties of the means. The grey solid lines show the power law fit to our model. For comparison, we show the observed mean sizes from multiple studies. We see that our fiducial model agrees with observations, while the no supernova model significantly underestimates the galaxy sizes. The redshift evolution of galaxy sizes provides another important measurement in addition to the luminosity dependence [e.g.][2004ApJ...600L.107F, 2004ApJ...611L...1B, 2010ApJ...709L..21O, 2012A&A...547A..51G, 2013ApJ...777..155O, 2015ApJ...804..103K, 2015ApJ...808....6H, 2015ApJS..219...15S]. The figure shows the redshift evolution of the effective radius predicted by our model. To compare with observations of size evolution, galaxies were selected using their luminosity in specific ranges. These luminosity ranges correspond to UV magnitudes from -21.0 to -19.7 and from -19.7 to -18.7 respectively."}
{"text": "Both fiducial and no supernova feedback models are shown in the figure. For comparison the observed galaxy sizes from [2004ApJ...611L...1B], [2010ApJ...709L..21O], [2013ApJ...777..155O], [2015ApJ...804..103K], [2015ApJ...808....6H] and [2015ApJS..219...15S] are also shown. We see that the evolution of galaxy sizes from our fiducial model is in good agreement with observations. However, the galaxy sizes in the no supernova feedback model are underestimated at each redshift. For example, sizes at fixed luminosity in the no supernova feedback model are approximately 60 (70) percent of those in the fiducial model at z~5 (10). This corresponds to surface brightness densities which are approximately 3 (2) times larger than the fiducial model prediction. These are distinguishable differences. To investigate the influence of parameter calibration in the no-supernova model, we have also run an uncalibrated no-supernova feedback simulation and find a qualitatively similar result. Therefore, we conclude that the galaxy size evolution provides an additional observable for determining the importance of supernova feedback in early galaxy formation."}
{"text": "Figure 4 caption: Confidence ellipses with delta chi-squared = 1, which projects 1-sigma uncertainties on m and R_e axes. The red, blue and green contours are z > 5 only observations from [2004ApJ...611L...1B], [2010ApJ...709L..21O] and [2013ApJ...777..155O] respectively. The black contours are from all observations shown in the previous figure. Our best-fitting values are shown as black filled circles. We fit the model size evolution at z~5 to 10 using R_e is proportional to (1+z) to the power of -m and find m = 2.00 for the brighter luminosity range and m = 2.02 for the fainter range. The fitted relations are shown as grey solid lines in the previous figure. We also show confidence intervals using the observations. Here we only include the observational data at z>5. We see that the fitted m from our model is comparable to observations. For example, m = 1.64 and m = 1.82 are derived using the combined observations shown in the figure for the two luminosity ranges."}
{"text": "Before concluding, we discuss the applicability of R_d as a measure of galaxy size. In observations, morphologies of LBGs are often found to be irregular and clumpy, sometimes showing multiple components [e.g.][1996ApJ...470..189G, 2006ApJ...652..963R, 2016MNRAS.457..440C, 2016ApJ...821...72S, 2015ApJ...800...39G, 2016arXiv160505325B]. This could be due to two different formation mechanisms: (i) galaxy interactions, such as mergers [e.g.][2006ApJ...636..592L, 2008ApJ...677...37O]; (ii) distributed and clumpy star formation regions within the same collapsing cloud due to instabilities [e.g.][2002ApJ...568..651G, 2007ApJ...656....1L, 2009ApJ...703..785D, 2010ApJ...709L..21O, 2013ApJ...773..153J, 2016ApJ...819L...2B]. Morphological studies at very high redshift are more challenging. [2016ApJ...821...72S] investigated the evolution of clumpy galaxies with large HST samples and found that the clumpy fraction increases from z~0 to z~1 but subsequently decreases from z~1 to 3 to z~8."}
{"text": "On the other hand, high-resolution cosmological simulations show that galaxies at z greater than or equal to 6 are dominated by disc morphologies [e.g.][2011ApJ...731...54P, 2011ApJ...738L..19R, 2015ApJ...808L..17F]. For example, using the large-volume BlueTide simulation, [2015ApJ...808L..17F] found that at z=8 to 10, up to 70 per cent of the galaxy population more massive than 10^10 solar masses are disc galaxies. Detailed measurement of more compact and clumpy galaxies are limited by the angular resolution of instruments, and the origin of observed clumpy morphologies at high-redshift is still under debate. [2016arXiv160505325B] recently published size measurements for a sample of extremely luminous galaxies at z~7. [2016arXiv160505325B] divided the sample into two groups (single and multi-component) according to their morphologies. We see that the size-luminosity relation for the single morphology galaxies is in good agreement with our model while including clumpy morphology galaxies leads to larger sizes. This may suggest that the multi-component galaxies are merging systems [2016arXiv160505325B]."}
{"text": "We have used the semi-analytic model MERAXES to study the dependence of galaxy size on UV luminosity, stellar mass and redshift at z~5 to 10. We also studied the effect of supernova feedback on the evolution of galaxy sizes. We show that the rotationally supported disc model generally adopted in semi-analytic models can be used to study the sizes of high-redshift galaxies. Our primary findings are that: The effective radius scales with UV luminosity as R_e is proportional to L to the power of 0.25 for galaxies with luminosity M_UV less than or equal to -14. Galaxies with the same disc size in the no supernova feedback model have brighter UV magnitudes than in the fiducial model. Our fiducial model with strong supernova feedback successfully reproduces the redshift evolution of average galaxy sizes at z>5, which is slightly steeper than z<5 observations. The model with no supernova feedback produces a significantly smaller radius at fixed luminosity than the fiducial model."}
{"text": "The recently identified luminous galaxy GN-z11 at z~11 [2016ApJ...819..129O] lies on our model-fitted size-luminosity relation. The fitted relation is also in agreement with the size measurements of very luminous galaxies containing single components and with individual components of luminous multi-component systems at z~7 [2016arXiv160505325B]. A significant fraction of z>8 galaxies will not be resolved by JWST. However, GMT will have the ability to resolve all galaxies in haloes above the atomic cooling limit. We conclude that galaxy sizes provide an important additional constraint on galaxy formation physics during reionization, and that current observations of galaxy size and evolution reinforce the importance of supernova feedback. These findings are in agreement with results based on the stellar mass function and luminosity function."}
{"text": "This research was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant ref. UOM0005, on its Peak Computing Facility hosted at the University of Melbourne, an initiative of the Victorian Government, Australia. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne and the Australian Governments Education Investment Fund. This research programme is funded by the Australian Research Council through the ARC Laureate Fellowship FL110100072 awarded to JSBW. AM acknowledges support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 638809 AIDA)."}
{"text": "We investigate how the hydrostatic suppression of baryonic accretion affects the growth rate of dark matter haloes during the Epoch of Reionization. By comparing halo properties in a simplistic hydrodynamic simulation in which gas only cools adiabatically, with its collisionless equivalent, we find that halo growth is slowed as hydrostatic forces prevent gas from collapsing. In our simulations, at the high redshifts relevant for reionization (between redshift of approximately 6 and approximately 11), haloes that host dwarf galaxies (less than or equal to 10^9 solar masses) can be reduced by up to a factor of 2 in mass due to the hydrostatic pressure of baryons. Consequently, the inclusion of baryonic effects reduces the amplitude of the low mass tail of the halo mass function by factors of 2-4. In addition, we find that the fraction of baryons in dark matter haloes hosting dwarf galaxies at high redshift never exceeds approximately 90 per cent of the cosmic baryon fraction. When implementing baryonic processes, including cooling, star formation, supernova feedback and reionization, the suppression effects become more significant with further reductions of approximately 30-60 per cent. Although convergence tests suggest that the suppression may become weaker in higher resolution simulations, this suppressed growth will be important for semi-analytic models of galaxy formation, in which the halo mass inherited from an underlying N-body simulation directly determines galaxy properties. Based on the adiabatic simulation, we provide tables to account for these effects in N-body simulations, and present a modification of the halo mass function along with explanatory analytic calculations."}
{"text": "In recent years, a number of groups have run large volume N-body simulations and used these to investigate the properties of large-scale structure (e.g. Hubble Volume, [Jenkins2001]; Millennium, [springel2005simulating]; CubeP3M, [iliev2008simulating]; Millennium-II, [Boylan_Kolchin2009]; Bolshoi, [Klypin2010]; MICE, [Crocce2010]). In order to connect the observable galaxy population to the halo properties produced by those simulations, semi-analytic models (SAMs) built on dark matter halo merger trees have also been developed (e.g. [Cole2000]; [Hatton2003]; [Baugh2005]; [croton2006many]; [DeLucia2007]; [Somerville2008]; [guo2011dwarf]). SAMs approximate the physics in hydrodynamic simulations (e.g. Illustris, [vogelsberger2014properties]; EAGLE, [Schaye2014]) using analytic descriptions. A crucial difference is that while baryons and dark matter evolve together in hydrodynamic simulations, SAMs explore the properties of galaxies based on the halo properties read from collisionless halo merger trees. This method, therefore, assumes that baryons have little influence on halo properties and that a pure dark matter N-body simulation can provide SAMs with a reliable halo merger tree."}
{"text": "However, recent studies at low redshift have shown that this may not be the case. Both the GIMIC [Sawala2013] and EAGLE [Schaller2014] projects discovered that the mass ratio between haloes extracted from full-hydrodynamic simulations and N-body simulations is less than unity, especially for low-mass haloes. [Sawala2013] found that without baryons, N-body simulations overpredict the halo mass by 30 per cent, 20 per cent and 10 per cent for haloes whose masses are less than or equal to 10^10, approximately 10^11 and approximately 10^12 solar masses, respectively. [Schaller2014] discovered similar differences with an overprediction of approximately 15 per cent for approximately 10^12 solar masses haloes resulting from AGN feedback. The Magneticum project [Bocquet2016] also found that the inclusion of baryons decreases the mass of galaxy clusters (10^12 - 10^15 solar masses) with the effect becoming smaller for larger halo masses. In this work, we analyse the effect of baryons on dark matter halo growth at high redshift (redshift greater than 5) in the mass range relevant for reionization."}
{"text": "Using a suite of high resolution hydrodynamic simulations for comparison with a collisionless N-body simulation, we investigate the baryonic effect, due to a range of galaxy physics, including gas pressure, cooling, star formation, reionization and supernova feedback. We also modify halo mass functions in the collisionless scenario through linear perturbation theory to account for the baryonic effect. This paper is organized as follows. We present simulations in Section 2, and discuss the comparison between full-hydrodynamic simulations and the collisionless case, including mass and baryon fractions. In Section 3.2, we calculate the simulated halo mass functions and provide a modification of halo mass functions from collisionless simulations or analytic calculations. Conclusions are given in Section 5. In this work, we adopt cosmological parameters from WMAP7 (Omega_m, Omega_b, Omega_Lambda, h, sigma_8, n_s = 0.275, 0.0458, 0.725, 0.702, 0.816, 0.968; [Komatsu2011])."}
{"text": "To make a quantitative investigation of baryonic effects, we utilize results from a suite of hydrodynamic simulations (Smaug, [duffy2014low]) performed as a part of the Dark-ages Reionization And Galaxy formation Observables from Numerical Simulations (DRAGONS) project. Each simulation has 512^3 baryonic and 512^3 dark matter particles within a cube of comoving side 10 h^-1 Mpc. This equates to a mass resolution of 4.7(0.9) x 10^5 h^-1 solar masses per dark matter (gas) particle. All simulations have identical initial conditions generated with the grafic package [Bertschinger2001] at z=199 using the Zel'dovich approximation [Zeldovich1970]. The simulations implement different physics and were run with an updated version of the gadget-2 N-body/hydrodynamic code [springel2005cosmological] to redshift z=5. The exceptions are the ADIAB and N-body simulations, which were run to z = 2 and 0, respectively, and will be introduced later. The particle IDs are consistent in the Smaug suite in order to match haloes across different simulations. A brief summary of the simulations is shown as follows, while further details can be found in [duffy2014low] and [Schaye2010]."}
{"text": "A collisionless N-body simulation (hereafter N-body) was performed using the same initial conditions from the full simulation but without hydrodynamic forces from the baryonic component. In the ADIAB simulation, gas only cools adiabatically and there is no stellar physics or reionization included. This simple model can be used to investigate the isolated effect on the dark matter halo growth of the hydrostatic suppression of baryonic accretion into the growing potential well. In the set of NOSN_NOSZCOOL simulations, radiative cooling [Wiersma2009] from primordial elements (hydrogen and helium) is turned on and star formation [Schaye2008] is implemented by converting gas particles into collisionless star particles, which represent a single stellar population specified by the Chabrier initial mass function [Chabrier2003]. However, the feedback due to supernova explosion is not included in these models. Moreover, an instantaneous UV/X-ray background [Haardt2001] is switched on at z=9 or 6.5 (NOSN_NOSZCOOL_LateRe) for early and late reionization to ensure the gas is heated to approximately 10^4K when reionization begins [Wiersma2009]. In addition, a NOSN_NOSZCOOL model without reionization is also performed for comparison (NOSN_NOSZCOOL_NoRe)."}
{"text": "In the REF simulation, stellar particles explode as Type II supernovae with the feedback coupled by randomly 'kicking' 2 of its neighbours with a velocity of 600 km/s [DallaVecchia2008]. This equates to 40 per cent of the available energy produced by supernova feedback coupled to driving a wind and is termed kinetic feedback. Additionally, radiative cooling from metal elements including carbon, nitrogen, oxygen, neon, magnesium, silicon, sulphur, calcium and iron are pre-tabulated using the public photoionization package cloudy [Ferland1998] and implemented in the simulation. Similarly to the REF simulation, in the REF_EFF model, 3 of the neighbours of a newly formed stellar particle are kicked with a wind velocity of 774.6 km/s. Here, all of the supernova energy is used for kinetic feedback and is used to represent the maximal kinetic feedback from supernovae. An alternative method of modelling supernova feedback is to heat the nearby gas stochastically by increasing the temperature of gas particles, which is termed thermal feedback [DallaVecchia2012]. This feedback is implemented in the WTHERM model, with gas particles heated to 10^7.5 K. We have found that WTHERM disagrees with REF_EFF, indicating that even with the high resolution of Smaug the method of coupling supernova feedback does play a (secondary) role in galaxy formation at our mass scales of interest [duffy2014low]."}
{"text": "A summary of the simulations utilized in this study. Structures were identified in all simulations using subfind [Springel2001]. It identifies collapsed regions with a friends-of-friends (fof) algorithm using a standard linking length of b=0.2, then splits them into several self-bound subhaloes according to their local overdensities. In this work, we adopted fof haloes (hereafter haloes for short). However, we note that the differences in the following results between subhaloes and haloes are usually less than 15 per cent, and there are also some offsets between the most massive subhalo within a fof group and their satellites."}
{"text": "First, we match haloes between full-hydrodynamic simulations and the N-body simulation according to their particle IDs. For each halo, if the majority of its particles are located within the corresponding halo of the other simulation, they will be considered as a matched candidate. We only include haloes that are matched bidirectionally to reduce the chance of mismatch. Then we calculate the mass ratio of the matched haloes between the hydrodynamic and the N-body simulations (M_hydro/M_Nbody). In this work, we adopt a spherical top-hat mass for haloes defined as the mass of all the particles (including dark matter, gas and star particles) within a sphere of average density Delta is approximately 18*pi^2 ([Duffy2010], 18*pi^2 for short) times the critical density (we also test our result with the fof halo mass, which is defined as the mass of all the particles linked by the fof halo finder (see Appendix A.1) and find that the difference is less than 15 per cent). We only use haloes with masses higher than 10^7.5 solar masses in the N-body simulation which corresponds to 40 particles [duffy2014low]."}
{"text": "Top panels: the evolution of mass ratio, M_hydro/M_Nbody, which is defined as the mass ratio of the matched haloes between hydrodynamic simulations and the corresponding N-body simulation. The spherical top-hat mass, which includes both dark matter and baryonic particles within a sphere of average density equal to 18*pi^2 times the critical density is adopted. The mean values with uncertainties showing 95 per cent confidence intervals around the mean using 100,000 bootstrap re-samples are shown in four mass bins with different colours (based on the top-hat mass in the N-body simulation). In the clockwise direction from the top left panel, these panels represent, respectively, (1) ADIAB, where gas is included and allowed to cool adiabatically compared to the N-body simulation; (2) NOSN_NOZCOOL_NoRe, where radiative cooling from primordial elements and star formation are turned on; (3) NOSN_NOZCOOL and NOSN_NOZCOOL_LateRe (dashed lines), where an instantaneous reionization background is switched on at z=9 or 6.5; (4) REF, where metal cooling and kinetic supernova feedback are implemented; (5) REF_EFF, where a maximal kinetic supernova feedback is adopted; (6) WTHERM, where a maximal thermal supernova feedback is adopted (see more in Table 1). For comparison, the ADIAB result for haloes around 10^9 solar masses is shown as black dotted line in panels (2) to (6). Bottom panels: the ratio of (2) ADIAB to NOSN_NOZCOOL_NoRe, (3) NOSN_NOZCOOL and NOSN_NOZCOOL_LateRe (dashed lines) to NOSN_NOZCOOL_NoRe, (4) REF to NOSN_NOZCOOL, (5) REF_EFF to REF and (6) WTHERM to REF_EFF. Redshifts that reionization background is switched on at are shown with vertical dashed lines. We present the evolution of mass ratios, M_hydro/M_Nbody, in Fig. 1 for different simulations. There are several points to note."}
{"text": "Mass ratios between the ADIAB and N-body simulations are shown in the top left panel of Fig. 1 in four mass bins, based on the N-body simulation. At all redshifts and mass bins, the ratio is less than 1. Since gas can only cool adiabatically in the ADIAB simulation, it is clear that hydrostatic pressure between gas particles keeps baryons from collapsing ([Somerville2002, Simpson2013, Sobacchi2013, Onorbe2015]), which in turn decreases the gravitational potential compared to an N-body simulation and delays the accretion of dark matter as well as baryons. Therefore, the halo mass is smaller at fixed time when baryons are included with the effect being more significant for less massive haloes. At the high redshifts relevant for reionization (between redshift of approximately 6 and approximately 11), haloes that host dwarf galaxies (less than or equal to 10^9 solar masses) are significantly reduced in mass, by up to a factor of 2. In addition, mass ratios rise towards lower redshift, suggesting a decreasing effect of baryons on halo mass."}
{"text": "Although our simulations have a relatively small population of large objects, it is likely that the baryonic effect from purely hydrostatic pressure asymptotes to a constant level in massive haloes (approximately 10^9.0 solar masses) at given redshift (e.g. 65 per cent at redshift of approximately 10). The mass ratios between the NOSN_NOZCOOL_NoRe and the N-body simulations are shown in the top middle panel of Fig. 1 (for comparison the bottom sub-panel shows the ratio of NOSN_NOZCOOL_NoRe to the ADIAB result). This comparison demonstrates the effect due to cooling and star formation. The mass ratio becomes higher compared to ADIAB (less than approximately 10 per cent), suggesting that when galaxies are able to cool and remove gas through forming stars, the effect of hydrostatic suppression naturally becomes smaller. Cooling and star formation also show an increasing effect at later time and a complex dependence on halo mass."}
{"text": "Mass ratios between the NOSN_NOZCOOL, NOSN_NOZCOOL_LateRe and N-body simulations are shown in the top right panel of Fig. 1, compared to the NOSN_NOZCOOL_NoRe simulation. When reionization is switched on at z=9 or 6.5, mass ratios decrease dramatically (by up to 30 per cent compared to the model without reionization) because of the heating of the intergalactic medium (IGM) from the UV/X-ray background. Moreover, there is a delay between the onset of reionization and this decrement as the now overpressurized mass can only respond on dynamical time-scales. It is clear that photoionization suppression by reionization only has a significant impact on smaller objects, as seen by comparing the ratio of the bottom sub-panel across different mass bins (there is no discernible effects for haloes >10^9.5 solar masses, in orange). We note that in the simulations with reionization, the IGM cools adiabatically until reionization starts. In reality there may well be an impact from other heating sources such as X-ray binaries, which are not included in our simulations. In Smaug, the UV/X-ray heating is only implemented following reionization through the assumption of a [Haardt2001] UV/X-ray background."}
{"text": "Since the growth rate is affected by the photoionization/heating of the IGM, the physics of stellar feedback is expected to have an impact as well [Governato2009, Trujillo-Gomez2014]. The bottom right panel of Fig. 1 shows the effect of supernovae feedback on the halo growth rate (less than approximately 20 per cent). The top and bottom sub-panels show the result from the REF simulation and its ratio to the NOSN_NOZCOOL simulation, respectively. We see that supernova feedback has an increasing impact on the halo mass at lower redshift and larger objects. In addition, we expect that for much larger haloes (greater than or equal to 10^11 solar masses), supernova feedback will have less influence, while AGNs become the dominant heating source [Somerville2015]. When supernova feedback becomes stronger, the mass ratio is further suppressed (less than or equal to 10 per cent, see the REF_EFF result in the bottom middle panel of Fig. 1)."}
{"text": "In the left bottom panel of Fig. 1, the REF_EFF and WTHERM simulations show slightly different mass ratios (less than 5 per cent) although they both have a strong supernovae feedback mechanism coupling 100 per cent of available supernovae energy. However, the supernovae feedback in the REF_EFF simulation is implemented kinetically [DallaVecchia2008], so that it uses the supernovae energy to drive winds and expel gas particles from galaxies. On the other hand, the thermal feedback in the WTHERM simulation stochastically heats the neighbouring gas particles and increases the temperature of heated gas by a certain value [DallaVecchia2012]. In practice, WTHERM removes more baryons for haloes less massive than 10^10 solar masses, and consequently reduces the mass ratio by a greater amount."}
{"text": "Mass ratio versus halo mass for all subhaloes. The red triangles and dashed line are from the data and fitting function in [Sawala2013] at z=6, while the grey points indicate the result from our REF simulation with 256^3 particles at z=5. The square-solid line shows the median value in each mass bin. Halo masses in our result are rescaled to have a consistent cosmology. The circle-solid line indicates the result from the REF simulation with 512^3 particles. [Sawala2013] use the GIMIC [Crain2009] simulations, which assume instantaneous reionization at z is approximately 9 [Haardt2001], and include star formation [Schaye2008], metal cooling [Wiersma2009] and kinetic supernovae feedback [DallaVecchia2008]. Their particle masses are 9.05 and 1.98x10^6 solar masses per dark matter and baryon particle, respectively. This value lies between our REF simulations with 256^3 (closer) and 512^3 particles (see the convergence test in Appendix B)."}
{"text": "We compare our results to theirs at redshift approximately 6 in Fig. 2. In order to have a consistent cosmology during the comparison [Angulo2010], we rescale the halo masses of our simulations, multiplying by (Omega_m' / Omega_m) * (H'^2 / H^2) * s^3, where H, H' are the Hubble constants in the two cosmologies, Omega_m' = 0.25 and s=0.83. The mass ratio of all subhaloes at redshift approximately 5 are in excellent agreement with the result at z=6 from [Sawala2013]. This result gives us confidence in our quantitative results for lower masses at higher redshifts."}
{"text": "Top panels: the evolution of baryon fraction, f_b, which is defined as the mass ratio of the baryonic particles to all particles including baryons and dark matter within a sphere of average density equal to 18*pi^2 times the critical density. The mean values with uncertainties showing 95 per cent confidence intervals around the mean using 100,000 bootstrap re-samples are shown in four mass bins with different colours (based on the top-hat mass in the N-body simulation). In the clockwise direction from the top left panel, these panels represent, respectively (1) ADIAB, where gas is included and allowed to cool adiabatically compared to the N-body simulation; (2) NOSN_NOZCOOL_NoRe, where radiative cooling from primordial elements and star formation are turned on; (3) NOSN_NOZCOOL and NOSN_NOZCOOL_LateRe (dashed lines), where an instantaneous reionization background is switched on at z=9 or 6.5; (4) REF, where metal cooling and kinetic supernova feedback are implemented; (5) REF_EFF, where a maximal kinetic supernova feedback is adopted; (6) WTHERM, where a maximal thermal supernova feedback is adopted (see more in Table 1). For comparison, the ADIAB result for haloes around 10^9 solar masses is shown as black dotted line in panels (2) to (6). Bottom panels: the ratio of (2) ADIAB to NOSN_NOZCOOL_NoRe, (3) NOSN_NOZCOOL and NOSN_NOZCOOL_LateRe (dashed lines) to NOSN_NOZCOOL_NoRe, (4) REF to NOSN_NOZCOOL, (5) REF_EFF to REF and (6) WTHERM to REF_EFF. Redshifts that reionization background is switched on at are shown with vertical dashed lines. The baryonic effect on halo mass shown in the previous section represents a combined impact on collapse of dark matter and baryons. The change in the dark matter component is essentially a consequence of the change in gravitational potential caused by baryons. Therefore, we expect a more significant impact on the baryonic component. In this section, we discuss the fraction of baryons present in a dark matter halo."}
{"text": "In Fig. 3 baryon fractions, f_b, are shown in the same mass bins (binned by the halo mass in the N-body simulation) for different hydrodynamic simulations. The baryon fraction of a halo is calculated through the mass ratio of the baryonic particles to all particles within a sphere of average density equal to 18*pi^2 times the critical density. The different behaviour of the baryon fraction using the fof mass is shown and discussed in Appendix A.1. We see that the fraction of baryons in dark matter haloes hosting dwarf galaxies at high redshift never exceeds approximately 90 per cent of the cosmic mean, Omega_b/Omega_m, in the presence of hydrostatic pressure (in agreement with [Crain2007] but here even with no cooling or feedback, see the top left panel of Fig. 3); the baryon fraction f_b also becomes larger for massive haloes, suggesting that more massive haloes have a deep enough potential well to overcome the hydrostatic pressure of the baryons [Gnedin2000, Hoeft2006, Okamoto2008, Noh2014]. However, unlike the mass ratio, the baryon fraction depends weakly on time, indicating that the growth rate of baryons is close to the dark matter component within the virial radius (at least, see Appendix A.1)."}
{"text": "Top panels: halo mass functions at redshifts from 13 to 2 (clockwise direction from the top left panel). Different simulations are shown using different colours. Bottom panels: ratios of halo mass functions from the full-hydrodynamic simulations to the N-body simulation. Cooling and star formation help haloes retain more baryons, so that haloes have approximately 20 per cent more baryons in the NOSN_NOZCOOL_NoRe simulations compared to ADIAB. The ratio of baryon fractions between NOSN_NOZCOOL_NoRe and ADIAB reaches its maximum of approximately 1.25 when the halo mass is around 10^8.5 solar masses, with a decrement for larger objects, illustrating that the combination of cooling and star formation has a non-monotonic response to halo mass. In contrast to ADIAB, the NOSN_NOZCOOL_NoRe simulation allows star formation, which decreases the heating due to virial shocks. Because there is no feedback to prevent gas from cooling and forming stars, star formation can consume plenty of gas and make a significant difference to the strength of shock heating. This decrement of shock heating also helps haloes retain more baryons. However, this decrement of shock heating has less effect to the mass of more massive haloes. This is because their gravitational potentials are strong enough to retain the ejecting particles or reincorporate the ejected gas regardless of this runaway star formation."}
{"text": "Reionization plays a significant role in reducing the baryon fraction [Somerville2002, Simpson2013, Sobacchi2013, Onorbe2015]. In the top right panel of Fig. 3, baryon fractions decrease rapidly when reionization starts. Moreover, reionization is able to remove the majority of baryons (by up to 90 per cent) in the haloes hosting dwarf galaxies, with the suppression becoming smaller in massive objects; supernova feedback also has a noticeable impact on baryon fractions ([Governato2009, Trujillo-Gomez2014], see the bottom right panel of Fig. 3). The ratio between REF and NOSN_NOZCOOL shows an increased effect in more massive haloes before reionization, indicating that supernova feedback also regulates galaxy formation in haloes with 10^8-10^10 solar masses. When supernova feedback becomes stronger, baryon fractions get further suppressed (by up to 40 per cent, see the bottom left and middle panels of Fig. 3); These calculations of mass ratio and baryon fractions for ADIAB and WTHERM simulations can be included into SAMs, in order to account for the loss of baryons due to hydrostatic pressure alone in the former and in the latter with additional feedback induced gas removal. This will be discussed further in Section 4.1. We also provide a simple analytic model to illustrate this baryonic effect in Appendix C."}
{"text": "In this section, we discuss the effect of baryons on the dark matter halo mass function. The previous sections demonstrated a suppression of halo mass due to the inclusion of baryons. We therefore expect an impact on the halo mass function. We first present the halo mass functions from the hydrodynamic simulations and their ratios to the N-body simulation at z=13, 9, 5 and 2 in Fig. 4 (clockwise direction from the top left panel). We see that baryons suppress the halo mass function [Sawala2013,Vogelsberger2014,Velliscig2014,Schaller2014,Bocquet2016]. The effect is dramatic at high redshift, with the number density reduced by as much as a half at redshift approximately 13, but converges at later times. This suggests that the halo mass function extracted from N-body simulations is biased significantly at high redshift. The halo mass function is further suppressed when more complete physics is considered [Velliscig2014], with the effect varying at different stages."}
{"text": "At high redshift (redshift greater than or equal to 9), stellar physics has little impact on the halo mass function (less than approximately 5 per cent). However, at later times, the effects of cooling and supernovae feedback become noticeable across the halo mass range of interest (10^8-10^10 solar masses) for reionization (redshift approximately 11 to 6). After the Epoch of Reionization, the number densities of haloes with masses between 10^7.5 and 10^9 solar masses get further suppressed by the global UV/X-ray background. This reduction by photoionization is enhanced for simulations with stronger supernova feedback as noted by [Pawlik2009]."}
{"text": "By connecting collapsed haloes with their initial density field, the Press-Schechter formalism (PS, [Press1974, Bond1991, Lacey1993]) provides an approximation to the halo mass function. It assumes the initial density fluctuations were Gaussian, and can be implemented using the standard spherical collapse model or the ellipsoidal model (SMT, [Sheth2001]). The PS formalism describes the halo mass function as Equation 1, where sigma is the mass variance. The halo mass function has also been further updated with new parameters and functional forms to better match N-body simulations. For instance, [Tinker2010] performed a large set of collisionless N-body simulations with the flat LambdaCDM cosmology and the spherical overdensity halo finder. They tested several overdensity thresholds and provided fitting functions of the halo mass function as Equation 4, where coefficients alpha, beta, eta and gamma are functions of mass and redshift (see more examples in [Reed2007, Tinker2008, Tinker2010, Watson2013], or the summary in [Murray2013])."}
{"text": "In this section, rather than parametrizing the halo mass function from the full-hydrodynamic simulation, we instead develop a simple method to account for the hydrostatic suppression of baryonic accretion, and use this to modify the halo mass function found in the theoretical collisionless scenario described above. We take the ADIAB simulation as an example. However, the same method can be employed for the other simulations with more complete physics regimes although they do not show significant differences from ADIAB in the halo mass function at the mass and redshift ranges tested (see Fig. 4). First, we match fof haloes in the ADIAB and N-body simulations at a given redshift, z. In the N-body simulation, we then search for the redshift z' when M_Nbody(z') = M_hydro(z) by following the most massive progenitor in the halo merger tree. We calculate the ratio of (1+z') to (1+z) and plot its median value as a function of mass (M_adiab, the virial halo mass in the ADIAB simulation) in Fig. 5 for z=7, 9 and 12. The 2D histogram illustrates the distribution of these quantities at z=7. We see that the ratios of (1+z') to (1+z) are nearly constant for 10^7.5 - 10^10 solar masses haloes and very weakly dependent on redshift in the early universe."}
{"text": "2D histograms of (1+z')/(1+z) versus M_adiab at z =7. The solid, dashed and dash-dotted lines indicate the median values at z=7, 9 and 12, respectively. Note that the lines overlap, which suggests a very week evolution of (1+z')/(1+z)."}
{"text": "Top panels: halo mass functions at redshift from 13 to 2 (clockwise direction from the top left panel). The filled and empty circles are from the ADIAB and N-body simulations while the dashed and solid lines indicate the original and modified SMT halo mass functions [Sheth2001], respectively. The error bar indicates the 1-sigma Poisson uncertainties. Bottom panels: the circles represent the ratios of halo mass functions from ADIAB to N-body while the solid lines indicate the ratios of modified SMT halo mass functions to the original collisionless halo mass functions. In the collisionless scenario, when the initial overdensity reaches the critical value, delta_c = 1.686*D^-1(z'), haloes collapse at z' with masses equal to M. However, when baryons are included, because of the hydrostatic suppression, haloes with the same initial overdensities suffer delayed formation and attain the same mass only at later times, z < z' as shown in Fig. 5. As a result, haloes with the same overdensity, 1.686*D^-1(z'), will collapse at redshift z in the presence of baryons. We use the median value of (1+z')/(1+z) to modify the collisionless halo mass function at z by replacing delta_c from 1.686*D^-1(z) to 1.686*D^-1(z')."}
{"text": "We present the modified SMT halo mass functions compared with the original collisionless halo mass function and their ratios in Fig. 6 for z=13, 9, 5, 2 (clockwise direction from the top left panel). Since the halo mass functions in Fig. 6 are calibrated against the ADIAB simulation, we show the simulated halo mass functions from ADIAB (filled circles) for comparison with the N-body simulation (empty circles) in the top panels. In the bottom panels of Fig. 6, ratios between halo mass functions from ADIAB and N-body simulations are shown with circles. Again, we see that the number densities of haloes are significantly reduced with the inclusion of baryons and the offsets between scenarios with and without baryons vanish at the high mass end and towards lower redshift."}
{"text": "This method provides an accurate modification of the collisionless halo mass function. In the bottom panels of Fig. 6, the difference between lines and circles is less than 0.1 for haloes larger than 10^8 solar masses but starts to increase at the low mass end when approaching the resolution limit. This significant effect has been missed in previous work, which mainly focused on lower redshift where this effect is subdominant. However, this modification of the halo mass function is a very important consideration for galaxy formation modelling at high redshift during the Epoch of Reionization."}
{"text": "Mass ratio at redshift approximately 5 for the ADIAB simulation. Tables of mass ratios, baryon fractions and redshift ratios for the ADIAB and WTHERM simulations are available in a machine-readable form in the online journal and in the HDF5 format on the DRAGONS website: http://dragons.ph.unimelb.edu.au/resources/smaug.html. z: redshift; log10(mass_lower): lower limit of the mass bin in logarithm. The unit of mass is solar masses; log10(mass_upper): upper limit of the mass bin in logarithm; mass_mean: average mass in the unit of solar masses; mass_errl: lower bond of the uncertainty in mass_mean. The uncertainty is the 95 per cent confidence interval around the mean using 100,000 bootstrap re-samples; mass_erru: upper bond of uncertainty in mass_mean; ratio_mean: average mass ratio; ratio_errl: lower bond of the uncertainty in ratio_mean; ratio_erru: upper bond of the uncertainty in ratio_mean;"}
{"text": "Tabulated values of mass ratios (see Table 2), baryon fractions and redshift ratios are provided online as functions of halo mass in the collisionless simulation and redshift for the ADIAB and WTHERM simulations, which are shown in the left panels of Figs 1, 3 and 5. We note that the provided tables are based on our simulations [duffy2014low] with 512^3 particles within 10h^-1 comoving Mpc boxes running with an updated version of the gadget-2 code. The quantities are based on top hat properties. However, different codes, box sizes, property definitions (see Appendix A.1) or resolutions (see Appendix B) might have different quantitative results. The WTHERM result can be used to evaluate the baryon fraction and the baryonic effect on halo mass within a more complicated physics paradigm, including radiative cooling, stellar evolution and reionization."}
{"text": "The simplistic ADIAB simulation's result can be incorporated into SAMs, in order to account for the baryonic effect on halo mass from the hydrostatic pressure in the presence of gas and improve the connection between halo merger trees and galaxy formation compared to use of pure dark matter collisionless simulations. We note that if one intends to use the result of the WTHERM simulation, which includes additional astrophysical processes, the baryonic effect on predicted galaxy properties will be double-counted. The first time is from the feedback on baryons in the hydrodynamic simulation while the second is due to calculations of feedback in the SAM. Therefore, one should use the ADIAB simulation to modify the halo mass first, then calculate the galaxy properties. If one wants to compare the properties between galaxies and their host haloes, the simulation including all astrophysical effects can then be used after calculating the galaxy properties because SAMs usually do not alter the halo properties."}
{"text": "Whilst we advocate this approach to approximate the baryonic effect on halo growth in SAMs, we note that modifying halo mass using ADIAB is not self consistent. This is because the additional baryonic physics also has an impact on the halo mass and consequently affects galaxy properties, especially at lower redshifts (see Figs 1, 3 and 4). However, most of these baryonic processes such as radiative cooling, supernovae feedback, reionization heating are implemented in SAMs for the purpose of gaining sensible galaxy properties, which can also be calibrated through the related free parameters representing efficiencies."}
{"text": "Through hydrodynamic simulations, we have found that simulated halo masses during the reionization era are significantly reduced when baryons are included. For example, in a simulation where gas only cools adiabatically and no stellar physics is involved, the mass reduction is approximately 45 per cent for 10^8 solar masses haloes, and approximately 30 per cent for 10^9 - 10^10 solar masses haloes at z = 10 compared to a collisionless N-body simulation. We note that this result is not converged (see Appendix B) for haloes with masses less than 10^9.5 solar masses. Therefore, the suppression is weaker in higher resolution simulations. We have also found that the suppressed growth of dark matter haloes becomes more dramatic at lower masses and at higher redshifts. The size of this effect depends on the physics of feedback and star formation as well. When supernovae feedback or reionization is implemented, halo masses are further suppressed because these act to remove gas or prevent its accretion."}
{"text": "In addition, we have found that while the mass ratios between hydrodynamic simulations and N-body simulations increase with time (before reionization starts), the baryon fractions of haloes usually have no dependence on time. The reduction of halo mass in the presence of baryons has important implications for the halo mass function during reionization. We found that simulated mass function amplitudes are reduced by factors of 2-4 in hydrodynamic models compared to the N-body simulation for low-mass galaxies during reionization. Motivated by this, we have developed a methodology to modify the collisionless halo mass function, in order to take baryons into account, which is calibrated against hydrodynamic simulations. The modifications of halo mass and baryon fraction will have important consequences for SAMs that utilize the halo merger tree constructed from N-body simulations, particularly for simulations of low-mass systems at high redshift. Merger trees generated from N-body simulations should therefore be modified to account for dark matter growth in the presence of baryons. To aid this we have provided tables online for the modified halo mass and baryon fraction, which can be utilized in SAMs to more accurately describe the growth of galaxies during and after reionization."}
{"text": "We would like to thank the anonymous referees for providing helpful suggestions that improves the paper substantially. This research was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant ref. UOM0005, on its Peak Computing Facility hosted at the University of Melbourne, an initiative of the Victorian Government, Australia. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne and the Australian Governments Education Investment Fund. This research programme is funded by the Australian Research Council through the ARC Laureate Fellowship FL110100072 awarded to JSBW. This work was supported by the Flagship Allocation Scheme of the NCI National Facility at the ANU, generous allocations of time through the iVEC Partner Share and Australian Supercomputer Time Allocation Committee. AM acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 638809 -- AIDA)."}
{"text": "Top: mass ratio, M_hydro/M_Nbody versus redshift from the ADIAB simulation. The halo mass is defined as the total mass of particles included in each fof halo. Bottom: baryon fraction, f_b as a function of redshift from the ADIAB simulation. The baryon fraction is defined as the mass ratio of the baryonic particles to all particles linked by the fof halo finder. The result using top hat properties (see the top left panels of Figs 1 and 3) is also shown here with dashed lines for comparison. In this work, we extract structures using a fof halo finder [Springel2001] and adopt a spherical top-hat profile to calculate mass. To check whether this introduces any bias, in Fig. A1, we plot instead the mass ratio, M_hydro/M_Nbody between the ADIAB and N-body simulations using the fof halo mass. This is the total mass of particles in each fof halo, modified to correct for the bias introduced by the fof halo finder as described in [Watson2013]. We find that the fof mass ratio evolves similarly to the top-hat mass ratio, supporting the conclusion that the suppressed growth of dark matter haloes is indeed due to the inclusion of baryons."}
{"text": "Top panel: the average normalized cumulative mass versus radius in the unit of virial radius. The radial profiles of dark matter, gas and total components from the ADIAB simulation are shown with black dash-dotted, dashed and solid lines, respectively for comparison with the N-body simulation shown with red solid line. Bottom panel: the ratio of the total components from ADIAB and N-body simulations shown in the top panel. The vertical and horizontal dotted lines indicate the radius and the value of ratio where R = R_vir. However, the offset between the fof mass and the top-hat mass cases suggests that a fixed overdensity cut (approximately 18*pi^2) may unfairly miss more mass at large radius in the simulations with baryons. Therefore, we plot the average radial profile for haloes with masses higher than 10^7.5 solar masses at z=5. In the top panel of Fig. A2, the average normalized cumulative mass (normalized by the fof halo mass) is shown as a function of radius in units of virial radius (defined as the top-hat radius) for the N-body simulation and the dark matter, gas and total components from the ADIAB simulation, respectively."}
{"text": "We see that the radial profile becomes flat at R is approximately 1.5*R_vir for each component, indicating that the fof halo finder includes the majority of the particles belonging to each halo. However, at R = R_vir, the ratio of mass between the ADIAB and N-body simulations (the bottom panel of Fig. A2) is approximately 0.96, which results in the offset between the mass ratios shown in Fig. A1 (at z=5). Additionally, baryon fractions calculated using all particles linked by the fof halo finder are shown in the bottom panel of Fig. A1, compared to the calculation with particles within the top-hat radius. Although for larger objects, the fraction of baryons within the entire fof halo is slightly smaller than within the virial radius, using fof properties generally shows larger baryon fractions for haloes less massive than 10^9 solar masses, indicating that the concentration of baryons is smaller than the collisionless component in those haloes due to the hydrostatic pressure. Moreover, while the growth rate of baryons is close to the dark matter component within the virial radius (see Section 2.3), baryon fractions within the entire fof halo decreases with time suggesting a slower growth of baryons compared to dark matter, and a baryon flow towards the inner region of haloes."}
{"text": "The results presented in this work are based on a suite of simulations, each of which has n x 512^3 (n=1 for DMONLY and n=2 for the baryon-included simulations) particles within a cube of comoving side 10 h^-1 Mpc. We present convergence tests of our results (mass ratio, baryon fraction and halo mass function) in Fig. B1 with simulations having the same volume, but different numbers of particles (N_part = n x 256^3 and 128^3). The left panels of Fig. B1 show the evolution of mass ratio and of baryon fraction for haloes with masses in the range of 10^9 to 10^10 solar masses, while the right panel shows the halo mass functions from ADIAB and N-body simulations. We see that the simulations are not formally converged in mass ratio for masses less than or equal to 10^9.5 solar masses. However, the baryon fraction and halo mass function show better convergence. In particular, the baryon fraction of massive objects is converged to 90 per cent as shown in the bottom left panel of Fig. B1. This is in agreement with [Crain2007], who studied the baryon fraction in a suite of non-radiative gas-dynamical simulations with different resolutions and also found that the baryon fraction of dark matter haloes can only reach 90 per cent of the cosmic mean with a decreasing value towards low mass end."}
{"text": "Resolution test on the mass ratio (top left), the baryon fraction (bottom left) and the halo mass function (right). On the left panels, results for halo mass around 10^9 to 10^10 solar masses are shown with different colours. On the right panel, mass functions from N-body and ADIAB simulations are indicated with different colours as well. Solid, dashed and dash-dotted lines illustrate simulations with 512^3, 256^3 and 128^3 particles within a cube of comoving side 10h^-1 Mpc, respectively. The convergence of the baryon fraction gives us confidence in our conclusions regarding mass ratio. As pointed out by [Schaye2014], due to the sub-grid baryonic physics applied, hydrodynamic simulations show different levels of the hydrostatic suppression. In particular, with decreasing resolutions, mass ratios and baryon fractions become smaller at a given redshift. Additionally, resolution also has an impact on the growth rate of baryons. While baryon fractions slightly increase in the simulation with the highest resolution, they decrease in the simulations with lower resolutions in the studied mass range. The rate of decrease increases if resolution is reduced. In addition, better convergence can be observed within larger objects. Since the offset results from the sub-grid physics of baryons, we also expect differences in the mass ratio and baryon fraction in simulations with more complex physics when different resolutions are adopted (see Section 2.2.1)."}
{"text": "Although the qualitative conclusions presented in this paper do not change, the weak convergence shown in Fig. B1 indicates that one might need to pay attention to specific resolution requirements when calculating quantitative modifications of halo masses and baryon fractions to be used for running SAMs on halo merger trees constructed from collisionless simulations."}
{"text": "The hydrodynamic simulations indicate that baryons have a significant impact on halo growth for the galaxies thought to drive reionization, owing to pressure gradients that impede the growth of the gravitational potential well [Sawala2013,Schaller2014,Bocquet2016]. Motivated by these results, we create a simple analytic model that describes the growth of matter fluctuations and illustrates the difference of halo growth due to the inclusion of hydrostatic pressure of the baryons. In a collisionless universe, the linear overdensity (delta_t' = (rho/rho_crit)-1, where rho_crit is the critical background density) evolution in Fourier k-space is described by Equation 5 [Pace2010], where the expansion factor, a, is the independent variable. In the LambdaCDM model for redshifts of interest to this study, E(a) = sqrt(Omega_m*a^-3 + Omega_Lambda). We see that delta_t' increases with time, and only depends on the cosmological parameters and initial conditions. Moreover, in the absence of baryons, the evolution of the overdensity is independent of scale, owing to the lack of explicit dependence on the spatial wavenumber, k."}
{"text": "In order to evaluate the co-evolution of baryonic and dark matter density fields, we write delta_dm and delta_b as the dark matter and baryonic overdensities, respectively, and set rho = a^-3 * (rho_dm0*(1+delta_dm) + rho_b0*(1+delta_b)), where rho_dm0 = rho_crit*(1-(Omega_b/Omega_m)) and rho_b0 = rho_crit*(Omega_b/Omega_m) are the current (i.e. a=1) background densities for dark matter and baryons, respectively. With these definitions, the equations for dark matter and baryonic overdensities are, respectively given by Equation 6 (e.g. [Barkana2000]), where k_b, mu=0.59, m_p and H_0 are, respectively the Boltzmann constant, the mean molecular weight of ionized primordial gas in atomic units, the mass of the proton and the current Hubble constant. The quantity T is the temperature of gas as a function of the expansion factor. We assume a uniform temperature for all gas in the universe and adopt two piecewise functions shown in the top left panel of Fig. C1."}
{"text": "Prior to z of approximately 200, the gas temperature is coupled to the cosmic microwave background (CMB) through Compton scattering and decreases as (1+z). At later times (30 less than or equal to z less than or equal to 200), the gas has decoupled from the CMB and cools adiabatically, with temperature decreasing as (1+z)^2. When the first stars form and heat their environment (the heating is likely through X-rays), the gas temperature rises as approximately (1+z)^-4.9 and finally reaches 10^4 K following reionization at z of approximately 7 [Pritchard2008]. We note that the temperature evolution parametrized from the work of [Pritchard2008] is illustrative of the gas evolution. However, there is significant uncertainty regarding the role of X-ray sources in the pre-reionization epoch (e.g. intermediate-mass black holes, [Madau2004]; high-mass X-ray binaries, [Mineo2012]). This introduces uncertainties in the scaling of the temperature with redshift, since it depends on the evolution of the X-ray emissivity [Mesinger2014]."}
{"text": "In order to make a direct comparison with simulations, we incorporate the IGM temperature from the ADIAB simulation, in which gas only cools adiabatically. However, due to shock-heating from structure growth in the simulation, the temperature evolution does not strictly follow (1+z). Therefore, for z greater than or equal to 60, we adopt the [Pritchard2008] model for the analytic calculation. The dark matter and baryonic overdensities in Equation (6) are coupled, and there is a mass dependence in the pressure term in Equation (6). The mass of a collapsed halo is related to the scale, k, following Equation 7, where lambda is the size of the density fluctuation and k=2*pi/lambda. This makes the pressure term in Equation (6) smaller at high masses, so that the hydrostatic suppression of baryons on halo growth becomes weaker. Below, we use these equations to illustrate the effect of the pressure term on the evolution of dark matter and baryonic overdensities."}
{"text": "In order to solve Equations (5) and (6), we require initial conditions for delta_t', delta_dm, delta_b and their first-order derivatives in the linear regime. In the LambdaCDM model, the linear critical overdensity for a dark matter halo collapsing at redshift z_col is delta_c = 3/20*(12*pi)^(2/3). Using the growth factor D(z), where D(z=0)=1, we set the initial conditions for the overdensity of collisionless fluctuations at z = z_i to be given by Equations 8 and 9."}
{"text": "Top left: chosen parameterizations of the uniform temperature for the gas in the universe. Before z of approximately 200, the gas temperature is coupled to the CMB through Compton scattering and decreases as (1+z). At later times, gas cools adiabatically and its temperature drops as (1+z)^2. When the first stars form and heat their environment (the heating is likely from X-rays from the first galaxies), the gas temperature rises as approximately (1+z)^-4.9 and finally reaches 10^4 K following reionization at z of approximately 7 ([Pritchard2008], PL08 shown with the solid line). In the ADIAB model, the IGM temperature decrease as shown with the dash-dotted line instead of (1+z)^2 due to the shock-heating. For z greater than or equal to 60, the gas temperature evolution is extrapolated with the PL08 curve. Top right, Bottom left and Bottom right: the evolution of dark matter (delta_dm), baryonic (delta_b) and total overdensities (delta_t), normalized by the overdensity in a collisionless universe (delta_t'). Halos in this example are assumed to collapse at z = 7 with masses between 10^8.0 solar masses and 10^10.0 solar masses, which are indicated with different colours."}
{"text": "In order to investigate the effect of baryons on halo growth at the collapse redshift z_col, we set the initial overdensities of dark matter delta_dm_i and baryons delta_b_i to the same value as the collisionless case delta_t_i', and also set their derivatives equal to the derivative of delta_t_i'. In this work, we adopt a large initial redshift (z_i = 999) to ensure the initial overdensity is within the linear regime. The top right and bottom panels of Fig. C1 show the resulting evolutions of dark matter (delta_dm), baryonic (delta_b) and total (delta_t = Omega_b/Omega_m * delta_dm + (1-Omega_b/Omega_m) * delta_b) overdensities normalized by the corresponding dark matter overdensity in a collisionless universe (delta_t'). The spatial frequency scale, k, is varied corresponding to halo masses from 10^8 solar masses to 10^10 solar masses (see Equation 7), for a collapse redshift of z_col = 7."}
{"text": "We see that baryonic overdensities collapse slower than the corresponding dark matter overdensity due to the hydrostatic pressure from the baryons. This effect increases when the halo mass is smaller. Comparing different models, we see that when the IGM becomes heated by X-rays from the first galaxies, resulting in more hydrostatic pressure against baryonic accretion, baryonic overdensities are suppressed significantly [Naoz2005, Naoz2012]. Fig. C1 also illustrates that the inclusion of baryons causes the dark matter halo overdensity to increase more slowly than in the collisionless case. This effect is larger for smaller haloes as expected from the scale dependence in Equation (6)."}
{"text": "We next investigate the delay in dark matter halo formation (when delta_t reaches delta_c) due to the inclusion of baryons. From Fig. C1, it is clear that it takes longer for the total matter overdensities to evolve to the linear critical overdensity delta_c owing to the suppressed collapse of baryons, especially when the system is smaller. Equivalently, a halo that formed with mass M_t' at z_col' in a collisionless universe will only reach that same mass later at z_col < z_col' if baryons are included such that M_t(z=z_col) = M_t'(z=z_col'). Given this delay and with the halo mass accretion history, one is able to estimate the halo mass, M_t at z_col', and predict the suppression of halo mass, M_t(z=z_col') / M_t'(z=z_col')."}
{"text": "[Correa2015a,Correa2015b,Correa2015c] introduced an analytic calculation of accretion history for dark matter based on the extended Press-Schechter theory ([Press1974,Bond1991,Lacey1993], see Section 3.2) given by Equation 10, where alpha and beta are given by Equations 11 and 12, and q is given by Equation 13. [Correa2015a] also provide a fitting function for the relation between halo formation redshift z_f and the halo mass M given by Equation 14. With these equations, we estimate the total mass M_t(z=z_col') of the corresponding halo whose mass is equal to M_t'(z=z_col') in the dark matter only universe. Fig. C2 shows the ratio of M_t to M_t' as a function of redshift, for five halo masses (from M_t'=10^8 to 10^10 solar masses), where M_t and M_t' are the halo mass at z=z_col' in the scenario with and without baryons. Calculations using the [Pritchard2008] and ADIAB gas temperature evolutions (see the top left panel of Fig. C1) are shown with solid and dash-dotted lines, respectively."}
{"text": "Mass ratio between haloes collapsing in the universe with and without baryons, M_t/M_t' as a function of redshift, z=z_col'. The calculation is shown with different colours for 4 halo masses, M_t(z=z_col') from 10^8 to 10^10 solar masses. Calculations with [Pritchard2008] and ADIAB gas temperature evolutions are shown with solid and dash-dotted lines, respectively. The PL08 result shows that at early times, the suppression is less than or equal to 5 per cent. However, when heating becomes important, the mass ratio is significantly suppressed. For example, we find the mass ratio is approximately 60 per cent at z=5 for haloes around 10^8 solar masses. This mass suppression becomes more dramatic in less massive haloes. From Equation (10), we can calculate the specific halo mass growth rate given by Equation 15. Since beta increases with decreasing mass [Correa2015a], the specific halo mass growth rate at a given redshift decreases towards less massive haloes, and hence the mass ratio becomes higher."}
{"text": "The analytic calculation of mass ratio for the ADIAB simulation IGM temperature evolution results in a similar trend to the simulation (mass ratios are smaller for less massive haloes and at higher redshift, see the top left panel of Fig. 1). However, it predicts far less suppression of halo masses (e.g. the mass ratio is less than or equal to 5 per cent for 10^8 solar masses haloes) than the ADIAB simulation (e.g. the mass ratio is around 50 per cent for 10^8 solar masses haloes at z=14 in the simulation). There are several possible reasons for this quantitative difference. Compared to the analytic model, which uses a simple IGM temperature evolution to calculate the pressure of baryons, the numerical simulation is much more complicated due to non-linear physics. Although the temperature decreases to less than 10^2K for gas particles identified as IGM, the gas temperature can be heated to more than 10^4-10^5K once falling close by or into haloes due to shocks, resulting in stronger pressure gradients and more dramatic mass suppression shown in the simulation."}
{"text": "In order to prevent gas particles being too close to each other, resulting in an extremely small calculation time step and dramatically increasing the computational cost, there is an existing minimum gas temperature in the simulation, which is approximately 5K. This will enhance the mass suppression due to a minimum effective hydrostatic pressure in the simulation (although typically this at very small scales only). There are also many limitations in the analytic model. For instance, the hypothesis of uniform gas temperature may lead to an underestimation of the baryonic overdensity [Naoz2005], while setting the same initial conditions for the baryonic and dark matter overdensities overestimates the baryonic fluctuations on small scales [Naoz2011]. Nonetheless, the analytic calculation provides a frame work to interpret the mass reduction observed in simulations."}
{"text": "Motivated by recent measurements of the number density of faint AGN at high redshift, we investigate the contribution of quasars to reionization by tracking the growth of central supermassive black holes in an update of the Meraxes semi-analytic model. The model is calibrated against the observed stellar mass function at redshift z from approximately 0.6 to 7, the black hole mass function at redshift z less than or approximately equal to 0.5, the global ionizing emissivity at redshift z from approximately 2 to 5 and the Thomson scattering optical depth. The model reproduces a Magorrian relation in agreement with observations at redshift z < 0.5 and predicts a decreasing black hole mass towards higher redshifts at fixed total stellar mass. With the implementation of an opening angle of 80 deg for quasar radiation, corresponding to an observable fraction of approximately 23.4 per cent due to obscuration by dust, the model is able to reproduce the observed quasar luminosity function at redshift z from approximately 0.6 to 6. The stellar light from galaxies hosting faint AGN contributes a significant or dominant fraction of the UV flux."}
{"text": "At high redshift, the model is consistent with the bright end quasar luminosity function and suggests that the recent faint redshift z~4 AGN sample compiled by [Giallongo2015] includes a significant fraction of stellar light. Direct application of this luminosity function to the calculation of AGN ionizing emissivity consequently overestimates the number of ionizing photons produced by quasars by a factor of 3 at redshift z~6. We conclude that quasars are unlikely to make a significant contribution to reionization. The epoch of reionization (EoR) is the phase of the Universe when neutral hydrogen in the intergalactic medium (IGM) was reionized. Star-forming galaxies at high redshift are believed to be one of the dominant sources of ionizing UV photons provided one assumes a high average escape fraction of Lyman continuum radiation (an escape fraction for stars greater than or approximately equal to 10 per cent) and extends the UV luminosity function to faint dwarf galaxies [Kuhlen2012, duffy2014low, Feng2016, Mesinger2016]. However, the value of the escape fraction for stars is very uncertain."}
{"text": "Observations of star-forming galaxies at low redshift usually indicate a much lower escape fraction. For example, by measuring the ratio of Lyman alpha to H-beta line emission, [Ciardullo2014] derived an escape fraction of 4.4 per cent while [Matthee2016] measured a median escape fraction of 1.6 per cent using stacking of H-alpha-selected galaxies. Moreover, some theoretical works also suggest a low escape fraction for stars [Gnedin2007, Hassan2016, Sun2015]. In order to reconcile the difference between low-redshift observations and the photon budget at high redshift, some propose a rapid increase of the escape fraction for stars with redshift [Haardt2012, Khaire2016, Price2016, Sharma2016] and with decreasing mass [Paardekooper2013, Kimm2014, Wise2014]. This is supported by identifying local analogues of high-redshift galaxies and extrapolating the observed escape fraction for stars using indicators such as the [OIII]/[OII] ratio to high redshift ([Faisst2016] and references therein)."}
{"text": "On the other hand, additional contributors to reionization may also be present. For example, [Ma2016] included a binary population into a set of radiative transfer cosmological simulations and found that they produced significantly more ionizing photons among the old stellar population compared to a model without binaries, reducing the requirement of high escape fraction. In addition, these photons produced at later times can escape from galaxies more easily since the local feedback efficiently clears out nearby gas, leading to a lower required escape fraction on average. With a high escape fraction (an escape fraction for quasars of approximately 1, [Barkana2000]), quasars (AGN) are potential contributors to reionization [Volonteri2009, Fontanot2014, Madau2015, Mitra2015], despite their relatively low number. Recently, [Giallongo2015] identified faint AGN candidates in the CANDELS GOODS-South field and suggested that there is a high number density of faint AGN at redshift z=4-6. These faint quasars provide a new source of reionization [Madau2015]."}
{"text": "However, it is still debated whether there are enough luminous quasars at high redshift to make a significant contribution [Bouwens2015, Weigel2015, Manti2017, Parsa2017] and whether the escape fraction of high-redshift low-luminosity AGN is of order of unity [Cristiani2016, Micheva2016]. To explore the consequences for galaxy formation and reionization from theses faint quasars, this paper describes the addition of a population of evolving black holes to the Meraxes semi-analytic model of galaxy formation and reionization [Mutch2016]. This new model enables a detailed exploration of the relative role of quasars during the EoR. The paper is organized as follows. We begin with a description of the semi-analytic model in Section 2, in which the black hole growth model is introduced in detail. We present the black hole properties in Section 3 and explore reionization from quasars in Sections 4 and 5. Conclusions are given in Section 6. In this work, we adopt cosmological parameters from the Planck 2015 results (Omega_m, Omega_b, Omega_Lambda, h, sigma_8, n_s = 0.308, 0.0484, 0.692, 0.678, 0.815, 0.968; [PlanckCollaboration2015])."}
{"text": "Built on halo merger trees constructed from the Tiamat collisionless N-body simulation [Poole2015], the Meraxes semi-analytic model [Mutch2016] was specifically designed to study galaxy formation and reionization at high redshift. The model computes galaxy properties according to different astrophysical processes including gas infall, cooling, star formation, supernova feedback, metal enrichment, mergers and reionization. In order to properly track the evolution of galaxies during reionization, Tiamat provide 100 snapshots between redshift z=35 and 5 with a time interval of approximately 11.1 Myr and 64 additional snapshots between redshift z=5 and 2 separated equally in units of Hubble time. The mass resolution of Tiamat is approximately 2.64x10^6 per h solar masses and the box size is 67.8 per h Mpc. Additionally, in order to obtain information of more massive objects and lower redshifts, we also take advantages of the dark matter halo merger trees generated from the Tiamat-125-HR simulation (Poople et al. in prep)."}
{"text": "The Tiamat-125-HR simulation shares identical cosmology with Tiamat but has a lower mass resolution of 0.12x10^9 per h solar masses in a bigger simulation volume, with side lengths equal to 125 per h Mpc. The Tiamat-125-HR trees are constructed down to redshift z=0.56 with the same snapshot separation strategy as the Tiamat trees. In the following subsections, we briefly describe the galaxy formation in Meraxes and introduce the new implementation of black hole growth and feedback in detail. More details about the implemented galaxy formation physics can be found in [Mutch2016]. In the Meraxes semi-analytic model, cooling and star formation are assumed to be negligible in haloes below the atomic cooling mass threshold, approximately 10^8 solar masses. Thus, once a halo grows larger than the atomic cooling limit it is designated as a galaxy, which has three baryonic components: gas, stars and a central black hole."}
{"text": "During one time step, Delta t, additional gas falls into the hot gas component of a galaxy from the IGM when the mass fraction of baryons in the halo is lower than the cosmic mean value, f_b = Omega_b / Omega_m: The change in hot gas mass, Delta m_hot, is calculated as the maximum of zero or the difference between the required baryon mass (chi_r times f_b times M_vir) and the existing baryonic mass (stars + cold gas + hot gas + ejected gas), where m_star, m_cold, m_hot and m_eject are the masses of the stellar component, cold gas, hot gas and ejected gas, respectively, and M_vir is the virial mass of the host halo in which the galaxy forms. chi_r is a baryon fraction modifier to take account of reionization feedback and will be introduced later in Section 4.1. Some of the hot gas, m_cool, cools and collapses on to the cold disc. Assuming the cooling process is in quasi-static thermal equilibrium, one can calculate the cooling time by the cooling time t_cool(r) equals (3 times mu bar times m_p times k times T_hot) divided by (2 times rho_hot(r) times Lambda(T_hot, Z_hot))."}
{"text": "Following [croton2006many], we calculate the cooling radius, r_cool, at which the cooling time is equal to the halo dynamical time... Cooling is sufficient within r_cool and we estimate the cooling mass by the cooling mass m_cool is defined as m_hot times the minimum of [1, min(1, r_cool / R_vir) times (Delta t / t_cool)], which is removed from the hot gas reservoir and redistributed into the cold gas disc, Delta m_hot = -Delta m_cold = -m_cool. From this, we see that depending on the ratio of r_cool to R_vir, cooling is separated into two regimes: static hot halo (r_cool > R_vir) and rapid cooling (r_cool < R_vir, see more in [croton2006many]). When the galaxy collects enough cold gas, m_cold > m_crit, based on [kennicutt1998global] and [kauffmann1996disc], it forms new stars, Delta m_star, through a burst."}
{"text": "The change in stellar mass Delta m_star equals the minimum of [(alpha_sf times max(0, m_cold - m_crit) times Delta t) / t_dyn,disc, m_cold], where t_dyn,disc is the dynamical time of the cold gas disc and alpha_sf is a free parameter corresponding to the star formation efficiency. This mass is removed from the cold gas reservoir. The new stellar mass is assumed to form following a [Salpeter1955ApJ...121..161S] initial mass function (IMF). Ultimately some of these stars recycle their mass back to the interstellar medium (ISM) through type-II supernovae explosion. The energy produced by these supernovae heats the ISM and converts some of the cold gas to the hot phase or, if there is sufficient energy, even ejects a fraction of hot gas from the galaxy. Assuming that the efficiency for supernovae energy coupling with the ISM scales with mass and is in proportion to a free parameter [guo2011dwarf], alpha_energy, then the total energy released by supernovae that couples to the ISM is calculated."}
{"text": "Since a massive star (greater than or approximately equal to 8 solar masses) takes approximately 40 million years, or 4 snapshots, before reaching its type-II supernova stage, Meraxes accounts for supernovae not only from the current snapshot, j, but also from the stars formed in the previous 4 snapshots. Therefore, the total energy released during one snapshot is the sum of the total energy from snapshots i=j to i=j-4. Since the hot gas shares the same virial temperature as the host halo, assuming the mass loading factor for reheating cold gas is a free parameter, alpha_mass, the energy utilized in gas heating can be calculated by the reheating energy E_reheat equals 1/2 times alpha_mass times Delta m_star times V_vir^2. Depending on the available energy, E_total, and the required energy for re-heating, E_reheat, the reheated mass is calculated. This mass is removed from the cold gas reservoir and redistributed in the hot gas component."}
{"text": "If there is still some energy left after reheating, the supernovae feedback will further remove hot gas from the galaxy, adding it to the ejected component. In addition, the metals produced by supernovae enrich the environment, which then enhances the cooling rate. Moreover, mergers drive strong turbulence and hence increase the possibility of star formation. Major mergers generally introduce more energetic bursts than minor mergers since they induce strong inflows and easily trigger bar-like instabilities in the cloud [Somerville2001]. Therefore, following mergers, Meraxes also includes a starburst mechanism. Reionization feedback will be introduced in Section 4.1. There are more details of the semi-analytic model in [Mutch2016]. This work extends the current model with a detailed black hole growth prescription based on [Croton2016] and is described in the following subsection."}
{"text": "In the updated model, every newly formed galaxy is seeded with a central black hole of mass 1000 per h solar masses. The two gas reservoirs in the galaxy (i.e. hot and cold) lead to two different black hole growth scenarios, termed radio and quasar modes [Croton2016]. In the normal quiescent state, black holes only accrete mass from the hot gas reservoir, resulting in radio emission in the centre of galaxy. However, mergers trigger rapid accretion on to the black hole from the cold gas disc, causing them to radiate as quasars. In this work, we do not distinguish AGN with different types and refer to them all as quasars unless specified otherwise. Whenever there is a static hot gas reservoir, m_hot, around the galaxy, some of it will cool, m_cool, and form a cold gas disc, m_cold, while some will be directly accreted by the central black hole."}
{"text": "We adopt the Bondi-Hoyle accretion model proposed in [Croton2016] to describe this hot gas accretion. The Bondi-Hoyle accretion rate is given by the Bondi-Hoyle accretion rate, dot m_Bondi, equals (2.5 times pi times G^2 times m_bh^2 times rho_hot) divided by c_s^3, where G, m_bh, c_s and rho_hot are the gravitational constant, the black hole mass, the speed of sound and the density of the hot gas reservoir, respectively. Then, assuming the accretion rate does not change during one time step, Delta t, the accretion mass is the change in black hole mass from hot gas, Delta m_bh,hot, equals the minimum of (m_hot, m_Edd, k_h times dot m_Bondi times Delta t), where k_h is a free parameter, used to adjust the efficiency of black hole growth in the radio mode. This mass is removed from the hot gas reservoir. Assuming a fraction, eta, of the accreted mass is radiated, the black hole only grows by the change in black hole mass Delta m_bh equals (1-eta) times Delta m_bh,hot."}
{"text": "Moreover, the radiation acting outward is limited by the Eddington luminosity... By integrating this through one time step, this provides the second limitation... the Eddington mass limit m_Edd equals m_bh times [exp((epsilon times Delta t) / (eta times t_Edd)) - 1], where t_Edd is the Eddington accretion time-scale and m_bh is the black hole mass at the beginning of this time step. Assuming adiabatic heating and that a fraction of the radiated energy, kappa_r, is coupled to the surrounding gas and therefore can contribute to feedback, then the heated mass due to black hole feedback can be calculated through the heated mass m_heat equals (kappa_r times eta times Delta m_bh,hot times c^2) / (0.5 times V_vir^2), which is subtracted from the cooling flow. However, if the heating from black hole feedback is too strong... it will significantly suppress the cooling flow, which will consequently restrain the black hole accretion of hot gas. This suppression is referred to as radio mode feedback."}
{"text": "In this case, following [Croton2016], Delta m_bh,hot is rescaled to be the amount of mass within the cooling radius... and the heated mass consequently shrinks to be the cooling mass, resulting in a complete quenching of cooling. Radio mode feedback limits gas condensation in cluster cooling flows and regulates star formation in massive galaxies [croton2006many]. We note that this does not have a significant impact on the results from Tiamat at redshift z>=2 due to the limited number of massive objects in the box. However, black hole feedback is important in more massive objects at lower redshifts, which can be observed using the Tiamat-125-HR halo merger trees. We note that at high redshift, accreted hot gas does not contribute significantly to black hole growth, with the accreted mass during the radio mode typically being only approximately 0.1 per cent of the mass from the quasar mode. Additionally, because the radio mode accretion rate is approximately 3 orders of magnitude smaller than the Eddington accretion rate, we ignore the energy due to the radio mode for the calculation of the quasar luminosity."}
{"text": "Many binary AGN have been detected in merging galaxies [Shields2012, Comerford2013, Comerford2014, Comerford2015, Muller-Sanchez2015]. This suggests that galaxy mergers might trigger AGN activity, which is also supported by hydrodynamic simulations of galaxy mergers [Capelo2015, Volonteri2015b, Volonteri2015a, Steinborn2016]. Following [Croton2016], when a merger occurs between two galaxies, the central black holes coalesce and their masses combine. As mergers drive strong gas inflows towards the central region [Capelo2015], cold gas is funnelled to the central black hole of the resulting merged galaxy, significantly increasing its mass. The amount of accretion can be estimated by [Bonoli2009, Croton2016]... where m_cold is the amount of mass available in the cold gas disc, k_c is a free parameter used to modulate the strength of black hole accretion and gamma is the mass ratio between the two merging galaxies, respectively. The term Delta m_bh,max' corresponds to the accretion mass left from the quasar mode in the previous snapshot, which will be introduced later."}
{"text": "Unlike the radio mode, black holes grow dramatically during the quasar mode. The AGN activity lifetime is much longer than the 11Myr time step at redshift z>5. In some cases, this leaves the central black hole insufficient time to consume all of the newly accreted gas, Delta m_bh,max, at the Eddington limit. Therefore, the mass actually accreted by the black hole is the change in black hole mass from cold gas Delta m_bh,cold equals the minimum of (m_Edd, Delta m_bh,max), which is removed from the cold gas reservoir. In our model, during the quasar mode black holes are assumed to either accrete and radiate at the Eddington rate or stay quiescent if the accretion mass is not sufficient. Therefore, depending on the total available mass brought in, Delta m_bh,max, and the Eddington limit, m_Edd, there are two possible scenarios when the central black hole is undergoing a merger: 1) Delta m_bh,max < m_Edd... 2) Delta m_bh,max >= m_Edd."}
{"text": "In the case of Delta m_bh,max > m_Edd, instead of consuming this instantaneously, causing a super-Eddington accretion event, some of the mass is accreted by the central black hole, limited by the Eddington rate, while the rest is stored in the accretion disc to be consumed in the next time step. Similarly, when this quasar is observed at t_obs, the bolometric luminosity can be calculated. It is suggested that during mergers, black holes undergo rapid accretion for a certain time period, which is followed by a long quiescent phase [Hopkins2005c, Hopkins2005a, Hopkins2005d, Hopkins2005b]. The assumption that black holes are either accreting at the Eddington rate (epsilon=1) or stay quiescent has been shown to provide a good description of black hole growth for the majority of black holes at high redshift [Bonoli2009]. The energy injected into galactic gas during the quasar mode is given by kappa_q times eta times Delta m_bh,cold times c^2, where kappa_q represents the mass coupling factor in the quasar mode."}
{"text": "Unlike the radio mode, this energy generates a wind, which heats the gas in the cold disc into the hot reservoir. Depending on the amount of energy provided by the quasar, the wind can further unbind and eject the hot gas in a manner similar to the stellar feedback prescription presented in Section 2.1. In order to compare the predicted black hole population in our model with observations, the intrinsic B-band and UV 1450 Angstrom band luminosities of quasars are calculated as follows: 1. We calculate the bolometric magnitude... 2. We calculate the B-band magnitude in the Vega magnitude system using the bolometric correction proposed by [Hopkins2007]... 3. We convert the B-band magnitude from the Vega system to the AB system following [Glikman2010]... 4. We extrapolate the B-band magnitude of which the effective wavelength is 4344 Angstrom [Blanton2007] to the 1450 Angstrom magnitude, assuming the quasar continuum between 1450 and 4344 Angstrom has a power-law slope of alpha_q,optical = 0.44 relative to wavelength [Schirber2003]."}
{"text": "We summarize the relevant model parameters in Table 1 compared to the original value adopted in [Mutch2016]. In this work, we constrain our model against: the observed evolution of the galaxy stellar mass function between redshift z from approximately 0.6 and 7; the observed black hole mass function and Magorrian relation at low redshift (redshift z less than or approximately equal to 0.5); the latest integrated free electron Thomson scattering optical depth measurement [PlanckCollaboration2016]; the predicted global ionizing emissivity from Lyman alpha opacities [Becker2013]. The black hole mass functions at redshift z from approximately 8.0 to 0.6 are shown with different colours in the left-hand panel of Fig. 1. The results calculated using the Tiamat and Tiamat-125-HR trees are shown with thick and thin lines, respectively. The shaded regions represent the 1-sigma Poisson uncertainties."}
{"text": "Estimates of the local black hole mass function are shown with points and grey shaded regions. We see that the discrepancy between various observations is substantial. This is a result of inconsistent correlations between black hole mass and observable quantities, such as the Sersic indices, bulge velocity dispersion or luminosity and galaxy geometry, and from the intrinsic scatter of these adopted scaling relations. Extrapolations of these observed scaling relations have impacts on the black hole mass function at the high-mass end, while different treatments of the spiral galaxy bulge can significantly change the low-mass end [Shankar2009]. In this work, the model is therefore calibrated against the black hole mass function between 10^7.5 solar masses and 10^9 solar masses. In the bottom left-hand panel of Fig. 1, we see that the mass function converges at lower redshifts above a black hole mass of 10^6 solar masses (shown as the vertical dotted line)."}
{"text": "The different mass resolutions of Tiamat and Tiamat-125-HR result in different merger rates, especially when approaching the resolution limit. At high redshift, because the growth of black hole is dominated by the merger triggered quasar mode, the number density of small black holes is relatively lower in the Tiamat-125-HR result (e.g. comparing the redshift z=8.0 thick and thin lines). At low redshift, redshift z~0.6, the model is in agreement with the observational estimations. The middle panel of Fig. 1 shows the relation between black hole mass and stellar mass (the Magorrian relation). The 2D histogram indicates the distribution of galaxies in logarithm from the fiducial model using the Tiamat-125-HR halo merger trees at redshift z~0.6 while the solid line represents the mean. The Magorrian relations at redshift z=2, 5 and 7 from Tiamat-125-HR are also shown with dash-dotted, dashed and dash-dot-dotted lines, respectively."}
{"text": "The right bottom subplot shows the redshift z=2, 5 and 7 Magorrian relations of the Tiamat result with thick lines compared with the redshift z~0.6 Tiamat-125-HR Magorrian relation. Observations from the local Universe are indicated with different symbols. We see that the model predicts a similar Magorrian relation at redshift z~0.6 compared to the local observations and we find an increasing normalization towards lower redshifts in the mass range of 10^10 solar masses < M_* < 10^12 solar masses. The evolution of the Magorrian relation in our model is due to the black hole and stellar mass evolving with the underlying dark matter halo mass differently. In [Mutch2016], we have shown that the median relation between stellar mass and virial mass does not evolve in our model and can be described by M_* is proportional to M_vir^7/5 in the range of 10^8 solar masses < M_* < 10^11 solar masses, which is supported by a simple analytic model of supernova energy conversation [Wyithe2003]."}
{"text": "On the other hand, haloes with a given virial mass host less massive black holes at earlier times in our model (see the right-hand panel of Fig. 1). These result in an increasing normalization of the Magorrian relation towards lower redshifts. From the right-hand panel of Fig. 1, we see that the M_bh - M_vir scaling relation does not get suppressed in massive haloes (at least to M_vir ~ 10^14 solar masses or M_bh ~ 10^9 solar masses). Both black holes and stars grow from the cold gas disc. However, AGN feedback significantly suppresses the cooling flow in massive galaxies [croton2006many], preventing stellar mass from growing. On the other hand, black holes are able to continue accreting until there is enough energy in feedback to overcome the halo potential and unbind the gas [Booth2010]. Because of these, the slope becomes steeper in the Magorrian relation at black hole mass M_bh > 10^8 solar masses."}
{"text": "Fig. 2 presents the galaxy stellar mass functions from our fiducial model for comparison with the available observational data at redshifts 7 to approximately 0.6. The results calculated using the Tiamat and Tiamat-125-HR trees are shown with thick and thin lines, respectively. The shaded regions represent the 1-sigma Poisson uncertainties. We see that the fiducial model is able to reproduce the observed galaxy stellar mass function across the redshift range of redshift z=7-0.6. We also present two additional models in Fig. 2, Mutch2016 and M16BH. Mutch2016 adopts identical parameters as the redshift varying escape fraction for stars model presented in [Mutch2016]. This model is able to reproduce the evolution of the stellar mass function at high redshift (redshift z>5)."}
{"text": "The redshift dependence of the escape fraction for stars, f_esc,*,M16, was chosen to simultaneously reproduce the normalization and flat slope of the [McQuinn2011] emissivity measurement at redshift z~5 and the Planck 2015 optical depth measurement ([PlanckCollaboration2015]). Details of the Mutch2016 model at high redshift (redshift z>5) can be found in [Mutch2016]. In this work, we extend the model to lower redshifts and find that, without AGN feedback regulating galaxy formation, the model fails to reproduce the observed stellar mass functions at redshift z<2, especially in larger mass ranges (stellar mass M_* > 10^11 solar masses). However, when AGN feedback is implemented, shown as the M16BH model, the model shows better agreement with observations [croton2006many]. These two models also suggest that radio-mode feedback does not play a significant role in galaxy formation during the EoR, and because reionization is dominated by low-mass galaxies ([Liu2016MNRAS.462..235L], see also Section 5), AGN feedback is expected to have no significant impact on reionization."}
{"text": "With respect to Mutch2016, the fiducial model presented in this work employs a stronger star formation efficiency (alpha_sf) with maximized supernova feedback (alpha_energy and alpha_mass) and more intense radio mode feedback (k_h), in order to gain better agreement with the observed stellar mass function in the intermediate mass range (10^9 solar masses < M_* < 10^11 solar masses) at 1<z<2. Semi-analytic models can predict quasar bolometric luminosity through the modelled central black hole mass. In order to compare with observations, three corrections are usually required: bolometric corrections, duty cycles and obscured fractions. In our model, we calculate the duty cycle self-consistently by assuming Eddington accretion of available gas and a random observation time between snapshots. Black holes that are inactive when observed are not considered in the census."}
{"text": "We convert the total luminosity into a particular band using the bolometric correction of [Hopkins2007]. Finally, we need to take the obscuration due to the presence of a dusty torus surrounding the AGN into account. In practice, each quasar is weighted by 1 - cos(theta/2), where theta represents the opening angle of AGN radiation, during the calculation of the quasar luminosity function. We note that the dependence of theta or the obscured fraction (the ratio of obscured to unobscured AGN) is very complicated. It has been suggested that theta may depend on wavelength, redshift and luminosity [Elvis1994, Hopkins2007]. For simplicity, we only consider constant theta. The opening angle is a free parameter in our model, chosen to reproduce the quasar luminosity function amplitude. In this work, theta=80 deg is adopted. This corresponds to a fraction of visible objects, f_obs, to be ~23.4 per cent, in agreement with [Hopkins2007]."}
{"text": "We present the UV 1450 Angstrom luminosity functions of quasars at redshift 6, 5, 4 and 3, and the B-band luminosity functions at redshift z~2, 1.5, 1.3 and 0.6 in Fig. 3, compared to the observational data. The results calculated using the Tiamat and Tiamat-125-HR trees are shown with thick and thin lines, respectively. The shaded regions represent the 95 per cent confidence intervals around the mean using 100000 bootstrap re-samples. Similarly to the black hole mass functions, the Tiamat-125-HR results show a lower number density at high redshift compared to the Tiamat results, and they converge at lower redshifts (redshift z less than or approximately equal to 4). We see that the model shows good agreement with observations across a large redshift range (redshift z~6-0.6)."}
{"text": "At high redshift the model is consistent with the samples of bright quasars [willott10, Shen2012, McGreer2013, Jiang2016] while it predicts a lower number density of faint quasars compared to the [Giallongo2015] sample. On the other hand, the model produces a significant number of faint quasars. The turnover (not shown here) of the predicted UV luminosity function is around UV magnitude M_1450 ~ -11, which is much fainter than the observed faintest quasars, UV magnitude M_1450 ~ -18 ([Giallongo2015]). In addition, the observed population of bright quasars (UV magnitude M_1450 < -23) at high redshift is not present in our model due to our limited simulation volume. All of these factors may have an impact on the contribution of AGN to the reionization history, which is discussed in Section 4. The large number of faint AGN identified by [Giallongo2015] has prompted renewed discussion of the contribution of quasars to reionization [Madau2015, Mitra2015, Kulkarni2017]."}
{"text": "We therefore further discuss the low number density in the faint end predicted by the model compared with the G15 data. When constructing an observed AGN luminosity function, the sample is typically identified spectroscopically or via colour-colour selections if spectra are not available, following which contamination from host galaxies is removed. However, this may not be the case for faint AGN. In particular, the G15 AGN sample is selected using X-ray activity and no AGN-galaxy separation is possible. Thus, the total UV luminosity may have a large fraction of stellar light, suggesting that the G15 sample may be potentially impacted by stellar light contamination. Despite the recent claim that only 12 of the 22 reported X-ray detections in G15 are high-redshift AGN [Parsa2017], this conjecture is supported by [Ricci2017], who used X-ray observations as a proxy and derived the quasar UV luminosity function down to much fainter ranges."}
{"text": "They showed that the luminosity function is in agreement with UV/optical observations (e.g. [Croom2009, Glikman2010, Masters2012, Palanque-Delabrouille13]), and have much lower amplitudes than the G15 results, and that the high number density of faint AGN in G15 can be explained by the contribution from the luminosity of host galaxy with UV magnitude M_1450 ~ -20. In order to account for this, we calculate the galaxy UV luminosity by integrating model SEDs based on the modelled star formation history [Liu2016MNRAS.462..235L] and add the stellar light to mimic the observed total UV luminosity (AGN+galaxy). We present the resulting luminosity function of faint objects in Fig. 3 with dashed lines. We see that including stellar light can significantly increase the number density of faint AGN inferred at high redshift, by up to approximately 1 order of magnitude. The fitting functions provided by [Giallongo2015] as shown with thin black dashed lines in Fig. 3 are more consistent with the AGN+galaxy luminosity function."}
{"text": "If this is the case, the estimated emissivity at high redshift based on [Giallongo2015] is likely overestimated. Motivated by the G15 sample, which suggests a numerous population of faint AGN at redshift z=4-6 ([Giallongo2015]), [Madau2015] extrapolated the emissivity calculated from [Giallongo2015] to higher redshifts and assessed a model of reionization, in which quasars are the dominant ionizing sources. They found that due to the high escape fraction of ionizing photons produced by those luminous objects, quasars are able to ionize the neutral hydrogen by redshift z~5.7 if the high emissivity of quasars derived at redshift z~5 continues to higher redshifts. Later, [Mitra2015] revisited the model with a revised extrapolation and also found that quasars have a significant role during the EoR. However, their analysis still prefers models with a non-zero escape fraction of approximately 12 per cent from galaxies."}
{"text": "It is worth noting that with different formalism, [Manti2017] fit the observed quasar UV luminosity function at redshift z=0.5-6.5, including the G15 sample. They recalculated the emissivity by integrating the luminosity function and confirmed a large number of ionizing photons from quasars at high redshift using the Schechter luminosity function. However, the fitting result using a double power law presents a rapidly decreasing emissivity at redshift z>6, suggesting that the extrapolated high-redshift quasar emissivity is strongly dependent on the assumed shape of the quasar luminosity function. Taking advantage of the Meraxes semi-analytic model with 21cmFAST [Mesinger2011], we investigate the contribution of quasars to reionization, within a frame work that accounts for black hole growth and feedback on star formation. The semi-numerical reionization code 21cmFAST [Mesinger2011] uses an excursion set formalism to identify HII bubbles in which the cumulative number of ionizing photons is more than the number of absorbing atoms."}
{"text": "The reionization condition is: N_star * N_gamma,star * f_esc,star + N_q * N_gamma,q * f_obs * f_esc,q >= (1 + N_rec_bar) * N_HI, where N_star and N_q are the numbers of baryons in stars and quasars, N_gamma,star ~ 4000 [Loeb2001] and N_gamma,q are the mean numbers of ionizing photons produced per baryon incorporated into the stellar or quasar components. The parameters f_esc,star and f_esc,q are the escape fractions of ionizing photons produced by stars and quasars. f_obs ~ 0.234 represents the observable fraction due to obscuration. N_HI is the cumulative number of atoms being ionized and N_rec_bar is the mean number of recombinations per baryon. Inhomogeneous recombinations are ignored, which can have a large impact [Sobacchi2014]. In this work, N_rec_bar is set to be 0 as suggested by the high-redshift Lyman alpha forest in the IGM [Bolton2007, McQuinn2011]."}
{"text": "When the local volume around a galaxy is ionized, the UV background provides an extra heating mechanism, which modifies the baryonic fraction of the host halo. Following [Sobacchi2013], when the virial mass, M_vir is smaller than a filtering mass, which can be calculated through M_filt = 2.8x10^9 solar masses * J_21^0.17 * ((1+z)/10)^-2.1 * [1 - ((1+z)/(1+z_ion))^2]^2.5, the suppression of gas becomes significant. Here, z_ion is the redshift when the local volume is first ionized. J_21 represents the intensity of the local UV background. This can be calculated through an equation involving the mean-free path of ionizing photons, which is approximated by the HII bubble radius, R. The parameters alpha_star=5.0 [Loeb2001] and alpha_q=1.57 ([Giallongo2015]) are the spectral indexes for a stellar-driven and a quasar-driven spectra in the UV band. m_dot_star and m_dot_q are the growth rates of stellar mass and black hole mass, respectively."}
{"text": "Fig. 4 shows the instantaneous ionizing emissivity averaged over the entire Tiamat simulation volume from different models as a function of redshift... From the Lyman alpha opacity, several measurements of the total emissivity (AGN and stars) at high redshift have been estimated [Bolton2007, McQuinn2011, Becker2013]. There are relatively large uncertainties in these measurements. In this work, we compare our models using the most recent data from [Becker2013]. The top panel of Fig. 4 shows that the fiducial model agrees with the [Becker2013] data and the bottom shows the ratio between ionizing photons from black holes and stars in the fiducial model, suggesting that during the EoR, quasars are subdominant in our model. The evolutions of the mass-weighted global neutral hydrogen fraction and the integrated Thomson scattering optical depth are shown in Fig. 5."}
{"text": "It shows that the fiducial model has a reasonable reionization history, with the mean global neutral hydrogen fraction decreasing from 90 per cent at redshift z~10 to 0 by redshift z~6 and a Thomson scattering optical depth in agreement with the latest Planck limits ([PlanckCollaboration2016]). There are two additional models in the top panel of Fig. 4 as well as in Fig. 5: StellarReion and QuasarReion. The ionizing source in the StellarReion model is only stars, with an evolving escape fraction and zero escape fraction for quasars, while quasars are the only reionization contributor in the QuasarReion model, with an escape fraction of 1 for quasars and 0 for stars. Note that only changing the feedback from reionization has little impact on the stellar mass function, the quasar luminosity function or the Magorrian relation. By preventing gas infall, reionization only affects less massive objects in our model."}
{"text": "In Fig. 4, we see that the emissivity of quasars grows rapidly in the QuasarReion model by a factor of 10 from redshift z~7-5. However, if quasars are the only reionization contributor, even with an escape fraction of 1 for quasars, the number of ionizing photons cannot reach the [Becker2013] data. Moreover, due to the deficiency in the photon budget at high redshift, quasars can only start reionization at redshift z~6 resulting in an end at redshift z~3. Together with the predicted optical depth, our model rules out the quasar-only reionization scenario. One may recalibrate the model with a more efficient black hole growth rate at high redshift in order to match the G15 luminosity function and the estimated emissivity. [Mitra2015] also suggest that if G15 emissivity is correct, quasar-only reionization is possible and it results in a small value of tau_e due to the rapid evolution of the Lyman-limit systems."}
{"text": "However, simultaneously matching the model with the G15 faint AGN luminosity function and the other observations of bright systems at high redshift is difficult. For example, comparing to observations at redshift z~6, our models produce a flatter luminosity function, which is more consistent with the bright quasar sample. This suggests that a mass-dependent black hole growth efficiency would be required, in order to steepen the luminosity function and produce more small quasars. In the following sections, we explore the relative contribution of quasars to reionization based only on the presented black hole growth model. Comparing the neutral hydrogen fraction and the optical depth between the fiducial and StellarReion models also suggests that quasars do not have a significant role in reionization in this model. Their contribution helps finish reionization earlier by a redshift interval Delta z less than or approximately equal to 0.1 and decreases the optical depth by less than 10 per cent."}
{"text": "Our models are calibrated against the black hole - galaxy scaling relation and quasar luminosity function, in order to reproduce a realistic AGN catalogue for the study of the contribution of quasars to hydrogen reionization. However, it has recently been suggested that the black hole sample used to derive scaling relations is likely different from the entire population, leading to a selection bias [Bernardi2007]. For instance, using Monte Carlo simulations [Shankar2016] recovered the intrinsic scaling relation assuming the selection bias comes from unresolved black holes and showed that such a bias can lead to factors of >= 3 and ~50-100 higher normalizations of the M_bh - sigma_* and M_bh - M_* relations, respectively. We note that a Magorrian relation with a smaller normalization can be achieved in our model using a smaller black hole growth efficiency."}
{"text": "In this case, the reconstructed black hole population becomes less massive, more efficient AGN feedback and a larger fraction of observable AGN in the UV band are required to simultaneously reproduce the observed stellar mass function and quasar luminosity function. With the model calibrated against the quasar luminosity function, the black hole - galaxy scaling relation is coupled with the observable AGN fraction - a lower Magorrian relation requires a larger fraction of observable AGN. We note that the total emissivity of quasars is integrated from the luminosity function. Therefore, scaling relations do not have a significant impact on reionization in this work. Noting the difficulty of observationally determining the fraction of obscured AGN and the large uncertainties in the black hole - galaxy scaling relation, in this section we use a range of models which predict similar Magorrian relations as shown in Fig. 1 and explore the contribution of quasars to reionization."}
{"text": "We have shown that with an opening angle of 80 deg, the model is able to reproduce the observed quasar luminosity function from redshift z~6-0.6. However, at high redshift, the model predicts significant stellar contribution to UV flux in the G15 sample, and consequently less ionizing photons from AGN. Based on this, we find that quasars do not have a significant role during EoR. In the top panel of Fig. 5, we show the estimated total emissivity from [Giallongo2015] with the model proposed by [Haardt2012, Madau2015] and [Mitra2015]. The modelled emissivity from QuasarReion is shown for comparison. Our quasar reionization-only model (QuasarReion) predicts lower emissivities compared to these two estimations, with only a third of the G15 value at redshift z~6. Consequently, in disagreement with [Madau2015] and [Mitra2015] we conclude that quasars cannot be the dominate sources during reionization."}
{"text": "We could increase the emissivity by excluding the obscuration from dust (setting theta=180, shown as QuasarReion_nodust in Fig. 5), which gives a closer emissivity compared to the G15 estimation and in agreement with the model proposed by [Mitra2015]. In this model, quasars have a more significant role during the EoR and can reionize the IGM alone by redshift z~4.5. However, this model overestimates the number density of bright and low-redshift AGN, leading to an incorrect evolution of the quasar luminosity function. A lower fraction of observable AGN, f_obs, towards brighter luminosities and lower redshifts is required to solve this conflict. However, observations suggest the opposite trend in optical, infrared and X-ray bands [Hopkins2007] and more constraints are required to clearly establish a f_obs - z relation. In this section, we explore possible combinations of stars and quasars that could result in an overall photon budget at redshift z>5 consistent with the observed optical depth and ionizing flux at redshift z~2-5."}
{"text": "Noting this requirement, in this section we assume constant escape fractions both for simplicity and to ease interpretation. Motivated by the recent claim that the escape fraction of low-luminosity AGN is possibly less than unity at high redshift [Micheva2016], we run Meraxes with different combinations of the escape fraction for stars, f_esc,star, and the escape fraction for quasars, f_esc,q, without any changes to the other parameters. In the top panel of Fig. 6, the left-hand panel shows the Thomson scattering optical depth, tau_e. For comparison, shaded regions are shown corresponding to the best fit and 1-sigma range of the [PlanckCollaboration2016] measurements. Based on the [Becker2013] data at redshift z~2-5 and the [PlanckCollaboration2016] measurement, the top right two panels show the 68, 90 and 99 per cent confidence contours on each parameter of the best fit via the standard minimum-chi-squared technique. The 2D histogram shows the distribution of the ratios of quasar emissivity to stellar emissivity at redshift z~6."}
{"text": "We see that a lower escape fraction of ionizing photons from stars, f_esc,star requires a higher contribution from quasars, in order to reach the observational constraint. This also returns a higher ratio of quasar emissivity to stellar emissivity. However, because there is not a significant number of quasars at high redshift, changing the escape fraction for quasars, f_esc,q, has little impact to the optical depth. Through the best fitting contours, we see that if the escape fraction of ionizing photons from stars is only a few percent (<5 per cent; [Ciardullo2014, Matthee2016b]), the model requires an escape fraction for quasars, f_esc,q, of approximately 1.0. Although the escape fraction of ionizing photons depends on the local environment, many theoretical and observational works suggest an evolving or mass-dependent escape fraction with a decreasing average value at lower redshifts or in more massive galaxies [Kuhlen2012, Haardt2012, Paardekooper2013, Kimm2014, Wise2014, Bauer2015, Price2016]."}
{"text": "Therefore, as discussed in [Mutch2016], in order to simultaneously match the normalization and flat slope of the observed ionizing emissivity at redshift z less than or approximately equal to 6, and the Planck tau_e measurements, a redshift-dependent escape fraction for galaxies was proposed: the escape fraction for stars as a function of redshift, f_esc,*(z), equals the minimum of [f_esc,* at z=5 times ((1+z)/6)^beta, 1]. We have shown two models with evolving escape fractions (fiducial and StellarReion) in Section 4. In this section, we further explore the possible evolution of the escape fraction by running the semi-analytic model with different combinations of the escape fraction for stars at z=5 and beta. Note that all of the ionizing photons from quasars are included in this section (the escape fraction for quasars f_esc,q = 1) in order to investigate the evolution of the stellar escape fraction with the contribution of quasars to reionization."}
{"text": "The bottom panels of Fig. 6 show the optical depth and the best-fitting confidence limits as functions of the normalization of the escape fraction for stars as a function of redshift, f_esc,*(z), the escape fraction for stars at z=5, and the scaling, beta, when the escape fraction for quasars f_esc,q = 1. We see that because a larger scaling suppresses the escape fraction at lower redshifts, which results in a lower emissivity at redshift z less than or approximately equal to 5, a larger normalization is required. In addition, a larger beta gives less ionizing photons at redshift z~8, which slows the process of reionization and consequently increases the optical depth. When the escape fraction for stars at z=5 reaches 0, the model becomes quasar-dominated, returning a low tau_e of around a half of the [PlanckCollaboration2016] measurement (see Fig. 5). We see that when including the contribution from quasars, the model prefers a combination of an escape fraction for stars at z=5 of approximately 6 per cent and beta of approximately 0.5."}
{"text": "This corresponds to an escape fraction for stars, f_esc,*, of approximately 6.5 per cent at redshift z=6 with a ratio between the emissivities of quasars and stars of approximately 0.12. In addition to the possibility that quasars do not have a very high escape fraction [Barkana2000], we note that the very faintest quasars predicted in the model are not observed. The recent detection by [Giallongo2015] only reaches to UV magnitude M_1450 ~ -18, while our fiducial models predict a significant population of faint quasars down to UV magnitude M_1450 ~ -11. Whether those undetected quasars are able to contribute a significant amount of ionizing photons is still unknown. For instance, they might be buried in the dust with a large obscuration fraction [Hopkins2007]. The critical mass above which quasars can contribute ionizing photons, coupled with the previously discussed escape fraction, represents limiting cases of a mass-dependent escape fraction for quasars."}
{"text": "In the top panel of Fig. 7, we present the cumulative fraction of ionizing photons as a function of black hole mass (or the corresponding UV magnitude M_1450 during the Eddington state as shown in the top axis) assuming an escape fraction for quasars f_esc,q = 1 from the fiducial model using the Tiamat simulation. We see that quasars fainter than UV magnitude M_1450 = -18 contribute approximately 80 per cent of the total emissivity at redshift z~7 with a decreasing contribution towards lower redshifts (10 per cent at redshift z~3, the end of the EoR in the QuasarReion model). This suggests that the number of fainter quasars becomes relatively smaller at later times, which can also be observed from the slope of the predicted quasar luminosity function becoming flatter from redshift z~7-3 (see Fig. 3). However, at redshifts higher than redshift z~6, the total emissivity from quasars is low."}
{"text": "For example, the total emissivity at redshift z~7 is five times lower than redshift z~5, suggesting that faint quasars below current observational limits provide only a small contribution to reionization. In addition, the AGN light curve adopted in this work, which assumes that black holes are either accreting with epsilon=1 or stay quiescent (epsilon=0) depending on the amount of accretion mass, has been shown to underestimate the number density of faint AGN at low redshift [Bonoli2009]. For instance, allowing epsilon to decrease progressively when the accretion disc has been mostly consumed predicts more faint AGN with M_B ~ -16 by a factor of 2 at redshift z~0.1. However, the impact becomes insignificant at brighter ranges and higher redshifts. Due to the small contribution of ionizing photons from faint quasars, AGN light curves are therefore not expected to have a significant impact on our conclusions regarding reionization."}
{"text": "On the other hand, due to the limited simulation volume the brightest quasars at high redshift (redshift z>=4) in our model only reach UV magnitude M_1450 ~ -23, above which the contribution of ionizing photons is not considered. However, the G15 emissivity accounts for bright quasars up to UV magnitude M_1450 = -28, 100 times brighter than the brightest quasar in our model. In order to estimate the emissivity of the missing bright quasars, we integrate the fitting functions provided by [Giallongo2015] with a magnitude interval of -28 < M_1450 < -23. We find that the total emissivity at high redshift increases by less than 1 per cent with the inclusion of the ionizing photons from these quasars. Therefore, the conclusion that quasars do not have a significant role during the EoR is not affected by the volume size. However, with the flattening luminosity function at lower redshifts (redshift z<4), bright quasars become more important and their contribution to reionization is not ignorable."}
{"text": "We note that including these objects will bring forward reionization in the QuasarReion model, but have no impact to the fiducial model. Our choice of black hole seed mass, 1000 per h solar masses lies between the light seed (approximately 10^2 - 10^3 solar masses) from a remnant Pop III star and the massive seed (approximately 10^3 - 10^5 solar masses) from the direct collapse of a gas cloud at early times [Greene2012]. The massive seed mass is frequently used to initialize massive haloes in hydrodynamic simulations [Springel2005, Vogelsberger2014, Schaye2014, Feng2016] while the approximately 10^3 solar masses seeds are also often adopted in semi-analytic models [Somerville2008, Bonoli2009]. We note that this seed mass assumption only affects the black hole mass at early times and in the least massive galaxies. The main conclusions of this work are not significantly affected by this assumption."}
{"text": "For example, with exactly the same adopted parameters but 10 times larger seed mass, the properties such as the black hole mass function, the Magorrian relation and the UV luminosity function are changed by less than 5 per cent in massive galaxies (stellar mass M_* > 10^9 solar masses). On the other hand, the model predicts a significant number of less massive black holes with masses approximately 10^5 solar masses, which is more than approximately 1 order of magnitude larger than the [Shankar2009] sample. However, this has negligible impact on the total instantaneous emissivity and consequently, the reionization history does not change significantly. Fig. 8 presents the evolution of emissivity, neutral hydrogen fraction and optical depth for the fiducial and QuasarReion models with larger black hole seed masses of 10^4 per h solar masses. Compared to the original models, we see that the quasar emissivity increases with a larger seed mass while the stellar emissivity decreases due to the stronger feedback from black holes."}
{"text": "However, the changes are negligible, resulting in a small perturbation to the reionization history and optical depth. We have updated the Meraxes semi-analytic model ([Mutch2016]) with a detailed prescription of black hole evolution as part of the Dark-ages Reionization And Galaxy formation Observables from Numerical Simulations (DRAGONS) project to study the role of AGN in reionization and galaxy formation at high redshift. The model is calibrated against the observed stellar mass function (redshift z~7-0.6), black hole mass function (redshift z less than or approximately equal to 0.5), quasar luminosity function (redshift z~6-0.6), ionizing emissivity (redshift z~5-2) and the Thomson scattering optical depth. The model is in agreement with the observed Magorrian relation at low redshift (redshift z<0.5) and predicts a decreasing black hole mass towards higher redshifts at a fixed stellar mass."}
{"text": "An opening angle of 80 deg, which corresponds to an un-obscured fraction of approximately 23.4 per cent, allows the model to reproduce the observed quasar luminosity function across a large redshift range (redshift z~6-0.6). Our model suggests that the radiation observed from recently discovered faint AGN at high redshift [Giallongo2015] may include a significant fraction of UV flux from stars. Previous direct estimates of quasar contributions to reionization based on these observations [Madau2015, Mitra2015] therefore result in an overestimate of the emissivity of quasars by a factor of 3 at redshift z~6. When we include the contribution of AGN to reionization, we find that quasars do not dominate the ionizing photon budget at redshift z>6. In a quasar-only reionization model, where the escape fractions of ionizing photons are 1 and 0 for quasars and stars, respectively, we find that reionization happens very late, redshift z~3, with a Thomson scattering optical depth of only half of the [PlanckCollaboration2016] measurement ([PlanckCollaboration2016])."}
{"text": "However, at low redshift, quasars are able to provide a large number of ionizing photons. With quasars contributing all of their ionizing photons (the escape fraction for quasars f_esc,q = 1), our model prefers a redshift-dependent escape fraction for stars, having the form of the escape fraction for stars as a function of redshift, f_esc,*(z), equals the minimum of [0.06 times ((1+z)/6)^0.5, 1]. This corresponds to quasars contributing 10 per cent of the total ionizing photons at redshift z~6. During one time step, for a black hole with a given initial mass of M_BH, its bolometric luminosity at Eddington rate can be calculated through the right hand of equation (17). Since the bolometric correction [Hopkins2007] adopted in this work is dependent on the bolometric luminosity, the UV magnitude, M_1450 of the quasar changes during its accretion, so does the emissivity."}
{"text": "In our model, because the accretion mass is always smaller than the black hole mass (Delta M_BH < M_BH, see Fig. A1), for the sake of calculation speed, we estimate the mean number of ionizing photons produced per black hole, N_gamma,q with the bolometric luminosity at the beginning of accretion. We calculate N_gamma,q as follows: 1. We calculate the UV magnitude, M_1450 using equations (19)-(22). 2. We calculate the UV flux with M_1450 in units of erg per second per Hz... 3. We calculate the flux at Lyman limit following [Giallongo2015]... 4. We calculate the instantaneous emissivity by the rate of ionizing photons dot N_ion is defined as the integral from nu_912 to infinity of F_912 * (nu/nu_912)^-alpha_q * dnu/(h*nu), which equals F_912 / (h*alpha_q). 5. The duration of accreting mass, Delta M_BH can be calculated... Therefore, the total number of ionizing photons emitted is the rate of ionizing photons dot N_ion times t_acc and the mean number of ionizing photons produced per black hole is N_gamma,q which is approximately equal to (dot N_ion at t=t_acc/2 * t_acc) / ((1-eta) * Delta M_BH / m_p)."}
{"text": "We note that during the accretion, with an exponential increase of black hole mass, the AGN bolometric luminosity, L_bol increases exponentially. Since the B-band bolometric correction, k_B, decreases with increasing luminosity following a double power law, the rate of ionizing photons dot N_ion is a convex function of time. Therefore, the approximation in the equation for N_gamma,q underestimates the number of ionizing photons produced by black hole. In order to test whether this has a significant impact on our conclusion, we rerun the QuasarReion model assuming a constant bolometric correction with k_B(t) approximately equal to k_B at t=t_acc. Eliminating the complex dependence of time from k_B, N_gamma,q can be analytically calculated by integrating the AGN light curve. However, we note that since k_B(t) <= k_B at t=t_acc, this approximation overestimates N_gamma,q. Fig. A2 presents the evolution of emissivity, neutral hydrogen fraction and optical depth for different QuasarReion models assuming constant dot N_ion (QuasarReion) and k_B (QuasarReion_kB), respectively."}
{"text": "Since the time interval between two snapshots is much smaller than the Eddington accretion time-scale (t_Edd ~ 450 Myr), the black hole mass increment is still within the linear regime and therefore we see that the impact from the calculation of N_gamma,q is not significant."}
{"text": "Correlations between black holes and their host galaxies provide insight into what drives black hole--host co-evolution. We use the Meraxes semi-analytic model to investigate the growth of black holes and their host galaxies from high redshift to the present day. Our modelling finds no significant evolution in the black hole--bulge and black hole--total stellar mass relations out to a redshift of 8. The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. In our modelling the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. We find that black hole growth is dominated by instability-driven or secular quasar-mode growth and not by merger-driven growth at all redshifts. Our model also predicts that disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation, in agreement with recent observations and hydrodynamical simulations."}
{"text": "Extensive low-redshift studies reveal a complex interplay between galaxies and the supermassive black holes that reside at their centres, with clear correlations observed between black hole mass and host bulge mass, total stellar mass, velocity dispersion and luminosity [Magorrian1998, Gebhardt2000, Merritt2001, Tremaine2002, Marconi2003, Haring2004, Bentz2009, Kormendy2013, Reines2015]; see the review by [Heckman2014]. These tight correlations suggest a co-evolution between galaxies and supermassive black holes, which may be causal, due to feedback from the active galactic nucleus [AGN; e.g.][Silk1998, Matteo2005, Bower2006, Ciotti2010] or the efficiency with which the galaxy can fuel the black hole [e.g.][Hopkins2010, Cen2015, AnglesAlcazar2017], or coincidental, simply due to mergers causing both black hole and galaxy growth [e.g.][Haehnelt2000, Croton2006b, Peng2007, Gaskell2011, Jahnke2011]. To understand what drives black hole--host co-evolution, it is necessary to study how these correlations change with redshift."}
{"text": "Observing high-redshift black hole--host correlations is fraught with difficulties. Host galaxies are hard to detect since they are often completely outshined by the AGN light, particularly in the rest-frame optical where common stellar mass estimators can be used [e.g.][Zibetti2009, Taylor2011]. Subtracting the quasar light has resulted in host detections out to redshift z is approximately equal to 2 [Jahnke2009, Mechtley2016], but is yet to be successful for detecting the highest redshift quasars at redshift z is approximately equal to 6 [Mechtley2012]. For these quasars, host masses are often estimated using the widths of observed submillimeter and millimeter emission lines, such as the [CII] 158 micron and CO (6--5) lines [e.g.][Wang2013]. However, dynamical masses determined from emission line widths are highly dependent on the assumptions made, such as the gas-disc geometries and inclination angles [e.g.][Valiante2014]. In fact, inclination angle assumptions can change the determined black hole mass to bulge mass ratio measurements by roughly 3 orders of magnitude [Wang2013]."}
{"text": "In addition, the emission regions may not trace the spatial distribution of the stellar component of the galaxy, meaning that these dynamical masses may not be representative of the total stellar mass [Narayanan2009]. Determining the black hole masses of high-z quasars is also difficult, with emission-line based estimators relying on calibrations at low redshift. Where these observations are unavailable, Eddington accretion rates are instead often assumed to estimate the black hole mass [as in e.g.][Wang2013, Willott2017], which also leads to large uncertainties. High-redshift studies of the black hole--host mass relations are thus very uncertain. With this in mind, high redshift observations find black holes that are more massive than expected by the local relation, where the canonical black hole--bulge mass ratio is 10 to the power of (-2.31 +/- 0.05) for a bulge mass of 10^11 solar masses [Kormendy2013]."}
{"text": "For example, ALMA observations of five redshift z is approximately equal to 6 quasar hosts show black hole to dynamical mass ratios ranging from 10 to the power of -1.9 to 10 to the power of -1.5 [Wang2013]. Similar studies at redshift z is approximately equal to 4--7 [e.g.][Maiolino2007, Riechers2008, Venemans2012] also give estimates for individual quasars of a black hole mass to dynamical mass ratio greater than or approximately equal to 10 to the power of -2, which is significantly larger than the local value if dynamical masses and bulge masses are assumed to be roughly equivalent. This suggests a faster evolution of the first supermassive black holes relative to their host galaxies [Valiante2014], which could potentially be a result of super-Eddington accretion [Volonteri2015]. The high observed black hole mass to dynamical mass ratio relation at high redshift could, however, be a result of selection effects [Lauer2007, Schulze2011, Schulze2014, DeGraf2015, Willott2017]."}
{"text": "[Willott2017] suggest that since only the most massive z>6 black holes are observed, if the relation has a wide dispersion then one would expect to see a higher value due to the Lauer bias [Lauer2007]: since the luminosity function falls off rapidly at high masses, the most massive black holes occur more often as outliers in galaxies of smaller masses than as typical black holes in the most massive galaxies. Indeed, [Willott2017] found that black holes with mass less than 10^9 solar masses at redshift z>6 fall below the black hole mass--dynamical mass relation for low redshift galaxies, in contrast to the opposite being true for higher mass black holes. Similarly, [Schulze2014] claim that selection effects are the reason for the observed evolution of the black hole mass--bulge mass relation; on applying a fitting method to correct for selection effects, they find no statistical evidence for a cosmological evolution in the black hole mass--bulge mass relation."}
{"text": "A lack of evolution in the black hole--host relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016], which observes very little evolution in the black hole mass--stellar mass relation from redshift z=0 to 5, and BlueTides [Huang2018], which finds a black hole mass--stellar mass relation at redshift z=8 that is consistent with the local [Kormendy2013] relation. [DeGraf2015], on the other hand, found that the relation evolves slightly for redshift z greater than or equal to 1 for the highest mass black holes, with a steeper slope at the high-mass end at higher redshifts, making selection effects important. The more statistical study of [Schindler2016] found that the ratio of the black hole to stellar mass density is constant within the uncertainties from redshift z=0 to 5, with a slight decrease in the ratio at redshifts between 3 and 5; this is also consistent with no cosmological evolution in the black hole mass--stellar mass relation."}
{"text": "In this work we explore the evolution of the black hole--host relations with the Meraxes semi-analytic model [Mutch2016]. Meraxes is designed specifically to study galaxy formation and evolution at high redshifts, making it ideal for studying the evolution of black holes and their host galaxies. In this work we use Meraxes, a semi-analytic model designed to study galaxy evolution at high redshifts [Mutch2016]. Using the properties of dark matter halos from an N-body simulation, Meraxes analytically models the physics involved in galaxy formation and evolution. We run Meraxes on the collisionless N-body simulations Tiamat and Tiamat-125-HR [Poole2016, Poole2017]. Tiamat is ideal for studying high redshifts, with a high mass and temporal resolution. Tiamat runs from redshift z=35 to z=1.8, with a box size of (67.8 per h Mpc)^3, 2160^3 particles of mass 2.64x10^6 per h solar masses, and a high cadence of 11.1 Myr per output snapshot at redshift z>5."}
{"text": "Tiamat-125-HR is a low-redshift counterpart to Tiamat, running from redshift z=35 to z=0 with the same temporal resolution, but with a lower mass resolution (1080^3 particles of mass 1.33x10^8 per h solar masses) and larger box size of (125 per h Mpc)^3, more suited for low-redshift studies. Throughout this work, we use the higher resolution Tiamat at high-redshifts, and Tiamat-125-HR for redshift z<2, unless otherwise specified. Meraxes assumes that galaxies reside in the centre of dark matter haloes produced by the N-body simulation. Using the properties of these haloes, Meraxes analytically models the baryonic physics involved in galaxy formation and evolution, such as gas cooling, star formation, black hole growth, and supernova and black hole feedback. These analytical prescriptions involve a range of free parameters, which must be calibrated using observations such as the stellar mass function."}
{"text": "In Meraxes, stars in galaxies reside in three components: an exponential disc, a spheroidal merger-driven bulge and a disc-like instability-driven bulge. Bulges grow through both galaxy-galaxy mergers and disc-instabilities. In Meraxes, we assume that galaxy mergers with merger ratio greater than 0.01 trigger a burst of star formation, by causing shocks and turbulence in the cold gas of the parent galaxy. The galaxy will also accumulate the mass of the secondary galaxy. We assume that the dominant mass component of the primary galaxy will regulate where these stars produced by the burst and the secondary's mass will be deposited. If the primary is dominated by a discy component, the mass is added to the instability-driven bulge. Otherwise, we assume that the new stars will accumulate in shells around the spheroidal merger-driven bulge. In major mergers, where the merger ratio is greater than 0.1 or 0.3, we assume that the stellar disc and instability-driven bulges are destroyed, with all stars placed into the merger-driven bulge."}
{"text": "In our model we assume that the galaxy discs are thin, with an exponential surface density and flat rotation curve. Such discs become unstable if the disc mass is greater than the disc velocity squared times the scale radius divided by the gravitational constant, which equals the critical mass [Efstathiou1982, Mo1998]. Here, we take the disc mass as the combined mass of both gas and stars in the disc, and the disc velocity and scale radius as the mass-weighted velocity and scale radius of the stellar and gas discs. If such a disc instability occurs, Meraxes returns the disc to stability by transferring the unstable mass of stars from the disc to the instability-driven bulge. The Meraxes black hole model was introduced in Q17, and updated to include instability-driven growth in M19. In Meraxes, black holes are seeded in every newly-formed galaxy, with a seed mass of 10^4 solar masses. Black holes then grow by accretion of both hot and cold gas, through the radio- and quasar modes, respectively."}
{"text": "We also assume that black holes grow in galaxy mergers, with the black holes in each galaxy merging together. Black holes accrete hot gas from the static hot gas reservoir around the galaxy, at a fraction of the Bondi-Hoyle accretion rate. We consider this fraction a free parameter, which adjusts the efficiency of radio-mode black hole growth [Croton2016]. This accretion is limited by the amount of hot gas in the reservoir and the Eddington limit. A fraction of this accretion mass is radiated away and so during one snapshot, black holes grow through the radio-mode by the remaining mass. We include the effects of radio-mode AGN feedback by assuming that a fraction of the radiated energy is coupled to the surrounding gas, adiabatically heating a mass which is subtracted from the cooling flow, regulating the accretion of new gas onto the black hole [Croton2006a, Croton2016]. This AGN feedback has no significant effect on the results of Tiamat at redshift z greater than or equal to 2."}
{"text": "Black holes accrete cold gas from the galaxy, when triggered by either a galaxy-galaxy merger or a disc instability. During such an event, the black hole mass grows by a certain amount, where the virial velocity and a free parameter adjust the growth efficiency. For merger-triggered growth, we take the efficiency parameter to be proportional to the merger ratio. For instability driven growth, we consider two separate free parameters. During the quasar mode, black holes are assumed to accrete at the Eddington rate, and thus the mass accreted by the black hole during one simulation snapshot is limited. This can result in the mass being accreted over multiple simulation snapshots. We incorporate quasar-mode AGN feedback by considering the energy injected into the gas during a simulation time-step. We assume that this energy generates a wind that heats the cold disc gas and transfers it to the hot gas reservoir, depleting the supply of cold gas available for the black hole to accrete. If sufficient energy is injected by the quasar, this wind can also eject the hot gas."}
{"text": "We calculate the bolometric luminosities of each black hole in the model following the Q17 method, which assumes Eddington luminosity for all accreting black holes, and self-consistently calculates the duty cycle. We consider the luminosities from both the quasar- and radio-modes of accretion. At high-redshifts the contribution from the radio-mode is negligible. At the lowest redshifts (redshift z less than or equal to 2), the radio-mode becomes a more significant growth mechanism for the most massive black holes, and so their luminosities are enhanced slightly by the addition of the radio-mode luminosity. We convert from bolometric to B-band luminosities using the [Hopkins2007] bolometric correction, and then assume a continuum slope of 0.44 to convert to UV luminosities. We also account for obscuration due to quasar orientation, by scaling the UV luminosity function by a factor related to the opening angle of quasar radiation. In our model we assume a constant opening angle, for simplicity, which is a free parameter in our model."}
{"text": "In M19 we calibrated the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8, and the black hole--bulge mass relation at redshift z=0. Using this model, we find that the black hole mass function and quasar luminosity functions are much larger than predicted by the observations. In addition, we note that [Shankar2016] find significant selection biases in the black hole--bulge mass relation---a topic of recent debate [see e.g.][Kormendy2019]. Due to the M19 predictions and this potential bias, we assume that the [Shankar2009] redshift z=0 black hole mass function is a less biased indicator of the local black hole population, and retune the model here to better reproduce the black hole observations. Note that we use the same parameter values for Tiamat and Tiamat-125-HR, and use both simulations to tune the model: Tiamat for matching redshift z greater than or equal to 2 observations and Tiamat-125-HR for redshift z<2."}
{"text": "We find that our results from the two simulations are generally consistent at redshift z is approximately equal to 2, with broad qualitative agreement at higher redshifts. We calibrate the free parameters in the model to match the observed stellar mass functions at redshift z=0--8, the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0, and the quasar X-ray luminosity functions from redshift z=5 to 2. Since [Shankar2016] find that the observed black hole--bulge mass relation is biased to high black hole masses, we also require our model to not over-predict this relation, however we do not otherwise tune to it. We note that our best models produce black hole--host mass relations lower than the observations, consistent with the expectations of [Shankar2009], and have steeper slopes. We find that these criteria are met by a range of free parameter values for the merger-driven black hole growth efficiency, and the definition of a major merger."}
{"text": "We note that all of these parameter sets produce very similar results. As a further check of the black hole population, we plot the black hole accretion rate density as a function of redshift for models with these different merger-driven black hole growth efficiencies. We find that the models with lower efficiencies give black hole accretion histories in approximate agreement with the observations. The larger efficiencies overproduce measurements of the black hole accretion rate density [e.g.][Delvecchio2014]. The opening angle of AGN radiation, theta, adjusts the normalization of the UV luminosity function. We tune this to match the observations, finding a preferred theta of 70 degrees, corresponding to an observable fraction of UV quasars of 18 per cent. We show the quasar X-ray luminosity functions at redshift z=5--0, with X-ray luminosities calculated using the [Hopkins2007] bolometric to X-ray correction."}
{"text": "At redshift z=2 the model and the observations agree remarkably well. At redshift z>2 the model over-predicts the observed quasar X-ray luminosity function at intermediate luminosities, by up to ~0.7 dex at redshift z=4, while at redshift z<2 the model under-predicts the luminosity function at these luminosities. Our model shows better agreement with the observations than previous versions of Meraxes. While the observations show a slight increase in the X-ray quasar luminosity functions from redshift z=4 to 2, the model predicts a slight decrease. In fact, we cannot find a combination of black hole parameters that results in a redshift evolution that matches that of the observed X-ray quasar luminosity function at redshift z>2. However, the key quantity of black hole accretion rate density is predicted by the model to peak at redshift z=2 as observed."}
{"text": "In addition to published uncertainties in the observations, it may also be the case that at higher redshifts X-ray AGN are more likely to be obscured, which is consistent with evidence from a range of X-ray observations [Treister2006, Vito2014, Buchner2015]. Thus we argue that the inability of our model to match the redshift evolution of the X-ray quasar luminosity function may not represent a significant concern. We show the quasar UV luminosity functions at redshift z=5--0. We find that, as with the X-ray luminosity function, the UV luminosity function decreases from redshift z=5 to 0, though it agrees well with observations at redshift z>2. At redshift z<2, however, we note that the faint-end of the UV luminosity function becomes flat, and by redshift z<1 there is a significant disagreement with the observations, with the model producing too many luminous quasars."}
{"text": "As seen in analysis, the black hole accretion rate density becomes significantly higher than the observations at redshift z<1, consistent with the quasar luminosities being overestimated at these redshifts. This excess black hole accretion is most likely a result of the model missing important physics required for modelling low-redshift galaxy evolution, particularly in the quenching of massive galaxies, or due to the simplifications assumed in the model such as a constant black hole accretion efficiency. However, as the overall accretion rate density at these redshifts is low, this will not have a significant impact on the black hole mass, an integrated quantity. Thus, while the redshift z<1 black hole accretion rates are overestimated, the black hole mass function and black hole--host mass relations are reliable at low redshifts. Indeed, we find that assuming a lower Eddington ratio significantly improves the match between the model and observed UV luminosity functions at redshift z<1."}
{"text": "However, this causes the model to no longer match the observations at higher redshifts. Thus, some evolving Eddington ratio is necessary for Meraxes to accurately reproduce the redshift z<1 quasar UV luminosity function. We now use the model described in Sections 2 and 3 to explore black hole growth. We investigate the redshift evolution of the black hole--host scaling relations. To investigate the redshift evolution of the black hole--bulge and black hole--total stellar mass relations we first perform linear least squares fits to the relations at a range of redshifts. We only include galaxies with mass > 10^9.5 solar masses in our fits, so that they are not biased by the large number of low-mass galaxies. Both relations have a slope and normalization that increase with redshift from redshift z=0 to 2, with much weaker evolution for redshift z>2. Relative to the scatter in the relations, we see minimal evolution in both the black hole--bulge and black hole--total stellar mass relations from redshift z=0 to 6."}
{"text": "This lack of evolution in the black hole--host mass relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016] and BlueTides [Huang2018]. We find that our black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. While the black hole mass has a slightly stronger relationship with the bulge stellar mass, the black hole and total stellar mass are still tightly correlated. The scatter in the relations is slightly larger than the 0.28 dex observed by [Kormendy2013] locally. However, they are very consistent with those from the BlueTides simulation at high redshift. The scatter decreases with increasing stellar mass. The median black hole mass to total stellar mass ratio as a function of redshift for galaxies with black hole mass > 10^6 solar masses shows no statistically-significant evolution out to redshift z is approximately equal to 8."}
{"text": "This is consistent with current high redshift observations; when selection effects are accounted for, the observations at high redshift are consistent with no cosmological evolution in these relations [Schulze2014]. Our model predicts no significant evolution in the black hole--host mass relations, with the scatter in the relations decreasing at the highest redshifts. This indicates that there is a connection between the growth of black holes and their host galaxies. Indeed, our model includes joint triggering of star formation and black hole growth during galaxy mergers, and black hole feedback which regulates star formation, meaning that the co-evolution of black holes and galaxies is implicit in our model. This is not consistent with the scenario proposed by [Peng2007] and [Jahnke2011], for example, where the black hole and galaxy growth is uncorrelated and the relationships are generated naturally within a merger driven galaxy evolution framework, due to a central-limit-like tendency."}
{"text": "The median black hole mass to total stellar mass ratio as a function of redshift with galaxies split into black hole mass bins shows that lower mass black holes have lower ratios than higher mass black holes. This will lead to a notable selection bias, since when observing the most massive black holes, the measured ratio will be higher than that of the entire population. This is generally expected for any sample selected by black hole mass or luminosity where the scatter in the relation is large [e.g.][Lauer2007]. Finally, we note an interesting effect of changing the parameter controlling the black hole efficiency for converting mass to energy. For a higher efficiency, the median black hole--stellar mass ratio decreases at redshifts z greater than or approximately equal to 6, instead of remaining constant with redshift. We investigate the cause of this high-redshift decrease in the black hole--host relation by considering the Eddington limit. Increasing the efficiency from 0.06 to 0.2 decreases the Eddington limit."}
{"text": "This results in many black holes having Eddington-limited growth at the highest redshifts (redshift z greater than or approximately equal to 6), which is not the case for the lower efficiency model. This causes black holes to grow slower than their host galaxies at high redshifts, resulting in a decreased black hole--stellar mass ratio. Observing the high-redshift black hole--stellar mass relation may therefore probe the Eddington limit and the efficiency of black holes in converting mass to energy. We consider the cumulative fraction of black hole mass formed through each of the mechanisms in our model: black hole seeding, merger-driven quasar-mode accretion, instability-driven quasar-mode accretion, radio-mode accretion and black hole--black hole coalescence in galaxy mergers. The merger-driven growth mode becomes more important at low redshifts, at both low- and high-black hole masses. On average, instabilities grow the majority of mass in black holes at all redshifts, except for galaxies with black hole mass > 10^9 solar masses at redshift z is approximately equal to 0, whose black hole growth becomes dominated by galaxy mergers."}
{"text": "Radio-mode growth slowly increases in significance with redshift, yet still has only contributed to a small proportion of the total black hole mass by redshift z=0, except at the highest masses. Note that we consider growth from disc instabilities that are triggered by earlier galaxy mergers as growth via the instability-driven mode. We also consider the instantaneous growth fractions of black hole mass formed through each mechanism as a function of redshift. As discussed, the model produces unreliable black hole accretion rates at redshift z<1, and so we only consider these black hole growth rates at redshift z>1. The instability-driven growth mode is the dominant growth mechanism, on average, at all redshifts, regardless of black hole mass. The merger-driven quasar mode and black hole--black hole coalescence mode are sub-dominant at all redshifts. The radio-mode grows more mass at low redshift and in the most massive galaxies, with the percentage of total instantaneous black hole growth from this mode increasing from only 0.1 per cent at redshift z=5 to almost 5 per cent at redshift z is approximately equal to 1."}
{"text": "Our finding that mergers are not the dominant mechanism for growing black holes is in agreement with a range of observations. For example, [Koss2010] find that only 25 per cent of local, moderate luminosity X-ray AGN show signs of mergers, though the fraction is much higher for luminous AGN [Hong2015]. From redshift z from approximately 0.3 to 1.0, [Cisternas2010] find that the vast majority (>85 per cent) of X-ray selected AGN do not show signs of mergers, suggesting that the bulk of their black hole accretion has been triggered by some other mechanism. This is also consistent with the findings of [Georgakakis2009], [Villforth2018], [Schawinski2012], [Mechtley2016], [DelMoro2015] and [Marian2019] for AGN at various redshifts. Our result that disc instabilities cause the majority of black hole growth is also consistent with predictions from other simulations."}
{"text": "In the GALFORM semi-analytic model, [Fanidakis2011] found that the growth of black holes is dominated by accretion due to disc instabilities, with the fraction of mass in black holes produced by disc instabilities more than an order of magnitude larger than that produced by mergers, at all redshifts. Using an updated GALFORM model, [Griffin2019] found that accretion of hot gas dominates the growth of black holes at redshift z<2, with disc-instabilities dominant at higher redshifts. [Hirschmann2012] found that instability-driven black hole growth was required to reproduce AGN downsizing, and that while major mergers are the dominant trigger for luminous AGN, especially at high redshift, disc instabilities cause the majority of black hole growth in moderately luminous Seyfert galaxies at low redshift. [Menci2014] find that in their semi-analytic model disc instabilities can provide enough black hole accretion to reproduce the observed AGN luminosity functions up to redshift z is approximately equal to 4.5, but are not likely to be dominant for the highest luminosity AGN or at the highest redshifts."}
{"text": "In contrast, [Shirakata2018] find that the primary trigger of AGN at redshift z less than or equal to 4 in their semi-analytic model is mergers, while disc instabilities are essential for fuelling moderate luminosity AGN at higher redshifts. The hydrodynamical simulation Horizon-AGN found that only ~35 per cent of black hole mass in local massive galaxies is directly attributable to merging, with the majority of black hole growth instead growing via secular processes [Martin2018]. The Magneticum Pathfinder Simulation also found that merger events are not the dominant fuelling mechanism for black holes in redshift z=0--2, with merger fractions less than 20 per cent, except for very luminous quasars at redshift z is approximately equal to 2 [Steinborn2018]. Finally, we comment on the effect of the efficiency parameters for merger-driven and instability-driven black hole growth in the model. We find the instability-driven efficiency from tuning the model, whereas the merger-driven efficiency is less constrained, with several values producing reasonable model results."}
{"text": "Having a merger growth efficiency that is twice, six times or even 18 times larger than the instability-driven growth efficiency may have an effect on the conclusions outlined above. We find, as expected, that models with larger merger efficiencies result in more merger-driven growth. For a merger efficiency twice the instability efficiency, the instability-driven mode still dominates at redshift z=2, while for a six times larger efficiency, the merger-driven mode begins to dominate at the highest black hole masses. For the model with an 18 times larger merger efficiency, the merger-driven mode contributes even more black hole growth, but is still not the dominant growth mode for black holes with mass between 10^6 and 10^9 solar masses. Thus, while the efficiency parameter for merger-driven growth has some effect on the relative distributions of the instability-driven and merger-driven growth modes, the instability-driven mode is still dominant for the majority of black holes, even if the merger growth efficiency is as much as 18 times larger than the secular growth efficiency."}
{"text": "A popular explanation for the black hole--host correlations is that major mergers drive the growth of both black holes and bulges [e.g.][Haehnelt2000, Croton2006b]. If this were the case, one would expect that black holes would only correlate with galaxy properties directly related to the merger process, such as bulge mass, and not, for example, total stellar mass. [Simmons2017] consider a sample of 101 disc-dominated AGN hosts from the SDSS, which they assume must have a major merger-free history since redshift z is approximately equal to 2. They found that these galaxies lie on the typical black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation. This indicates that the substantial and ongoing black hole growth in these merger-free disc galaxies must be due to a process other than major mergers, and that major mergers cannot be the primary mechanism behind the black hole--host correlations."}
{"text": "We plot the black hole mass--total stellar mass and black hole mass--bulge mass relation for disc-dominated and bulge-dominated galaxies at redshift z=0. Our simulated disc galaxies lie on the black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation, as they have small bulges relative to their black hole mass. This is consistent with the [Simmons2017] observations, and the results from the Horizon-AGN hydrodynamical simulation [Martin2018]. However, we see a less significant offset, which occurs at lower black hole masses than [Simmons2017] and [Martin2018], since the black holes in our disc-dominated galaxies are less massive in comparison. [Mutlu-Pakdil2017] also find no dependence of the black hole mass--total stellar mass relation on galaxy type in the Illustris hydrodynamical simulation. [Martin2018] suggest that major mergers therefore cannot be primarily responsible for feeding black holes, otherwise major-merger free disc galaxies should have less massive black holes than are observed and simulated."}
{"text": "This is consistent with our finding that the instability-driven mode is the dominant growth mechanism for black holes. We use the Meraxes semi-analytic model to investigate the evolution of black holes and their relations to their host galaxies. We find the following key predictions of our model: There is minimal statistically-significant evolution in the black hole--bulge and black hole--total stellar mass relations out to high redshifts (redshift z is approximately equal to 8). The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. This indicates that the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. Higher mass black holes have higher black hole--total stellar mass ratios, leading to a significant selection effect in measurements of this ratio when observing only the most massive black holes."}
{"text": "The instability-driven or secular quasar-mode growth is the dominant growth mechanism for black holes at all redshifts. The contribution from merger-driven quasar-mode growth only becomes significant at low redshift for black holes with mass greater than or approximately equal to 10^9 solar masses. Disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation. Our simulation is limited in making predictions for the highest redshift quasars at redshift z=6--7 due to the simulation box size and resolution. In future work we will run Meraxes on larger N-body simulations in order to make predictions for these objects. We calibrate the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8 and the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0. The black hole mass functions produced by Tiamat and Tiamat-125-HR are converged at redshift z=2 for black holes with mass > 10^7.1 solar masses [see Marshall2019], with Tiamat-125-HR producing more low-mass black holes."}
{"text": "We therefore focus on matching the observed black hole mass functions at masses > 10^7.1 solar masses. While the [Shankar2009] and [Davis2014] relations are different, particularly at black hole mass ~ 10^8.5 solar masses, they are similar relative to the freedom we have in adjusting our model black hole mass function, and so when calibrating we found the most reasonable fit to both. In the model stellar mass function, we also plot the Meraxes stellar mass function produced when AGN feedback is switched off. This shows that AGN feedback has no effect on galaxies in Tiamat at redshift z greater than or equal to 2, but suppresses the growth of the most massive galaxies at lower redshifts as seen in Tiamat-125-HR. Throughout this work, we use the higher resolution Tiamat simulation at redshift z greater than or equal to 2, and Tiamat-125-HR for redshift z<2, where Tiamat is unavailable."}
{"text": "We find that the results discussed in this paper are generally consistent between the two simulations at redshift z is approximately equal to 2. However, one notable result is that the best-fitting black hole--stellar mass relations change rapidly between redshift z=2 (using Tiamat) and z=1 (using Tiamat-125-HR). To verify that this jump is not purely a result of the simulation change, we show the best-fitting relations from redshift z=6--0 using Tiamat-125-HR. The Tiamat-125-HR simulation shows similar results to those found using Tiamat at redshift z greater than or equal to 2, with a slightly milder but still relatively rapid evolution from redshift z=2 to z=1. The qualitative result of the evolution being insignificant relative to the scatter in the relation still holds. Thus, while the change in simulation slightly amplifies the rapid change in the black hole--stellar mass relations from redshift z=2 to z=1, this does not change our conclusions."}
{"text": "We also note that where the black hole mass functions are converged, the black hole--stellar mass relations are in good agreement between the two simulations."}
{"text": "Massive quiescent galaxies (MQGs) are thought to have formed stars rapidly at early times followed by a long period of quiescence. The recent discovery of a MQG, ZF-COSMOS-20115 at a redshift of approximately 4, only 1.5 Gyr after the big bang, places new constraints on galaxy growth and the role of feedback in early star formation[cite: 3]. Spectroscopic follow-up confirmed ZF-COSMOS-20115 as a MQG at a redshift of 3.717 with an estimated stellar mass of approximately 10 to the power of 11 solar masses, showing no evidence of recent star formation[cite: 4]. We use the Meraxes semi-analytic model to investigate how ZF-COSMOS-20115 analogues build stellar mass, and why they become quiescent[cite: 5]. We identify three analogue galaxies with similar properties to ZF-COSMOS-20115[cite: 6]. We find that ZF-COSMOS-20115 is likely hosted by a massive halo with virial mass of approximately 10 to the power of 13 solar masses, having been through significant mergers at early times[cite: 7]. These merger events drove intense growth of the nucleus, which later prevented cooling and quenched star formation[cite: 8]. Therefore, ZF-COSMOS-20115 is unlikely to have experienced strong or extended star formation events at a redshift less than 3.7[cite: 9]. We find that the analogues host the most massive black holes in our simulation and were luminous quasars at a redshift of approximately 5, indicating that ZF-COSMOS-20115 and other MQGs may be the descendants of high-redshift quasars[cite: 10]. In addition, the model suggests that ZF-COSMOS-20115 formed in a region of intergalactic medium that was reionized early[cite: 11]."}
{"text": "Massive quiescent galaxies (MQGs) are galaxies with stellar masses of the order of 10 to the power of 11 solar masses, and low or null star formation rate (SFR). It is thought that these objects formed rapidly at early times, followed by a long state of quiescence [Ilbert2013]. Due to the absence of recent star-forming events in MQGs, they are observationally challenging to study, especially at high redshift[cite: 13]. Using the ultra deep imaging from the FourStar Galaxy Evolution Survey (ZFOURGE), [Straatman2014] identified 15 MQGs at a redshift of 3.4-4.2 with an estimated number density of MQGs (hereafter the S14 sample) of (1.8 plus or minus 0.7) times 10 to the power of -5 per cubic Megaparsec[cite: 14]. Despite the large uncertainties, this number density is significantly higher than the value expected from extrapolations using observations at lower redshifts [Bell2003, Muzzin2013], leading to an unexpectedly high MQG fraction of 34 plus or minus 13 per cent at a redshift of approximately 4[cite: 15]. Recently, spectroscopic follow-up [Glazebrook2017] was performed on the brightest MQG in the S14 sample, ZF-COSMOS-20115[cite: 16]. Their analysis revealed that ZF-COSMOS-20115 has a stellar mass of M_*=1.7 with uncertainty +0.12/-0.24 times 10 to the power of 11 solar masses (see a more recent study of [Simpson2017]), and redshift of 3.717 plus or minus 0.001, but no detectable ongoing star formation based on Balmer absorption lines (i.e. H-beta, H-gamma and H-delta), implying a current SFR less than 0.2 solar masses per year[cite: 17]."}
{"text": "Furthermore, modelling the spectral evolution of the stellar population [1999astro.ph.12179F] suggests rapid growth of stellar mass with a SFR greater than 990 solar masses per year at the peak of activity and a formation time-scale less than 250 Myr[cite: 18]. In this paper we use the Meraxes semi-analytic model [Mutch2016a] within the Dark-ages Reionization And Galaxy formation Observables from Numerical Simulations (DRAGONS) programme to investigate the galaxy formation history of MQGs at high redshift[cite: 19]. We note that cosmological simulations have had difficulty producing MQGs at high redshift [Lee2013, Wellons2015, Dave2016, Behroozi2016][cite: 20]. However, we identify three galaxies with properties similar to ZF-COSMOS-20115[cite: 21]. This paper is organized as follows. We begin with a brief overview of the DRAGONS framework in Section 2 and present the modelled galaxy property in Section 3[cite: 22]. We show the ZF-COSMOS-20115 analogues in our model in Section 4 and discuss the history and future of ZF-COSMOS-20115 in Sections 5 and 6[cite: 23]. Conclusions are given in Section 7[cite: 24]. In this work, we adopt cosmological parameters from the Planck 2015 results (Omega_m, Omega_b, Omega_Lambda, h, sigma_8, n_s = 0.308, 0.0484, 0.692, 0.678, 0.815, 0.968; [PlanckCollaboration2015])[cite: 24]."}
{"text": "The Meraxes semi-analytic model [Mutch2016a] was specifically designed to study galaxy formation at high redshift and the epoch of reionization (EoR)[cite: 25]. In this work, we use the updated version of Meraxes [Qin2017], which includes a detailed prescription of black hole growth and AGN feedback[cite: 26]. Our fiducial model was run on the Tiamat-125-HR dark matter halo merger trees[cite: 27]. We briefly review the model here and refer the interested reader to the aforementioned references for details[cite: 28]. The underlying Tiamat-125-HR dark matter halo merger trees provide 100 snapshots between a redshift of 35 and 5 with a time interval of approximately 11.1 Myr and 114 additional snapshots between a redshift of 5 and 0.56 separated equally in units of Hubble time (Poole et al. in preparation)[cite: 29]. The particle mass resolution of Tiamat-125-HR is approximately 1.2 times 10 to the power of 8 per h solar masses and the box size is 125 per h Mpc[cite: 30]. In order to show convergence, Meraxes was also run using the Tiamat halo merger trees [Poole2015], which were constructed from an N-body simulation sharing identical cosmology with Tiamat-125-HR but at a higher mass resolution (2.6 times 10 to the power of 6 per h solar masses) and smaller volume (67.8 per h Mpc)[cite: 31]. These results are presented in Section 5 for comparison[cite: 32]."}
{"text": "The Meraxes semi-analytic model consists of a number of important astrophysical processes, including gas infall, cooling, star formation, supernova feedback, AGN feedback, metal enrichment, mergers and reionization [Mutch2016a, Qin2017]. The model was calibrated against the observed stellar mass function at a redshift of approximately 7-0.56 (see the galaxy stellar mass function at a redshift of 2-4 in the top panels of Fig. 1), black hole mass function at a redshift less than or approximately equal to 0.5, ionizing emissivity at a redshift of approximately 5-2 and the Thomson scattering optical depth[cite: 33]. The model is in agreement with the observed Magorrian relation at a redshift less than 0.56 as well as the observed quasar luminosity function across a large redshift range (a redshift of approximately 6-0.56) when an opening angle of 80 deg is chosen to account for obscuration by dust[cite: 34]. Compared to other simulations (e.g. the Millennium simulation; [Rong2017]), several features of this model are well suited to study of high-redshift MQGs[cite: 35]. We note that the cadence of our model is about 11 Myr at a redshift greater than or equal to 5 and reaches 30 Myr at a redshift of 3.7[cite: 36]. This high temporal resolution enables us to not only resolve the dynamical time of the disc and simulate the bursty nature of star formation events, but also investigate the evolution of galaxies in more detail[cite: 37]."}
{"text": "In addition, the agreement between our model and observations, including the stellar mass function at a redshift of approximately 7-0.56 and quasar luminosity function at a redshift of approximately 6-0.56, suggests that the model galaxy and AGN catalogues we have constructed are able to represent the relevant observables across cosmic time[cite: 38]. This is crucial for investigation of individual galaxy analogues within a cosmological context (e.g. [Mutch2016b, Waters2016])[cite: 39]. A list of the properties of the ZF-COSMOS-20115 analogues at a redshift of approximately 3.7 and the time of peak star formation. The estimated properties of ZF-COSMOS-20115 by [Glazebrook2017] are shown for comparison[cite: 40, 41]. A brief overview of how the ZF-COSMOS-20115 properties were estimated: stellar mass at a redshift of 3.7 from SED fitting; SFR at a redshift of 3.7 from Balmer lines [cite: 42]; virial mass at a redshift of 3.7 from galaxy number density and halo mass function; peak redshift, SFR at peak redshift from spectral evolution of stellar population modelling[cite: 43, 44]."}
{"text": "Top panels: galaxy stellar mass function at a redshift of 2-4 compared to the observational data sets. The shaded regions represent the 1-sigma Poisson uncertainties[cite: 45]. Bottom left panel: number density of galaxies with masses above M_* at a redshift of 3.7. Dashed, dash-dotted, solid and dotted thick lines represent samples of i) all galaxies; ii) galaxies with SFR less than 100 solar masses per year [cite: 46]; iii) SFR less than 30 solar masses per year and iv) SFR less than 1 solar mass per year[cite: 47]. The black circle indicates the observationally estimated value and uncertainties from the S14 sample [Straatman2014]. Bottom middle panel: evolution of the number density of massive galaxies with log base 10 of M_*/solar mass greater than 10.6[cite: 48]. The observational data at lower redshifts (a redshift less than 3; [Straatman2015]) is indicated with grey circles[cite: 49]. Bottom right panel: evolution of the MQG fraction. The MQG fraction with SFR less than 1 solar mass per year of the model running with Eddington ratio, epsilon=0.1 is shown with the dotted thin line for comparison[cite: 50]."}
{"text": "In the top panels of Fig. 1 we plot the evolution of the model galaxy stellar mass function between a redshift of 2 and 4. The agreement with observed mass functions demonstrates the ability of the model to reproduce the observed growth of stellar mass across the broad range of cosmic time relevant to this work [Qin2017]. The bottom left panel of Fig. 1 presents the predicted cumulative galaxy stellar mass function at a redshift of 3.7 for four different samples in our model: i) all galaxies; ii) SFR less than 100 solar masses per year; iii) SFR less than 30 solar masses per year and iv) SFR less than 1 solar mass per year[cite: 51, 52]. We note that there are 15 MQGs detected in the S14 sample, corresponding to a number density of (1.8 plus or minus 0.7) times 10 to the power of -5 per cubic Megaparsec. This is shown in Fig. 1 for comparison[cite: 53]. In addition, SFRs derived from stellar population modelling vary from 0 to approximately 32 solar masses per year in the S14 sample. We see that the number density of MQGs predicted by our model with SFRs in this range is in good agreement with the S14 sample[cite: 54]. We also show the evolution of the number density of massive galaxies and the MQG fraction in Fig. 1[cite: 55]. The model is consistent with observations at lower redshifts (a redshift less than 3; [Straatman2015])[cite: 56]."}
{"text": "We note that, despite the large uncertainty, observations may suggest that the MQG fraction stops decreasing at a redshift of approximately 4 while a continuously decreasing trend towards higher redshifts is usually presented in theoretical models ([Glazebrook2017]; see the bottom right panel of Fig. 1)[cite: 57]. The MQG fraction in the S14 sample is 34 plus or minus 13 per cent at a redshift of approximately 4[cite: 58]. This was compared to Illustris [Vogelsberger2014], a suite of hydrodynamical simulations of galaxy formation. Only approximately 20 per cent of massive galaxies in Illustris are MQGs (in agreement with our model, see the SFR less than 30 solar masses per year line in the bottom right panel of Fig. 1)[cite: 59]. Based on this, [Straatman2015] suggested that quenching is likely to occur at early times in massive galaxies[cite: 60]. However, we note that only one object in the S14 sample, ZF-COSMOS-20115, has been spectroscopically confirmed to be a MQG and, due to the limited volume of the ZFOURGE survey and potential contaminations from dust obscured star-forming galaxies [Straatman2015], the MQG population at high redshift is not well constrained[cite: 61]. Therefore, instead of making attempts to interpret the high MQG fraction at high redshift, in this work, we focus on finding analogues of the spectroscopically confirmed ZF-COSMOS-20115 and discuss the possible evolutionary history and future of this galaxy in order to identify the potential quenching mechanism and possible progenitors of high-redshift MQGs[cite: 62]."}
{"text": "In order to identify the analogues of ZF-COSMOS-20115 in our model, we consider the following two properties. The stellar mass of ZF-COSMOS-20115 was constrained [Glazebrook2017] from the equivalent width of the observed spectral energy distribution (SED) and is considered a robust observed property[cite: 64]. However, [Simpson2017] recently argued that due to contaminations from a nearby dusty starburst, the stellar mass of ZF-COSMOS-20115 was overestimated by 50 per cent[cite: 65]. Therefore, according to [Simpson2017], we set a threshold of stellar mass greater than 0.8 times 10 to the power of 11 solar masses, which returns 139 massive galaxies[cite: 66]. Based on the Balmer absorption lines (or the lack of H-beta emission line), the current SFR was reported to be less than 0.2 (or 4) solar masses per year. We note that in the alternate case that ZF-COSMOS-20115 is an obscured star-forming galaxy, the SFR would be less than 70 - 100 solar masses per year, which is inferred from the non-detection threshold of the Herschel/PACS imaging [Straatman2014][cite: 67]. In this work, we focus on the MQG scenario and select ZF-COSMOS-20115 analogues with SFR less than 0.4 solar masses per year[cite: 68]. This selection returns 10 MQGs, corresponding to 7 per cent of the 139 massive galaxies[cite: 69]."}
{"text": "Using spectral evolution models of stellar population [1999astro.ph.12179F], and the assumption that the stellar mass of ZF-COSMOS-20115 increases with a constant SFR for a certain period followed by a long state of quiescence, [Glazebrook2017] found that ZF-COSMOS-20115 has a stellar age of 500-1050 Myr with a formation time-scale of less than 250 Myr[cite: 69]. This implies that ZF-COSMOS-20115 formed at a redshift of approximately 5.8 with uncertainty +2.3/-0.8 with a star-forming period of a redshift interval less than 1.5 with uncertainty +2.1/-0.4[cite: 70]. We note that strong star formation at a redshift less than 4.5 creates significantly excess flux in the spectrum at wavelengths shorter than H-alpha compared to the observed SED of ZF-COSMOS-20115[cite: 71]. Therefore, we exclude galaxies with SFR greater than 100 solar masses per year at a redshift less than 4.5 from the sample[cite: 72]. Based on these specific criteria, we identify three analogues which we will henceforth refer to as ZF-1 to ZF-3[cite: 73]. However, we note that the choice of the stellar mass and SFR thresholds does not have a significant impact to our conclusion[cite: 74]. The ZF-COSMOS-20115 analogues in our model have stellar masses of around 10 to the power of 11 solar masses and negligible star formation at a redshift of approximately 3.7 with peak SFRs greater than or equal to 500 solar masses per year at a redshift of approximately 5-6[cite: 75]."}
{"text": "We summarize their properties at a redshift of approximately 3.7 and at the time of peak star formation in Table 1, for comparison to the ZF-COSMOS-20115 properties estimated by [Glazebrook2017][cite: 75]. We see that, due to the limited volume of our parent N-body simulation, the candidates are slightly less massive (by up to 30 per cent) than ZF-COSMOS-20115[cite: 76]. However, their halo masses (approximately 10 to the power of 13 solar masses) are larger than the value (10 to the power of 12.5 solar masses) estimated from the galaxy number density and the halo mass function at a redshift of 4[cite: 77]. This implies that the three analogues have larger stellar mass to halo mass ratios by factors of 2-3, suggesting that these MQGs are hosted in relatively large haloes[cite: 78]. During the calculation, we consider Lyman-alpha absorption while dust extinction is not included (dust extinction A_V between 0.4 and 0.6; [Glazebrook2017])[cite: 80]. The result is presented in Figure 2, compared to the photometry measurements from [Glazebrook2017][cite: 81]. We see that the 4 galaxies are fainter than ZF-COSMOS-20115 and show strong Balmer and 0.4 micron breaks (D_4000)[cite: 82]. The D_4000 break is also an indicator of the absence of recent star formation [Poggianti1997, Kauffmann2003][cite: 83]."}
{"text": "Observed SEDs of the ZF-COSMOS-20115 candidates. The points with error bars represent the photometry measurements and their 1-sigma uncertainties. Vertical dotted lines indicate the Lyman and Balmer series and breaks, and D_4000 at a redshift of approximately 3.7[cite: 85]. As discussed above, owing to the mass of ZF-COSMOS-20115 and the absence of recent star formation, there must have been a period of intense star formation at early times [Glazebrook2017][cite: 86]. In order to identify why this star formation was subsequently quenched, we investigate the history of the three analogues by tracking their most massive progenitors along the dark matter halo merger trees[cite: 87]."}
{"text": "Histories of the three analogues, ZF-1, ZF-2, ZF-3, in terms of, from top to bottom, the star formation rate, stellar mass, cold gas mass, cooling mass, virial mass, central black hole mass, heating mass due to AGN feedback, intrinsic quasar UV magnitude and baryonic merger ratio[cite: 88]. Results with different Eddington ratios, epsilon=1.0, 0.3, 0.1, are shown with solid, dashed and dotted lines, respectively[cite: 89]. Note that the virial masses are the same in different models and only the fiducial model with epsilon=1.0 is shown in the merger ratio panels with the black star symbol[cite: 90]. In the cold gas mass panels, thin black lines represent the critical mass in the fiducial model, above which galaxies are able to form stars[cite: 91]. In the intrinsic quasar UV magnitude panels, thin black lines indicate the UV magnitude of the host galaxy in the fiducial model for comparison[cite: 92]. The values of SFR, stellar mass and virial mass at a redshift of 3.7 are shown in each corresponding panel for the three models[cite: 93]. The thin grey lines and small squares represent the full set of z=3.7 massive star-forming galaxies with stellar mass greater than 0.8 times 10 to the power of 11 solar masses and SFR greater than 70 solar masses per year, the Herschel/PACS non-detection threshold, in the fiducial model[cite: 94]."}
{"text": "The derived stellar mass and SFR limits, virial mass of ZF-COSMOS-20115 [Glazebrook2017] are shown with black and grey circles[cite: 95]. There are two SFR limits at a redshift of approximately 5.8, representing the 68 and 95 per cent confidences and three SFR limits at a redshift of approximately 3.7, indicating the values inferred from the Balmer absorption lines, H-beta emission lines and Herschel non-detection threshold, respectively[cite: 96]. The vertical dashed line represents the spectroscopic redshift of ZF-COSMOS-20115, a redshift of 3.717[cite: 97]. The vertical dotted line with shaded regions show the estimated time of the peak of star formation of ZF-COSMOS-20115, a redshift of 5.8 with uncertainty +2.3/-0.8[cite: 98]. The horizontal dashed line indicates merger ratio equal to a third[cite: 99]. Note that merger ratios less than 1 per cent are shown with tick marks on the x-axis for the three analogues[cite: 99]."}
{"text": "Fig. 3 shows the histories of the three analogues at a redshift of approximately 15-3.5 (corresponding to a lookback time of t of approximately 13.5-12.0 Gyr)[cite: 100]. We show, from top to bottom with thick black lines and star symbols representing the fiducial model, the SFR, stellar mass, cold gas mass, cooling mass, virial mass, central black hole mass, heating mass due to AGN feedback, intrinsic quasar UV magnitude and baryonic merger ratio[cite: 101]. In the background, with thin grey lines and squares we also plot the histories of all massive star-forming galaxies with stellar mass greater than 0.8 times 10 to the power of 11 solar masses and SFR greater than 70 solar masses per year[cite: 102]. The derived properties and limits of ZF-COSMOS-20115 are shown as circles for comparison. As shown in the histories of virial mass, the analogues are hosted by relatively massive haloes compared to star-forming galaxies with similar stellar masses, with masses of M_vir of approximately 10 to the power of 13 solar masses[cite: 105]. Mergers trigger the most intense star formation event in the history of each of ZF-1, ZF-2 and ZF-3 at a redshift of 5.1, 4.9 and 5.7 with SFRs of approximately 600, 800 and 1000 solar masses per year, and merger ratios of approximately 0.18, 0.34 and 0.14, respectively[cite: 106]."}
{"text": "However, unlike the star formation history modelling performed in [Glazebrook2017], where the galaxy is assumed to form stars with a constant SFR of greater than 990 solar masses per year for only less than 250 Myr, the three analogues have longer star formation time-scales of approximately 500 Myr to 1 Gyr with milder evolutions of SFR[cite: 107]. After the mergers, cooling is significantly suppressed and the galaxies consume the available cold gas on short time-scales (approximately 100-300 Myr)[cite: 108]. When there is insufficient cold gas in the galaxies (m_cold is less than m_crit, see equation 6 in [Mutch2016a]), star formation is quenched and the analogues become fainter in the UV band[cite: 109]. Mergers drive black hole growth in our model. The central massive black holes of the three galaxies therefore grow significantly after the merger event[cite: 110]. At the time when cooling stops, their black hole masses become 1-1.5 orders of magnitude larger than in star-forming galaxies with the same stellar mass[cite: 111]. During the accretion phase, the central black hole radiates energy and heats the surrounding interstellar medium (ISM)[cite: 112]. In our model, AGN feedback limits gas condensation by suppressing the cooling flow [croton2006many][cite: 113]. When the black hole becomes massive enough, AGN feedback is able to completely neutralize the cooling mass, leading to quenching of star formation in the three analogues[cite: 114]."}
{"text": "Because of the dramatic accretion following a significant merger event, the nucleus is triggered into a quasar phase [Qin2017][cite: 115]. However, the finite accreted mass can only support central massive black hole activity for a finite period of time[cite: 116]. In the second last row of Fig. 3, we show the intrinsic quasar UV magnitude (solid thick black lines) in comparison with the magnitude of the host galaxy (solid thin black lines)[cite: 117]. We see that, before the merger, the total UV magnitude is dominated by stellar light, but that the accretion briefly dominates UV flux during the quasar phase following the merger[cite: 118]. However later, at a redshift of 3.7, the nucleus has become inactive (but still provides AGN feedback through the radio mode, see more details in [Qin2017])[cite: 119]. This explains the lack of significant UV to optical radiation from the central massive black hole in the observed SED of ZF-COSMOS-20115, which can be well fit with a stellar population model [Glazebrook2017] without AGN contributions[cite: 120]."}
{"text": "In our fiducial model, black holes are assumed to either accrete and radiate at the Eddington rate (epsilon=1, where epsilon is the Eddington ratio) or stay quiescent if there is no accretion[cite: 121]. This assumption has been shown to provide a good description of black hole growth for the majority of black holes at the relevant redshifts [Bonoli2009]. In order to directly investigate the importance of the Eddington ratio in determining whether our three analogues are quenched by AGN feedback, we set the Eddington ratio to epsilon=0.3 (dashed thick black lines in Fig. 3) and epsilon=0.1 (dotted thick black lines)[cite: 123]. We note that without AGN feedback, in the Tiamat-125-HR volume the model can still reproduce the observed galaxy stellar mass function at a redshift greater than 4 but overestimates the number of more massive galaxies at a redshift less than 2 [Qin2017][cite: 124]. With epsilon=0.1, we find that while the number of massive galaxies with stellar mass greater than 0.8 times 10 to the power of 11 solar masses increases to 198, the fraction of MQGs decreases significantly at high redshift (see the thin dotted line in the bottom right panel of Fig. 1)[cite: 125]."}
{"text": "Moreover, amongst these galaxies, only five are quiescent galaxies. However, they cannot be considered analogues due to intense recent star formation events at a redshift less than 4.5 that violate the selection criterion 2[cite: 126]. Whilst no ZF-COSMOS-20115 analogues are found in the case of sub-Eddington accretion, it is illuminating to look at the variation in the evolution of ZF-1, ZF-2 and ZF-3 with lower black hole growth efficiencies[cite: 127]. We see that when the central massive black hole is sub-Eddington, the black hole growth becomes slower, providing weaker feedback to galaxy formation and having a longer quasar phase with a fainter luminosity[cite: 128]. With epsilon=0.3, the central black holes are inactive at a redshift of 3.7 but the analogues form stars for a longer period down to a redshift less than 4.5[cite: 129]. This violates selection criterion (ii) and results in a stronger UV excess in the spectrum at wavelengths shorter than H-alpha compared to ZF-COSMOS-20115[cite: 130]. With a lower Eddington ratio of epsilon=0.1, black hole growth becomes significantly slower compared to the model with Eddington accretion, and the heating mass due to AGN becomes insignificant[cite: 131]. We find that with epsilon=0.1, the analogues are star-forming galaxies at a redshift of 3.7[cite: 132]. Our model therefore predicts that the intense growth of a massive black hole (epsilon of approximately 1) in the centre of ZF-COSMOS-20115, likely induced by mergers, resulted in persistent AGN feedback which quenched subsequent star formation[cite: 133]."}
{"text": "Our model suggests the existence of greater than 10 to the power of 8 solar masses supermassive black holes and a significant role of AGN feedback in galaxy formation at a redshift of approximately 5-6 when the Universe was less than approximately 1 Gyr old[cite: 134]. In particular, we find that the three ZF-COSMOS-20115 analogues in our model are quenched due to persistent AGN feedback[cite: 135]. This could be potentially examined using far-infrared (FIR) and radio observations[cite: 136]. For instance, [Gobat2017] constructed a median SED in the range of 10-10^6 micrometers using stacked images of approximately 1000 MQGs at a redshift of approximately 2[cite: 137]. They discovered significant emissions in the FIR and radio bands of MQGs, which suggests a large content of dust (approximately 10 to the power of 8 solar masses) and gas (approximately 10 to the power of 10 solar masses)[cite: 138]. This is in contrast to local early-type galaxies that are usually found to be gas poor[cite: 139]. If present, this gas must be consumed with a low efficiency in order to keep MQGs quiescent across cosmic time[cite: 140]. This is likely due to AGN feedback and is supported by a significant excess of radio emission (approximately 5 times 10 to the power of 22 W/Hz) in the stacked SED compared to a dust only spectral model[cite: 141]."}
{"text": "The SED of ZF-COSMOS-20115 in the observer frame [Glazebrook2017], the sensitivities of ZFOURGE NIR and MIR instruments [Dickinson2003, Straatman2016], the expected JWST 10-sigma point source detection limits [Cowley2017] with approximately 3h exposure time, the designed 5-sigma detection limits of the WFIRST high latitude survey [Spergel2013] with approximately 200s exposure time and the 1.4 GHz magnitude limits of the VLA-COSMOS Deep [Schinnerer2010], ASKAP-EMU and SKA-SUR surveys [2015aska.confE.173K]. Conclusive evidence for this becomes observationally more challenging at a redshift of approximately 4[cite: 142]. We note that the near-infrared (NIR) emission of ZF-COSMOS-20115 is less than 3 microJanskys (Spitzer/MIPS 24 micrometers) and no mid-infrared detection was reported by Herschel/PACS (MIR, 100-160 micrometers, [Straatman2015])[cite: 143]. In addition, within a 20 arcsec box around ZF-COSMOS-20115 there is no radio source in the COSMOS VLA Deep catalogue [Schinnerer2010], the typical rms and resolution of which are 7.5 microJanskys and 1.7 arcsec[cite: 144]. Next-generation telescopes are expected to provide enormously improved sensitivity and resolution covering a wide range of wavelengths[cite: 145]."}
{"text": "We summarize the detection capabilities of JWST, WFIRST, ASKAP and SKA in Fig. 4 compared to the SED of ZF-COSMOS-20115 in the observed frame [Glazebrook2017], the sensitivities of the NIR and MIR instruments employed by ZFOURGE [Dickinson2003, Straatman2016] and the VLA-COSMOS Deep Survey[cite: 146]. Within the context of high-redshift quiescent galaxies, JWST will provide broad-band imaging from 0.7 to 28.5 micrometers with sensitivities of approximately 10 to the power of -2 microJanskys to 1-10 microJanskys (3h exposure) from NIR to MIR [Greene2007, 2011ASPC..446..331R, Bouchet2015][cite: 147]. With a sufficient high-redshift MQG sample becoming available from JWST, radio flux can be estimated using the stacking technique with telescopes such as ASKAP [Norris2011][cite: 148]. In addition, the high latitude survey of WFIRST [Spergel2013, Gehrels2015] will cover 6 per cent of the entire sky, a region that is 20000 times larger than ZFROUGE with AB magnitude limits of ~27 in the NIR (0.7-2 micrometers)[cite: 149]. Together with the planned SKA-SUR all sky survey [2015aska.confE.173K], this will enable direct evaluation of AGN activity in MQGs[cite: 150]."}
{"text": "Fig. 3 shows that the UV fluxes of the three analogues for most of their histories are dominated by stellar light, and that at a redshift of approximately 3.7 their central nuclei have become inactive[cite: 158]. However, the central massive black holes of the three analogues have previously grown significantly (approximately 10 to the power of 8 solar masses) during the quasar phase at a redshift of approximately 5 when accretion becomes important to or even dominates the total UV luminosity[cite: 159]. Fig. 5 shows the correlation between black hole mass and stellar mass of the three analogues at a redshift of 4.9, 4.5 and 5.3 when their AGN activities reached a peak[cite: 160]. Note that the model has been shown to successfully reproduce the observed Magorrian relation at a redshift less than or approximately equal to 0.5 [Qin2017][cite: 161]. We see that at a redshift of approximately 5, the three analogues have larger black holes than other galaxies in our model, and in particular, that ZF-3 hosts the most massive black hole in the model at a redshift of 5.3, and has a luminosity corresponding to that of a SDSS quasar [Glikman2011, Shen2012, McGreer2013][cite: 162]."}
{"text": "Correlation between black hole mass and stellar mass compared to ZF-1, ZF-2 and ZF-3 at a redshift of 4.9, 4.5 and 5.3, respectively. The three analogues at the corresponding redshift are indicated by black circles and their UV magnitudes of AGN and stellar light are shown in the top left corners[cite: 151]. Indeed at the time of peak AGN activity, the quasar UV luminosities of ZF-1, ZF-2 and ZF-3 increase to M_1450 = -23.0, -24.7 and -24.8, up to approximately 2.5 magnitudes brighter than the host galaxies[cite: 163]. We show the predicted quasar luminosity function at a redshift of 5 in the top panel of Fig. 6[cite: 164]. The result using the Tiamat halo merger trees is shown for comparison and to indicate the convergence of the quasar luminosity function at a redshift of approximately 5[cite: 165]. The model is in agreement with observations at the bright end [Shen2012, McGreer2013][cite: 166]. We indicate the quasar luminosities of the three analogues in the top panel of Fig. 6 and find that the progenitors of ZF-1, ZF-2 and ZF-3 are bright quasars in the range that optical surveys such as SDSS are able to detect[cite: 167]."}
{"text": "This suggests that ZF-COSMOS-20115 is likely the descendent of a high-redshift quasar and illustrates the possible connection between MQGs and high-redshift quasars [2012MNRAS.425L..66M][cite: 168]. In order to better demonstrate this, for each massive galaxy selected at a redshift of 5.3, we present the correlation between black hole mass and subsequent SFR at a redshift of 3.7 in the bottom panel of Fig. 6[cite: 169]. ZF-3 is indicated with a filled circle. We see that galaxies with less massive black holes (M_BH less than 10 to the power of 7.5 solar masses) can have a range of subsequent star formation levels[cite: 170]. This is due to self-regulated stellar feedback being the dominant mechanism in these galaxies[cite: 171]. However, due to persistent AGN feedback, galaxies with more massive black holes do not have intense subsequent star formation[cite: 172]. This indicates that a high-redshift bright quasar will likely become a MQG at later times, when its accretion disc has been completely consumed[cite: 173]. Top panel: quasar UV 1450 Angstrom luminosity function at a redshift of approximately 5[cite: 152]. The results using the Tiamat-125-HR and Tiamat halo merger trees are shown with solid and dashed lines, respectively[cite: 153]. The shaded regions represent the 95 per cent confidence intervals around the mean using 100000 bootstrap re-samples for the Tiamat-125-HR result[cite: 154]."}
{"text": "The observational data is shown with different symbols: [Shen2012] using SDSS DR7 data at a redshift of approximately 4.75 and [McGreer2013] using SDSS, UKIDSS and MMT at a redshift of approximately 4.7-5.1[cite: 155]. From left to right, the vertical lines indicate the quasar UV magnitudes of ZF-1, ZF-2 and ZF-3, respectively[cite: 156]. Bottom panel: correlation between high-redshift black hole mass (z=5) and low-redshift SFR (z=3.7)[cite: 157]. The size of the empty circle represents different stellar masses and ZF-3 is indicated with the filled circle[cite: 157]. The three ZF-COSMOS-20115 analogues are hosted by massive haloes, which provide deep gravitational potentials that efficiently accrete baryons[cite: 175]. The high baryon accretion efficiency induces intense star formation at high redshift, providing a significant number of ionizing photons that reionize surrounding hydrogen at a very early time[cite: 176]. In this section, we discuss the reionization history of ZF-COSMOS-20115[cite: 177]."}
{"text": "The evolution of the average neutral hydrogen fraction within boxes of lengths around 3.6, 6.5 and 9.4 Mpc around the three ZF-COSMOS-20115 analogues[cite: 174]. The result within the entire Tiamat-125-HR and Tiamat volumes are shown for comparison[cite: 174]. In Fig. 7, we show the evolution of the average neutral hydrogen fraction within boxes with different sizes around the three analogues[cite: 185]. The neutral hydrogen fraction is calculated using 21cmFAST [Mesinger2011] with the galaxy catalogue provided by Meraxes (see more details in [Mutch2016a])[cite: 186]. We see that the analogues start ionizing the intergalactic medium (IGM) at a redshift greater than or equal to 14 with inner regions becoming ionized first[cite: 187]. For example, ZF-1, ZF-2 and ZF-3 (and their nearby galaxies) reionize 3.6Mpc regions at a redshift of approximately 9.5, 9 and 10.5, respectively, and 9.4Mpc regions by a redshift of approximately 7, 6.5 and 8[cite: 188]. We also present the average neutral hydrogen fraction of the entire Tiamat-125-HR box in Fig. 7[cite: 189]. Due to the simulation not resolving dwarf galaxies, reionization only finishes at a redshift less than 5 in the Tiamat-125-HR volume[cite: 190]."}
{"text": "We therefore also show the result calculated using the higher resolution Tiamat halo merger trees for comparison[cite: 191]. This higher resolution model has been shown [Qin2017] to match the observed ionizing emissivity at a redshift of approximately 5-2 [Becker2013] and the Thomson scattering optical depth [PlanckCollaboration2016][cite: 192]. Comparing the average evolution in ionized fraction between the two simulations illustrates that reionization predicted are delayed by a redshift interval of approximately 1 in the low-resolution simulation[cite: 193]. The model suggests that ZF-COSMOS-20115 is located in a region of IGM that was ionized early in the reionization era[cite: 194]. In this section, we use the Meraxes semi-analytic model to explore possible scenarios for the subsequent evolution of ZF-COSMOS-20115 at a redshift less than 3.7[cite: 195]. Fig. 8 shows the future of the three analogues from a redshift of approximately 4 to a redshift of approximately 0.56[cite: 196]. We see that AGN feedback keeps gas in the analogues from cooling, and that without a major merger it is unlikely that a galaxy like ZF-COSMOS-20115 will have a further strong star formation event at a redshift less than 3.7[cite: 197]. However, depending on the halo properties or merger ratios, starbursts can in some cases be triggered[cite: 198]."}
{"text": "Futures of the three analogues, ZF-1, ZF-2, ZF-3, in terms of, from top to bottom, the star formation rate (and the baryonic merger ratio on the right y-axis), stellar mass, cold gas mass, cooling mass, virial mass, halo spin parameter, central black hole mass, heating mass due to AGN feedback and intrinsic quasar UV magnitude[cite: 178]. In the cold gas mass panels, thin black lines represent the critical mass, above which galaxies are able to form stars[cite: 179]. In the intrinsic quasar UV magnitude panels, thin black lines indicate the UV magnitude of the host galaxy for comparison[cite: 180]. Thin grey lines represent the full sample of massive star-forming galaxies with stellar mass greater than 0.8 times 10 to the power of 11 solar masses and SFR greater than 70 solar masses per year, the Herschel/PACS non-detection threshold[cite: 181]. The derived stellar mass, virial mass and SFR limits of ZF-COSMOS-20115 [Glazebrook2017] are shown with black and grey circles[cite: 182]. The vertical dashed line represents the spectroscopic redshift of ZF-COSMOS-20115, a redshift of 3.717[cite: 183]. The horizontal dashed line indicates merger ratio equal to a third[cite: 184]. Because ZF-COSMOS-20115 is likely to be cold gas poor due to AGN heating, subsequent starburst events would only persist for a short time period[cite: 199]."}
{"text": "When there is a merger, the three analogues increase their stellar masses by absorbing baryons from their merging companions[cite: 200]. The UV flux changes due to different star-forming histories of the merging companion (most likely the companion is a star-forming galaxy and therefore the UV flux increases after the merger), as well as the merger-triggered starburst[cite: 201]. However, depending on the merger ratio, only a small fraction of mergers can trigger additional large starbursts[cite: 202]. For example, ZF-1 stays quiescent until a redshift of approximately 1.1 when several galaxies merge with it, inducing a minor star-forming event with a SFR of approximately 25 solar masses per year[cite: 203]. With the central supermassive black hole heating the ISM, continuous star formation is unlikely to occur[cite: 204]. However, there are three short (a redshift interval less than 0.1) star formation events in ZF-3 at a redshift of approximately 2-3, when the cold gas mass, which gradually increases from stellar mass recycling [Mutch2016a], exceeds the critical value[cite: 205]. We note that the star formation law in our model depends on a critical mass, above which galaxies are able to form stars[cite: 206]."}
{"text": "This critical mass is inferred from the host halo properties and increases with virial mass and halo angular momentum (based on [kennicutt1998global] and [kauffmann1996disc])[cite: 207]. While the halo mass of ZF-3 grows smoothly, the spin parameter, which is a measure of specific angular momentum, decreases by a factor of 2 during the star-forming events[cite: 208]. Assuming full conservation of specific angular momentum for newly cooling gas [Mutch2016a], the cold gas disc contracts, resulting in higher gas densities[cite: 209]. Under circumstances where the cold gas density becomes larger than the critical value, star formation can occur[cite: 210]. ZF-2 merges with a larger galaxy at a redshift of approximately 2.5-1.2[cite: 214]. The host halo of ZF-2 initially becomes smaller due to tidal stripping from the merging companion, and eventually merges into the more massive halo with a baryonic merger ratio of approximately 1.4[cite: 215]. When the halo is being stripped, the host galaxy loses its gas component which becomes unbound[cite: 216]. Consequently, without gas falling into the centre, the central massive black hole stops accreting and there is no AGN feedback or heating in ZF-2 during the stripping period[cite: 217]."}
{"text": "On the other hand, the cold gas disc is considered to be gravitationally bound in our model and remains intact during galaxy stripping[cite: 218]. When the halo mass becomes smaller, the disc size and hence the critical mass required for star formation decreases[cite: 219]. This results in star formation activity which quickly consumes the available gas. ZF-COSMOS-20115 is a MQG at a redshift of approximately 3.7[cite: 220]. We model MQGs using the Meraxes semi-analytic model and identify three ZF-COSMOS-20115 analogues in the fiducial model presented in [Qin2017][cite: 221]. These analogues have properties that are in agreement with the observed constraints on ZF-COSMOS-20115 inferred from the recent spectroscopic follow-up of [Glazebrook2017][cite: 222]. We find that the three analogues are hosted by more massive haloes (10 to the power of 13 solar masses) compared to other star-forming galaxies with similar stellar masses[cite: 223]. Following the most massive progenitor, we track the history of the three analogues and identify significant merger events at a redshift of approximately 5[cite: 224]. We find that when the mergers drive intense Eddington-limited growth of the central massive black hole, the cooling flow is significantly suppressed by the resulting AGN feedback[cite: 225]."}
{"text": "We further investigate scenarios when black holes accrete at sub-Eddington rates and find insufficient heating energy from AGN feedback to suppress star formation[cite: 226]. In particular, with black holes accreting at a third of the Eddington rate, the ZF-COSMOS-20115 analogues still have high SFRs at a redshift of approximately 4.5, while, with the Eddington ratio of 0.1, they are star-forming galaxies at a redshift of approximately 3.7[cite: 227]. Our model therefore suggests that there was a period when the central massive black hole grew rapidly in ZF-COSMOS-20115, probably triggered by mergers, and that the persistent feedback from AGN quenched the subsequent star formation[cite: 228]. In addition, we find the three analogues host the most massive black holes in our simulation, and that they were luminous quasars (M_1450 less than or approximately equal to -23) at a redshift of approximately 5[cite: 229]. Moreover, all galaxies with massive black holes at a redshift of approximately 5 have quenched star formation by a redshift of approximately 3.7[cite: 230]. This suggests that ZF-COSMOS-20115 is the descendent of a high-redshift quasars similar to those detected in SDSS[cite: 231]. By investigating the ionizing regions around the three analogues, we find that ZF-COSMOS-20115 formed in a region that was reionized early[cite: 232]. We also follow the future of our ZF-COSMOS-20115 analogues down to a redshift of 0.56 and find that further strong or continuous star formation events are unlikely to occur in ZF-COSMOS-20115 at a redshift less than 3.7[cite: 233]."}
{"text": "This research was supported by the Victorian Life Sciences Computation Initiative (VLSCI), grant ref. UOM0005, on its Peak Computing Facility hosted at the University of Melbourne, an initiative of the Victorian Government, Australia[cite: 234]. Part of this work was performed on the gSTAR national facility at Swinburne University of Technology [cite: 235]. gSTAR is funded by Swinburne and the Australian Governments Education Investment Fund[cite: 236]. This work was supported by the Flagship Allocation Scheme of the NCI National Facility at the ANU, generous allocations of time through the iVEC Partner Share and Australian Supercomputer Time Allocation Committee[cite: 237]. AM acknowledges support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 638809 -- AIDA)[cite: 238]."}
{"text": "Direct detection of regions of ionized hydrogen (HII) has been suggested as a promising probe of cosmic reionization. Observing the redshifted 21-cm signal of hydrogen from the epoch of reionization (EoR) is a key scientific driver behind new-generation, low-frequency radio interferometers. We investigate the feasibility of combining low-frequency observations with the Square Kilometre Array and near infra-red survey data of the Wide-Field Infrared Survey Telescope to detect cosmic reionization by imaging HII bubbles surrounding massive galaxies during the cosmic dawn. While individual bubbles will be too small to be detected, we find that by stacking redshifted 21-cm spectra centred on known galaxies, it will be possible to directly detect the EoR at redshifts of approximately 9 to 12, and to place qualitative constraints on the evolution of the spin temperature of the intergalactic medium (IGM) at redshifts greater than or similar to 9. In particular, given a detection of ionized bubbles using this technique, it is possible to determine if the IGM surrounding them is typically in absorption or emission. Determining the globally-averaged neutral fraction of the IGM using this method will prove more difficult due to degeneracy with the average size of HII regions."}
{"text": "Cosmic hydrogen is believed to have been reionized by ultraviolet (UV) radiation produced by stars and quasars. The period from the formation of the first ionizing sources to when the intergalactic medium (IGM) was completely ionized is commonly known as the epoch of reionization (EoR). However, due to formidable challenges in observation and simulation, our knowledge of this process is lacking. Knowing how reionization occurred, both in time and space, would not only dramatically improve our understanding of the evolution and properties the IGM, but also the formation and role of the ionizing sources responsible during this period. Observations of high-redshift sources and the cosmic microwave background (CMB) have allowed some constraints to be placed on the timing and duration of the EoR. For example, Gunn-Peterson absorption troughs in quasar Lyman-alpha spectra set a lower limit for the end of reionization at a redshift of approximately 6 [Fan2006, Mortlock2011]. Additionally, CMB observations provide a measure of the total optical depth to electron scattering. Since this is an integrated quantity from the surface of last scattering (redshift of approximately 1100), it cannot, on its own, distinguish between different reionization histories."}
{"text": "However, depending on the model of reionization adopted, the average redshift at which reionization is half complete is found to lie between z = 7.8 and 8.8 [PLANCK2016]. Recent analysis by [Greig2016] implies that reionization is not yet complete by z = 7.1, with the volume-weighted IGM neutral fraction constrained to 0.40 (+0.41, -0.32) at 2 sigma. A far more promising observational strategy to constrain reionization is to directly measure the emission from the 21-cm spin-flip transition of neutral hydrogen. Due to cosmic expansion, the frequency of this radiation is now less than 200 MHz. Various experiments are underway or planned to measure the cosmic 21-cm signal as a function of frequency. One approach is to measure the spatially-averaged global signal using a single-dipole antenna, e.g., EDGES, DARE, SARAS [Bowman2008, DARE2012, SARAS2013]. Another is to measure the signal's spatial fluctuations interferometrically (using, e.g., LOFAR, GMRT, PAPER, MWA, HERA, SKA). For some instruments the latter approach can yield both high-resolution tomographic images of the ionized structure and statistical measurements (such as the 21-cm power spectrum) allowing us to learn about the properties of the reionization sources and sinks in far greater detail [MW2010, Koopmans2015]."}
{"text": "In this work we use simulations to investigate structures of ionized hydrogen (HII) surrounding the first galaxies during the early stages of the EoR (redshifts greater than or similar to 9). During this era---known also as the cosmic dawn---these regions appear as isolated 'bubbles'. We begin by discussing the ionized regions associated with simulation analogues of the highest-known redshift galaxy to date (GN-z11). We then move on to consider the wider population of bubbles in our simulation, establishing a relationship between their size, and redshift and luminosity of the brightest galaxy within them. We apply this simulation-based empirical relationship to explore the utility of an image regime-based EoR detection strategy that synergises the proposed Wide-Field Infrared Survey Telescope's (WFIRST) High Latitude Survey (HLS) and deep integrations of the redshifted 21-cm signal using the planned low-frequency Square Kilometre Array (SKA1-LOW). Our direct detection stategy is similar to those proposed targeting regions of ionized hydrogen surrounding high-luminosity quasars but is able to push the detection redshift beyond what is possible using quasars alone due to their relatively low population at redshifts greater than 8 [Wyithe2005, Kohler2005, Geil2008]."}
{"text": "Other techniques for probing individual sources have been presented, both midway through the EoR and at very high redshift (z ~ 15), such as visibility-based methods using matched filtering [Datta2007, Datta2012, Majumdar2012, Ghara2016], and using imaging [Ghara2017]. Some of these works also assess the prospects of constraining properties of the high-redshift IGM (such as its globally-averaged neutral fraction) and the sources responsible for its reionization. This paper is structured as follows. In Section 2 we give a brief overview of the DRAGONS simulation used in this paper. Section 3 explains the motivation behind this work and presents our bubble size--galaxy redshift and luminosity relation. Section 4 describes our detection strategy and presents our detectability results. Section 5 explores simple methods to constrain the spin temperature and globally-averaged ionization state of the high-redshift IGM. We address some additional details that may potentially impact our results in Section 6 before presenting a summary in Section 7. All globally-averaged quantities are volume weighted, and distances are given in comoving units unless stated otherwise. Absolute magnitudes used throughout are given in the AB system [OG1983], are intrinsic, and have been calculated assuming a standard Salpeter initial mass function [Salpeter1955]."}
{"text": "The Dark-ages, Reionization And Galaxy-formation Observables from Numerical Simulations (DRAGONS) project was specifically designed to study the formation of the first galaxies and cosmic reionization. It integrates a semi-numerical calculation of reionization (21cmfast) within a semi-analytic model of galaxy formation (Meraxes) built upon an N-body simulation (Tiamat). This gives a self-consistantly coupled reionization model which accounts for feedback due to both supernovae (SN) and the ionizing UV background from stars within galaxies. A unique feature of DRAGONS is that it utilises horizontal rather than vertical dark matter halo merger trees. This allows it to correctly simulate how galaxies influence each others' evolution by way of their ionizing flux. Tiamat has a sufficently large volume (cube of sides 100 Mpc in length) to investigate cosmic evolution while still achieving a mass resolution approaching the atomic cooling mass threshold. Tiamat also has excellent temporal resolution with 100 equally-spaced snapshots between redshifts 5-35, giving a cadence of about 11 Myr. This means the stochastic effects of star formation and SN feedback on reionization are accurately captured. Complete descriptions of Tiamat and Meraxes are given in Paper-I [DRAGONS1] and Paper-III [DRAGONS3], respectively, while details of the 21cmfast algorithm are described in [MFC2011]."}
{"text": "Paper-V [DRAGONS5] investigates the effect of galaxy-formation physics on the morphology and statistical signatures of reionization. The Meraxes model used in this work is the fiducial model described in Papers-III and V. This model has been calibrated so as to reproduce the observed evolution of the galaxy stellar mass function from z = 5-7 (see Paper-III) and the latest Planck optical depth measurements [PLANCK2015]. All output fields (e.g. density, stellar mass and ionization fraction) have been regularly gridded over 512-cubed voxels. Motivated by the identification of the surprisingly bright and massive galaxy GN-z11 at z = 11.1 by [OESCH2016], Paper-VI [DRAGONS6] investigates the origin and fate of such objects using DRAGONS. Two analogue galaxies of similar luminosity and stellar mass to GN-z11, labelled DR-1 and DR-2, were found within the Tiamat volume and show excellent agreement with all available observationally derived properties of this object. Maintaining this motivation, here we briefly summarise aspects of these objects' impact on the IGM in terms of reionization."}
{"text": "With the Tiamat volume gridded to 512-cubed, the voxels containing DR-1 and DR-2 are first fully ionized at redshifts 17.8 and 17.1, respectively. While these objects were not the first sources to begin ionizing the IGM in our simulation, they were among the first, with the majority of voxels being ionized after a redshift of approximately 7.9. This is not surprising given these objects' early star formation histories (see Paper-VI) and the fact that they are found in highly overdense regions. The ionized bubbles surrounding DR-1 and DR-2 (and the other less massive and less luminous galaxies within them) at z = 11.1 are approximately spherical. This is due to the lack of overlapping bubbles surrounding other galaxies in their vicinity. At this redshift both DR-1 and DR-2 lie close to the centroid of their bubbles. We estimate individual bubble size using a three-dimensional ray tracing technique, centred upon the brightest galaxy in the bubble, which measures the distance to an ionization phase transition in 1000 or more randomly chosen directions. In the case of DR-1 and DR-2 at z = 11.1 this provides an accurate and precise estimate of bubble radius."}
{"text": "However, at later times (when there is overlap and the brightest galaxy in the bubble may be off-centre) the resulting sampled radius distribution has higher variance. Using this method we find that the average diameters of the bubbles surrounding DR-1 and DR-2 at z = 11.1 are approximately 10 and 8 Mpc, respectively. At this redshift the globally-averaged neutral fraction of our fiducially-modelled IGM is 0.976, hence these two bubbles alone (out of more than 600) make up just under 3 per cent of the total ionized volume. Figure 1 shows zoomed-in slices through the ionization fields surrounding DR-1 and DR-2 at selected redshifts, showing the evolution of bubble size. The area of each galaxy's marker is proportional to its UV luminosity. By visual inspection these bubbles cease to be isolated regions, and are also driven by many less luminous galaxies, from a redshift of approximately 9. In order to compare the bubbles surrounding DR-1 and DR-2 to others in the simulation, Figure 2 shows where they lie in the size distribution of all ionized regions in the simulation as a function of redshift (and lookback time)."}
{"text": "The average size of the bubbles surrounding DR-1 and DR-2 are shown by the thick red and thinner blue lines, respectively. Dashed extensions of the lines show when the error in radius is more than half the radius of the bubble, marking the approximate transition from an isolated bubble to an overlapping region. For comparison, the sizes of other ionized regions in the simulation are shown by the distributions. The bubble size distribution for each snapshot is calculated using the Monte Carlo method described in [MF2007]. In this section we turn our attention to the population of bubbles surrounding a deep selection of galaxies in our simulation. Our main objective here is to investigate the expected connection between the size of such regions and the luminosity of the brighest galaxy within them, aiming to establish a simple relationship between these properties as a function of redshift. We do so anticipating its use in Section 4, where we examine the prospects of detecting ionized regions at high redshift. Note that our galaxy number density predictions are based on intrinsic luminosities and do not include dust attenuation as this is not expected to be significant at such high redshifts (z greater than or equal to 9)."}
{"text": "This also maintains the good agreement between the BlueTides UVLFs used in this work [WATERS2016] and the results of [OESCH2016]. Before demonstrating our average radius versus absolute UV magnitude fitting procedure we show a sample of zoomed-in slices through the ionization fields of the first 40 (unique) bubbles surrounding the brightest galaxies at z = 11.1 in Figure 3. Note that for the purpose of detecting the EoR by stacking bubble 21-cm spectra, we are interested in the relationship between bubble size and the luminosity of the brightest galaxy in the bubble. Hence, only one datum contributes to the model fitting for each bubble and therefore the bubbles shown are unique. In general, there is no one-to-one correspondence between bubbles and galaxies due to clustering. The average radius of each bubble has been estimated using the individual bubble method described previously. We include Figure 3 in order to demonstrate the variation in geometry of these regions at this redshift. The plot of average bubble radius against the absolute UV magnitude of the brightest galaxy within each bubble (considering galaxies brighter than M_UV = -17.25 only) at z = 11.1 is shown in Figure 4."}
{"text": "The error bars represent the plus or minus 1 sigma range in radius. Histograms on the top and right axes indicate the marginalised distributions of UV magnitude and bubble radius, respectively. For reference, the 5 sigma detection limit of the WFIRST HLS [Spergel2013] and the 8 sigma detection limit of a wide-field survey using the James Webb Space Telescope (JWST) [Mason2015] at this redshift are indicated. We use this result, and similar results at other redshifts, to perform an error-weighted Markov Chain Monte Carlo (MCMC) parameter estimation to the linear average radius versus absolute UV magnitude model, at 18 redshifts between z ~ 9-12. We also fit for an estimate of the variance in the intercept. Specific results for z = 9.2, 10.2 and 11.1 are given in Table 1. While one may expect a non-linear relationship, the many other galaxies in the neighbourhood of the brightest galaxy in each bubble enhance the local ionizing photon budget. Bias and clustering of these sources conspire to complicate this relationship. We choose to fit a linear model for both simplicity and the fact that it describes the luminosity enhancement well."}
{"text": "Having established a functional relationship between the typical size of bubbles as a function of both the luminosity of the brightest galaxy within them and its redshift, we now investigate prospects for their detectability. The two principal competing components we consider to be at play here are the strength of the cosmic 21-cm signal and instrumental noise. The relevant cosmic signal is the spatially-dependent 21-cm differential brightness temperature, delta T_b, between hydrogen gas and the CMB along the line of sight [FOB2006]. For high redshifts, it can be written as an equation dependent on the neutral hydrogen fraction, local dark matter overdensity, spin temperature, and CMB temperature. By using this formulation we ignore redshift-space distortions. When spin temperature equals the CMB temperature the 21-cm signal from the IGM vanishes. Similarly, as reionization progresses and the neutral hydrogen fraction approaches zero, the 21-cm signal diminishes. When the spin temperature is less than (or greater than) the CMB temperature, the 21-cm signal appears in absorption (or emission)."}
{"text": "In the post-heating regime, where X-rays heat the IGM and the Lyman-alpha background acts to decouple the 21-cm transition from the CMB (such that spin temperature is much greater than the CMB temperature), the 21-cm signal saturates and it appears in emission. This is demonstrated in the top panel of Figure 5, which shows the evolution of the volume-averaged spin tempertaure, according to the Evolution Of 21cm Structure (EOS) simulation by [Mesinger2016] using their 'bright galaxies' model. In this model, reionization is dominated by galaxies inside greater than 10 to the power of 10 solar mass haloes (roughly corresponding to a UV magnitude less than or similar to -17). The bottom panel shows the corresponding volume-averaged 21-cm differential brightness temperature for both the unsaturated and saturated signal case. The EOS simulation incorporates extremely efficient SNe feedback and closely matches the global reionization history of our fiducial model. For computational efficiency, we apply the temperature differential factor homogenously to our differential brightness temperature fields using the EOS spin temperature model."}
{"text": "We simulate the instrumental noise of SKA1-LOW based on the imaging performance results provided by [SKAdoc] (hereafter SKA2015). As our detection strategy involves using line-of-sight redshifted 21-cm spectra, the spatial structure of the noise does not concern us. Rather, all that is required is the rms noise, for an observation made at a specific frequency, with a given frequency channel width, integrated over time, and smoothed using a synthesised beam of a given full width half maximum. In order to provide a sense of the relative brightness temperatures of signals and noise involved, consider the bubble surrounding DR-1 at z = 11.1 (117.6 MHz). According to our simulation the globally-averaged neutral fraction of the surounding IGM is 0.98. Therefore, assuming saturation, the bubble appears as a near-spherical, approximately 30 mK deep 'hole' of radius approximately 5 Mpc. The instrumental noise, smoothed in both the sky plane and frequency space on a scale equal to the radius of the bubble has an rms of approximately 100 mK. Not assuming saturation gives a approximately 100 mK signal. The situation improves at z = 9.2, but detection is still unlikely."}
{"text": "Given the unlikely prospect of detecting individual bubbles surrounding galaxies, we turn our attention to stack-averaging multiple line-of-sight 21-cm spectra in order to improve the signal-to-noise ratio. As an example, we look at the case using the deep and wide near-infrared High Latitude Survey by WFIRST to obtain sky position, redshift and UV magnitude data of galaxies that lie within the SKA deep integration field. As WFIRST's planned spectroscopic survey will not be sufficiently deep to detect the same, relatively faint, galaxy candidates as identified by the HLS imaging survey, accurate redshift determination will require follow-up grism spectroscopy. Redshifts would be estimated by fitting a spectral energy distribution to the spectra, as was done by [OESCH2016] for GN-z11's spectra. Furthermore, without emission lines, these galaxies will need to be Lyman break galaxies. The presence of emission lines would likely improve redshift determination considering the high spectral resolution of WFIRST's grism [Spergel2013]. At the redshifts investigated in this work, it is reasonable to expect that most of the detectable galaxies will exhibit a Lyman break due to the low ionization fraction of the intervening IGM. We also note that spectroscopic follow-up could also be performed using other instruments, e.g. JWST."}
{"text": "These sky position, redshift and UV magnitude data are then used to stack-average the line-of-sight redshifted 21-cm spectra centred on each target galaxy. Ideally, this would overlay the bubbles' spectral profiles on top of each other, however, since the redshift upon which each spectrum is centred will be subject to an uncertainty (which we denote by sigma_z), the bubbles will be scattered along the line-of-sight axis. For the case of GN-z11, [OESCH2016] used HST-WFC3 grism spectroscopy in combination with photometric data from the CANDELS survey to place this object at z = 11.09 (+0.08, -0.12). Even at half this uncertainty the spatial equivalent of this redshift error at this redshift is approximately twice the size of the bubble surrounding DR-1. Given the design specifications based on the slitless spectroscopic survey capability requirements, [Spergel2013] report that WFIRST should be able to determine redshift within an uncertainty less than or equal to 0.001 * (1 + z). We make a conservative assumption in this work by first setting our fiducial redshift error to sigma_z = 0.05 for all redshifts investigated."}
{"text": "We simulate the expected redshifted 21-cm stacked spectrum using the WFIRST-HLS galaxy survey as follows. First, we only stack spectra corresponding to galaxies brighter than some UV magnitude cutoff, and which have a redshift that falls within some range. Next, we calculate the number of such galaxies in a single SKA1-LOW field using the predicted intrinsic UVLFs provided by [WATERS2016] based on the BlueTides simulation. We find this number to be greater than 300 for the redshifts of interest in this work. We randomly sample these UVLFs to obtain a redshift and magnitude for each galaxy. Then, using our average radius-magnitude-redshift model, we form a randomly sampled mock observation set consisting of the tuple (redshift, magnitude, bubble radius, spatial offset) for each galaxy. The effective SKA1-LOW field of view has been calculated by applying diffraction theory to a circular aperture and depends on both the observed wavelength and station diameter. Since we find that the number of spectra required for detection is roughly less than half of what we predict is available the field of view is not an active constraint in this work."}
{"text": "There are three points to consider. First, despite the high temporal cadence of our simulation, we have a relatively limited number of snapshots between z ~ 9-11. Furthermore, since the Tiamat volume is much smaller than the SKA survey volume, the number of bubbles around galaxies available to stack at each redshift is in deficit. Also, as demonstrated previously, the ionized regions surrounding the brightest galaxies are relatively spherical and isolated at the redshifts investigated in this work. For this reason, we generate synthetic spherical bubbles. Second, in order to beat the instrumental noise down to an acceptable level the number of spectra required to be stacked is greater than or similar to 50. Stack-averaging this number of randomly selected fields results in a relatively smooth spectrum. We therefore make the approximation of embedding our synthetic bubbles in a flat IGM whose globally-averaged brightness temperature is set by the standard equation. Third, in the large number of spectra limit, the stack-averaged signal can be approximated by the convolution of the redshift error probability distribution and the spectral profile of a bubble of average size, smoothed in the sky plane by the SKA1-LOW beam."}
{"text": "Taking these issues into consideration, we construct synthetic redshifted 21-cm spectra in the following manner: For each galaxy in the mock observation set, we embed a spherical bubble of radius R in a flat IGM volume with a brightness temperature set by the standard equation. Each volume is centred on redshift z and the bubble is offset from the volume centre by a random distance. The brightness temperature field is binned in frequency space and smoothed in the sky plane using a Gaussian beam with a FWHM equal to the average diameter of the bubbles in the set. The 'image' in each channel is zero-meaned as interferometers do not measure the DC mode. The line-of-sight spectrum through the centre of the bubble is then taken and zero-meaned to simulate removal of spectrally-smooth extragalactic foregrounds. Instrumental noise for each spectrum is simulated by randomly sampling a value for each channel. We centre the noise realisation for all individual spectra on the central redshift. The stack-average of each of these spectral components is then calculated."}
{"text": "Here we demonstrate our spectral stacking strategy with example realisations. Figure 6 shows the stack-average of 100 redshifted 21-cm spectra centred on galaxies brighter than a magnitude of -21.88 at a redshift of 11 +/- 1.5. We assume an error in grism-determined redshifts of 0.05 and a 1000 hr integration by SKA. The left-hand panels show the unsaturated case, while the right-hand panels show the saturated case. The upper panels show the two independent components: the cosmic signal and instrumental noise. The total signal is shown in the middle panels together with the best-fitting Gaussian model. The Gaussian model is described by two parameters (depth and standard deviation). We calculate the signal-to-noise ratio (SNR) using the resulting marginalised depth distribution. The SNR for these example realisations are 5.0 and 3.7 for the unsaturated and saturated cases, respectively. The lower panels show the difference between the input cosmic signal and the best-fitting model. The degree of fluctuation in a randomly stack-avererged IGM for these examples is much less than the signal depth for both cases."}
{"text": "Naturally, the resulting SNR varies with each realisation. For this observation parameter set an ensemble of realisations gives SNRs of 5.6 +/- 0.9 and 3.1 +/- 0.9 for the unsaturated and saturated cases, respectively. As expected, stack-averaging a larger number of spectra leads to an improvement, e.g. stacking the brightest 300 give SNRs of 7.5 +/- 0.9 and 4.6 +/- 0.5 for the unsaturated and saturated cases, respectively. We now go on to explore the full observational parameter space using ensembles of simulations to gauge detectability. The kind of realisations previously described can be performed anywhere in the valid observation space. In this section we discuss the average and scatter in SNRs for all the possible observation sets with central redshifts of 9.5 and 11, for both the unsaturated and saturated signal case. We calculate these by creating an ensemble of 50 realisations at 100 points in the planes shown in Figure 7. The number of stacked spectra are shown by the dashed line contours, while the colourmaps and unbroken contours show the average SNR (the bold contours mark a constant SNR of 5, which we use as our threshold for detectibility)."}
{"text": "The temperature differential-dependent modality of the 21-cm signal enables a qualitative constraint to be placed on the average spin-temperature of the IGM with respect to the CMB temperature. Given a detection of ionized bubbles using the technique described in the previous section, it is possible to determine if the IGM surrounding them is typically in absorption or emission. If the IGM is, on average, in absorption, then spin temperature is less than the CMB temperature. On the other hand, if the IGM is, on average, in emission, then spin temperature is greater than the CMB temperature. Furthermore, if the signal mode of the IGM was found to change over a range of redshifts this can be used to provide a quantitative measure of the redshift at which the spin temperature is equal to the CMB temperature. This is not possible for the reionization model presented in this work as the bubbles begin to overlap significantly before the IGM begins to appear in emission. However, this may not be the case in reality as heating by unmodelled sources/mechanisms may occur earlier."}
{"text": "Another IGM property of interest is its globally-averaged neutral fraction. Unfortunately, even if an accurate measurement of the differential brightness temperature is made, this signal depends on both neutral fraction and spin temperature. Therefore, without knowledge of the spin temperature, the neutral fraction can only be determined when the signal from the IGM is saturated. Assuming the IGM is fully heated and the signal appears in saturated emission, we may still be left with a degeneracy in the stacked 21-cm spectra between the average size of the stacked bubbles and the average ionization state of the IGM in which they are embedded. This is because a stack of small bubbles has a similar signature to a stack of larger bubbles in a more ionized IGM. This arises due to the grism's limited accuracy and is therefore an observationally-introduced degeneracy, not a physical one. We now demonstrate a method which breaks this degeneracy by taking advantage of the non-Gaussianity and/or constant width of the stacked spectral signal observed where uncertainty in the grism-determined redshifts is small."}
{"text": "Using a redshift uncertainty of approximately 0.001 * (1 + z) as WFIRST's spectroscopic redshift survey capability [Spergel2013], we have a redshift uncertainty at z=10 of 0.011, equivalent to 2.4 Mpc. Note that this is less than half of the typical radius of bubbles surrounding galaxies detectable by WFIRST at z = 10 according to our simulation. Therefore, the bubbles are relatively tightly aligned on top of each other in the stacked spectrum. As a consequence, their stack-averaged spectrum resembles an instrumentally-smoothed bubble profile rather than a Gaussian. Having confirmed this, fitting the analytic model for an instrumentally-smoothed stack of spectra provides estimates for the average radius and average brightness temperature. This technique is demonstrated for a central redshift of 9.5 in Figure 8. Fitting was performed using an MCMC parameter estimation technique. The resulting best-fitting parameter estimates are an average radius of 6.9 (+0.5, -0.4) Mpc (input value of 6.8 Mpc) and an average brightness temperature of 23.5 (+2.7, -3.6) mK (input value of 24.5 mK). Using the standard equation, we estimate the neutral fraction to be 0.85 +/- 0.13 (input value of 0.89)."}
{"text": "Some sources embedded in an IGM with a spin temperature less than the CMB temperature will not only ionize their surroundings to form a bubble, but will also heat the gas in their proximity through soft X-ray emission. This will give rise to a relatively thin shell of 21-cm emission beyond the bubble [Tozzi2000, WL2004, Ghara2016]. The brightness temperature profile of these sources will therefore resemble a top-hat with 'horns'. In order to be conservative we have ignored these effects, although they would improve the signal-to-noise of the stacked spectra used for our detectability predictions. Foregrounds were anticipated and have proven to be a significant challenge to detecting the cosmic signal due to their brightness and the chromatic response of the new generation of low-frequency interferometers [POBER2016]. In this work we have assumed anthropogenic RFI and both Galactic and extragalactic point sources have been removed from the observation data leaving no residual. We have also assumed there are no contamination or removal effects by diffuse Galactic foregrounds (synchrotron emission) apart from the mean removal for each line-of-sight spectra. Previous work has shown that it is possible to subtract this foreground in the imaging regime using a polynomial fitting-based method [MCQUINN2006, WANG2006, Geil2008b, PandO2011, ALONSO2015]."}
{"text": "We have investigated the feasibility of directly detecting regions of ionized hydrogen surrounding galaxies by stacking redshifted 21-cm observations around optically-identified luminous galaxies during early stages of the EoR. In particular, we look at utilising low-frequency observations by the SKA and near infra-red survey data of WFIRST in order to image bubbles surrounding massive galaxies at redshifts greater than or similar to 9.5. Our main results can be summarised as follows. We find that our modelling, using the DRAGONS simulation suite, predicts a linear relationship between the size of ionized bubbles and the luminosity of the brighest galaxy within them which evolves with redshift. We provide a fit for this relation and its scatter as a function of redshift. Individual bubbles will not be detected with SKA1-LOW. However, by stacking 100 or more redshifted 21-cm spectra it is possible to detect the EoR directly with a significance of at least 5 sigma at z ~ 9-12. Both the spin temperature of the IGM and the accuracy of the grism-determined redshifts of the galaxies have a significant impact on the detectibility of reionization."}
{"text": "It is possible to place qualitative constraints on the evolution of the spin temperature of the IGM at redshifts greater than or similar to 9 and it may be possible to quantitatively measure the redshift at which it is equal to the CMB temperature. Measuring the average size of bubbles and globally-averaged neutral fraction of the IGM is a difficult task due to the degeneracy of these properties' contribution to the cosmic signal. However, if the IGM can be assumed to be fully heated and the accuracy of the grism-determined redshifts of the galaxies is sufficiently high then this degeneracy may be broken and both the average bubble size and neutral fraction can be accurately determined. We conclude that imaging 21-cm emission around samples of luminous galaxies from the EoR will provide an additional and complementary probe of cosmic reionization. This work was supported by the Victorian Life Sciences Computation Initiative (VLSCI). Part of this work was performed on the gSTAR national facility at Swinburne University of Technology. AM acknowledges support from the European Research Council. This research was funded by the Australian Research Council (ARC), including through the ARC Centre of Excellence for All-sky Astrophysics (CAASTRO)."}
{"text": "The typical radius of a cosmological Strömgren sphere, R_S, generated by a source of UV luminosity L_UV scales as R_S is proportional to L_UV to the power of 1/3 [CH2000]. In terms of absolute UV magnitude, this gives a non-linear relation. The average radius vs absolute UV magnitude plot in Figure 4, however, shows average bubble radius as a function of the absolute UV magnitude of the brightest galaxy only in each bubble. Of course many other galaxies contribute ionizing photons toward the formation of an ionized region. These galaxies are both clustered and biased and therefore any enhancement they perform effectively depends on the luminosity of the brightest galaxy in the bubble, and the size of the region. The total luminosity of galaxies in a region may therefore be written as the sum of the brightest galaxy's luminosity and the luminosity of the non-centrals. The important thing to note here is that the data do not suggest a power law relation between total luminosity and the brightest galaxy's luminosity. Hence the cube root Strömgren sphere relation cannot hold. A reduced chi-squared analysis fails to show that any model describes the data significantly better than any other."}
{"text": "In Section 3.2 we calculated the best-fitting error-weighted model parameter values for eighteen different redshifts between z ~ 9-12. To each parameter (a1, a0 and sigma-squared_0) we fit the same exponential functional form, given by f(z) = c0 * exp[-c1 * (z - c2)]. The resulting best-fitting values for these functional coefficients are given in Table A2. This appendix describes how we simulate the instrumental noise of SKA1-LOW. For a comprehensive and authoritative overview of interferometric techniques for radio astronomy, see [TMS]. The image-space noise realisations used throughout this work were generated based on instrumental specifications provided by [SKAdoc] (hereafter SKA2015). In particular, we use their simulated brightness temperature sensitivity results for a deep (1000 hr) integration as a function of frequency and synthesised beam FWHM. This uses a fiducial frequency channel width of 1 MHz, however, calculating the sensitivity for different integration times and/or frequency channel widths is possible by noting that the rms noise is proportional to 1 / sqrt(channel width * integration time)."}
{"text": "In this work we have used the following double power law to describe the predicted intrinsic UV luminosity functions for galaxies at z = 9-11: a Schechter function [Bowler2014]. Here phi*, M*, alpha and beta are the normalisation, characteristic magnitude, faint end slope and bright end slope, respectively. We use the best-fitting values to these parameters, found using the BlueTides simulation by [WATERS2016]. The equations for these parameters are provided as functions of redshift."}
{"text": "We introduce Meraxes, a new, purpose-built semi-analytic galaxy formation model designed for studying galaxy growth during reionization. Meraxes is the first model of its type to include a temporally and spatially coupled treatment of reionization and is built upon a custom (100 Mpc)^3 N-body simulation with high temporal and mass resolution, allowing us to resolve the galaxy and star formation physics relevant to early galaxy formation. Our fiducial model with supernova feedback reproduces the observed optical depth to electron scattering and evolution of the galaxy stellar mass function between z=5 and 7, predicting that a broad range of halo masses contribute to reionization. Using a constant escape fraction and global recombination rate, our model is unable to simultaneously match the observed ionizing emissivity at z<~6."}
{"text": "However, the use of an evolving escape fraction of 0.05--0.1 at z~6, increasing towards higher redshift, is able to satisfy these three constraints. We also demonstrate that photoionization suppression of low mass galaxy formation during reionization has only a small effect on the ionization history of the inter-galactic medium. This lack of `self-regulation' arises due to the already efficient quenching of star formation by supernova feedback. It is only in models with gas supply-limited star formation that reionization feedback is effective at regulating galaxy growth. We similarly find that reionization has only a small effect on the stellar mass function, with no observationally detectable imprint at stellar masses greater than 10^7.5 solar masses. However, patchy reionization has significant effects on individual galaxy masses, with variations of factors of 2--3 at z=5 that correlate with environment."}
{"text": "There are several key observational areas in which substantial progress will be made in the study of the first galaxies during the coming decade. Of particular importance will be forthcoming programmes searching for galaxies beyond the current redshift frontier using the Hubble Space Telescope and, in the future, the James Webb Space Telescope. However, even next generation surveys will not extend to the faint luminosities of the faintest galaxies thought to drive the reionization of inter-galactic neutral hydrogen in the early Universe. Thus, alongside new probes provided by high redshift gamma-ray bursts and metal pollution of the inter-galactic medium (IGM), an important new observational window for study of the first galaxies will be provided by experiments to measure the redshifted 21 cm radio signal. These observations will both provide the first direct probe of the neutral hydrogen content in the high redshift Universe and, through modelling, provide a route to study the early dwarf galaxies thought to exist during reionization alongside their more massive counterparts whose star formation can be directly detected."}
{"text": "Within this context, the development of theoretical models that include a self-consistent treatment of the physics of galaxy formation and intergalactic hydrogen will play a key role. Traditional approaches to the study of galaxies and their effects on the IGM utilize either numerical simulation or analytic modelling. The latter allows investigation of average behaviours on large scales but the calculations are inherently linear, meaning that complex feedback processes cannot be addressed. Numerical simulations, on the other hand, include non-linear effects but at the expense of computational cost. To achieve a volume sufficiently large to study ionized structure, a popular and effective approach to simulating reionization is to begin with a collisionless N-body simulation and use a simple prescription to relate halo mass to ionizing luminosity. A radiative transfer method can then be used to calculate the ionization structure on large scales."}
{"text": "In recent years, new hybrid, or semi-numerical models have been developed that combine N-body simulations with analytical methods to enable the calculation of reionization structure in very large volumes with high efficiency. These methods have elucidated the primary features of the ionization structure during reionization, but do not capture the physics of galaxy formation. Therefore, to better understand the physics of galaxy formation, many authors have performed hydrodynamic simulations of galaxy formation which are able to directly model the growth of stellar mass in high-redshift galaxies when coupled with sub-grid models for processes including metal enrichment and feedback. These simulations are able to broadly reproduce the luminosity function of galaxies at high redshift, however, computational expense limits their ability to self-consistently model reionization in volumes large enough to statistically describe the spatial evolution of this process. Instead, a common approach is to impose a simple parametrized model to approximate the average ionizing background as a function of redshift, independent of the properties of the ionizing source population or their spatial distribution."}
{"text": "Recently, hydrodynamical simulations of galaxy formation with coupled radiative transfer have been used to compute the effects of reionization on galaxy formation self-consistently for the first time. However, the extreme computational expense of these simulations limit their size to relatively small volumes and/or few variations on galaxy formation physics or reionization scenarios that can be explored. In addition, the modelling of sub-grid physical processes remains uncertain, requiring systematic studies of the available parameter space in order to draw robust conclusions. Such studies represent an extreme computational challenge which has yet to be overcome. Another approach to the realistic modelling of high redshift galaxies has been through the use of semi-analytic galaxy formation models. While large volumes are available to such models, until now they have not been fully coupled to an accurate description of reionization."}
{"text": "This is in part due to the structure of most existing semi-analytic models, which utilize so-called `vertical' halo merger trees in which galaxies belonging to each tree branch are evolved independently from the rest of the simulation volume. Since galaxies drive the process of reionization, which in turn affects their subsequent evolution, galaxies spatially separated by tens of Mpc cannot be considered and evolved independently as has traditionally been the case. Self-consistently studying reionization instead requires a semi-analytic model designed to run on `horizontal' merger trees where all haloes at each snapshot of the parent N-body simulation are processed simultaneously. Additionally, the reduced dynamical time of dark matter haloes at high redshift requires snapshots with a much higher cadence than is needed to model galaxy formation at lower redshifts."}
{"text": "This is the third paper in a series describing the Dark-ages Reionization And Galaxy Observables from Numerical Simulations (DRAGONS) project, which integrates detailed semi-analytic models constructed specifically to study galaxy formation at high redshift, with semi-numerical models of the galaxy–reionization process interaction. In this work, we introduce Meraxes, the new semi-analytic model of galaxy formation developed for DRAGONS, integrating the 21cmFAST semi-numerical model for ionization structure described in [Mesinger2007]. Meraxes is implemented within the large-volume, high-resolution, and high-cadence Tiamat N-body simulation described in [Poole2016] and [Angel2016]. In subsequent papers we will use Meraxes to carry out a range of studies including the investigation of the high redshift galaxy luminosity function [Liu2015], and the ionization structure of the IGM [Geil2015]. Complimentary, high resolution hydrodynamic simulations are described in [Duffy2014]."}
{"text": "Modern semi-analytic galaxy formation models are capable of providing statistically accurate representations of the global properties of galaxies across a broad range of redshifts, and are therefore able to describe the distribution and evolution of the ionizing photons which drive the process of cosmic reionization. These photons generate regions of ionized hydrogen (H II) with characteristic sizes of tens of Mpc during reionization. Thus, in order to take advantage of this information and to self-consistently model the effect of these photons on the growth of galaxies, one must consider the contributions of galaxies separated by similar scales. Traditionally, semi-analytic models have therefore used parametrized descriptions to include the average effect of reionization and the associated photo-suppression of baryonic infall on the growth of galaxies. These parametrizations are typically calibrated using radiative transfer simulations and are provided as a function of redshift and halo mass alone."}
{"text": "Whilst it is computationally efficient to include reionization in this manner, there are a number of important drawbacks. First, the progression of reionization is not self-consistently modified by the growth of the galaxies which are driving it. Therefore it is impossible to investigate how different galaxy physics affect the ionization state of the IGM or to quantify the potential back-reaction on galaxy evolution. Secondly, these simple reionization prescriptions miss the potentially important effects of spatially dependent self-regulation, whereby massive galaxies located at the peaks in the density distribution can reionize their surroundings, delaying or preventing the onset of star formation in nearby lower mass haloes. Our new semi-analytic galaxy formation model, Meraxes, has been written from the ground up to facilitate these modelling requirements. Its key features include the `horizontal' processing of merger trees constructed from a purpose run N-body simulation (Tiamat) and the incorporation of the semi-numerical reionization algorithm, 21cmFAST, as a core component."}
{"text": "When combined, these features allow Meraxes to efficiently couple the growth of galaxies to the process of reionization, both temporally and spatially. It can therefore be used to investigate the potentially complex effects of various reionization models on the properties of high-z galaxies, as well as to test for observational discriminants of different galaxy physics in the distribution and evolution of inter-galactic neutral hydrogen. In order to develop confidence in our newly developed framework, as well as provide a solid foundation for future additions and improvements, our initial implementation of the baryonic physics processes in Meraxes is heavily based on the well-studied L-Galaxies semi-analytic model, in particular the version described in [Croton2006] and extended in [Guo2011]. However, as well as our improved treatment of reionization, the excellent temporal resolution provided to us by the Tiamat merger trees has also necessitated the development of a number of important updates to the treatment of supernova feedback and stellar mass recycling."}
{"text": "The Tiamat collisionless N-body simulation has been designed for the DRAGONS study of high-redshift galaxy formation and the epoch of reionization (EoR). It contains 2160^3 dark matter particles within a 100 Mpc (comoving) periodic box and was run using a modified version of the GADGET-2 N-body code and the latest Planck 2015 cosmology. The volume of Tiamat allows for the investigation of the statistical signatures of reionization and its 21 cm observational signal, whilst the resulting particle mass of 3.89x10^6 solar masses provides the necessary resolution to identify the low-mass sources thought to be driving this process. Furthermore, Tiamat provides high temporal resolution in the form of 100 output snapshots evenly spaced in cosmic time between z=35 and 5, resulting in a cadence of 11.1 Myr per snapshot. This level of temporal resolution is a unique feature of Tiamat which allows our semi-analytic model to accurately simulate the stochastic nature of star formation in a regime where the dynamical time of a typical galactic disc is shorter than the lifetime of the least massive Type II supernova progenitor (~40 Myr)."}
{"text": "In addition to the main Tiamat volume, a suite of smaller, higher mass resolution N-body simulations have been run as part of the DRAGONS programme (Paper-I). For this work we make particular use of the TinyTiamat and MediTiamat volumes in order to quantify the effect of resolution on our results. TinyTiamat is the highest resolution simulation of the DRAGONS suite, with a particle mass of 10^5 solar masses in a small box of side length 14.8 Mpc, whilst MediTiamat bridges the resolution gap with the main simulation by providing a particle mass of 1.16x10^6 solar masses in a 33.3 Mpc box. Both simulations maintain the same snapshot cadence as the main Tiamat volume and are described in detail in Paper-I. Halo identification in all simulations used in this work was carried out using the Subfind real-space halo finder down to a minimum mass of 32 particles. The resulting halo catalogues comprise of friends-of-friends (FoF) groups of gravitationally bound particles which themselves are made up of a single mass dominant `central' subhalo along with zero or more sub-dominant `satellite' subhaloes."}
{"text": "The formation history of subhaloes, in the form of hierarchical merger trees, acts as the raw input to Meraxes and is used to define the positions and growth of galaxies. Many traditional semi-analytic models process such trees in a depth-first (or `vertical') order, whereby small collections of directly interacting dark matter haloes are processed one after the other from high to low redshift and independently of each other. Whilst computationally efficient in terms of minimizing the memory overhead required to process the simulation, the inherent assumption is that haloes (and by extension galaxies) which do not directly interact do not affect each other's evolution. This assumption breaks down when considering the process of reionization during which ionizing photons from galaxies tens of Mpc away can heat the IGM, raising the local Jeans mass and altering the accretion rate of baryons. Meraxes instead processes trees breadth-first (or `horizontally'). In this method all of the haloes in the entire volume are loaded into memory and the associated galaxies evolved for each snapshot sequentially."}
{"text": "We begin by making the standard assumption that as FoF groups grow, any freshly accreted mass, always carries with it the universal baryon fraction, f_b, in the form of pristine primordial gas. However, the fraction of these infalling baryons which will remain bound to the FoF group and participate in galaxy formation may be reduced by a number of factors. In particular, ionizing ultraviolet background (UVB) radiation from both local and external sources can heat the IGM, increasing the local Jeans mass and leading to a non-negligible reduction in the amount of baryons successfully captured by low mass systems. We parametrize this reduction in terms of a baryon fraction modifier, f_mod, which represents the attenuation of the total baryon mass that could have ever been successfully captured by an FoF group in its lifetime. Any baryons which are successfully captured are assumed to be shocked to the virial temperature of the host FoF group and added to a diffuse hydrostatic hot reservoir where they mix with any already present hot gas."}
{"text": "At each time step in the simulation some fraction of the hydrostatic hot reservoir may cool and condense down into the central regions of the group where it can then participate in galaxy formation. In order to calculate the rate at which this occurs we follow the commonly employed methodology outlined in [White1991]. In this model, the cooling time of a quasi-static isothermal hot halo is given by the ratio of the specific thermal energy to cooling rate per unit volume. We assume that the hot gas is shocked to the virial temperature of the FoF group and that it follows a singular isothermal sphere density profile. The cooling model naturally leads to three distinct regimes. When the cooling radius is greater than or equal to the virial radius, any infalling gas will cool so rapidly that there will be no time for a stable shock to form. In this case we assume that the infalling material flows directly into the central regions of the halo over a dynamical time. When the cooling radius is less than the virial radius, the cooling time will be sufficiently long that a quasi-static hot atmosphere will form, and the cooling rate can be calculated from a simple continuity equation."}
{"text": "When the virial temperature is less than or equal to 10^4 K, we set the cooling radius to 0 and no cooling occurs. In the standard model of galaxy formation, haloes with this temperature represent the lowest mass scale for galaxy formation. Below this, the primary mechanism for gas cooling is via molecular hydrogen which is easily photo-dissociated by trace amounts of star formation, making it an inefficient pathway for Pop II star formation. Above this temperature, atomic line cooling provides an efficient mechanism to dissipate energy and remove pressure support. The mass resolution of our input N-body simulation, Tiamat, was chosen such that the minimum halo mass at z=5 is close to the atomic cooling mass threshold of 10^4 K. All material which successfully cools into the central regions of the FoF group is assumed to be deposited directly into the cold gas reservoir of the galaxy hosted by the central halo."}
{"text": "We assume that cooled gas settles into a rotationally supported cold gas disc with an exponential surface density profile. Under the simplifying assumption of full conservation of specific angular momentum, the scale radius of the disc can be approximated from the spin of the host dark matter halo. Based on the well-established observational work of [Kennicutt1998], the star formation rate of local spiral galaxies can be related to the surface density of cold gas above a given threshold. The value of this threshold can be understood in terms of the gravitational instability required to form massive star-forming clouds. If the total amount of cold gas in the disc is greater than the critical mass, the star formation rate is assumed to be a fraction (the star formation efficiency) of the gas mass above the critical value, divided by the disc's dynamical time."}
{"text": "Galaxy mergers can drive strong shocks and turbulence in any participating cold gas, driving this material towards the inner regions of the parent galaxy and resulting in an efficient burst of star formation. We model the fraction of cold gas consumed by such a burst using the prescription introduced by [Somerville2001]. This relation agrees well with the results of numerical simulations of mergers with baryonic mass ratios in the range 0.1--1.0. For merger events where the mass ratio is less than 0.1, we suppress any merger-driven star formation. For simplicity, we assume that all of the stars formed in a merger-driven burst do so within a single snapshot. At z~8, the median dynamical time of a galaxy disc in Meraxes is ~60% of the time between two consecutive snapshots of Tiamat (~11.2 Myr). Hence, this approximation is roughly equivalent to the assumption that the merger-driven burst occurs on a time-scale approximately less than one disc dynamical time for the majority of galaxies."}
{"text": "The radiative and mechanical energy liberated by supernovae can have a profound impact on galaxy evolution, potentially heating significant amounts of gas and even ejecting it from a galaxy or host dark matter halo entirely. This is especially so at high redshift where haloes are on average less massive than in the local Universe, and possess correspondingly shallower potential wells. Many semi-analytic models make the simplifying assumption that all supernova feedback energy is released instantaneously. This approximation is motivated by the reasonable further assumption that the majority of supernova feedback energy is released by massive stars which have short lifetimes. In the cases where the time span between each simulation snapshot is large, the approximation of the instantaneous deposition of all supernova energy into the ISM is valid. However, motivated by the short dynamical time of systems at high redshift, the separation between snapshots in our input simulation is approximately 11.1 Myr. It therefore takes at least three snapshots after a single coeval star formation episode for all stars more massive than 8 solar masses to have gone supernova."}
{"text": "In order to accommodate this matching of time-scales in Meraxes, we have implemented a simple delayed supernova feedback scheme. The basic methodology of our delayed feedback scheme is to calculate the total amount of energy which should be injected into the ISM by a single star formation episode, and to release this energy gradually over time in proportion to the fraction of SN-II which will have occurred. We assume a standard Salpeter initial mass function (IMF) with upper and lower mass limits of 0.1 and 120 solar masses respectively. The number fraction of stars that will end their lives as type II supernovae is then calculated by integrating the IMF. If we further assume that each supernova produced injects a constant 10^51 erg of energy into the ISM then, for a burst of a given mass, the total amount of energy deposited into the ISM is calculated, where a free parameter describes the efficiency with which the supernova energy couples to the surrounding gas."}
{"text": "As is common practice, we model the mass of gas which is reheated by this energy deposition as a mass loading factor. We follow [Guo2013] who adopted parametrizations for the energy coupling efficiency and mass loading factor that scale with the halo's maximum circular velocity. The total amount of supernova energy released by a galaxy at any given snapshot will be dependent on the mass of stars formed both in the current and previous snapshots. We therefore explicitly track the total mass of stars formed in each galaxy for the last 4 snapshots (corresponding to 40 Myr). The eventual fate of the reheated material depends on both its mass and the amount of energy injected. If there is more energy injected into the reheated gas than is required to raise it to the virial temperature of the halo, we assume the gas to be added to the hot halo of the host FoF group. Any excess energy is assumed to then go into ejecting some fraction of the FoF group hot reservoir from the system entirely."}
{"text": "If instead only a fraction of the total reheated mass can be raised to the virial temperature, only that energetically feasible fraction is added to the FoF group hot reservoir, with the rest raining back down on to the galaxy in a galactic fountain. Any gas and metals which are successfully expelled from the system entirely are placed into a separate `ejected' reservoir. Here they are assumed to play no further role in the evolution of the galaxies in the host FoF group until the group falls into a more massive system. At this point, the ejected material is assumed to be re-accreted into the new group and is added to its hot halo component. We implement a simple metal enrichment scheme whereby a fixed yield of metals is released into the ISM per unit mass of stars formed. We assume that these metals are released predominantly by massive stars which end their lives as SN-II and we gradually release them over time as these supernovae occur."}
{"text": "A common assumption of many semi-analytic models is the instantaneous recycling approximation (IRA), in which some fixed fraction of the stellar mass formed during each time step is instantaneously recycled back into the ISM. Given our choice of IMF, a recycle fraction of 40% corresponds to all stars more massive than approximately 1 solar mass instantaneously going supernova. However, the lifetime of a 1 solar mass star is close to the current age of the Universe and hence the IRA can only be considered valid for galaxies around z=0. At z>~2, where the majority of galaxies have stellar populations dominated by recent star formation, this approximation becomes invalid and we are forced to consider a more realistic alternative. Our stellar mass recycling prescription is divided into two parts: we assume that the initial stellar mass of all supernovae is returned to the cold gas reservoir of the galaxy and we explicitly track the star formation history of each galaxy for the last 4 snapshots to calculate the recycled mass from older stars."}
{"text": "As haloes inspiral towards more massive systems, tidal forces experienced during repeated pericentric passages can lead to the stripping of loosely bound material from the outer regions. In Meraxes, if the mass of an FoF group drops, then a pro rata fraction of the ejected and/or hot baryonic content of the halo is also removed. This material is taken first from the ejected reservoir, with further mass being removed from the hot halo component if required. No baryons are ever taken from the cold gas or stellar mass reservoirs. Further to these long-range tidal forces, galaxies infalling into groups or clusters are observed to be subjected to a number of dynamical processes which remove gas from the outskirts of the system, including ram-pressure stripping, strangulation, and harassment. We model the combined effects of these processes by assuming that all FoF groups are instantly stripped of their entire hot and ejected gas reservoirs upon infall into a more massive structure, with their combined mass and metals being added to the hot component of the new parent."}
{"text": "Mergers play an important role in the build up of galaxy stellar mass, both through hierarchical mass assembly and induced star formation. This is particularly so at high-z where their prevalence is enhanced. In Meraxes these galaxy merger events are triggered by the merging of the corresponding host dark matter haloes. Following [Croton2006], when a dark matter halo is marked as having merged, we utilize dynamical friction arguments to approximate the time taken for the orbit of the incoming galaxy to decay and the corresponding galaxy--galaxy merger to occur. Galaxy mergers can drive strong shocks and turbulence in any participating cold gas, driving this material towards the inner regions of the parent galaxy and resulting in an efficient burst of star formation. We model the fraction of cold gas consumed by such a burst using the prescription introduced by [Somerville2001]. For merger events where the mass ratio is less than 0.1, we suppress any merger-driven star formation."}
{"text": "A ghost dark matter halo is one which is temporarily unresolved in our input merger trees. This can be due to a number of reasons, but is most commonly a result of a smaller halo passing through or nearby a much more massive structure. The Tiamat merger trees used in this work are carefully constructed to identify these artefacts, resulting in the skipping of a potentially large number of snapshots between haloes and their descendants. In many semi-analytic models, the galaxies hosted by such haloes are simply ignored until their halo is later re-identified. However, we must ensure that we correctly include these objects at all snapshots in order to account for their ionizing photon contribution. Due to the lack of knowledge of the properties of a ghost's host dark matter halo, we are unable to implement many of the physics prescriptions outlined above. We therefore simply allow these galaxies to passively evolve during the time over which they are identified as ghosts, forming no new stars but experiencing the delayed supernova feedback from previously formed generations."}
{"text": "The free parameters of the model were manually calibrated to replicate the observed evolution of the galaxy stellar mass function between redshifts 5 and 7, as well as the integrated free electron Thomson scattering optical depth measurements. The evolution of the stellar mass function has been shown by previous statistical investigations of semi-analytic models to provide a tight constraint on both the star formation efficiency and supernova feedback parameters. By combining this with the Thomson scattering optical observations, we can additionally put constraints on the escape fraction of ionizing photons, and thus all of the free parameters of our model. We make use of the mass functions estimated by [Gonzalez2011], [Duncan2014], [Grazian2014], and [Song2015]. Both [Duncan2014] and [Grazian2014] utilize data collected from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) GOODS South field with stellar masses directly obtained from SED fitting of combined optical and near-infrared space-based observations, and include the effects of both nebular line and continuum emission."}
{"text": "We are able to achieve an excellent match to the normalization, shape, and evolution of the observed mass function across all plotted redshifts. At z=5, where there is the largest divergence between different observational data sets, we chose parameter values which provided a reasonable compromise between each. However, at the low-mass end we have chosen to follow the observations of [Duncan2014] as they use a large data set with stellar masses obtained from SED fitting and provide actual data points rather than a Schechter fit. The quality of the agreement between our model and the observational data gives us faith that our implemented physical prescriptions are both reasonable and applicable at the high redshifts of interest in this work. Although typically producing fewer ionizing photons than their more massive counterparts, low mass galaxies with stellar mass less than the observational limit are expected to contribute a large fraction of the overall ionizing photon budget due to their high number density. For this reason, the low-mass slope of the stellar mass function is of particular importance to reionization."}
{"text": "The median stellar mass--virial mass relation is well described by a power law with a slope of ~1.4. This shows good agreement with simple energy conservation arguments which suggest a slope of ~1.7 for supernova feedback-regulated galaxy growth and a fixed cold gas mass fraction. However, at FoF group masses below approximately 10^9.5 solar masses there is a rapid increase in the spread of stellar mass values. This is due to a combination of supernova and reionization feedback effects, as well as a low star formation efficiency in these small, often diffuse haloes. Interestingly, there is no statistically significant evolution in either the slope or normalization of the relation with redshift. However, the same simple energy conservation arguments which provided a good agreement for the slope of the relation suggest that the normalization should evolve with redshift. Despite this, our model indicates that in order to reproduce the observed evolution of the galaxy stellar mass function over the redshifts considered in this work, the efficiency of galaxy formation and the associated feedback processes must conspire to provide a constant star formation efficieny in haloes of a fixed mass."}
{"text": "Our fiducial model provides an integrated optical depth which is in excellent agreement with the Planck results. An important consideration when assessing the results of any cosmological simulation is the potential loss of stellar mass (and therefore ionizing photon contribution) due to finite mass resolution. This issue is explored in detail for Meraxes and the Tiamat suite of simulations in the appendix. In summary, we find that the halo mass function of the full Tiamat simulation is complete down to approximately 0.5 dex above the atomic cooling mass threshold at z=5, whilst the lower volume but higher mass resolution MediTiamat is fully complete down to this mass limit. Using MediTiamat to quantify the fraction of total stellar mass missing from the full simulation, we find that at z=10 we miss approximately 25% of stellar mass from low mass, unresolved systems. By z=6 this fraction falls to less than 5%."}
{"text": "The ionization structure of a 4 Mpc thick slab produced by Meraxes shows that at early times, ionized bubbles surround the peaks in the density field where the first galaxies form. As reionization progresses the bubbles begin to overlap, and by a neutral fraction of 0.3, a large `lane' of ionized hydrogen, extending the entire length of the simulation volume is formed. The ability to investigate the distribution and evolution of bubble morphologies and the associated observable 21 cm power spectra is a key feature of our Meraxes framework. We find that supernova feedback is the dominant physical mechanism for regulating the growth of galaxy stellar mass both during and immediately prior to reionization. We find that it is only in the absence of supernova feedback that suppression of star formation due to the presence of an ionizing UVB reaches significant levels, and even then, only if star formation is efficient enough so as to be gas supply limited."}
{"text": "We further find that the reionization history of the IGM is similarly insensitive to reionization feedback. This implies that the process of reionization is not self-regulated. However, we note that if the process of reionization is more extended than is predicted by our model (for example, due to inhomogeneous recombinations in the IGM) then reionization feedback may play a more effective role. The fiducial model also predicts that a broad range of halo masses contribute to ionizing photon production during reionization. The reionization feedback is most effective in low mass haloes. However, supernova feedback of the level required to reproduce the observed high-z stellar mass functions dominates the suppression of star formation across all halo masses. The strong halo mass dependence of the stellar mass fraction contrasts the constant value assumed by the majority of reionization structure studies."}
{"text": "The evolution of the instantaneous ionizing emissivity in our fiducial model, which has a constant escape fraction, predicts a high and steeply increasing ionizing emissivity at z=5 that is inconsistent with the observational data from the Lyman-alpha forest. A model with a lower escape fraction, which is only marginally consistent with the Planck optical depth measurements, still fails to reproduce the observational data. However, an evolving escape fraction, with 0.05 <~ f_esc <~ 0.1 at z~6 and a redshift scaling proportional to (1+z)^kappa, where kappa~3, does allow our model to simultaneously satisfy these constraints. The large escape fraction in this model at high-z leads to an early onset of reionization. However, since the escape fraction decreases over time, the speed at which reionization progresses declines with decreasing neutral fraction, resulting in an extended EoR."}
{"text": "By comparing to a simple, homogeneous reionization prescription of the kind traditionally used in semi-analytic models, we find that the inclusion of a self-consistent patchy reionization model can result in significant, environmentally dependent variations in the stellar masses of individual galaxies by factors of 2--3. The distribution in galaxy mass ratios at a fixed stellar mass is largely symmetric, meaning that the total stellar functions produced by these two prescriptions remain in good agreement. However, the different predictions for individual galaxy masses may have important consequences for galaxy clustering statistics and 21cm power spectra owing to the Poisson noise that this scatter adds between the halo and galaxy clustering. This highlights that despite the good agreement in stellar mass functions, there can be important consequences of using a self-consistent, spatially dependent model of reionization that is not fully encoded in a parametrized homogeneous description."}
{"text": "The patchy fiducial model predicts a photoionization suppression which depends on environment with up to an order of magnitude difference in the filtering mass between over- and underdense regions. The trend of increasing filtering mass with increasing over-density is due to the contribution of ionizing flux from nearby galaxies which is not self-consistently included in the homogeneous model. At higher local densities, there is an increase in the average number and mass of nearby sources contributing ionizing photons which in the fiducial, patchy reionization model results in an increased filtering mass value. The inability of parametrized global reionization prescriptions to capture the density-dependent spread in filtering masses, as well as the trend of increasing filtering mass with density, could have important consequences for the galaxy clustering and cross-correlation statistics."}
{"text": "It is important to note that we were only able to calibrate the homogeneous variation through the use of our full fiducial run with self-consistently coupled reionization. Any change to the free model parameters, or underlying cosmological model, would require the mean filtering mass--redshift relationship to be recalculated."}
{"text": "We study dwarf galaxy formation at high redshift (redshift z greater than or equal to 5) using a suite of high-resolution, cosmological hydrodynamic simulations and a semi-analytic model (SAM). We focus on gas accretion, cooling and star formation in this work by isolating the relevant process from reionization and supernova feedback, which will be further discussed in a companion paper. We apply the SAM to halo merger trees constructed from a collisionless N-body simulation sharing identical initial conditions to the hydrodynamic suite, and calibrate the free parameters against the stellar mass function predicted by the hydrodynamic simulations at redshift z=5. By making comparisons of the star formation history and gas components calculated by the two modelling techniques, we find that semi-analytic prescriptions that are commonly adopted in the literature of low-redshift galaxy formation do not accurately represent dwarf galaxy properties in the hydrodynamic simulation at earlier times."}
{"text": "We propose 3 modifications to SAMs that will provide more accurate high-redshift simulations. These include 1) the halo mass and baryon fraction which are overestimated by collisionless N-body simulations; 2) the star formation efficiency which follows a different cosmic evolutionary path from the hydrodynamic simulation; and 3) the cooling rate which is not well defined for dwarf galaxies at high redshift. Accurate semi-analytic modelling of dwarf galaxy formation informed by detailed hydrodynamical modelling will facilitate reliable semi-analytic predictions over the large volumes needed for the study of reionization. About 150 Myr after the Big Bang, the Universe entered the Epoch of Reionization (EoR; [Planck2016A&A...596A.108P]), when the first stars and galaxies were created and started to photoionize the intergalactic neutral hydrogen. Over the past decade, there have been significant advances in the study of galaxies during the EoR and the evolution of the ionized intergalactic medium (IGM)."}
{"text": "High-redshift galaxies thought to have sourced reionization have been discovered all the way to redshift z~11 [Oesch2016], when the Universe was only 400 Myr old. However, the sample of these early galaxies remains small with only approximately 1000 candidates at redshift z>6 identified using advanced space-based instruments [Bouwens2014, Bouwens2015]. Achieving a physical understanding between galaxies and the progress of reionization is therefore aided by numerical simulations (see e.g. [Bertschinger1998, Baugh2006, Dolag2008, Somerville2015]). Two of the main numerical approaches to model galaxy formation are hydrodynamic simulations and semi-analytic models (SAMs) applied to dark matter halo merger trees constructed from cosmological N-body simulations. Since they adopt different approximations, their strengths and requirements are diverse. Hydrodynamic simulations include baryons as well as dark matter, and simulate the complex baryonic physics more directly (e.g. [Crain2009, Schaye2010, vogelsberger2014properties, Schaye2014, feng2015bluetides, Pawlik2017])."}
{"text": "However, while galaxies form and evolve in the presence of gravity and hydrodynamical forces in a simulation volume, its large computational expense limits the capability of simultaneously resolving small-scale regions and capturing massive systems. For instance, in order to study reionization and galaxy formation during the EoR, simulations are required to have a volume size of at least 10^6 Mpc^3 [Iliev2014MNRAS.439..725I] and a particle resolution that is able to resolve haloes with masses around 5x10^7 solar masses (i.e. >10 billion particles; [Barkana1999ApJ...523...54B]). While it remains challenging to explore the relevant parameter space in hydrodynamic simulations, SAMs, with their advantages of low expense on computational resources, become the alternative in this case. N-body simulations (e.g. [Navarro1997, springel2005simulating, iliev2008simulating, Boylan_Kolchin2009, Klypin2010, Garrison2017]) solve for the gravitational force on each collisionless dark matter particle but neglect the baryonic physics."}
{"text": "In order to implement the galaxy formation physics of baryons into these simulations, halo merger trees are constructed and based on the properties inherited from the merger trees, SAMs parametrize baryonic processes to evolve galaxies, offering an efficient approach to simulate galaxies in a cosmological context [e.g.][Cole2000, Hatton2003, Baugh2005, croton2006many, DeLucia2007, Somerville2008, guo2011dwarf, Henriques2015]. In general, a SAM first designates haloes as galaxies and endows them with stellar components and several gas reservoirs of varied functionalities. The latter usually include a cold gas disc where star formation occurs and a hot halo of non-star-forming gas. Mass is then manipulated and transferred between these baryonic sectors as a result of varied baryonic processes including accretion, cooling, star formation and feedback from supernovae or active galactic nuclei (AGN). These processes are implemented using scaling functions of astrophysics that are motivated either from first principles, from observations, or from more complicated simulations."}
{"text": "Despite these improvements recently implemented into modern SAMs, some prescriptions are still commonly adopted by many of these models. For instance, in order to initialize the baryonic component of haloes from dark matter only N-body simulations, the universal baryon fraction is applied to every virialized system with a further suppression due to reionization feedback. These baryons are considered as infalling gas and are usually assumed to share the virial temperature of the host halo as a result of experiencing shock--heating. However, we note that the degeneracy between parameters of SAMs, as well as their time and mass dependencies introduced by these simplified baryonic prescriptions are not well understood. In addition, lack of available observational data means that semi-analytic predictions have generally been tested against observables that are massive and in the nearby Universe [croton2006many, guo2011dwarf, Stevens2016]. Their consistency and performance in the low-mass regime or at high redshift remain unclear."}
{"text": "This motivates us to 1) test the performance of SAMs at high redshift, which were originally developed from the literature of low-redshift galaxy formation; and 2) inform more accurate semi-analytic modelling of dwarf galaxies, which will be applied to large-volume simulations to study the EoR in the future. In the absence of detailed observational data, constraints on the properties of SAM galaxies can be supplemented through comparisons against physics-rich hydrodynamic simulations, which are expected to predict galaxies that are more representative than simplified calculations using semi-analytic approaches [e.g. Guo2016, mitchell:2017je, stevens:2017fi, cote:2017uh]. In this work, we take the Meraxes SAM [Mutch2016a] as an example, and apply it to the halo merger trees constructed from a collisionless N-body simulation sharing identical initial conditions to the Smaug suite of hydrodynamic simulations [duffy2014low]."}
{"text": "We calibrate the SAM against the Smaug hydrodynamic simulations and make direct comparisons of the calculated galaxy properties using the two modelling techniques. This paper focuses on modelling of gas accretion, cooling and star formation, the implementation of which is common among many modern SAMs [croton2006many, Somerville2008, guo2011dwarf, Henriques2015]. The effect of feedback on star formation is excluded and will be presented in a companion paper. We begin with a brief introduction of the N-body/hydrodynamic simulations and SAM utilized in this work in Section 2. Then we discuss the consequence of applying SAMs directly to collisionless N-body simulations and propose modifications accordingly in Section 3. In Section 4, we proceed with the proposed modifications and calibrate the SAM to reproduce the hydrodynamic result. We investigate galaxy properties in detail and make comparisons between the hydrodynamic simulation and the SAM results. We conclude in Section 5."}
{"text": "In this work, we adopt cosmological parameters from WMAP7 (Omega_m, Omega_b, Omega_Lambda, h, sigma_8, n_s = 0.275, 0.0458, 0.725, 0.702, 0.816, 0.968; [Komatsu2011]) in all simulations. The Dark-ages Reionization And Galaxy Formation Observable from Numerical Simulation (DRAGONS) project employs N-body simulations [Poole2016], hydrodynamic simulations [duffy2014low, Qin2017a] and SAMs [Mutch2016a, Qin2017c] to study reionization and galaxy formation at high redshift (redshift z greater than or equal to 5, [Geil2016, Geil2017, Liu2016, Liu2017, Mutch2016b, Park2017, Duffy2017, Qin2017b]). The resulting galaxy catalogues from both the hydrodynamic simulation and SAM with feedback included are in good agreement with observations including the stellar mass and galaxy UV luminosity functions across cosmic time."}
{"text": "In this work, we focus on high-redshift modelling (redshift z greater than or equal to 5) of currently unobservable dwarf galaxies (virial mass M_vir less than or approximately equal to 10^10.5 solar masses) which are believed to be the dominant source of ionizing photons driving reionization [duffy2014low, Liu2016]. Using simplified models, we isolate prescriptions of gas accretion, cooling and star formation from reionization and supernova feedback, which will be further discussed in a companion paper. In the following two subsections, we summarize the DRAGONS SAM and hydrodynamic simulation, named Meraxes and Smaug, respectively. Meraxes is based on the Munich SAM [croton2006many, guo2011dwarf] and optimized to study galaxy formation at high redshift. Based on halo properties read from merger trees, it evolves galaxies using simplified prescriptions, which calculate baryonic infall, cooling, star formation, supernova feedback, metal enrichment, stellar mass recycling, AGN feedback and mergers."}
{"text": "In addition, Meraxes incorporates 21cmFAST [Mesinger2010], a semi-numerical approach to evolve ionization fields, for the purpose of investigating reionization feedback and exploring the IGM state during the EoR. We refer the interested reader to [Mutch2016a] and [Qin2017c] for a detailed description of Meraxes and provide a brief review of the relevant modelling prescriptions in this section. To connect N-body simulations of dark matter with baryonic physics, the first implementation is the accretion of gas. Following convention, a universal baryon fraction with suppression due to reionization heating is applied and each halo group accretes gas from the IGM. The change in hot gas mass Delta m_hot equals f_mod*f_b*M_vir - sum over N_halo of m_baryon, where m_baryon is the total baryonic mass including hot gas, cold gas and stellar mass. In the case of Delta m_hot > 0, all of the mass is assumed to be accreted by the central halo."}
{"text": "Gas falling into a halo is stored in the hot gas reservoir, which is assumed to share the halo virial temperature, T_vir, due to shock heating. It then cools within a certain time-scale. Assuming the hot gas follows a singular isothermal sphere (SIS) profile, we calculate the cooling radius, r_cool, at which the cooling time is equal to the halo dynamical time. Based on the ratio of the cooling radius to the virial radius, we calculate the cooling rate and consider two scenarios: static hot halo (r_cool < R_vir) and rapid cooling (r_cool >= R_vir). Therefore, the cooling rate can be calculated by the cooling rate dot m_cool equals (m_hot / t_dyn) times the minimum of (1, r_cool / R_vir). Cooling leads to the build-up of a cold gas reservoir, which is assumed to form a rotationally supported disc, where stars form, with an exponential surface density profile."}
{"text": "When the cold gas mass, m_cold, exceeds a critical value, m_crit, we use a phenomenological relation suggested by observations [kennicutt1998global] to calculate the star formation rate (SFR). The star formation rate dot m_star equals alpha_sf times (max(0, m_cold - m_crit)) / t_dyn,disc, where t_dyn,disc is the dynamical time of the cold gas disc inferred by the halo spin parameter [bullock2001apj...555..240b]. A free parameter, alpha_sf, is introduced for the purpose of adjusting the star formation efficiency. We note that, in order to be consistent with the hydrodynamic simulations, the newly formed stars are assumed to follow an initial mass function in the mass range of 0.1-120 solar masses with the form from [chabrier2003galactic]. Smaug is a series of high-resolution hydrodynamic simulations which were run with a modified GADGET-2 N-body/hydrodynamics code [springel2005cosmological]. These models follow the OverWhelmingly Large Simulations project (OWLS; [Schaye2010])."}
{"text": "These models have been shown to successfully reproduce observed galaxy properties at low redshift including the cosmic star formation history [Schaye2010] and the stellar mass function at redshift z<2 [Haas2013]. In addition, [Katsianis2017] recently showed that the EAGLE simulations, an extension of OWLS, are also in agreement with the observed SFR function across cosmic time (redshift z from approximately 0 to 8). These achievements motivate us to make use of the hydrodynamic simulations and to investigate the validity of semi-analytic prescriptions at high redshift where observational constraints are unavailable. In this work, the simulation from Smaug comprises 512^3 baryon and 512^3 dark matter particles within a cube of comoving side of 10 per h Mpc. This equates to a mass resolution of 4.7 (0.9) x 10^5 per h solar masses per dark matter (gas) particle."}
{"text": "The time interval between two outputs is around 11 Myr, and the initial conditions were generated with the grafic package [Bertschinger2001] at redshift z=199 using the Zel'dovich approximation [Zeldovich1970]. We summarize the subgrid physics adopted in Smaug in terms of cooling and star formation for comparison with the semi-analytic prescriptions. Cooling [Wiersma2009a] consists of only primordial elements and is pre-tabulated using the cloudy package [ferland1998cloudy]. Star formation [Schaye2008] occurs by stochastically converting gas particles to star particles in the ISM. When the gas density exceeds a critical value, the gas particle is assumed to be multiphase ISM with pressure proportional to density to the power of 4/3. The gas depletion time, t_g, in the hydrodynamic simulation is calculated based on the observed KS ([kennicutt1998global]) star formation law, and the SFR is given by the gas mass divided by the depletion time."}
{"text": "The two simulations used in this work are (1) DMONLY, a collisionless N-body simulation performed using the same initial conditions from the full simulation but neglecting hydrodynamic forces from the baryonic component. (2) NOSN_NOZCOOL_NoRe, a toy model with cooling in the absence of metal line emissions and reionization heating. It ignores feedback from exploding supernovae and heating due to reionization, and will be used to compare with the SAM for the purpose of investigating gas accretion, cooling and star formation without impacts from any feedback. The top left panel of Fig. 2 presents an example of the gas density distribution at redshift z=5 in the NOSN_NOZCOOL_NoRe Smaug simulation. In the SAM, cold gas is considered as potentially star-formation gas. In order to facilitate direct comparisons of the gas reservoir with the semi-analytic calculation, we specify, for each galaxy in the hydrodynamic simulation, a star-formation gas component."}
{"text": "This reservoir comprises all potential star forming particles of the galaxy, making it comparable to the assumption adopted in the SAM. As mentioned before, a gas particle located in a cold dense region is considered as multiphase and can potentially form stars. More specifically in Smaug, this requires the particle to satisfy a combination of four criteria [Schaye2010]: A) a high physical density; B) a high comoving density; C) a high physical density and a low temperature; D) a low temperature. Hot gas in the SAM represents a reservoir where the temperature is as high as the halo virial temperature as a result of shock--heating during gas accretion. Therefore, in order to define a hot gas component for a galaxy in hydrodynamic simulations, which can be compared with the SAM, we first exclude all potential star forming particles from the galaxy."}
{"text": "We plot the temperature distribution of non-star-forming gas particles of two haloes in the NOSN_NOZCOOL_NoRe Smaug simulation in the top panels of Fig. 1. In the more massive halo, three populations can be observed, corresponding to, from right to left, (1) infall hot gas; (2) infall gas that has been through cooling, and the cooling rate decreases significantly when temperature drops to a few 10^4 K [Wiersma2009a]; and (3) cold gas which is about to reach the multiphase ISM disc and become dense enough to form stars. However, we can only identify the group of less dense (non-star-forming) cold gas in the less massive halo. Based on the density--temperature phase diagram of the non-star-forming gas particles of a galaxy, the hot gas mass and temperature of the galaxy can be determined. In practice, we use the KMeans clustering algorithm. We consider two features (density and temperature) and separate the non-star-forming gas particles into two groups."}
{"text": "Hydrostatic pressure keeps gas from collapsing into shallow potential wells of low-mass haloes, which consequently decreases the gravitational potential within these haloes and slows their growths compared to a collisionless universe. This has been illustrated using comparisons between hydrodynamic simulations and N-body simulations of dark matter only [Sawala2013, Schaller2014, Velliscig2014], which show that the inclusion of baryons significantly reduces halo masses. We investigated the same baryonic effect in dwarf galaxies at high redshift (redshift z>5) in [Qin2017a]. We found that the reduction of mass can be up to a factor of 2 and that the fraction of baryons in haloes with masses between 10^7 and 10^9 solar masses, which host dwarf galaxies, never exceeds 90 per cent of the cosmic mean during reionization. Thus, applying SAMs to halo merger trees generated from a collisionless N-body simulation and assuming the universal baryon fraction overestimates halo and baryon masses of dwarf galaxies at high redshift."}
{"text": "We proposed two modifiers using a simplified hydrodynamic simulation in [Qin2017a] -- ADIAB, where gas only cools adiabatically with no stellar or galactic physics involved. In this work, which aims to inform a better semi-analytic description of high-redshift dwarf galaxies, we make use of these two modifiers, which are shown in the top panels of Fig. 2 as functions of halo mass at redshift z=13-5. In practice, the halo mass modifier is included when halo properties are read from the merger trees and the baryon fraction modifier is embedded in f_mod. However, we also point out the fact that these modifiers do not offer a consistent modification accounting for all aspects of astrophysical processes. In [Qin2017a], these have been shown to provide additional approximately 10 per cent alterations to halo mass due to radiative cooling, star formation and supernova feedback. Reionization, on the other hand, provides a more dramatic suppression."}
{"text": "In order to demonstrate the effect of incorporating the modifiers within semi-analytic galaxy formation modelling, we apply Meraxes with different implementations. We first apply the SAM with both the halo mass and baryon fraction modifiers implemented and calibrate the free parameters in the NOSN_NOZCOOL_NoRe regime where feedback is not included (SAM_HB). Next with all free parameters remaining the same, we then apply the SAM with only the halo mass modifier included (SAM_H) and without any modifiers (SAM). We see that compared to the hydrodynamic simulations, the collisionless N-body simulation as well as the uncorrected SAM overestimate the virial mass function, especially at higher redshifts. However, the halo mass modifier results in a SAM virial mass function that is in better agreement with the hydrodynamic calculation. This leads to a reduction as much as a factor of 2 in of the halo number density at redshift z~12 for a given mass, and since the growth of the system becomes suppressed, it harbours fewer baryons."}
{"text": "The first row of Fig. 3 presents the stellar mass function of matched galaxies between SAM_HB and Smaug at redshift z=13-5. We see that the two redshift z=5 mass functions are in agreement at stellar mass M_* > 10^7 solar masses, below which the models are limited by resolution and cooling mechanism. This indicates that the two modelled galaxy catalogues comprise similar stellar components at redshift z=5 in a cosmological context. However, the results diverge towards higher redshifts -- SAM_HB produces more massive galaxies than Smaug. This highlights the issue that stellar build-up proceeds faster in the SAM. As a consequence of the high-redshift modelling, the SAM produces more ionizing photons at earlier times compared to the hydrodynamic calculation, overestimating the contribution of high-redshift dwarf galaxies to reionization [Liu2016]."}
{"text": "We investigate the properties of individual galaxies in the two models, and show the comparisons of the total baryon mass, stellar mass and SFR predicted by the hydrodynamic simulation and SAM in the bottom three rows of Fig. 3. We see that the overall baryon mass is underestimated by the SAM, with the offset becoming larger at the low-mass end. This is because the NOSN_NOZCOOL_NoRe Smaug simulation predicts larger halo masses and baryon fractions than ADIAB due to cooling and star formation [Qin2017a]. Therefore, modifying the halo mass and baryon fraction using the ADIAB Smaug simulation overestimates the baryonic effect when feedback is not included. In addition, we see that both stellar mass and SFR are similar between the two models at redshift z=5, which are, however, underestimated in the SAM result when the stellar mass approaches 10^6 solar masses or SFR reaches 10^-2 solar masses per year. This causes an underestimation of the number of ionizing photons at the high redshifts."}
{"text": "We next discuss the involved prescriptions that might induce such discrepancies in the history of star formation. In the NOSN_NOZCOOL_NoRe case when feedback is not implemented, there are only two processes that might cause the different stellar growth histories between SAMs and hydrodynamic simulations: 1) star formation efficiency; and 2) gas fuelling and cooling efficiencies. We note again that since star formation is not resolved in cosmological simulations, both the hydrodynamic simulation and SAM start from an empirical relation between SFR and density -- the KS law [kennicutt1998global], which proposes that a galaxy is able to form stars when its surface density exceeds a critical value, and the surface SFR density can be estimated by a power law. We have shown that cooling is not well modelled in the SAM when the virial temperature is lower than the atomic cooling threshold, which leads to significant underestimations of the number of low stellar mass and SFR objects in Fig. 3."}
{"text": "In the hydrodynamic simulation, local 3D densities can be calculated through smoothing particle mass. Smaug converts the critical surface density to three dimensions assuming a self-gravitating disc. When the local pressure of a gas particle with a relatively low temperature (<10^5 K) exceeds the critical value, the particle is considered as a potential star forming region. This infers a SFR of dot m_star,hydro is proportional to (1+z)^1.1. On the other hand, the average SFR of a galaxy in the SAM is calculated using equation (6). For a given halo mass and with m_cold proportional to M_vir, the redshift dependency of the SAM SFR is approximately dot m_star,SAM is proportional to (1+z)^1.5. Comparing these equations, we find that although both numerical calculations of star formation are derived from the KS law, they possess different evolutionary histories for a given halo mass. This is essentially due to the different assumption of gas depletion time-scale adopted in the two modelling approaches."}
{"text": "In order to be consistent with the hydrodynamic simulation, a suppressed star formation efficiency of alpha_sf proportional to (1+z)^(-m) towards higher redshifts is required in the SAM. At higher redshifts, galaxies have larger velocity dispersions, indicating increased turbulence and thickened discs [Newman2012, Price2015]. Meanwhile, simulations suggest that mergers which happen frequently at high redshift [Poole2016] can also thicken discs [Moster2010, Moster2012]. Therefore, the assumption of a self-gravitating disc might not be valid at high redshift. If we assume an SIS profile for star-forming gas, the density scales as (1+z)^3, which leads to a larger value of m~0.7. Furthermore, during the experiment we find that, in the SAM, galaxies are more likely to have an insufficient cold gas reservoir at lower redshifts. This requires a more suppressed star formation efficiency at higher redshift, and in practice, m=1.3 is adopted in this work."}
{"text": "In Fig. 3, the semi-analytic result using the redshift-dependent star formation efficiency (SAM_HBS) is presented using dashed lines. We see that suppressing star formation at higher redshifts results in a better agreement of the stellar mass function, stellar mass and SFR with the hydrodynamic calculations. We define hot gas fraction as the mass ratio of the hot gas to the non-star-forming gas, and show its correlation with halo mass in Smaug at redshift z=13-5 in the left-hand panel of Fig. 4. We highlight galaxies above the atomic cooling threshold with red circles and we see that these galaxies in general comprise little or no hot gas. We see that the majority of galaxies at high redshift do not possess any hot gas, and their non-star-forming gas particles are identified as one group -- the cold non-star-forming gas."}
{"text": "However, due to the lack of molecular cooling, galaxies with virial mass M_vir less than or approximately equal to 10^8 solar masses do comprise two components. In the right-hand panel of Fig. 4, we show the 2D histograms of the hot (red) and cold (blue) non-star-forming gas temperatures as functions of halo mass in Smaug. We see that for galaxies with virial mass less than or approximately equal to 10^8 solar masses, their hot and cold non-star-forming gas particles possess median temperatures >10^3 K and <10^3 K, respectively. This broad distribution on the density--temperature phase diagram is from adiabatic cooling of the gas as the universe expands, which is also indicated by the decreasing median temperature at lower redshifts of these less massive objects. Gas in the IGM falls into the gravitational potential of a halo and fuels star formation in the host galaxy."}
{"text": "While gas particles cover a broad range of temperatures from approximately 10^3 - 10^8 K [Wiersma2009b] in the hydrodynamic simulation, (hot) gas initially accreted by a galaxy in the SAM is assumed to be shock-heated to the virial temperature. In order to test the validity of this simplified gas infall prescription for modelling of dwarf galaxies, we compare the temperature of non-star-forming gas in the hydrodynamic simulation to the halo virial temperature. In the right-hand panel of Fig. 4, we highlight galaxies with virial mass > 10^9 solar masses in Smaug with circles and show the correlation between virial temperature and halo mass with green solid lines. We see that fewer than 10 galaxies with virial mass > 10^9 solar masses in the Smaug simulation comprise hot gas at redshift z=5, and their hot gas temperatures are close to the virial temperatures, suggesting that theses galaxies have been heated through shocks."}
{"text": "However, the non-star-forming gas of most galaxies in Smaug is considered as cold with temperature T less than or approximately equal to 10^4 K, which is much lower than the virial temperature and becomes more common at higher redshifts. This is consistent with the prediction of EAGLE simulations [Schaye2014], where the mass ratio of hot to all baryons is less than 1 per cent on average for haloes around 10^10 solar masses [Correa2017], with the fraction decreasing towards higher redshifts and in less massive haloes. We see that in the SAM, cold and hot gas, where stars can and cannot form, are defined geometrically. They represent a star forming disc and the outer region, following an exponential and an SIS profile, respectively. However, we show that full virialization of infall gas might be problematic for high-redshift modelling of dwarf galaxy formation. In these less massive systems, virial shocks might not form and the infall gas could then only reach the virial temperature when it arrives at the star forming disc [Birnboim2003, Cattaneo2017]."}
{"text": "Instead, these cold and less dense non-star-forming gas particles of dwarf galaxies in Smaug represent a cold accretion mode [Keres2005, Keres2009, benson2011, Correa2017]. Therefore, in the SAM, instead of being fully virialized, the infall gas of dwarf galaxies should be separated into hot and cold components, which reach the disc and contribute to star formation on different time-scales. In addition, since the non-star-forming gas particles of the majority of high-redshift dwarf galaxies are not hot in the hydrodynamic simulation, we advocate that the terminology of hot gas becomes misleading in the redshift and mass ranges discussed in this work. The gas infall and cooling prescription adopted for the SAM distinguishes two regimes -- a static hot halo and rapid cooling gas. In the second regime, gas cools onto the disc at the dynamical time-scale, which has the properties of cold accretion if one combines the process of gas infall and rapid cooling."}
{"text": "Therefore, altering the rapid cooling rate is an alternative to incorporating cold accretion directly. The relative importance of the two cooling modes is determined by the ratio of the cooling radius to the virial radius, which is shown in the left panel of Fig. 6. We see that galaxies with stellar mass < 10^9 solar masses are mostly in the rapid cooling regime. The determination of static hot halo and rapid cooling regimes has been discussed in [croton2006many]. Comparing with hydrodynamic simulations, they found virial mass ~ 10^11 solar masses separates the two regimes, which is approximately independent with redshift up to redshift z~6 (see also [Correa2017]). This is in agreement with our finding of stellar mass ~ 10^9 solar masses. The balance of instantaneous cooling rate between the two numerical approaches can be inferred from the evolution of the mass ratio of star forming to non-star-forming gas. This is shown in the right panel of Fig. 6."}
{"text": "We see that while the SAM_HBS result is in agreement with the hydrodynamic calculation at low redshift, the ratio of star-forming to non-star-forming gas in the SAM is underestimated at higher redshifts. We have shown that in the SAM, dwarf galaxies at high redshift are identified as being in the rapid cooling regime. Therefore, in order to understand the different transition rates between non-star-forming reservoir and star-formation gas in Meraxes and Smaug, we next discuss the assumed SIS profile of hot gas reservoir in the SAM. We present the median radial profile of the non-star-forming gas of galaxies with stellar mass = 10^(7 +/- 0.5) solar masses in Smaug at redshift z=13-5 in Fig. 7. We see that the density of non-star-forming gas drops at the inner region when compared to an SIS mass profile. The non-star-forming gas particles 1) have a large dispersion up to greater than or approximately equal to 2 times the virial radius; and 2) are less concentrated at higher redshifts."}
{"text": "The SAM assumes the SIS profile for hot gas. Therefore, in the rapid cooling regime, the cooling mass during one time step can be calculated. We see that the SIS profile significantly overestimates the non-star-forming gas density in the inner region compared to the simulation result. Therefore, with the assumption that gas can only transform from non-star-forming to star forming gas when collapsing into the centre, the SIS profile leads to an overestimation of the inward collapse rate. However, due to the large radial region of star-formation gas observed in Fig. 7, this assumption might not be accurate. Gas particles in dwarf galaxies at redshift z>9 can be triggered as star forming regions as far as the virial radius. The combination of corresponding effects between the overestimated collapse rate from the assumed SIS profile and the underestimated transition radius of gas reservoir is the primary cause of the discrepancy in the ratio of star-forming to non-star-forming gas between Meraxes and Smaug."}
{"text": "Whilst adopting the correct gas profile and finding the accurate transition radius of gas reservoir can help explain the underestimation of the ratio of star-forming to non-star-forming gas in the SAM at high redshift, an analytic solution is not well defined. The large dispersion in the gas profile is mainly due to frequent mergers at these redshifts, which can be affected by numerical configurations, as well as by physics implementations including feedback. In order to take the underestimated cooling rate of dwarf galaxies at high redshift into account, we propose an alteration to the cooling equation and allow the free parameter, kappa_cool representing the maximum cooling factor to exceed unity at high redshift. We show the result of the ratio of star-forming to non-star-forming gas calculated with kappa_cool = min(5, (1+z)/6) in Fig. 6, and we see that with higher cooling rates, the semi-analytic calculation becomes more consistent with the hydrodynamic result at high redshift."}
{"text": "However, the stellar mass function becomes higher at redshift z=13 compared to the Smaug result (see Fig. 3), suggesting the necessity of stronger suppression of the star formation efficiency due to the relatively larger disc mass at higher redshifts in the SAM. Lastly, we point out that without a self-consistent radiative transfer calculation, atomic cooling and gas temperature might not be properly simulated in the hydrodynamic simulation either, which alters the importance of thermal radiation cooling. For instance, with local sources of ionizing radiation neglected, the cooling rate is potentially overestimated [Schaye2014], and since self-shielding cannot be properly captured in our hydrodynamic simulations, the cooling rate might be underestimated in dense regions [McQuinn2011]. Moreover, supernova feedback and reionization are expected to regulate galaxy formation through altering the gas component, which will be the topic of a forthcoming paper."}
{"text": "While most assumptions adopted for semi-analytic galaxy formation models, including the gas reservoirs, are in good agreement with hydrodynamic simulations for Milky Way size objects [Guo2016, Stevens2016b], they become less accurate for less massive galaxies at high redshift. In this work, we propose modifications to SAMs based on the comparison of dwarf galaxy properties calculated by the Meraxes SAM and the Smaug high-resolution hydrodynamic simulation. We focus on gas accretion, cooling and star formation at redshift z>=5, and consider scenarios in the absence of reionization and supernova feedback. We summarize the modifications below: The parent cosmological simulation of a SAM usually includes only collisionless particles, where baryonic physics is neglected. In making comparisons between N-body and hydrodynamic simulations starting from identical initial conditions, we previously showed ([Qin2017a]) that dwarf galaxy host halo masses are significantly overestimated when hydrostatic pressure is not considered, and that the fraction of baryons accreted by dwarf galaxies cannot reach the level of cosmic mean."}
{"text": "While inclusion of halo masses directly from N-body dark matter only simulation and assumption of a universal baryon fraction are standard features of SAMs, the impact of these assumptions becomes significant at high redshift and small scale. We find that the star formation prescription in the SAM that is based on the consumption of a cold gas reservoir does not represent the evolutionary path followed by gas in the hydrodynamic simulation, while both of the two modelling approaches start from the observational relation between surface density and SFR [kennicutt1998global]. We find that this results from variation in the calculated depletion time-scale of the gas reservoir. We address this by modifying the efficiency that modulates star formation in the SAM with a redshift dependency. In this work, we adopt alpha_sf(z) = 0.05 * [(1+z)/6]^-1.3, which allows the model to follow the NOSN_NOZCOOL_NoRe hydrodynamic simulation in the Smaug suite."}
{"text": "The majority of dwarf galaxies at high redshift are in the rapid cooling regime, where the infalling gas cannot form stable shocks or remain in hydrostatic equilibrium. This represents a cold accretion mode, which is not well modelled with the assumption that the hot gas reservoir follows the SIS profile and falls into the centre within the dynamical time. We find, in the hydrodynamic simulation, that gas in high-redshift dwarf galaxies can form stars as far as the virial radius and that the SIS profile overestimates the density in the inner regions of these low-mass objects. In order to take this into account, we propose of modulation of the cooling prescription with a redshift-dependent collapse rate where kappa_cool(z) = min[5, (1+z)/6] leads to an agreement with the hydrodynamic calculation on the cold gas mass evolution. Furthermore, we point out that the terminology of hot gas and cold gas becomes misleading when applying SAMs to the formation of high-redshift dwarf galaxies."}
{"text": "The hot gas representing non-star-forming gas within a galaxy does not experience full virialization and possess a median temperature that is much lower than the virial temperature of the host halo. In a future paper (Qin et al. in prep.), we will discuss star formation in the presence of feedback from reionization and supernovae. We will compare the SAM calculation with the most complete hydrodynamic simulation in the Smaug suite that considers reionization as an instantaneous heating background [Haardt2001] and distributes supernova energy in thermal form [DallaVecchia2012]. We will also consider an additional star formation prescription to the one shown in this work, in which molecular gas directly drives the star formation history [Lagos2011]. The goal of these two papers will be more complete and faithful recreation of hydrodynamic simulations at high redshift, which will further leverage the observations that we can make in this early history of our Universe."}
{"text": "In this work, we make direct comparisons of the semi-analytic and hydrodynamic galaxy properties calculated by Meraxes and Smaug, respectively. We connect galaxies produced by Meraxes to their host haloes in the N-body simulation, and then match galaxies in Meraxes with the corresponding hydrodynamic simulation. The same algorithm of matching haloes between snapshots is adopted to match between simulations. Dark matter (and baryon) particles evolve (co-evolve) in Smaug, and friend-of-friend (or fof) groups and subgroups (or haloes), to which particles belong are determined using a standard fof halo finder and subgroup finder ([subfind], [springel2008aquarius]) in post-processing. Then by tracking halo particles in consecutive snapshots, each halo can be linked to its progenitors and form a merger tree. This process is applied to all haloes at one snapshot, in order to horizontally construct the merger trees, which allows the SAM to evolve all galaxies at each snapshot and calculate reionization feedback self-consistently."}
{"text": "We next give a brief overview of the gbptrees algorithm used to build dark matter halo merger trees. For each halo, subfind sorts particles according to their kinetic and potential energies, with, in general, more bounded particles ranking higher. For each candidate, a pseudo-radial moment is defined. We define the goodness of a matching candidate as the difference between the pseudo-radial moment at m=-1 and m=0. The two halos are considered as a good match when this difference is > -0.2 [poole2017mnras.472.3659p]. Amongst all good matches, the best match is identified by maximizing the statistic of the pseudo-radial moment at m=-1 during the process of scanning for good matches forwards and backwards over 16 snapshots. A consequence of this algorithm is that matching is performed by tracking halo cores instead of the majority of halo particles. This central weighting algorithm allows us to build more realistic halo merger trees."}
{"text": "Meraxes reports the Most Bounded Particle (MBP) of the host halo for each galaxy, which bridges SAM galaxies and dark matter haloes in DMONLY. In order to further connect haloes in the collisionless N-body simulation with simulations including baryonic physics, we match haloes between simulations using the same matching strategy described in Appendix A.2. Instead of matching 33 snapshots in one simulation, we match haloes from two simulations (e.g. NOSN_NOZCOOL_NoRe and DMONLY) using their dark matter particles at each snapshot. This is achievable because all the Smaug simulations including DMONLY start from the identical cosmological initial conditions and their dark matter particles possess the same IDs over different simulations. However, with information from only two snapshots, mismatches and pathologies occur in particular when reaching the resolution limit. Therefore, final matched sample is limited to haloes which are matched bidirectionally."}
{"text": "Fig. A2 illustrates how galaxies are finally matched between Meraxes and Smaug with this two-step manner that MBPs connect galaxies from Meraxes to their host haloes which are matched with Smaug galaxies through dark matter particles. In this work, only central galaxies with virial masses exceeding the resolution threshold of 10^7.5 solar masses in the SAM results are considered, and in order to minimize the impact from central-satellites switching mentioned in Appendix A.2, satellite galaxies identified in the SAM are excluded from the final sample as well. In the NOSN_NOZCOOL_NoRe Smaug simulation, there are 195562 galaxies, in which 129043 galaxies (~ 66 per cent) are matched with Meraxes. In this work, we use a machine learning algorithm to spilt non-star-forming gas particles into hot and cold components. The two groups are considered as one when the offset between their median temperatures is small."}
{"text": "Fig. A3 shows the fraction of hot gas in the non-star-forming gas at redshift z=5 with different choices of the temperature offset threshold Delta_T,crit, and we see that a smaller Delta_T,crit introduces more galaxies with a hot gas fraction > 0. However, this only affects galaxies with inefficient cooling (i.e. below the atomic cooling thresholds) while the hot gas fraction of more massive galaxies remain zero or small. On the other hand, when non-star-forming gas particles of a galaxy are considered as one group, which is common for galaxies with efficient cooling, whether they are determined as hot or cold is based on their median temperature. We vary the minimum temperature of particles being identified as hot (T_crit) from 10^5 K to 10^4 K and we find that the hot gas fraction is insensitive to T_crit. Based on these, we note that the choice of temperature thresholds does not have a significant impact to our conclusion that high-redshift dwarf galaxies accrete gas in cold mode."}
{"text": "A numerical experiment evolves a galaxy by calculating physics processes in a predefined order. For instance, Meraxes in sequence calculates reionization, baryonic infall, cooling, star formation and the impact of supernova feedback. Thanks to the exquisite time step of calculation of hydrodynamic simulations, their outputs can be considered as instantaneous galaxy properties at a given redshift. However, this is not the case for the SAM used in this work, which records properties that either have or have not been processed or are average values during one time step. In the right panel of Fig. 6, we show the ratio of star-forming to non-star-forming gas, which is the mass ratio of cold to hot gas in the SAM. Three moments of calculation can be adopted: (1) after star formation; (2) before star formation and after cooling; (3) before cooling and after baryon infall. We note that case (1) is adopted in the main context, and we show the difference in Fig. A4. We see that because of the high cadence (~11Myr) of the SAM, the choice of calculation does not have a significant impact to our results."}
{"text": "We directly compare predictions of dwarf galaxy properties in a semi-analytic model (SAM) with those extracted from a high-resolution hydrodynamic simulation. We focus on galaxies with halo masses of 10^9 < virial mass / solar mass less than or approximately equal to 10^11 at high redshift (redshift z >= 5). We find that, with the modifications previously proposed in [qin2018], including to suppress the halo mass and baryon fraction, as well as to modulate gas cooling and star formation efficiencies, the SAM can reproduce the cosmic evolution of galaxy properties predicted by the hydrodynamic simulation. These include the galaxy stellar mass function, total baryonic mass, star-forming gas mass and star formation rate at redshift z~5-11. However, this agreement is only possible by reducing the star formation threshold relative to that suggested by local observations. Otherwise, too much star-forming gas is trapped in quenched dwarf galaxies."}
{"text": "We further find that dwarf galaxies rapidly build up their star-forming reservoirs in the early universe (redshift z>10), with the relevant time-scale becoming significantly longer towards lower redshifts. This indicates efficient accretion in cold mode in these low-mass objects at high redshift. Note that the improved SAM, which has been calibrated against hydrodynamic simulations, can provide more accurate predictions of high-redshift dwarf galaxy properties that are essential for reionization study. Reionization refers to an important process after the Big Bang, during which the intergalactic medium (IGM) was transiting from neutral hydrogen to its ionized state [Wyithe:2004kb]. According to the observed galaxy sample at high redshift [Bouwens2014, Bouwens2015, Stefanon2016arXiv161109354S, Oesch2016ApJ...819..129O], this process can only happen with ionizing photons from much fainter galaxies taken into account [Robertson2013ApJ...768...71R, duffy2014low, Bouwens:2015hk, Liu2016]."}
{"text": "Although there are still some debates on other possible sources that can dominate the high-redshift photon budget such as active galactic nuclei (AGN; [Giallongo2015A&A...578A..83G, Madau2015ApJ...813L...8M, Qin2017c, Hassan2018MNRAS.473..227H]), dwarf galaxies that are beyond our observational capabilities are generally thought to have driven the Epoch of Reionization (EoR). In this context, understanding the formation of these unobserved objects is crucial to studying the EoR and can only be probed at this stage with theoretical simulations. Hydrodynamic simulations evolve dark matter and baryonic particles simultaneously and provide direct insights into the relevant astrophysical process [Vogelsberger2014, Schaye2014, Hopkins2014MNRAS.445..581H, feng2015bluetides]. However, resolving dwarf galaxies within a cosmological volume for reionization studies usually involves more than a few billions of particles, which remains computationally challenging at this stage. A more efficient method is to apply semi-analytic models (SAMs; [croton2006many, Somerville2008, guo2011dwarf, Henriques2015]) to N-body simulations that only consider collisionless particles."}
{"text": "Using the halo properties inherited from the parent simulation, SAMs approximate baryonic physics such as gas accretion, star formation and feedback using simplified scaling relations. These relations are motivated directly from physical processes, or empirically from observational results and more complicated numerical techniques such as hydrodynamic simulations and radiative transfer calculations. The semi-analytic prescriptions that indirectly model galaxy formation introduce free parameters to describe efficiencies which are inevitably accompanied by parameter degeneracies [Mutch2013, Henriques2013]. This can make their predictions sometimes controversial, and potentially disconnected from the true behaviour in the universe. An alternative to validate SAMs in the absence of observations at high redshift is to compare their results against hydrodynamic calculations that start from identical cosmological initial conditions. The goal of this work is to capture emergent behaviours from the hydrodynamic simulations and to improve the parametrised modelling in SAMs as so to replicate these processes."}
{"text": "Under the assumption that hydrodynamic simulations are a more natural description of the astrophysical phenomenon and hence more representative of real galaxies, we can explore the semi-analytic prescriptions for quantities that are, in practice, unobservables and potentially reveal improper assumptions or missing physics in SAMs. [Guo2016] compared the L-galaxies [Cole2000, Bower2006] and GALFORM [Springel2005, Henriques2015] SAMs with the EAGLE hydrodynamic simulations [Schaye2014], and concluded that the models can reproduce the stellar mass function predicted by EAGLE. However, discrepancies were also found in the efficiencies of stellar and AGN feedback as well as the prediction of stellar mass-metallicity and size relations. [Mitchell:2017je] also used EAGLE to assess GALFORM and found the angular momentum as well as the baryon cycling might not be properly traced in the SAM, leading to inaccurate predictions of galaxy sizes."}
{"text": "[Stevens:2017fi], on the other hand, investigated cooling of Milk Way-like galaxies in EAGLE and addressed the necessity of updating the cooling prescription employed in most SAMs (see recent updates of the cooling model in [Hou2018mnras.475..543h, Hou2018arxiv180301923h]). We, in the previous paper [qin2018], also found that the cooling prescription needs revision for more accurate modelling of low-mass galaxies at high redshift and proposed an alternative modification to the current prescription, avoiding the introduction of a new model. [Cote:2017uh] recently extended the comparison from cosmological simulations of smoothed particles to zoom-in simulations of a system with a total mass of approximately 10^9 solar masses, and investigated the difference in dwarf galaxy formation between a SAM and hydrodynamic simulation. They found their SAM was successful in reproducing the hydrodynamic calculation of star formation history but with a prediction of a much narrower distribution of metallicity compared to the hydrodynamic result."}
{"text": "This is the second paper following the work of [qin2018], where we investigated the performance of SAMs when applied to high-redshift dwarf galaxies. We used the Meraxes SAM [Mutch2016a] as an example and focused on gas accretion, cooling and star formation with reionization and supernova feedback isolated. We compared the stellar and gas masses with a high-resolution hydrodynamic simulation from the Smaug suite, and found that, in the SAM, 1) due to the lack of hydrostatic pressure in parent N-body simulations, inheriting halo properties directly from the dark matter halo merger trees overestimates the total mass of haloes hosting dwarf galaxies; 2) the assumption that, in the absence of feedback, haloes consists of a baryonic reservoir with a mass of the cosmic baryon fraction of their total mass is not accurate for dwarf galaxy formation modelling; 3) star formation modelled by consuming the total gas disc in a few dynamical times of that disc cannot capture the evolutionary path of star formation implemented in hydrodynamic simulations; and 4) gas accreted by dwarf galaxies is cold."}
{"text": "Accordingly, we proposed modifications to SAMs, seeking for consistency with hydrodynamic simulations in calculations of the evolution of stellar and gas components of dwarf galaxies. In this work, we include these modifications as well as feedback from reionization and supernovae, and investigate whether the updated SAM can broadly agree with the hydrodynamic calculation of dwarf galaxies in the presence of feedback. We start with a brief review of the Meraxes SAM as well as the modifications proposed in [qin2018] and the Smaug hydrodynamic simulation suite in Section 2. We then present and discuss our comparison results in Section 3. Conclusions are given in Section 4. In this work, we adopt the Chabrier initial mass function (IMF) in the mass range of 0.1-120 solar masses and cosmological parameters from WMAP7."}
{"text": "The Dark-ages Reionization And Galaxy Formation Observable from Numerical Simulation (DRAGONS) project employs N-body simulations, hydrodynamic simulations and SAMs to study reionization and galaxy formation at high redshift (redshift z >= 5). In the previous publication of this series, we used the Meraxes SAM as an example and investigated the semi-analytic modelling prescriptions adopted in the literature. We focussed on comparisons of dwarf galaxy properties calculated by Meraxes with a simplified model that ignores feedback from the Smaug hydrodynamic simulation suite. Based on the comparison, we proposed modifications to the halo properties as well as the cooling and star formation prescriptions. In this work, we include reionization and supernova feedback, and extend the comparison of high-redshift dwarf galaxies modelling with a molecular-hydrogen-based star formation law in the SAM."}
{"text": "We briefly introduce the Meraxes SAM and Smaug hydrodynamic simulation in this section with emphasis on reionization and supernova feedback. Meraxes evolves galaxies with scaling relations capturing baryonic processes. These include gas infall, cooling, star formation, supernova feedback, metal enrichment, stellar mass recycling, reionization, supermassive black hole growth, AGN feedback and mergers. It also calculates the ionization state of the IGM using the 21cmFAST semi-numerical algorithm. Note that, in order to take hydrostatic pressure into account in this work, halo masses inherited from the merger trees that are constructed from collisionless N-body simulations as well as total baryonic masses are updated using the halo mass and baryon fraction modifiers provided in [Qin2017a]."}
{"text": "Gas falls into a halo from the IGM and cools through thermal radiation. Within a transition time-scale, this process leads to the formation of a star-forming disc, which is assumed to follow an exponential surface density profile. In previous DRAGONS publications, we follow [croton2006many], form stars by consuming the total star-forming gas, and calculate the star formation rate (SFR) by a formula where the depletion time-scale of total star-forming gas on the disc is proportional to the dynamical time-scale of the host halo. However, this was found to be inconsistent with the implementation in hydrodynamic simulations. In this work, we instead adopt a different equation and use free parameters to directly adjust the evolutionary path of the depletion time-scale. A second star formation prescription will be explored in this work, the detail of which will be presented in Mutch et al. (in prep.)."}
{"text": "Note that this prescription is based on the depletion of molecular hydrogen (see [Lagos2011] and references therein) and is considered as a more physically plausible model compared to the total-gas-based star formation prescription. First, we assume stars follow the same distribution as the interstellar medium (ISM) and they are considered as a stellar disc with an exponential surface density profile. We then calculate the pressure of the ISM accounting for both stars and hydrogen through the [Elmegreen1993] approximation. In order to split the disc into molecules and atoms, the observed relation between the ISM pressure and the surface density ratio of neutral to molecular hydrogen is implemented. [Blitz2006] investigated the neutral hydrogen, CO and stellar densities of 14 nearby galaxies and found a power-law relation between the ratio of neutral to molecular hydrogen surface densities and the ISM pressure. With this, we estimate the molecular hydrogen mass and calculate the SFR."}
{"text": "Inferred from the stellar lifetime-mass relation and the assumed IMF, we calculate the fraction of the newly formed stars which will have reached the supernova stage at the end of the current time step. These stars recycle their masses to the ISM, and the metals and energy produced by the supernovae provide feedback to the environment. In particular, the metals enhance the cooling rate through the metallicity dependent cooling function while the supernova energy leads to transition of gas between different reservoirs. In practice, supernova energy converts star-forming gas to hot (i.e. non-star-forming gas) and, in the case of strong supernova feedback, further ejects hot gas from the galaxy. In this work, we adopt the [guo2011dwarf] prescriptions to calculate the energy coupled to the surrounding gas. We consider two supernova feedback regimes: 1) contemporaneous feedback; and 2) delayed feedback where long-lived stars formed at earlier times are taken into account."}
{"text": "Therefore, the total energy released in the current snapshot is the sum of the supernova energy from stars formed in the current and previous 4 snapshots. On the other hand, the expected mass of gas that is heated by supernovae depends on the mass loading factor, which is assumed to follow the same form as the coupling efficiency. We first calculate the maximum reheated mass with an upper limit set to be 10 following [Mutch2016a], which is a typical value for high-redshift dwarf starburst galaxies [uhlig2012]. Note that, since the total supernova energy is finite, a galaxy might not be able to heat all the mass estimated from the loading factor. Therefore, we calculate the mass of actually reheated gas. While in the case of an intense supernova event, the energy released by supernovae further unbinds the hot gas which is removed from the galaxy and stored in a reservoir termed the ejected gas. We assume the ejected gas does not contribute to star formation."}
{"text": "In order to model the feedback from reionization, we further inhibit the local baryon fraction of haloes by a factor of f_mod which is defined as 2 to the power of (-M_crit / M_vir), where M_vir is the halo mass and M_crit represents a filtering mass below which haloes are not able to efficiently accrete baryons from the IGM. We calculate the critical mass for each halo following [Sobacchi2013a], where it depends on the local UV background intensity and the redshift at which the surrounding IGM was first ionized, which is determined using the 21cmFAST algorithm. Smaug, a high-resolution hydrodynamic simulation suite, was performed using a modified version of the GADGET-2 N-body/hydrodynamics code, following the same parameter configuration of the OverWhelmingly Large Simulations project (OWLS; [Schaye2010]). The simulations presented in this work start from the same initial conditions generated with the grafic package at redshift z=199 using the Zel'dovich approximation."}
{"text": "Each simulation evolves (2x)512^3 particles including dark matter (and baryons) within a periodic cube of comoving side of 10 per h Mpc. The Plummer-equivalent comoving softening length is 0.2 per h kpc and the particle resolution is 4.7 and 0.9 x 10^5 per h solar masses for dark matter and baryons or 5.7 x 10^5 per h solar masses if only dark matter particles are considered. We summarize the adopted subgrid physics prescriptions in this section. Cooling [Wiersma2009a] consists of both primordial elements and metal emission lines from carbon, nitrogen, oxygen, neon, magnesium, silicon, sulphur, calcium and iron. Star formation [Schaye2008] occurs in the ISM that is assumed to be multiphase. Supernova feedback can be simulated kinetically [DallaVecchia2008] or thermally [DallaVecchia2012]. In order to compare galaxy properties between Meraxes and Smaug, we focus on the hydrodynamic simulation with thermal supernova feedback implemented."}
{"text": "Reionization feedback is implemented as a UV/X-ray background with all gas particles being instantaneously heated to 10^4 K at a given redshift. Although this prescription is numerically achievable and is considered appropriate in the 10 per h Mpc volume of Smaug simulations, it is not an accurate calculation of reionization feedback. Therefore, the semi-analytic prescription of reionization feedback will be compared to two hydrodynamic simulations with reionization redshifts of 9 and 6.5, which bracket the observed CMB and Lyman-alpha forest boundaries of the EoR, and represent the strongest and weakest feedback scenarios, respectively. Simulations utilized in this study is summarized below: (1) DMONLY, a collisionless N-body simulation; (2) NOSN_NOZCOOL, NOSN_NOZCOOL_LateRe and NOSN_NOZCOOL_NoRe, three toy models with cooling in the absence of metal line emission and ignoring supernova feedback; and (3) WTHERM, a complete hydrodynamic simulation including radiative cooling from primordial elements and metals, as well as stellar evolution, thermal supernova feedback and instantaneous photoionization heating from a reionization background at redshift z=9."}
{"text": "In this work, with algorithms described in [qin2018], we 1) include the aforementioned modifications of the semi-analytic properties or prescriptions; 2) build halo merger trees using the DMONLY simulation; 3) match each individual galaxies between Meraxes and Smaug outputs; and 4) identify star-forming and hot gas in Smaug. We present the comparison result between dwarf galaxy properties predicted by the hydrodynamic simulation and SAM in this section. Reionization feedback in the SAM is incorporated by inhibiting the local baryon fraction of haloes using a filtering mass. In this work, we adopt the average filtering mass, which ignores the spatial distribution of the IGM ionization state and depends only on redshift. In order to assess the validity of this feedback prescription, we compare with two Smaug hydrodynamic simulations in which gas particles are instantaneously heated to 10^4 K at different redshifts."}
{"text": "Note that the suppression due to the ionizing background is quantified in the SAM using a baryon fraction modifier, which, in hydrodynamic simulations, can be informed by comparing the baryonic components of galaxies matched between the different reionization feedback runs. We see that, through photoionization heating, reionization plays a significant role in reducing the fraction of baryons, and that the baryon fraction modifier adopted in the SAM is in general agreement with the hydrodynamic result -- the modifier decreases in less massive haloes and towards lower redshifts. In a 10 per h Mpc volume, the UV/X-ray ionizing background adopted in the two hydrodynamic simulations represents the strongest and weakest feedback scenarios that are consistent with the CMB and Lyman-alpha observations. However, since reionization does not affect the gas component before the reionization redshift in these simulations, its feedback on the baryonic reservoirs cannot be captured by the simulations at higher redshifts."}
{"text": "Therefore, the time when reionization feedback becomes important is relatively late compared to the SAM where the onset of reionization is more gradual and realistic on large scales. As a result, the baryon fraction is overestimated in the hydrodynamic simulations at earlier times, which can potentially lead to an overproduction of stellar mass in dwarf galaxies. We next investigate the stellar evolution and feedback in Meraxes and Smaug, starting with a discussion of involved free parameters in the SAM. Cosmological SAMs are usually calibrated against the observed galaxy stellar mass functions where a sufficient sample is available. By doing this, the stellar component is assured to be well modelled in a statistical context, and with more upcoming observations, the parameter space becomes better constrained and missing physics in the SAM might be revealed. However, one of the issues about this calibration strategy is that it cannot guarantee the modelled galaxies are also representative of real galaxies in terms of their unobservable properties."}
{"text": "Taking the gas component as an example, although a handful of radio telescopes are capable of observing the gas component of distant galaxies, the current sample remains small, limiting our understanding of how galaxies accrete baryons and convert their hydrogen into stars in the early universe. In order to illustrate this, we use the total-gas-based star formation model with parameters adopted in [Mutch2016a] as an example. With a short depletion time-scale of the total star-forming gas, the dynamical time-scale for gas transition, and strong supernova feedback, Meraxes was able to reproduce the observed stellar mass function at redshift z=5-7 in [Mutch2016a]. We see that the semi-analytic prediction is in agreement with Smaug above the resolution limit. We next show more detailed galaxy property evolution, including the total baryonic mass, star-forming gas mass and SFR, from the two numerical experiments in two mass ranges."}
{"text": "We see that, although the SAM is in agreement with the hydrodynamic simulation on the stellar mass function at a large range of redshifts, they disagree on the evolutionary path of the gas component. We find that the baryonic mass is about 2-5 times smaller in the SAM compared to the hydrodynamic simulation, suggesting that too much supernova energy has been coupled to the ISM. In addition, the hydrodynamic simulation shows an increasing amount of star-forming gas towards higher redshifts for a given halo mass. This suggests that cooling (or cold-mode accretion) might be more efficient in the early universe. On the other hand, the SAM underestimates the star-forming gas reservoir at higher redshift but predicts a similar SFR. This suggests that the depletion time-scale might be set shorter in the SAM, which happens to result in an agreement with the hydrodynamic result on the stellar mass function."}
{"text": "We recalibrate our chosen parameters in order to simultaneously reproduce the evolutions of the stellar mass function of the hydrodynamic simulation, as well as the following three quantities: total baryonic mass, star-forming gas mass, and SFR. After exploring the parameter space, we identify a set of parameters that lead to a better agreement on the property evolution of galaxies with virial mass > 10^10 solar masses. This model is referred to as SAM_KS_limited. However, in the low-mass range where the virial mass is between 10^9 and 10^10 solar masses, this model fails to reproduce the evolutionary path of the star-forming gas reservoir calculated by the hydrodynamic simulation. During the experiment, we find that the star-forming gas mass at low redshift does not change by incorporating a larger mass loading factor, which is expected to further suppress the star-forming gas mass through supernova heating."}
{"text": "This suggests that the bulk of star-forming gas is stored in quenched galaxies where the star-forming gas mass is less than the critical mass for star formation. According to the total-gas-based star formation prescription, galaxies can only form stars when their gas reservoirs are adequate. This reservoir mass threshold is calculated based on observations at the local Universe. In the current DRAGONS series, we instead have adopted a lower critical mass. This is supported by [Henriques2015], which proposes to reduce the mass threshold of star-forming galaxies to reconcile the issue that previous SAMs have overpredicted the number of quenched galaxies in the low-mass range while these galaxies still possess a significant amount of star-forming gas reservoir. This might explain the evolution of star-forming gas mass of dwarf galaxies predicted by SAM_KS_limited and suggests that the threshold of star formation needs to be further reduced in these low-mass galaxies."}
{"text": "We next focus on the dwarf galaxies and recalibrate the model without any thresholds of star formation. The result of this model, SAM_KS_unlimited, shows that while SAM_KS_limited with a critical mass of approximately 10^8 solar masses is better at reproducing the hydrodynamically simulated high-mass galaxies, the updated model with no threshold is more consistent with the hydrodynamic result at the low mass range. This indicates high-redshift less massive galaxies, in general, possess lower thresholds of star formation as well. Note that in SAM_KS_unlimited, a rapidly evolving gas transition time-scale is crucial to reproducing the evolution of the star-forming gas mass calculated by the hydrodynamic simulation. However, it also leads to unrealistically rapid changes of the gas transition efficiency in the SAM. We note that, with more intense supernova heating to offset it, additional gas can be allowed to transition from hot to star-forming."}
{"text": "Therefore, incorporating a larger mass loading factor at lower redshifts will decrease the transition time-scale accordingly and allow moderate changes of the transition rate. However, as we will see, supernova heating only plays a secondary role in changing the evolution of star-forming gas of high-redshift dwarf galaxies. In these two SAM_KS models, stars form by consuming the total star-forming gas reservoir. However, due to the unknown time-scale of depleting the total gas, the degeneracy between the processes of cooling and heating exists. [Duffy2017] investigated the molecular hydrogen component of dwarf galaxies using the Smaug simulations and found the depletion time-scale of molecular hydrogen is approximately 0.3 Gyr, independent of the feedback regime. They also discussed the mass and redshift dependencies when applying SAMs with molecular hydrogen-based star formation laws and proposed a redshift-dependent depletion time-scale, the extrapolation of which agrees with the previous findings at the local Universe."}
{"text": "We note that the scaling index of the depletion time-scale was motivated from the KS law with an assumption that galactic discs are self-gravitating and follow exponential surface profiles. The latter might need revising for high-redshift dwarf galaxies. In the early universe, galaxies tend to possess larger velocity dispersions and both mergers and cold-mode accretion are significant. These all indicate that high-redshift galaxies might have thickened discs. In this section, we adopt a less steeply evolving redshift dependency due to thicker discs at high redshift, and then calibrate cooling and supernova feedback efficiencies to reproduce the dwarf galaxy properties from Smaug. We will further discuss the semi-analytic prediction when varying the depletion time-scale. We see that without any degeneracies, the molecular hydrogen-based model can still reproduce the hydrodynamic calculation of the properties of dwarf galaxies as well as the cosmic evolution of the stellar mass function."}
{"text": "Compared to the SAM_KS_unlimited result, SAM_H2 agrees better with Smaug on the evolution of the total baryonic mass of dwarf galaxies, and the calculation of massive galaxies. However, it still overestimates the total baryonic mass and underestimates the mass of star-forming gas and SFR of massive galaxies, suggesting that these galaxies might possess different cooling and supernova feedback efficiencies or shorter depletion time-scale of molecular hydrogen compared to less massive galaxies. The success of our SAM with the molecular hydrogen-based star formation prescription and a fixed molecular hydrogen depletion time-scale is encouraging. It indicates that the accretion-cooling-depletion-heating-and-ejection pathway of gas is still representative for dwarf galaxy formation at high redshift in terms of predicting the gas and stellar properties of the hydrodynamic simulation. We next use the molecular hydrogen-based SAM as an example and illustrate the impact of changing the relevant parameters with comparisons to the fiducial SAM_H2 model."}
{"text": "The gas transition time-scale of the fiducial SAM_H2 model results in a significantly larger value at low redshift. We show this scaling, as well as the result of assigning the transition time-scale with the free-fall time-scale (a common assumption adopted in the literature for the rapid cooling regime), and a time-scale that evolves slower towards higher redshifts compared to the fiducial model. We see that adopting a shorter transition time-scale results in the star-forming gas reservoir receiving more efficient replenishment. In the case of unchanged gas depletion time-scale, SFR increases. Consequently, more energy gets ejected from supernova explosions, leading to more suppressed total baryonic masses given that the energy coupling efficiency and mass loading factor for heating do not change. We see that without changing other parameters, a significantly evolving transition time-scale is required to reproduce the rapidly decreasing star-forming gas mass at lower redshifts as predicted by the hydrodynamic simulation."}
{"text": "The molecular hydrogen depletion time-scale is better constrained than that of the total gas. However, observational results still possess large variance even in the local Universe, from a half to a few Gyr. Therefore, we use the redshift-dependent molecular hydrogen depletion time-scale proposed in [Duffy2017]. For the fiducial model, we use a less steeply evolving redshift dependency due to thicker discs at high redshift. We show the property evolution of using the time-scales proposed by [Duffy2017] as well as a constant value, which is commonly adopted for SAMs in the literature. We see that by increasing the time-scale of converting hydrogen into stars, star formation quenches, leading to weaker supernova ejection and heating. With the current configuration of parameters, we see that a constant 2 Gyr depletion time-scale significantly underestimates star formation at high redshift in agreement with [Duffy2017] and the star-forming gas evolution gradient is not expected to change significantly by varying the redshift dependency."}
{"text": "Supernova explosions increase the thermal energy of the ISM and expel baryons in dwarf galaxies. However, since the relevant region cannot be resolved in cosmological simulations, subgrid physics with free parameters are adopted by both hydrodynamic and semi-analytic modelling approaches. The fraction of supernova energy that contributes to feedback is f_th and epsilon_energy in Smaug and Meraxes, respectively. Since f_th is chosen to be unity, with all the supernova energy being coupled to the ISM, one might expect epsilon_energy=1 as well. However, because SAMs ignore the thermal energy of the star-forming gas and assume the temperature of hot gas does not change during one time step, epsilon_sf-sf and epsilon_hot-hot are zero. This means that, despite all supernova energy being coupled to the ISM in the hydrodynamic simulation, only a fraction of it contributes to feedback in the SAM."}
{"text": "How much of the supernova energy is coupled to the ISM and used to heat gas is governed by free parameters describing the mass loading factor in the SAM while in the hydrodynamic simulation, it is the increment of gas temperature that determines the number of gas particles that are affected. This indicates that, in the hydrodynamic simulation, the mean number of instantaneously heated nearby gas particles per stellar baryon is approximately 1.34 [DallaVecchia2012]. This small mass loading factor places the heated gas in the Bremsstrahlung cooling regime, achieving an efficient supernova feedback mechanism through heating. Moreover, due to the increased pressure from the thermal feedback, gas particles within high overdensities tend to move outwards in a wind. As the wind particles travel, they further increase the thermal energy of the nearby gas particles along the path, leading to a much larger effective mass loading factor over a long period of time."}
{"text": "Since the SAM captures the average property over 11Myr, one might expect the SAM mass loading factor to be much larger than 1.34 as well. However, we have also shown that in hydrodynamically simulated dwarf galaxies, gas particles need not be fully virialized to become non-star-forming gas while on the other hand, SAMs ignore the thermal energy of the star-forming gas and assume the non-star-forming hot gas shares the virial temperature of host halo. Without properly tracking the thermal energy of varied gas reservoirs in the SAM, it is challenging to determine the energy-ISM coupling efficiency and mass loading factor. In this work, against the hydrodynamic result of WTHERM, we have calibrated our fiducial SAM. We see that when the mass loading factor is fixed, more coupled energy to the ISM leads to stronger suppression of the total baryonic mass, which subsequently decreases the mass of the star-forming disc and quenches star formation."}
{"text": "From the MaximumSNCoupling model, we see that with all supernova energy used to convert star-forming gas to hot and eject hot gas from the galaxy, the total baryonic mass and star-forming gas become significantly suppressed. On the other hand, when the supernova energy coupling efficiency is fixed, less heating leads to a larger reservoir of star-forming gas and enhanced star formation. Consequently, more supernova energy is coupled to the ISM. With less energy used for heating, more mass in the hot gas reservoir gets ejected. Depending on the increased amount of star-forming gas and stellar mass as well as the decreased hot gas mass, the total baryonic mass varies slightly. In addition, the property evolution does not change significantly between these three models. Therefore, we do not expect that, by changing the heating efficiency of supernovae, the issue of incorporating a rapidly evolving gas transition time-scale can be resolved."}
{"text": "Following [qin2018], we further investigate the semi-analytic modelling prescriptions of galaxy formation that are commonly adopted in the literature. In this work, we include supernova feedback and homogeneous reionization background in both the Meraxes SAM and Smaug high-resolution hydrodynamic simulation, and make comparisons between the stellar and gas reservoirs predicted by these two methods. We focus on galaxies with virial mass between 10^9 and 10^11 solar masses. With the modifications previously proposed in [qin2018] including adjustments to halo masses from the merger trees, suppression of baryon fractions accounting for hydrostatic pressures, and the modulation of time-scales for the transition of gas from hot to star-forming and from star-forming to stars, we find that the current SAM is able to reproduce the hydrodynamic calculation of the cosmic evolution of galaxies with virial mass > 10^10 solar masses at high redshift."}
{"text": "This includes the stellar mass function, total baryonic mass, star-forming gas mass and SFR between redshift z=5-11. However, in less massive galaxies with SFR calculated using the total star-forming gas, we identify a significant amount of star-forming gas stored in quenched galaxies due to the imposed mass threshold of star formation. After reducing the threshold, the SAM successfully mimics the evolution of dwarf galaxies in the hydrodynamic simulation. We also investigate a second star formation prescription, which splits the star-forming gas disc into molecular and atomic hydrogen and forms stars from molecules [Lagos2011]. Fixing the depletion time-scale of molecular hydrogen inferred from a previous study of the Smaug hydrodynamic simulation [Duffy2017], we find that, with only calibrations of the gas transition rate and supernova efficiencies, the SAM can also reproduce the dwarf galaxy properties calculated by the hydrodynamic simulation."}
{"text": "In addition, we find that when reionization and supernova feedback are included, dwarf galaxies tend to accrete a significant amount of star-forming gas at early times (redshift z>10), which quickly becomes suppressed towards lower redshifts. Future work needs to take this into account and incorporate modelling of cold-mode accretion to study dwarf galaxies in the early universe. We show the impact to the semi-analytic calculation, in the presence of reionization and supernova feedback, of incorporating the halo mass and baryon fraction modifiers, which correspond to the slower evolution of haloes and less efficient gas accretion due to hydrostatic pressure. We apply Meraxes with the total-gas-based star formation law and the same parameters adopted in [Mutch2016a] (SAM_PaperIII) but without the baryon fraction modifier (SAM_PaperIII_noB) and without any modifiers (SAM_PaperIII_noHB)."}
{"text": "We see that without the halo mass modifier, the halo mass function is overestimated compared to the hydrodynamic result at high redshift, which consequently increases the mass function of gas and stars. In addition, further excluding the baryon fraction modifier increases the amount of gas accreted by the host halo and subsequently causes more stars to form. However, we see that the modifications have an insignificant impact to the stellar mass function in the current observable range, which requires deeper surveys with upcoming space programs such as JWST. [qin2018] shows that in the absence of feedback, the majority of dwarf galaxies in the hydrodynamic simulation accrete gas particles with temperatures around a few of 10^4 K, which is much lower than their halo virial temperatures. This represents a cold-mode accretion of the infalling gas [Keres2005, Keres2009], which in the SAM is currently modelled through the cooling prescription of the rapid cooling regime proposed by [white1991]."}
{"text": "The infalling hot gas is also assumed to follow the singular isothermal sphere (SIS) profile. To ease demonstration in this paper, we term the time-scale of gas being transited from hot reservoir to the star-forming disc as a transition time-scale. We illustrate the cooling prescription in Fig. B1. Most massive haloes are able to create shocks and heat the infalling gas, resulting in hydrostatic equilibrium. In this case, which is termed the hot halo regime, the time-scale of hot gas transitioning to star-forming is determined by the thermal cooling time-scale. However, it is difficult to generate shock heating in less massive systems, leaving little support to prevent gas from infalling onto the central disc, and cooling becomes rapid. In this rapid cooling regime, the prescription assumes the star-forming gas disc is relatively small and such a process happens as free-fall. In making comparisons of the gas reservoir calculated by the SAM and hydrodynamic simulation in [qin2018], we found the transition time-scale equals the dynamical time-scale becomes less accurate when applying the rapid cooling prescription to high-redshift dwarf galaxy modelling."}
{"text": "This is due to the aforementioned two assumptions which lead to over- and under-estimations of the gas transited from hot to star-forming, respectively. 1) Assuming the SIS profile of the accreted mass overestimates the gas density in the inner regions. 2) star-forming gas particles of dwarf galaxies (in the hydrodynamic simulation) possess larger extensions and can be found as far as the virial radius. This means that assuming gas can only transfer from non-star-forming hot gas to star-forming when it reaches the galaxy centre introduces a longer inflow path and hence leads to an overestimated transition time-scale. In this case, the mass of hot gas transitioning to star-forming is underestimated instead. We note that when feedback is included, semi-analytic modelling of dwarf galaxies still suffers from these two factors. First, in order to demonstrate that most high-redshift dwarf galaxies in the SAM are still identified as in the rapid cooling regime when reionization and supernova feedback are included, we calculate the cooling radius, at which the time-scale of thermal cooling is equal to the halo dynamical time in the SAM."}
{"text": "Note that gas within the cooling radius is considered to have reached hydrostatic equilibrium and cool thermally if the cooling radius is less than the virial radius. However, in the case of a large cooling radius, the infalling gas will not be able to form stable shocks or remain in hydrostatic equilibrium. Accordingly, all of the accreted gas directly collapses into the central regions as free-fall. We see that most low-mass galaxies discussed in this work are considered to be in the rapid cooling regime. Next we discuss the gas density profile of galaxies with stellar mass of approximately 10^7 solar masses. We see that, compared to the NOSN_NOZCOOL_NoRe simulation where heating from supernova (and reionization) is not included, galaxies within the same stellar mass range are hosted by larger haloes with more gas particles identified as non-star-forming when the feedback is considered. However, the total gas mass does not change significantly, indicating suppressions of baryonic mass and self-regulation of star formation."}
{"text": "Moreover, although the star-forming regions become relatively smaller in WTHERM, they still possess a large dispersion at high redshift. This can also be observed from the large radius of the maximum rotation of the most massive halo, which suggests the necessity of an enhanced inflow rate between the circum-galactic medium and ISM at earlier times. More accurate semi-analytic modelling of gas accretion should not only distinguish the hot- and cold-mode inflows with gas reaching the star-forming disc on different time-scales, but also account for the larger disc size at higher redshifts. We consider these as a future project with a more complete cooling function implemented. For the purpose of accurately capturing the gas transition time-scale using the current rapid cooling prescription, in [qin2018], we proposed to change the cooling efficiency when galaxies are identified in this regime. We introduced a maximum cooling factor, which was used to modulate the gas transition time-scale based on the time-scale of free-fall."}
{"text": "In this work, we adopt this modification by incorporating a form of the transition time-scale as a function of redshift. However, considering the transition radius between star-forming and non-star-forming gas changes due to feedback, the normalization and scaling index are not expected to possess the same values as adopted in [qin2018]. Therefore, we leave them as free parameters and explore the transition time-scale in this work."}
{"text": "We investigate the dependence of galaxy clustering at redshift z from approximately 4 to 7 on UV-luminosity and stellar mass. Our sample consists of approximately 10,000 Lyman-break galaxies (LBGs) in the XDF and CANDELS fields. As part of our analysis, the stellar mass versus UV magnitude relation is estimated for the sample, which is found to have a nearly linear slope of the slope of the log10 stellar mass versus UV magnitude relation is approximately 0.44. We subsequently measure the angular correlation function and bias in different stellar mass and luminosity bins. We focus on comparing the clustering dependence on these two properties. While UV-luminosity is only related to recent starbursts of a galaxy, stellar mass reflects the integrated build-up of the whole star formation history, which should make it more tightly correlated with halo mass. Hence, the clustering segregation with stellar mass is expected to be larger than with luminosity. However, our measurements suggest that the segregation with luminosity is larger with approximately 90% confidence (neglecting contributions from systematic errors)."}
{"text": "We compare this unexpected result with predictions from the Meraxes semi-analytic galaxy formation model. Interestingly, the model reproduces the observed angular correlation functions, and also suggests stronger clustering segregation with luminosity. The comparison between our observations and the model provides evidence of multiple halo occupation in the small scale clustering. Galaxy clustering provides a probe of the host halo mass of galaxies. The clustering strength is commonly described by the two-point correlation function, which measures the probability of finding galaxy pairs at given spatial separations. [1996MNRAS.282..347M] used the extended Press-Schechter formalism [1991ApJ...379..440B] to show that the ratio between the correlation functions of halos and the underlying matter depends on halo mass. This ratio is known as bias. Since galaxies reside in halos, the bias links galaxy clustering to the mass of their host halos (see [2002PhR...372....1C] for a review)."}
{"text": "The dependence of clustering strength on galaxy properties is known as clustering segregation, and reveals the correlation between galaxy properties and halo mass. At high redshifts, clustering segregation is observed for Lyman-break galaxies (LBGs) with UV-luminosity [2006ApJ...642...63L, 2009A&A...498..725H, 2014ApJ...793...17B, 2016ApJ...821..123H, 2018PASJ...70S..11H] and stellar mass [,2017ApJ...841....8I, 2018A&A...612A..42D]. One basic conclusion from these studies is that more luminous and larger stellar mass galaxies are more clustered, and therefore reside in more massive halos. In the context of hierarchical galaxy formation, this correlation between halo and galaxy properties is unsurprising, since halo mass is closely related to the gas reservoir available for star formation and those processes which impact on it. For instance, in the low mass regime, supernova (SN) feedback can effectively suppress star formation [2013MNRAS.428.2741W, 2014MNRAS.445..581H, 2014MNRAS.443.3435D]. Therefore, it is of particular interest to explore which galaxy property is more tightly correlated with the host halo mass."}
{"text": "While UV-luminosity is directly related to the current star formation rate, stellar mass provides integrated information over the star formation history. For this reason, it is expected that, when splitting the same sample by luminosity and stellar mass, clustering segregation with stellar mass should be larger than with UV magnitude. In order to observe the difference between clustering segregation with stellar mass and luminosity, it is essential that the stellar mass is measured from SED fitting including rest-frame optical photometry. Recently, [2016ApJ...821..123H] carried out an analysis of clustering segregation with stellar mass in similar fields to our work. However, the stellar mass used in that study was obtained from a simple conversion of the UV- luminosity to mass using the stellar mass versus UV magnitude relation. Thus, the analysis could not self-consistently infer any difference of the clustering segregation between stellar mass and UV-luminosity. In this paper, we measure stellar masses from SED fitting including rest-frame optical Spitzer/IRAC data, which allows us to measure the clustering segregation in stellar mass at these redshifts for the first time."}
{"text": "Semi-analytic models (SAMs) of galaxy formation are based on halo merger trees provided by N-body simulations, and evolve galaxy properties within these halos using analytic or empirical prescriptions of baryonic physics and feedback processes. Since the theory which links galaxy clustering to dark matter halos also relies on N-body simulations [e.g][1996ApJ...462..563N, 2010ApJ...724..878T], a comparison between observed clustering and that predicted by a SAM tests the link between galaxy properties and halo mass. In this study, we compare our clustering measurements with results from the Meraxes SAM. This model has been shown to be successful in reproducing UV-luminosity functions and stellar mass functions over a wide range of redshifts [2016MNRAS.462..250M, 2016MNRAS.462..235L, 2017MNRAS.472.2009Q]. This somewhat contradicts the above expectation. Examining the clustering dependence beyond this redshift is the main purpose of this paper. This paper is organised as follows. We describe the observational catalogue used in the analysis, and measure the stellar mass versus UV magnitude relation in Section 2."}
{"text": "Methods to measure the angular correlation function (ACF) and galaxy bias are introduced in Section 3, and results are demonstrated in Section 4. We perform the comparison between the observations and predictions from Meraxes in Section 5. Finally, the work is summarised in Section 6. Throughout the paper, unless specified, the cosmology of (h, Omega_m, Omega_b, Omega_Lambda, sigma_8)=(0.678, 0.308, 0.0484, 0.692, 0.815) [2016A&A...594A...1P] is assumed. Magnitudes are in the AB system. The galaxy sample used for our measurements is based on the photometric catalogue from [2015ApJ...803...34B], who selected Lyman break galaxies (LBGs) at z~4-7 based on the Hubble Space Telescope (HST) data in all the CANDELS fields, as well as the very deep XDF and HUDF09 parallel fields."}
{"text": "In particular, our sample is drawn from the XDF [2013ApJS..209....6I], HUDF-091 and HUDF-092 [2011ApJ...737...90B], CANDELS-GN and CANDELS-GS [2011ApJS..197...35G, 2011ApJS..197...36K], ERS [2011ApJS..193...27W], and CANDELS-UDS, CANDELS-COSMOS and CANDELS-EGS [2011ApJS..197...35G, 2011ApJS..197...36K]. These survey regions span an aggregate of ~ 700 arcmin^2 in the sky, and ~ 10,000 LBGs are identified. Photometric redshifts of these sources are estimated using the EAZY code [Brammer08]. For more information on the LBG selection and the photometric redshifts see [2015ApJ...803...34B]. We combine the HST photometry with the large archive of Spitzer/IRAC legacy data available in the CANDELS fields [Ashby13, Ashby15], which includes the ultra-deep IGOODS/IUDF and GREATS surveys [Labbé et al. 2018, in prep.][2015ApJS..221...23L] in the GOODS fields. IRAC photometry is measured in circular apertures after subtracting the contaminating flux of neighboring galaxies using the code mophongo [Labbé et al., 2018, in prep.][Labbe06], which is similar to the code TPHOT [Merlin16]."}
{"text": "We measure stellar masses of galaxies based on SED fitting to the HST+Spitzer photometry using ZEBRA+ [Oesch10]. The synthetic template set used here is based on [BC03] with a constant star-formation history, sub-solar metallicities (0.2 Z_sun) and a [2003PASP..115..763C] initial mass function (IMF). Nebular continuum and emission lines are added self-consistently based on the number of ionizing photons emitted by each SED and assuming line ratios relative to H-beta as tabulated by [Anders03]. Dust extinction is applied using the attenuation curve by [Calzetti00]. Following [2015ApJ...803...34B], the absolute magnitudes, M_UV, are computed based on the fluxes in the photometric band that is closest to rest-frame 1600 Angstrom. We first fit the stellar mass versus UV magnitude relation for the LBG sample, which will be used in our clustering analysis to compare stellar mass and luminosity segregation. The form of the relation is assumed to be log10 of the fitted stellar mass M_star equals (d log10 M_star / dM_UV) times (M_UV + 19.5) + log10 of M_star at M_UV = -19.5."}
{"text": "The log-likelihood is then constructed as ln of the likelihood L equals -1/2 times the sum over all LBGs i of [(log10(observed M_star i / fitted M_star))^2 / Delta^2 + ln(2 pi Delta^2)], where the sum is over all LBGs, and Delta is a mass-independent free parameter representing scatter in the stellar mass versus UV magnitude relation. We adopt a Bayesian approach to perform the fit, assume constant priors for all parameters, and apply the emcee MCMC sampler developed by [2013PASP..125..306F]. The resulting stellar mass versus UV magnitude relations are shown in Figure 1. Best-fit parameters are given in Table 1. We find that the stellar mass versus UV magnitude relations are close to linear (M_star is proportional to L) and that the scatter in stellar mass at fixed luminosity is ~ 0.5 dex. Even though our best-fit slopes are slightly shallower, our measurements are consistent with the recent study from [2016ApJ...825....5S]."}
{"text": "In this work, every galaxy in our HST sample has an estimate of stellar mass irrespective of the quality of Spitzer data. Low S/N ratios of Spitzer bands could make the stellar masses less precise. To investigate this, in Figure 1, galaxies that have at least one Spitzer band (3.6 um and 4.5 um) with S/N > 3 are shown as yellow empty circles in Figure 1, while the others are shown as small blue dots. No systematic offset is found between them. Since the sample is large enough at z ~ 4, we use multiple stellar mass and luminosity bins for the clustering measurements, and avoid using bins that have no lower bound to reduce possible effects due to low S/N ratios of Spitzer data. The lower bound for the least massive stellar mass bin is shown as red dashed line in the corresponding panel of Figure 1. At all other redshifts, limited by the sample size, we include all galaxies and use two bins to examine clustering segregation with stellar mass and luminosity."}
{"text": "The fraction of LBGs that are included and have at least one Spitzer band with S/N > 3 is 74%, 63%, 53%, and 47% at z ~ 4, 5, 6, and 7 respectively. The advantage of this approach is that the completeness of sample LBGs, which is defined by the selection, is not affected by Spitzer data, and it is important to use the same set of galaxies to compare the clustering segregation between UV-luminosity and stellar mass. We will discuss possible effects on clustering measurements due to uncertainties in stellar mass in Section 4.2. Our approach follows [2014ApJ...793...17B]. We start by determining the angular correlation functions (ACFs), which measure the excess probability of finding galaxy pairs with angular separations between theta and theta + delta theta. The ACF estimator proposed by [1993ApJ...412...64L] is applied, i.e. the observed angular correlation function, omega_obs(theta), is estimated using the Landy-Szalay estimator as (DD(theta) - 2DR(theta) + RR(theta)) / RR(theta)."}
{"text": "DD(theta), DR(theta) and RR(theta) are the probability of finding galaxy-galaxy, galaxy-random and random-random pairs respectively. These probabilities are calculated by counting all pairs at separations between theta to theta + delta theta, and normalising by the total number of pairs. Estimates of DR(theta) and RR(theta) require a catalogue of uniformly-distributed random points. This is generated by a random Poisson process. For each field, the random catalogue contains 10,000 points uniformly placed within the corresponding survey regions. We measure the ACFs in logarithmic bins, and estimate errors by bootstrap resampling [1986MNRAS.223P..21L]. We construct bootstrap subsamples by replacing individual galaxies and perform the resampling for ~ 500 times. This approach is also used in [2014ApJ...793...17B] and [2016ApJ...821..123H]. In order to investigate the clustering dependence on both stellar mass and UV magnitude, the total sample is split into subsamples. We choose bins such that they satisfy the stellar mass versus UV magnitude relation at each redshift."}
{"text": "Since the area of each survey region is finite, the observed ACFs are affected by border effects. This is corrected by an additive constant, which is known as the intergral constrain (IC). Following [1999MNRAS.307..703R], we have the true angular correlation function, omega_true(theta), equals the observed angular correlation function, omega_obs(theta), plus the integral constraint, IC, with the integral constraint, IC, equals the double integral of omega_true(theta) over solid angles dOmega_1 and dOmega_2, divided by Omega^2, which equals the sum over i of RR(theta_i) times omega_true(theta_i) divided by the sum over i of RR(theta_i), where omega_true(theta) is the fitting model of the ACF. We assume the ACFs to be a power law, the true angular correlation function, omega_true(theta), equals the amplitude A_omega times (theta divided by 1 arcsecond) to the power of -beta, and construct the log-likelihood using ln of the likelihood L equals -1/2 times the sum over fields and bins i of [(omega_obs(theta_i) - A_omega(theta_i^-beta - IC/A_omega)) / sigma(theta_i)]^2."}
{"text": "This is equivalent to measuring the average ACF of all fields using inverse-variance weighting. Since this approach requires an estimate of the ACF in each individual field, we only include fields that are deep enough such that the mean separation of galaxy pairs is smaller than 100 arcsec. Moreover, the dependence of the IC on the fitting model results in some degeneracy between A_omega and beta [2006ApJ...642...63L], we therefore fix beta = 0.6 following [2006ApJ...642...63L] and [2014ApJ...793...17B]. In addition, since the area of XDF, HUDF-091, and HUDF-092 is only 4.7 arcmin^2 (i.e. one WFC3/IR pointing), the counted number of galaxy pairs in these fields decreases when the angular separation is greater than ~ 140 arcsec. We therefore only include separations smaller than that in the likelihood function. The amplitude of the ACF A_omega could be weakened by contamination of lower redshift sources."}
{"text": "We reduce this effect by removing all LBGs whose best-fit photometric redshift indicates that it might be a low redshift contaminant (photometric redshift z < 2). It is also noted that [2016ApJ...821..123H] used the contamination fraction estimated by [2015ApJ...803...34B] to correct for this effect. They found that the difference is insignificant compared with the statistical error. Thus, no further treatment is employed to correct the effect of contamination. Since linear bins are used in this work, we mainly measure the ACF at large scales, i.e. the 2-halo term. As pointed out by [2013MNRAS.429.2333J], the 2-halo term is mostly sensitive to the halo mass of central galaxies, since, at given stellar mass or luminosity bins, the satellite fraction is small. Real space parameters are obtained by applying the Limber transform to the ACFs."}
{"text": "The real-space correlation function, xi(r), provides three dimensional information on galaxy clustering, which is also approximated by a power law, the real-space correlation function, xi(r), is a power law defined as (r divided by r_0) to the power of -gamma, where r_0 is called the correlation length. In this case, the Limber transform takes the form [1980lssu.book.....P] beta equals gamma - 1, and the amplitude A_omega equals r_0^gamma times the Beta function B(1/2, (gamma-1)/2) times an integral over redshift z involving the redshift distribution N(z) squared, where B(x,y) is the beta function, N(z) is the redshift distribution function of sample galaxies, and H(z) is the Hubble parameter as a function of redshift. The above equations link A_omega and beta to the power law parameters in the real space. N(z) is estimated using the photometric redshifts of each LBG."}
{"text": "We derive the bias using the ratio between the variance of the galaxy and the matter correlation functions smoothed by a top-hat with radius 8 h^-1 Mpc: the bias b equals the galaxy variance sigma_8,g divided by the matter variance sigma_8, where [1980lssu.book.....P] the galaxy variance squared, sigma_8,g^2, equals 72 times (r_0 / 8 h^-1 Mpc)^gamma divided by [(3-gamma)(4-gamma)(6-gamma)2^gamma]. We employ the relation proposed by [2010ApJ...724..878T], which is based on a set of N-body simulations. Figure 2 shows measured ACFs and best-fit power laws for both stellar mass and luminosity subsamples. Results for the angular correlation function amplitude (A_omega), the correlation length (r_0), and bias (b) are summarised in Table 2. All quantities given in the table are the most probable value and the corresponding 1-sigma error."}
{"text": "Clustering segregation is observed with both stellar mass and luminosity. From Figure 2, it is clear that the ACFs increase with luminosity at all redshifts. Similar trends are also observed for different stellar mass subsamples. However, the segregation with stellar mass is found to be weaker than with luminosity. To further compare the clustering dependence of these two properties, we plot the measured bias as a function of mean stellar mass and flux in Figure 3. The bias increases with stellar mass, from b = 2.7 to 3.6 at z ~ 4, and b = 4.2 to 4.8 at z ~ 5. The segregation of bias with luminosity is more obvious. At z ~ 4, the bias for the brightest sample is b = 4.1, while that of the faintest sample is smaller at b = 2.5. Similarly, at z ~ 5, the bias has an increase between the faint and bright samples, from b = 3.8 to 5.3."}
{"text": "At z >= 6, the LBG sample is smaller, and uncertainties become much larger. While there is a small increase of the bias with mean UV flux at mean redshift z = 5.9, no significant segregation with stellar mass is detected. For samples at z ~ 7, we find that the bias increases from b = 7.4 to 11.7, and from b = 5.6 to 8.6, for stellar mass and luminosity bins respectively. As a comparison, we also plot the bias estimated by [2016ApJ...821..123H] from their power law fits as a function of mean UV magnitude. We find that the trends of clustering dependence on luminosity are consistent, while the offsets on biases themselves could be due to different methods of computing them. To summarise, we find that both more massive and more luminous galaxies are more highly clustered, implying that they are hosted by more massive dark matter halos."}
{"text": "On the other hand, the comparison of segregation between stellar mass and luminosity disagrees with our prior expectations, especially at mean redshift z = 3.8 and 5.0. In particular, we find that the clustering dependence is larger for luminosity than for stellar mass. In order to quantify this trend, we fit the measured biases of the lightest (faintest) and heaviest (brightest) by straight lines, i.e. the bias b equals the slope alpha_SM times log10(M_star / M_sun) + constant, and the bias b equals -1.1 times the slope alpha_UV times log10(L_UV / L_sun) + constant. If clustering segregation with both properties were the same, one would expect that the ratio of the slopes should recover the slope of the stellar mass versus UV magnitude relation. Therefore, we include a correction factor of -1.1 to equation 9 in order to make alpha_SM and alpha_UV comparable. The value -1.1 is based on the results in Table 1."}
{"text": "We combine the measured biases over all redshifts, assume the same slope but different intercepts for each redshift, and fit these five parameters using the emcee MCMC sampler developed by [2013PASP..125..306F], assuming flat priors. Best-fit results are shown in the left and middle panels of Figure 4. We illustrate the marginalised distributions of the slopes for stellar mass and luminosity subsamples as solid red and blue lines respectively in the bottom left panel of Figure 4. The median and 1-sigma percentiles of the slopes are summarised in the top right corner. We conclude that the slope in the stellar mass case is systematically smaller than in the luminosity case, which indicates larger clustering segregation with luminosity. The significance of this trend can be seen from the bottom right panel of the figure. The probability that the slope alpha_UV is greater than the slope alpha_SM is approximately 90 % (shaded region)."}
{"text": "However, UV magnitude only probes recent starbursts of a galaxy, while stellar mass is an integrated quantity, which reflects the whole star formation history. This argument suggests that a tighter relation is expected between stellar and halo mass, and therefore, clustering segregation with stellar mass should be larger. Both observational effects and astrophysical reasons could be responsible for this discrepancy. We investigate this issue further by comparing the results at z ~ 4 with predictions from the SAM Meraxes in the next section. The Meraxes SAM is part of the Dark-ages, Reionization And Galaxy-formation Observables Numerical Simulation (DRAGONS) project. It is designed to self-consistently model galaxy formation and evolution during and after the epoch of the reionisation. Physics implemented in the model is described in [2016MNRAS.462..250M] and [2017MNRAS.472.2009Q]."}
{"text": "In the present work, the model is run on the extended Tiamat N-body simulation [2016MNRAS.459.3025P, 2017MNRAS.472.3659P]. The simulation has 2160^3 dark matter particles, with particle mass m_p = 2.64 x 10^6 h^-1 M_sun, and side length 67.8 h^-1 Mpc. The simulation outputs 101 snapshots between z = 35 and z = 5 with time steps separated by ~ 11 Myr, and additional 63 snapshots from z = 5 to z = 1.8. The time steps of these additional snapshots are evenly spaced in dynamical time. We adopt the same parameter configuration as in [2017MNRAS.472.2009Q] for the SAM. All model stellar mass is subtracted by 0.24 dex in order to convert from a [1955ApJ...121..161S] IMF to a [2003PASP..115..763C] IMF."}
{"text": "The computation of photometry of model galaxies is described in [2016MNRAS.462..235L]. Progenitors of each model galaxy are treated a series of single stellar populations (SSPs), and integrated over the whole star formation history. We assume constant metallicity Z = 0.001 for the SSP. Recent hydrodynamical simulations [2016MNRAS.456.2140M, 2016MNRAS.462.3265D] predict a mass-metallicity relation that is close to this value at z ~ 4. [2017MNRAS.470.3006C] point out that intrinsic luminosities only weakly depend on the metallicity. Therefore, this assumption is valid for this work. SSPs templates are generated by starburst99 [1999ApJS..123....3L, 2005ApJ...621..695V, 2010ApJS..189..309L, 2014ApJS..212...14L] assuming the same IMF with meraxes. Modelling of the Lyman absorption due to the intergalactic medium (IGM) is critical for the simulated LBG selection."}
{"text": "We update the transmission curve of the IGM using a recent study from [2014MNRAS.442.1805I], which predicts a more consistent redshift distribution for selected model LBGs. In addition, we also update the dust correction using an empirical model proposed by [2015ApJ...813...21M], which is applicable at z < 4. We follow [2016MNRAS.461..176P, 2017MNRAS.472.1995P] to select model LBGs and calculate the ACFs. This approach mimics the incompleteness of the LBG sample by adding photometric scatter to the magnitudes of each LBG selection band. The level of the scatter is given by the 1-sigma field detection limits. In the present work, we assemble model LBGs according to the flux limits of the deepest field in the our observations, i.e. the XDF. The resulting redshift distribution of model selected LBGs is shown in Figure 5, which agrees with the observed one estimated by photometric redshifts."}
{"text": "In terms of the determination of the ACF, we compute the real-space correlation function across a sequence of snapshots directly from the spatial coordinates of each galaxy, and convert to an ACF by the Limber transform. The readers are referred to [2016MNRAS.461..176P, 2017MNRAS.472.1995P] for a more detailed description. We focus on the comparison between our model and observations at z ~ 4, where the measurements have the smallest errors. We plot predicted ACFs together with measured ACFs in Figure 4. The model ACFs agree very well with observations, and reproduce the observed clustering dependence on both stellar mass and luminosity. In order to check whether the model predicts larger clustering segregation with luminosity as indicated by our observations, we therefore calculate the bias from the model by the bias squared equals the real-space correlation function of galaxies xi(r) divided by the real-space correlation function of dark matter xi_DM(r,z), where xi(r) and xi_DM(r, z) are the real-space correlation functions of galaxies and dark matter."}
{"text": "An average value is taken in the range 5 Mpc <= r <= 10 Mpc. The estimated biases for the lightest (faintest) and heaviest (brightest) samples are shown using star symbols in the left (middle) panel in Figure 4. Subsequently, we derive the slope for these two points for comparison with observational data in Figure 4. Red and blue lines correspond to stellar mass and luminosity bins respectively. We conclude that the measured variation of bias with stellar mass and luminosity is consistent with predictions and that the clustering segregation with luminosity is larger than stellar mass in the model. In other words, the model predictions also contradict our expectation that stellar mass should be more tightly correlated with halo mass. The physical interpretation behind this could be complex, and we defer it to a subsequent paper. The observed clustering dependence on stellar mass could be weakened due to observational uncertainties on the estimations of stellar mass."}
{"text": "The uncertainties, for instance, can be due to the low S/N ratio of Spitzer data. We demonstrate this effect by adding 0.5 dex of Gaussian scatter to the stellar mass of selected model LBGs and remeasure the clustering in stellar mass bins. This level of scatter is also used in abundance matching studies [e.g.][2013MNRAS.428.3121M, 2013ApJ...770...57B]. The recalculated ACFs are shown as green lines in Figure 4. For the most massive bin, the ACF decreases at all scales, while for the other two bins, scatter in stellar mass only affects the small scale correlation functions. We also recalculate the bias and the corresponding slope. The results are demonstrated in Figure 4. In the right panel of Figure 4, the dot dashed line represents the slope in the case where scatter is added to the stellar mass, and shows that scatter reduces the slope relative to that of the original model, from alpha_SM = 1.3 to alpha_SM = 0.7."}
{"text": "This effect is most significant for the most massive bins, since the massive end has fewer galaxies. We can use this systematic error of model alpha_SM introduced by adding scatter to the stellar mass to estimate the effect on our measured alpha_SM. This indicates that accounting for uncertainties in stellar mass leads to clustering segregation that is similar for both mass and UV-luminosity, but which is not larger with stellar mass. Hence, although uncertainties in stellar mass can weaken the clustering dependence, the unexpected trend could still result from physical reasons. Another interesting finding from the comparison between observations and the model is the deviation of the ACFs from a power law at small scales (theta < 10 arcsec). In the model, this is due to the 1-halo term, arising from multiple halo occupation, where more than one galaxy resides in the same halo."}
{"text": "To provide evidence of this multiple halo occupation, we calculate the 1-halo and 2-halo terms explicitly from Meraxes by counting galaxy pairs in the same and different FoF groups. These two terms are shown as dashed and dot dashed lines in Figure 4, respectively, demonstrating that the steep increase of the ACFs at small scales is due to multiple halo occupation. Consistency is also found between observations and the model. It can also be seen that the transition of the model ACFs between the 1-halo and 2-halo terms becomes more rapid with decreasing stellar mass. However, there is no such trend in luminosity. This finding may suggest an additional feature of clustering segregation with stellar mass and luminosity, implying different satellite properties for the two cases. However, we caution that the satellite properties of Meraxes have yet to be fully explored and compared with observations, and that achieving realistic recent satellite star formation histories has traitionally been a challenging task for SAMs."}
{"text": "This difference can also be seen from the observed ACFs but with large uncertainties. At the very bright end, the smooth transition between 1-halo and 2-halo terms is observed in [2018PASJ...70S..11H], and explained using non-linear bias [2016MNRAS.463..270J]. Larger surveys with more complete samples might be used to investigate this phenomenon in more details for fainter and less massive galaxies. We have carried out a clustering analysis of LBGs over the range z ~ 4 - 7, with emphasis on the comparison between clustering segregation with stellar mass and luminosity. We also compare our measurements with predictions from the Meraxes SAM. Our findings can be summarised as follows: The observed ACF amplitude and bias generally increase with stellar mass and luminosity over z ~ 4 - 7. The ACFs obtained from the model are consistent with observations, and reproduce clustering segregation with both stellar mass and luminosity."}
{"text": "This suggests that more luminous and massive galaxies are more clustered, and hence hosted by more massive dark matter halos. By combining measurements over all redshifts, a systematic difference is found between clustering segregation with stellar mass and luminosity. In particular, it is observed that clustering strength is more tightly correlated with luminosity. This is in contrast to the expectation that stellar mass should be more tightly correlated with halo mass since stellar mass reflects the whole star formation history, while UV magnitude only corresponds to recent star formation. We find that the model also predicts this surprising result of larger clustering segregation with luminosity. At z ~ 4, the model predicts that the transition between the 1-halo and 2-halo terms of the ACFs is smoother for larger stellar mass galaxies, and that this trend does not appear for samples split by luminosity. Observations show similar behaviour but with large error bars."}
{"text": "This might suggest that samples split by stellar mass and luminosity have quite different satellite properties. Our results extend to higher redshift findings from the recent study at z ~ 3 by [2018A&A...612A..42D], who carried out a clustering analysis of 3236 galaxies discovered in the VIMOS Ultra Deep Survey. They measured the real space correlation functions, and also found a larger difference in the correlation lengths when splitting the sample by luminosity than by stellar mass. This unexpected trend of clustering segregation with stellar mass and luminosity may provide new clues of galaxy formation in the early universe. For instance, some high-redshift galaxies might be formed by a single starburst. In this case, stellar mass and UV-luminosity become similar indicators of the star formation history. Our study also motivates future spectroscopic surveys with the James Webb Space Telescope (JWST), which will provide more complete samples and more accurate stellar mass measurements substantially reducing the systematic errors in clustering studies."}
{"text": "We study the sizes, angular momenta and morphologies of high-redshift galaxies using an update of the Meraxes semi-analytic galaxy evolution model. Our model successfully reproduces a range of observations from redshifts z=0-10. We find that the effective radius of a galaxy disc scales with UV luminosity as R_e is proportional to L_UV^0.33 at z=5-10, and with stellar mass as R_e is proportional to M_*^0.24 at z=5 but with a slope that increases at higher redshifts. Our model predicts that the median galaxy size scales with redshift as R_e is proportional to (1+z)^-m, where m=1.98+/-0.07 for galaxies with (0.3-1)L*_(z=3) and m=2.15+/-0.05 for galaxies with (0.12-0.3)L*_(z=3). We find that the ratio between stellar and halo specific angular momentum is typically less than one and decreases with halo and stellar mass. This relation shows no redshift dependence, while the relation between specific angular momentum and stellar mass decreases by ~0.5 dex from z=7 to z=2."}
{"text": "Our model reproduces the distribution of local galaxy morphologies, with bulges formed predominantly through galaxy mergers for low-mass galaxies, disc-instabilities for galaxies with M_* is approximately 10^10 - 10^11.5 M_sun, and major mergers for the most massive galaxies. At high redshifts, we find galaxy morphologies that are predominantly bulge-dominated."}
{"text": "Size, angular momentum and morphology are three of the most fundamental galaxy properties, and are integral probes for understanding the structure and growth of galaxies. Observing these properties at high redshifts offers an invaluable insight into galaxy formation and evolution in the early Universe. The sizes of high-redshift Lyman-break galaxies have been measured using deep Hubble Space Telescope (HST) fields in a number of studies from z~6-12 ([e.g.][Oesch2010, Mosleh2012, Grazian2012, Ono2013, Huang2013, Holwerda2015, Kawamata2015, Shibuya2015, Kawamata2018]). They find sizes consistent with an evolution of the galaxy effective radius R_e is proportional to (1+z)^-m at fixed luminosity, with measurements of m typically in the range of 1 <~ m <~ 1.5. While observing galaxy morphologies at high-redshift is challenging ([see e.g.][Abraham2001]), observations generally find that high-redshift galaxies are more clumpy and irregular than those at low redshift ([Abraham2001, Papovich2005, Elmegreen2014])."}
{"text": "Several studies find that there is a larger fraction of spheroids at higher redshifts ([e.g.][Bundy2005, Franceschini2006, Ravindranath2006, Lotz2006, Dahlen2007]), though [Ravindranath2006] find that the z~2.5-5 population is not dominated by spheroids but by extended disc-like galaxies and irregulars or merger-like systems. Unfortunately, there are only a few observational studies of galaxy angular momentum at redshifts z>1 ([e.g.][Swinbank2017, Alcorn2018, Okamura2018]), since obtaining large spectroscopic samples to measure kinematics and thus specific angular momenta at high redshifts is difficult. [Okamura2018], for example, estimated the specific angular momentum of z~2, 3 and 4 galaxies from their measured disc sizes, using the analytic model of [Mo1998], and found little redshift evolution of the ratio of stellar to halo specific angular momentum. Because of the difficulty of observing these properties at high redshift, models and simulations play a necessary role for measuring and understanding their evolution in the early Universe."}
{"text": "In the hierarchical structure formation scenario, gas cools in the centres of dark matter haloes to form galaxies. The [Mo1998] analytical model of this process predicts that if galaxies are thin exponential discs with flat rotation curves, and specific angular momentum is conserved, the scale length of a galaxy disc R_s is given by Equation 1. Note that this model is an extension of the [Fall1983] model which assumed R_s = lambda * R_vir / sqrt(2), with J_d=J_H and M_d=M_vir. The virial radius of a dark matter halo is given by Equation 2. Hence, the simple model of [Mo1998] predicts that sizes of discs scale with redshift as (1+z)^-1.5 at fixed circular velocity, or (1+z)^-1 at fixed halo mass. Measurements of m typically lie between these two values ([e.g.][Bouwens2004, Oesch2010, Ono2013, Kawamata2015, Shibuya2015, Laporte2016, Kawamata2018])."}
{"text": "Semi-analytic models often use the [Fall1983] model and assume R_s = lambda * R_vir / sqrt(2) to predict the sizes of galaxies within their simulated dark matter haloes ([e.g.][Croton2006a, Mutch2016, Liu2016]). While simplistic, this model has had success in reproducing the size evolution of galaxies from z~5-9 [Liu2016]. More advanced semi-analytic models improve their disc size estimates by explicitly tracking the angular momentum of galaxy discs ([e.g.][Lagos2009, Guo2011, Benson2012, Stevens2016, Tonini2016, Xie2017, Zoldan2019]). Under the assumption that galaxy discs have a constant velocity profile and an exponential surface density profile, their specific angular momentum is j=2*R_s*V, and so their radii can be estimated as R_s=j/2V. These models generally assume that the velocity of the galaxy disc V is equal to the maximum circular velocity of the surrounding dark matter halo ([e.g.][Guo2011, Tonini2016, Zoldan2019])."}
{"text": "Meraxes [Mutch2016] is a semi-analytic galaxy formation model designed to study high-redshift galaxy evolution. In [Liu2016] (hereafter L16), Meraxes was used to investigate the sizes of high-redshift galaxies. This model assumed R_s = R_vir * lambda / sqrt(2), included no angular momentum tracking, and assumed that all galaxies were exponential discs for simplicity. In this paper, we use Meraxes to study the evolution of galaxy sizes, angular momentum and morphology. We implement a new method to determine galaxy sizes and velocities, introduce angular momentum tracking, and implement a bulge growth model to allow for morphological studies. This paper is organised as follows. In Section 2 we introduce Meraxes and detail these new model updates... We then make predictions for the high-redshift evolution of galaxy sizes in Section 4, angular momenta in Section 5 and morphologies in Section 6. We conclude in Section 7."}
{"text": "In this section we describe additions to the semi-analytic model Meraxes that allow calculation of the disc scale length, bulge mass, and angular momentum of galaxies in the model. Readers interested in the calibration and results may skip to Section 3. In this work, we apply Meraxes to two collisionless N-body dark matter simulations, Tiamat and Tiamat-125-HR. The Tiamat simulation [Poole2016, Poole2017] has a co-moving box size of (67.8h^-1 Mpc)^3, and contains 2160^3 particles each of mass 2.64x10^6 h^-1 M_sun. The high mass and temporal resolution of Tiamat make it an extremely accurate and ideal simulation for studying galaxy evolution at high-redshifts. Tiamat is used throughout this work unless otherwise specified. To investigate lower redshifts, we run Meraxes on Tiamat-125-HR [Poole2017], a low-redshift compliment to Tiamat, with the same cosmology and snapshot cadence extended to z=0."}
{"text": "Meraxes [Mutch2016] is a semi-analytic model specifically designed to study galaxy evolution during the Epoch of Reionization. Using the properties of the dark matter haloes from Tiamat and Tiamat-125-HR, Meraxes models the baryonic physics involved in galaxy formation and evolution analytically, including prescriptions for physical processes such as gas cooling, star formation, AGN and supernova feedback, and black hole growth. The various free parameters of the model are calibrated to reproduce certain observations, such as the evolution of the galaxy stellar mass function. This work introduces several extensions that have been made to Meraxes: i) we now split galaxies into bulge and disc components, ii) we introduce a new mechanism for black hole growth, iii) we implement a new model for determining galaxy disc sizes, iv) we use a more physical star formation prescription, and v) the angular momenta of the gas and stellar discs are now tracked."}
{"text": "Previously published versions of Meraxes made no attempt to decompose a galaxy into its morphological components, instead assuming that all cold gas and stars in a galaxy are contained in a disc component. Following previous semi-analytic models ([e.g.][Croton2006a, Lucia2006, Guo2011, Menci2014, Tonini2016]), we expand the model to include a second galaxy component---galaxy bulges. These are assumed to contain no gas, and have no angular momentum, for simplicity. Our model for bulge growth is analogous to that of [Tonini2016], with bulges growing during galaxy mergers and disc instabilities. As in [Tonini2016], we split galaxy bulges into two types---merger-driven and instability-driven. We assume that the instability-driven bulge is disc-like, with a mass distribution that is flattened in the disc direction, whereas the merger-driven bulge is spheroidal. These bulges are somewhat comparable to observed classical and 'pseudo' bulges."}
{"text": "When two galaxies merge, we first assume that the gas discs of the primary and secondary galaxies add. Galaxy mergers can induce an efficient burst of star formation. We assume that in a merger with merger ratio gamma = M_2/M_1 >= 0.01 the remnant undergoes a merger-driven starburst. This causes mass M_burst = 0.57 * gamma^0.7 * M_cold,1 to be converted from cold gas into stars [Somerville2001, Mutch2016]. Any gas that is not converted into stars during this burst remains in a gas disc. If the primary is dominated by a discy component, the mass deposition is likely to occur in the plane of the disc, and so these stars are added to the instability-driven bulge. Otherwise, the dominant mass component of the primary is the spheroidal merger-driven bulge, and so we assume that the newly formed stars accumulate in shells around it and are added to the merger-driven bulge."}
{"text": "If a galaxy undergoes a major merger, which we define as a merger with gamma>0.1, all stars and metals from both galaxies are placed into the merger-driven bulge of the remnant—major mergers are assumed to form pure bulge galaxies. In a minor merger (gamma <= 0.1) where the primary is disc-dominated, we assume that the stars from the secondary are added to the primary's disc. This causes a gravitational instability such that an amount of mass equal to the secondary's stellar mass is taken from the disc of the primary and placed into its instability-driven bulge [see][Tonini2016]. In a minor merger where the primary is bulge-dominated, the secondary's mass is simply added to the primary's bulge (either the instability-driven bulge or the merger-driven bulge, depending on which is dominant)."}
{"text": "For thin galaxy discs with an exponential surface density and flat rotation curve, a disc is stable if its mass M_disc < M_crit = V_disc^2 * R_s / G [Efstathiou1982, Mo1998]. Thus, we assume that if the galaxy disc accretes enough material such that M_disc > M_crit, then it is no longer in dynamical equilibrium and an amount M_unstable = M_disc - M_crit of this disc mass is unstable. To return the disc to equilibrium, we assume that the unstable stellar mass is transferred from the disc to the instability-driven bulge. We then assume that the disc instability can drive black hole growth. After this black hole growth, the remainder of the unstable gas is consumed in a 100 per cent efficient starburst, with the stars formed added to the instability-driven bulge."}
{"text": "We implement a new density-dependent star formation prescription equivalent to that in [Tonini2016]. This uses the mass of cold gas above the critical density for star formation to determine how many stars are formed. The original Meraxes prescription assumed that the gas in the gas disc was evenly distributed out to a radius of 3*R_s,g. The new model improves this by assuming that the gas in the disc is exponentially distributed. The gas surface density threshold for star formation is Sigma_crit = 10 M_sun/pc^2. For gas discs with an exponential surface density profile, the total mass of gas inside the critical radius is calculated, and we assume that this amount of gas is capable of forming stars. New stars form at a rate of SFR = epsilon * M_crit / t_dyn, where t_dyn is the dynamical time of the disc and epsilon is a free parameter describing the efficiency of star formation."}
{"text": "The simulated properties of dark matter haloes can jump significantly between adjacent snapshots due to errors in the halo-finding process. In previous versions of Meraxes, the scale radius of the disc R_s was approximated from the radius and spin of the host halo. This means that the galaxy properties can also jump significantly between adjacent snapshots due to such errors. Clearly this is unphysical, and decoupling the galaxy properties from the instantaneous halo properties to remove these errors would be ideal. We therefore introduce a new method for determining the scale radius of galaxy discs, in which the disc is evolved incrementally in response to changes that have occurred at each snapshot. In order to do so, we consider any changes to the mass of the disc as a sum (or subtraction) of two discs: the existing disc and a pseudo-disc of material to be added (or removed), and determine the size of the resulting disc using conservation of energy and angular momentum arguments."}
{"text": "This method requires that we also track the vector angular momentum of both the stellar and cold gas discs. We assume that the stellar and gas discs have: i) a constant velocity profile V(r)=V (a flat rotation curve) and ii) an exponential surface density profile, as in [Mo1998]. We consider the sum (or subtraction) of two such discs. If these discs have masses M1 and M2, and velocities V1 and V2, then from conservation of energy, the new velocity is V_new = sqrt((M1*V1^2 + M2*V2^2) / (M1+M2)). Assuming conservation of angular momentum, J1+J2=J_new, the angular momentum of the combined disc is calculated by summing the individual angular momentum vectors. The magnitude of angular momentum is |J| = 2*M_disc*V*R_s. Using these conservation laws, the new disc scale length can be calculated as R_new = |J_new| / (2*V_new*(M1+M2))."}
{"text": "This incremental method is applied to several physical processes. For gas cooling, we assume hot halo gas settles into a disc with the velocity and specific angular momentum of the host halo. For quiescent star formation, new stars form in a disc with the properties of the parent gas disc, and their mass and angular momentum are transferred from the gas to the stellar disc. For starbursts, new stars form in the bulge with zero angular momentum, and the gas disc's radius increases to conserve angular momentum. For minor mergers, we assume the secondary's disc retains its angular momentum and is added vectorially to the primary's. In major mergers, the stellar disc is destroyed and becomes a bulge, while gas discs are combined. For supernovae, gas ejected from the disc is added back to the gas disc, while gas from the bulge is ejected to the halo and re-accretes with the halo's angular momentum. For disc instabilities and AGN feedback, mass is removed from the disc while specific angular momentum is conserved, causing the disc radius to increase."}
{"text": "All analysis henceforth is conducted using model galaxies with M_*>10^7 M_sun, the resolution limit of Meraxes when run on the Tiamat simulation [Mutch2016]. To ensure that our conclusions are robust, we therefore only consider galaxies classified as centrals, except in the stellar mass and luminosity functions. We leave a detailed exploration of the effect of including satellite galaxies to future work. We use the same parameter values for both Tiamat and Tiamat-125-HR, and use both simulations to tune the model: Tiamat for matching z>=2 observations and Tiamat-125-HR for z<2. The stellar and black hole mass functions from the two simulations at z=2 are converged above M_*=10^8.6 M_sun and M_BH=10^7.1 M_sun, respectively. We therefore place no significance on the trends observed with Tiamat-125-HR for lower masses."}
{"text": "The free parameters in Meraxes are tuned to match the observed stellar mass functions at z=8-0 and the M_BH - M_bulge relation at z=0. We calibrate to the stellar mass function at a range of redshifts, as this has been shown to provide a tight constraint on both the star formation efficiency and supernova feedback parameters ([see e.g.][Mutch2013, Henriques2013]). We use the M_BH - M_bulge relation to calibrate the black hole growth parameters; we use this relation instead of the black hole mass function as it is a more direct observable, and our model now has the capability of modelling bulge masses. We place an emphasis on matching the canonical [Kormendy2013] observations at high stellar and bulge masses. To produce a median bulge fraction that is in better agreement with local observations at the highest stellar masses, we also modify the definition of a major merger to be one with gamma>0.1, instead of gamma>0.3 as used previously."}
{"text": "Once the model has been tuned, we verify the changes by comparing the output to a range of local observations: the stellar mass-disc size relation, bulge fractions, and angular momentum-mass relations. We present the sizes of model galaxies using the physical effective radius, or half-light radius, R_e. We estimate this as R_e=1.678*R_s, which is the half-light radius for a disc with an exponential surface density profile. Figure 5 shows the relation between the stellar disc effective radius and stellar mass at z=0. The model agrees reasonably well with the [Dutton2010], [Lange2016] and [Lapi2018] observations, with the median matching their relations closely for 10^9 < M_*/M_sun < 10^10.5. At higher masses, our model median jumps to higher radii, though is still reasonably consistent with the observations; this jump is most likely a result of the lower sample size of high-mass galaxies."}
{"text": "To verify that our bulge model is producing galaxies with reasonable morphologies, we consider the median fraction of stellar mass contained within galaxy bulges as a function of total stellar mass at z=0.1. Our model predicts that the majority of stellar mass for low mass galaxies (M_* is approximately 10^9 M_sun) is contained in the bulge component, discs contribute a peak of ~60 per cent of the stellar mass at M_* is approximately 10^9.5 M_sun, and bulges again dominate at larger masses. This dip in the bulge-to-total mass ratio B/T is due to the masses at which the two bulge growth mechanisms are dominant; the merger-driven growth mode peaks for galaxies with M_* is approximately 10^9 M_sun, while the instability-driven growth mode peaks at M_* is approximately 10^11 M_sun. This suggests that high-mass galaxy discs are likely to be unstable and thus form bulges, while it is predominantly only less massive galaxies which form their bulges via mergers."}
{"text": "We compare our results to the SDSS observations of [Thanjavur2016] and GAMA observations of [Moffett2016]. For stellar masses of >~10^11 M_sun the model predicts a bulge fraction in remarkable agreement with the observations. For masses 10^10 < M_* < 10^11 M_sun, our model overpredicts the total bulge fraction by approximately 10 per cent compared to SDSS, but up to 40% compared to GAMA. However, the GAMA analysis does not include pseudobulges, and this mass range is precisely where we predict the instability-driven or 'pseudo' bulge to dominate, which may explain this discrepancy. The trend our model predicts for the B/T ratio is qualitatively consistent with observations such as [Conselice2006], who found that the spiral fraction is largest in galaxies with 10^9 < M_* < 10^11 M_sun. The predictions of our model are also qualitatively very similar to those of the EAGLE simulation [Clauwens2018]."}
{"text": "In this section we investigate the success of our model at reproducing the angular momentum-mass relations observed in local galaxies. We consider only disc-dominated galaxies, with bulge-to-total mass ratio B/T<0.3. The correlation between stellar specific angular momentum j_* and total stellar mass M_* (the Fall relation) is claimed to be one of the most fundamental galaxy scaling relations. We show our predicted j_*-M_* relation at z=0 in Figure 8. We also show a range of observations, to which our model shows remarkable agreement. The [Posti2018] observations extend to low stellar masses, where they find that the j_*-M_* relation remains as a single, unbroken power-law, challenging models which predict a flattening at low masses. Our model shows no significant flattening, consistent with the [Posti2018] observations."}
{"text": "We predict a decreasing ratio of stellar-to-halo specific angular momentum (j_*/j_H) with decreasing stellar and halo mass. While our model contains galaxies with a wide range of j_*/j_H values, the distribution has a median lower than one, with j_*/j_H is approximately 0.5 at M_vir is approximately 10^12 M_sun. Our model therefore suggests that the majority of galaxies lose angular momentum as they evolve. Our predictions overlap with the confidence intervals of the [Lapi2018] and [Dutton2012] observations. We make different predictions to previous simulations and semi-analytic models, such as [Pedrosa2015], who find roughly no mass dependence of j_d/j_H, as does the Dark SAGE semi-analytic model [Stevens2016]."}
{"text": "Finally, we consider the morphological dependence of the specific angular momentum-mass relation, as observations suggest that mass, angular momentum and bulge-to-total ratio are strongly correlated. We plot the j_*-M_* relation for galaxies in our model, coloured by their bulge-to-total mass ratio B/T, in Figure 10. We see a clear trend of bulge-dominated galaxies lying below the disc-dominated sequence, consistent with the [Fall2018] observations. This trend arises naturally from our assumption that the bulge component has negligible angular momentum. The Illustris [Genel2015] and Magneticum Pathfinder [Teklu2015] simulations also predict a similar correlation between galaxy type and j_*. Overall, our model reproduces the local angular momentum-mass scaling relations well."}
{"text": "We investigate the relationship between the sizes of stellar discs and UV magnitude of galaxies in our model from z=5-10. We find that for all UV magnitudes, brighter galaxies tend to have larger sizes. This is in agreement with the [L16] predictions, however we see a steeper slope at the brightest magnitudes. This is due to the improvements of our new disc size model. In [L16], the galaxy radius was simply related to the halo radius. By tracing the evolution of disc-sizes more physically, our galaxies sizes do not show an artificial flattening at fainter magnitudes. Our model agrees well with the [Grazian2012], [Ono2013], [Huang2013] and [Holwerda2015] observations. At redshifts z=6, 7 and 8, the best-fit relation of [Kawamata2018] agrees well at the brightest magnitudes, but our model shows a flattening in the relation at lower magnitudes that is not seen in those observations."}
{"text": "The relations between the stellar disc effective radius and galaxy stellar mass from z=5-10 are shown in Figure 13. Our model shows a clear trend of increasing disc size with increasing stellar mass. The [Mosleh2012] observations match well with the model predictions at z=5 and 7, while being smaller than our median at z=6. The [Holwerda2015] galaxies also match well with our predictions. We fit the relation R_e = R_0 * (M_*/M_0)^b where M_0 = 10^9 M_sun, as in [Holwerda2015]. The normalization R_0 decreases from z=5 to z=10, while the slope b increases. Our values for b are consistent with some of those derived by [Holwerda2015], though their values vary significantly depending on the observations used."}
{"text": "We show the predictions of our model for the redshift evolution of the stellar disc effective radius in Figure 14. We split our galaxies into two luminosity bins to compare with observations. Our predictions are consistent with these observations, but are somewhat steeper. We fit the relation with the form R_e is proportional to (1+z)^-m. We obtain m=1.98+/-0.07 for galaxies with (0.3-1)L*_(z=3), and m=2.15+/-0.05 for galaxies with (0.12-0.3)L*_(z=3). These are within 3-sigma of the [L16] values. Our predictions are also consistent with the FIRE-2 hydrodynamical simulation [Ma2018], which predicts m=1-2. Our predictions for m are higher than those derived from the individual observational data sets, which all predict 1 <~ m <~ 1.5. However, [L16] show that a combined fit to z>5 observations produces larger values of m that are consistent with our predictions."}
{"text": "We plot the median total stellar specific angular momentum as a function of total stellar mass from z=7 to z=2 in Figure 15. The relation evolves to higher values of j_* for lower redshifts, at a fixed stellar mass. From z=7 to z=2, the relation increases by ~0.5 dex. At lower redshifts, observations show a range of results for the evolution of the j_*-M_* relation. Our model is consistent with the predictions of Dark SAGE [Stevens2016], which finds a weak trend for galaxies of fixed mass to have lower specific angular momentum at higher redshifts. In contrast, the hydrodynamical simulation of [Pedrosa2015] finds that the j_d-M_* relations are statistically unchanged up to z~2. The j_*/j_H - M_vir relation shows no significant redshift evolution."}
{"text": "In Section 3.2.2 we showed that Meraxes can reasonably reproduce the morphological distribution of observed low-redshift galaxies. Here we show the Meraxes predictions for galaxy morphologies at high-redshift. In Figure 16 we show the redshift evolution of the B/T ratio as a function of total stellar mass. As redshift increases, the dip in the B/T ratio becomes shallower and shifts to lower masses. This is a result of an evolution of the masses at which the merger- and instability-driven growth modes are effective. This results in an average B/T that is higher at high redshifts, suggesting that high-redshift galaxies are more likely to be bulge-dominated than those at low redshift. This is consistent with the current observations, which suggest that the spheroidal fraction increases to higher redshifts ([e.g.][Ravindranath2006, Lotz2006, Dahlen2007, Shibuya2015]). This is supported by the IllustrisTNG hydrosimulation [Pillepich2019]."}
{"text": "In this paper we introduce updates to the semi-analytic model Meraxes in order to investigate the evolution of sizes, angular momenta and morphologies of galaxies to high redshifts. These updates include a prescription for bulge formation and growth, tracking of angular momentum, and a new way of determining galaxy disc sizes. The model is calibrated to the observed stellar mass functions at z=8-0 and the black hole-bulge mass relation at z=0. At low redshifts, the model reproduces the observed galaxy size-mass relation well. We produce galaxy morphologies that are consistent with observations, with different bulge formation mechanisms dominating at different mass scales. We predict a specific angular momentum-mass relation that is consistent with observations, and shows no flattening at low-masses. We find that the specific angular momentum-mass relation depends on galaxy morphology, with bulge dominated galaxies lying below the disc-dominated sequence. We predict that the ratio between stellar and halo specific angular momentum is typically less than one and decreases with mass."}
{"text": "At high redshifts, our model predicts the following: The size-luminosity relation has a slope of beta is approximately 0.33, with a normalization that decreases with redshift. The size-mass relation has a slope b is approximately 0.24-0.28, which increases with redshift, while the normalization decreases. The median size of a galaxy disc decreases with redshift as R_e is proportional to (1+z)^-m, where m is approximately 2. The specific angular momentum-stellar mass relation evolves to higher values of j_* for lower redshifts, at a fixed stellar mass. The relation between the ratio of stellar and halo specific angular momentum j_*/j_H to stellar mass shows little evolution. Finally, galaxies at high redshifts are predominantly bulge-dominated. Meraxes can now predict a wide-range of relations that can be observed and tested by the next generation of telescopes, such as JWST."}
{"text": "Intergalactic medium temperature is a powerful probe of the epoch of reionisation, as information is retained long after reionisation itself. However, mean temperatures are highly degenerate with the timing of reionisation, with the amount heat injected during the epoch, and with the subsequent cooling rates. We post-process a suite of semi-analytic galaxy formation models to characterise how different thermal statistics of the intergalactic medium can be used to constrain reionisation. Temperature is highly correlated with redshift of reionisation for a period of time after the gas is heated. However as the gas cools, thermal memory of reionisation is lost, and a power-law temperature-density relation is formed, Temperature T equals T_0 times (1 + delta) to the power of (1 - gamma) with gamma approximately equal to 1.5. Constraining our model against observations of electron optical depth and temperature at mean density, we find that reionisation likely finished at redshift of reionization equals 6.8 with an uncertainty of +0.5 / -0.8 with a soft spectral slope of alpha equals 2.8 with an uncertainty of +1.2 / -1.0. By restricting spectral slope to the range [0.5,2.5] motivated by population II synthesis models, reionisation timing is further constrained to redshift of reionization equals 6.9 with an uncertainty of +0.4 / -0.5."}
{"text": "We find that, in the future, the degeneracies between reionisation timing and background spectrum can be broken using the scatter in temperatures and integrated thermal history. Over 13 billion years ago, when the universe was approximately 400,000 years old, it consisted mostly of a neutral atomic gas of hydrogen and helium. Over time the gas began to cool and collapse into the first stars and galaxies. Some of the radiation from these sources was energetic enough to strip electrons from the surrounding atomic gas, ionising it. This period of time, from the birth of the first stars until almost all of the atomic gas in the universe had been reionised, is referred to as the Epoch of Reionisation (EoR). The EoR is the last large-scale cosmic event to be studied in detail, and is of great interest to cosmology as it contains information about the formation processes behind the first galaxies in our universe via their effect on the intergalactic medium (IGM)."}
{"text": "There are many unanswered questions concerning the EoR, including details of its structure, duration, and effect on subsequent galaxies. However, observations of the EoR at optical to near infrared wavelengths are made difficult by the absorption of Lyman alpha photons by neutral hydrogen, which is optically thick to this wavelength even at low concentrations. Since all wavelengths below the Lyman alpha line will eventually redshift to that wavelength, measuring the presence of neutral hydrogen using Lyman alpha optical depth probes the tail end of reionisation [2017MNRAS.465.4838G], since the absorption saturates around neutral fractions of neutral hydrogen fraction less than or approximately equal to 10 to the power of -4 [2006ARA&A..44..415F]. While saturation varies between sightlines, the strength of this absorption line prohibits direct observations deeper into the EoR. In addition, we can infer the number of free electrons, and hence ionised gas, along a sightline by measuring the Thomson scattering of CMB photons. However this is an integrated measure that cannot distinguish between reionisation histories of different durations."}
{"text": "The reionisation of the IGM is accompanied by a large increase in temperature, to approximately 2 x 10^4 K, followed by cooling on a cosmological timescale [1994MNRAS.266..343M, 1997MNRAS.292...27H, 2000MNRAS.318..817S, 2003ApJ...596....9H, 2009ApJ...701...94F, 2016MNRAS.460.1885U, 2017ApJ...837..106O, 2018MNRAS.477.5501K, 2018arXiv180104931P, 2018arXiv181011683O, 2018arXiv181201016G, 2019arXiv190704860W]. As a result, the thermal imprint of reionisation will last much longer than reionisation itself. IGM temperature measurements are therefore a potentially powerful way to probe the EoR, as they contain information about the reionisation history of a region that lasts long after it reionises. Modeling the temperature evolution during the EoR allows us to relate various parameters of ionisation history to IGM temperature. Comparing observations of temperature at various redshifts to the model will place constraints on the nature of the EoR and the sources driving it [2002ApJ...567L.103T, 2012MNRAS.421.1969R, 2014ApJ...788..175L, 2017ApJ...847...63O, 2019ApJ...872..101B]."}
{"text": "Simulating the thermal history of the IGM is not a new idea, with many authors having studied IGM temperature under various assumptions of the background density and ionisation history. Instantaneous reionisation models [2002ApJ...567L.103T, 2003ApJ...596....9H, 2016MNRAS.460.1885U], radiative transfer [2018arXiv180104931P, 2018MNRAS.477.5501K], and inhomogeneous reionisation simulations [2009ApJ...701...94F, 2019ApJ...874..154D, 2012MNRAS.421.1969R] have all been utilised as a basis for IGM temperature models. Once the density field and ionising background are known, most temperature modelling follows a similar process, where photo-heating, adiabatic cooling due to structure growth and the Hubble flow, along with various cooling processes in the IGM are followed over time. The process used in our model is outlined in 2. This work uses the DRAGONS simulation suite, using the density grids from the N-body simulation Tiamat [2016MNRAS.459.3025P] and the ionising flux grids from the semi-analytic galaxy formation model Meraxes [2016MNRAS.462..250M] to determine temperature evolution over time."}
{"text": "The ionising flux model in Meraxes captures the inhomogeneous nature of reionisation, allowing us to study the entire thermal structure in our simulation. Importantly, Meraxes directly couples high-redshift galaxy formation to hydrogen reionisation, allowing us to constrain the properties of ionising sources using their effect on the IGM. Using the temperature to probe the EoR involves comparing our simulated temperature distribution to observations of thermal history, placing constraints on the timing of reionisation, and the sources driving it. Previous works studying IGM temperature have shown the relationships between the thermal state of the IGM and reionisation. Many of these works connected IGM temperature to statistics of the Lyman alpha forest and offered some measurements and constraints on the nautre of the EoR [2011MNRAS.410.1096B, 2013MNRAS.436.1023B, 2018arXiv180804367W, 2019ApJ...872..101B, 2018arXiv181011683O, 2019arXiv190704860W]. The hydrodynamic and radiative transfer simulations used in this manner have made it possible to make measurements of the IGM temperature, and draw connections between thermal variables and the EoR."}
{"text": "However these simulations are extremely computationally expensive. In order to compare these variables with a wide range of reionisation histories, a faster model is required. Using the DRAGONS simulation suite, we compare these observations to a wide range of reionisation scenarios in order to statistically constrain the global nature of the EoR. The paper is structured as follows. The DRAGONS simulations will be briefly described and the post-processing temperature model will be laid out in section 2. Overview of the model outputs is given in section 3. Our results, including an investigation of the constraints the IGM thermal history can offer and constraints from current observations, are in sections 4 and 5 respectively, before concluding in section 6. The cosmology utilised throughout this paper is the flat standard LambdaCDM from [2016A&A...594A..13P] with {Omega_m, Omega_b, Omega_Lambda, h, sigma_8, n_s} = {0.308, 0.0484, 0.692, 0.678, 0.815, 0.968}."}
{"text": "Meraxes couples early galaxy formation and reionisation in a spatially and temporally dependent way, tracking gas cooling, star formation, and feedback between galaxies and the IGM amongst other processes (see [2016MNRAS.462..250M] for more details). This paper utilises the 100 cMpc Tiamat simulation box [2016MNRAS.459.3025P] containing 2160^3 particles of mass 2.64 x 10^6 solar masses. We use GBPTREES merger trees [2017MNRAS.472.3659P] from redshifts z=35 to z=2. We use the fiducial parameter balues presented in [2017MNRAS.472.2009Q], apart from the variations listed in section 2.4. Meraxes includes a modified version of the excursion-set algorithm 21cmFAST [2007ApJ...669..663M] to track the progress of inhomogeneous reionisation in the simulated volume. Emissivity within an ionised bubble of radius r in Meraxes is calculated from the star formation rate within the bubble, the star formation rate within the bubble, star formation rate within the bubble(r)."}
{"text": "The emissivity is calculated as: the emissivity bar equals the fraction of ionising photons that escape the host galaxy times the number of ionising photons produced per stellar baryon, all divided by (4/3 times pi times r cubed times (1-0.75 times the Helium mass fraction) times the proton mass), multiplied by the star formation rate within the bubble(r), where f_esc is the fraction of ionising photons that escape the host galaxy, N_gamma is the number of ionising photons produced per stellar baryon, and m_p is the proton mass. The specific intensity at the hydrogen ionisation threshold, J_21, within the region is then computed from the emissivity, the specific intensity J bar at the hydrogen ionization threshold equals (1+z) squared divided by 4 pi, times the comoving mean-free path, times the Planck constant, times the assumed spectral power-law slope, times the emissivity bar, where h_p is the Planck constant. The comoving mean-free path, lambda_mfp, is equal to the ionised bubble radius during reionisation, and limited to 30 cMpc throughout the simulation, due to the maximum scale of the excursion-set algorithm. alpha is the assumed spectral power-law slope, a free parameter in our model where a small value corresponds to a harder UV background, such that the specific intensity J at frequency nu equals the specific intensity J bar at the hydrogen ionization threshold times (the frequency nu divided by the ionization threshold of hydrogen) to the power of -alpha, where nu_HI is the ionisation threshold of hydrogen."}
{"text": "Meraxes includes the quasar model detailed in [2017MNRAS.472.2009Q], where radiation from quasars is included when calculating reionisation structure and feedback, using equations analogous to 1 and 2, with a spectral slope of alpha_q = 1.57. Grids of the specific intensity from both galaxies and quasars, as well as density grids, are output from Meraxes. As stated in [2017MNRAS.472.2009Q] quasars have a sub-dominant effect on hydrogen reionisation in our model, due to the low number density of these luminous objects. DRAGONS combines a mass resolution small enough to capture low-mass galaxy formation, a volume large enough to study the structure of reionisation, and an inhomogeneous reionisation model based on galaxy physics. Meraxes can simultaneously reproduce the observed stellar mass function, as well as Thomson scattering optical depth and ionising emissivity measurements with certain parameter choices [2016MNRAS.462..250M]."}
{"text": "In this paper we introduce an IGM temperature model in order to better constrain the EoR within DRAGONS. The model is largely based on the semi-numerical approaches of [SRthesis] and [1997MNRAS.292...27H]. Using the ionising background and density grids from the DRAGONS semi-analytic framework, we calculate the temperature and ionisiation of the IGM within the simulated volume. Non-equilibrium photo-ionisation rates, Gamma_i and photo-heating rates, g_i, are calculated post-ionisation from the specific ionising intensity in Meraxes, J_21, assuming an optically thin IGM: the photo-ionization rate, Gamma_i, equals the integral from the ionization threshold nu_i to infinity of (4 pi times the specific intensity J_nu divided by (the Planck constant times nu)) times the frequency-dependent cross-section sigma_i(nu) dnu, the photo-heating rate, g_i, equals the integral from the ionization threshold nu_i to infinity of (4 pi times the specific intensity J_nu divided by nu) times (nu minus nu_i) times the frequency-dependent cross-section sigma_i(nu) dnu, where sigma_i(nu) is the frequency dependent cross-section taken from [1996ApJ...465..487V]."}
{"text": "The ionisation state of the IGM is then governed by the following differential equation: the change in the normalized abundance of species i, d(X tilde)_i/dt, equals -Gamma_i times (X tilde)_i plus the sum over species j,k of (X tilde)_j times (X tilde)_k times the recombination rate R_jk, times (the mean baryon density rho_b bar times (1 + delta) divided by the proton mass m_p) for each species i,j,k in {HI,HII,HeI,HeII} where R_jk is the recombination rate of species j and k resulting in i, including recombination and collisional ionisation. (X tilde)_i is defined as (X tilde)_i equals (n_i times m_p) divided by ((1 + delta) times rho_b bar), for the local overdensity, delta, and cosmic mean density, rho_b. The thermal state of the IGM is governed by the balance between photo-heating, adiabatic cooling under the Hubble flow, recombination cooling, and inverse Compton cooling, as well as changes in local overdensity according to [1997MNRAS.292...27H]."}
{"text": "The thermal state equation is: the change in temperature dT/dt equals (2 divided by (3 times the Boltzmann constant k_B times the sum over species i of (X tilde)_i)) times (the total photo-heating rate G(t) minus the total cooling rate Lambda(t, (X tilde)_i)) minus 2 times the Hubble parameter H times T plus (2T divided by (3 times (1 + delta))) times d(delta)/dt minus (T divided by the sum over species i of (X tilde)_i) times d(sum over species i of (X tilde)_i)/dt, where G is the total photo-heating rate of all species, G equals the sum over species i of g_i times (X tilde)_i, k_b is the Boltzmann constant, and H is the Hubble parameter. The cooling rate, Lambda, takes into account recombinations, collisions, bremsstrahlung, and inverse Compton cooling. We take the rates for these processes from [2015MNRAS.446.3697L]. Photo-ionisation and heating rates are calculated separately for stellar and quasar sources using the optically thin equations 4 and 5, then added together when solving equations 6 and 7."}
{"text": "Following [SRthesis], the coupled equations 6 and 7 are solved recursively, without assuming ionisation equilibrium, using a first order implicit integration scheme [1997NewA....2..209A, 2007MNRAS.374..493B] until they converge to a solution with the absolute value of the difference between the electron abundance at iteration k and k+1, |(X tilde)_e,k - (X tilde)_e,k+1|, is less than 10^-6 at a given attempt k, where we use the electron abundance as our convergence statistic. To improve the efficiency of our code, we adopt a variable timestep, where the timestep length is doubled for the next timestep each time a solution is found, or halved if a convergent solution cannot be found within 100 attempts. In the same manner, we follow the integrated thermal history via u, the total energy injected into the IGM per unit mass via photo-heating. This can be observed in Lyman alpha power spectra, distinct from temperature [2016MNRAS.463.2335N, 2019ApJ...872..101B] and can be used to simultaneously measure reionisation timing and amount of photo-heating that exists when only considering mean temperature."}
{"text": "The injected energy u is followed by simply integrating the photoheating rate over time. The value of u has been related to the small scale Jeans smoothing of the IGM, as it is dependent on the integrated thermal history throughout the EoR. We cannot calculate the Jeans scale directly in post-processing, but u provides a similar probe into the integrated thermal history throughout the EoR. In order to achieve the computational speeds required to run the model many times, we track the temperature within a 128^3 grid with cell side length approximately 800ckpc of the Tiamat 100 cMpc box; from the redshift of reionisation of each voxel, until z=4. The results for this paper use the same 10,000 (approximately 0.5%) randomly selected voxels in each box, unless otherwise stated, as a sample of the entire volume. As this is a post-processing model, the thermal state of each voxel is treated independently, although their ionising flux intensities and densities are already coupled within Meraxes and Tiamat."}
{"text": "We set the specific intensity above the helium ionisation threshold nu_HeII = 54.4 eV to zero, so that there is no reionisation of HeII to HeIII. This is because Meraxes only traces the size of HII bubbles, meaning it does not predict the mean-free path of photons above nu_HeII. This will restrict our temperature model to times earlier than HeII reionisation, thought to complete around z ~ 3 [2008ApJ...682...14F]. We include HeI reionisation, since we expect helium to be singly ionised at the same time as hydrogen [2003ApJ...586..693W]. When constraining the EoR, we also ignore the outputs of our model below z=4, to minimise confusion with the effects of HeII reionisation. In order to produce and test a large number of thermal and ionisation histories, we vary three parameters within Meraxes and the post-processing temperature model. Escape fraction normalisation and redshift-scaling, as well as background ionising spectral slope."}
{"text": "The temperature of the IGM is sensitive to the timing of reionisation, and the timing of reionisation is heavily dependent on the escape fraction of photons from galaxies. We utilise a redshift-dependent, uniform escape fraction for ionising photons, which was shown by [2016MNRAS.462..250M] to allow the model to match electron optical depth and ionising emissivity observations simultaneously. The escape fraction f_esc equals the minimum of [f_5 times ((1+z) divided by 6) to the power of beta, 1.0]. We vary f_5 between 0.03 and 0.12 and beta between 0 and 2.5 to vary the timing and duration of reionisation in the model. These values were chosen to bracket constraints from electron optical depth measurements, producing reionisation histories that finish between redshifts 5 and 10. The spectral shape of the ionising background sets the energy injected per photoionisation, which affects the reionisation temperature and the subsequent cooling rate. We model the stellar spectrum between 13.6 and 54.4 eV as a power law (equation 3), with a slope, alpha, between 0.2 and 5."}
{"text": "The quasar spectral slope in the same frequency range is fixed at 1.57 and the quasar escape fraction is fixed at 1, as in [2017MNRAS.472.2009Q]. The range of spectral slopes considered is both broader and softer than those often used in temperature modelling [2016MNRAS.460.1885U, 2019ApJ...874..154D], which are based on Population II stellar synthesis models. This range was chosen to produce at least one thermal history that is consistent with observations for each reionisation history. We investigate these scenarios when studying the correlations between heat injection, reionisation timing and temperature. When placing constraints on the EoR, however, we restrict alpha to be more consistent with these population synthesis models. For our fiducial model, we start with a 99 per cent ionised (HII and HeII) IGM, with the initial temperature calculated from the UV spectral slope at ionisation and the speed of the ionisation front in Meraxes using fits to radiative transfer simulations, performed by [2019ApJ...874..154D]."}
{"text": "If the ionisation front passes through the gas very quickly, the reionisation temperature is decided entirely by the average energy of the ionising photons, the average energy of a photon E_gamma. [2018MNRAS.477.5501K, 1997MNRAS.292...27H], yielding the reionization temperature T_reion is approximately equal to (1 divided by (3 times the Boltzmann constant k_b)) times the average energy of a photon E_gamma. However, [2019ApJ...874..154D] found using one dimensional radiative transfer simulations that the ionisation front can pass through slowly enough for collisional cooling within the hot, partially neutral gas to have a large effect on the reionisation temperaure. It was found that the speed of the ionisation front provided the best estimation for reionisation temperature, as the faster the ionisation front passes through the gas, the less time it spends in the hot, semi-neutral state where collisional cooling is efficient. Ionisation front speeds are calculated in each voxel by finding the distance between ionisation boundaries (where adjacent voxels have different ionisation snapshots) at successive snapshots, and assuming that fronts travel at a constant speed within each 11Myr snapshot."}
{"text": "We take the distance between random points in each voxel, representing our uncertainty at the grid resolution. The reionisation temperature is calculated from the front speeds and the spectral slope of the background, using fits provided by [2019ApJ...874..154D]. The distribution of reionisation temperatures in our box is presented in section 3.2, this approach introduces a correlation between ionising flux amplitude, gas density, and reionisation temperature, which further complicates the picture of patchy reionisation. Since we explore softer spectra than [2019ApJ...874..154D], initial temperatures for models with 3 < alpha <= 5 are given by the lowest of our two upper limits; from 1) the temperature at the speed of the ionisation front with alpha = 3 and 2) the maximum temperature given by the spectral slope in equation 11. This will slightly overestimate initial temperatures for the slower moving fronts, however softer spectra approach their maximum reionisation temperature at slower speeds, so this effect will be small."}
{"text": "The total photo-heating energy, u, is initialised to the mean excess energy of ionising photons, E_excess [2018arXiv180104931P]. Assuming total local absorption of ionising photons, the excess energy E_excess equals the integral from nu_i to infinity of (4 pi J_nu divided by (h_p nu)) times f_i dnu, divided by the integral from nu_i to infinity of (4 pi J_nu divided by (h_p nu)) times h_p(nu - nu_i) times f_i dnu where a factor that accounts for the preferential absorption of different frequencies by different species is f_i equals (n_i sigma_i) divided by the sum over j of n_j sigma_j and j sums over HI, HeI and HeII. Regardless of how long it takes the front to move through the gas, the total amount of energy imparted to the gas will depend only on the background spectrum, assuming the number of recombinations and collisional ionisations that occur as the front passes is small, and that all photons with energies between 1 and 4 Ryd are absorbed within the front."}
{"text": "We note that, in contrast to other works, the reionisation temperature is partly decoupled from the average photon energy. This occurs via collisional excitation cooling described above, from the models in [2019ApJ...874..154D], whereas most previous works assume reionisation occurs very quickly in each region with no cooling in the ionisation front. Using these models lowers Treion without changing the initial u_0, as u_0 only takes into account energy changes via photo-heating, as defined by [2016MNRAS.463.2335N] and [2019ApJ...872..101B]. As a result, we set the initial u_0 to the mean excess energy of the ionising background, described above. Gas on scales below our grid resolution is not homogeneous, and clumping on unresolved scales will increase recombination rates. Increasing the recombination rate will increase temperatures after reionisation by shifting ionisation equilibrium to a more neutral state, allowing more photoionisations to occur, which overcomes the increased cooling rates."}
{"text": "Large scale clumping is taken into account via our spatial grid, of voxel length ~800ckpc. We also expect reionisation to erase much of the small scale clumping due to Jeans smoothing. This still leaves some room for subgrid clumping to affect our results, on scales between our grid resolution and the Jeans length. The increased temperatures due to clumping, while reflective of the total heat inside a voxel, will not represent the wide distribution of temperatures that can exist within the voxel, as it will be dominated by the higher density clumps. In order to compare with higher resolution simulations (see appendix A), and produce a temperature independent of grid resolution, we set the clumping factor to 1. This implies that we are following the gas at the mean density of each voxel throughout the simulation, rather than each voxel as a whole. We note that there is an effect due to the subgrid structure on the background spectrum due to spectral filtering."}
{"text": "This is where intermediary absorbers harden the ionising background by preferentially absorbing lower frequency photons, as the HI ionisation cross-section scales approximately as frequency nu to the power of -3 near the ionisation edge. The amount of hardening is dependent on the structure and clumping of the IGM, as well as the structure or the ionising background. Theoretically this could harden the spectral slope by 3 (see [2009ApJ...703.1416F] appendix D) but measurements of the column density distribution of absorbers suggest a hardening of the spectral slope by approximately 1 [2010ApJ...721.1448S]. However modeling this filtering, as well as the spatially dependent spectrum of the ionising background, is beyond the scope of this work. Two approximations are made when evaluating temperature evolution that should be noted. First, equations 6 and 7 are applied to the Meraxes grids, rather than individual parcels of gas. Second, we calculate temperatures in post-processing, this assumes independence of each voxel with regards to the temperatures of other voxels, and that any gas influx is at the same temperature as the gas within the voxel."}
{"text": "These assumptions can cause some spurious heating or cooling as gas moves through the box, since this will be treated in the same way as structure growth (via the third term of equation 7). Since neighboring voxels tend to have similar ionisation histories and densities, combined with dark matter velocities that are fairly low compared to the voxel sizes, we do not expect this to have a large effect on temperatures. We tested the effect of gas diffusion on the model by running a model where an extra term was added to equation 7 to account for the gas of differing temperature entering the voxel. We keep track of the bulk flow of matter via the Tiamat velocity grids, and conservatively assumed that the temperatures of adjacent regions scaled with the maximum temperature density slope found in our other models, Temperature T is proportional to (1 + delta) to the power of 0.6. Under these assumptions, heating rate differences of order ~ 10% were observed in high density regions, and changes of order ~ 1% were observed at mean density."}
{"text": "Considering that this model overestimates the heating changes due to gas diffusion (nearby voxels are likely to be at similar temperatures shortly after reionisation), we believe that the independence of voxels is a safe approximation for the purposes of this work. The independence of voxels within our model also excludes a treatment of recombination emission, since inhomogeneous recombinations are not yet included in Meraxes. The effects of recombination emission are detailed in [2009ApJ...703.1416F] where they find it can contribute up to 10% of the ionising background for hydrogen. The effect of a 10% increase in the photo-ionisation rate will not greatly affect our results (see Appendix B). However, recombination emission could soften the background spectrum by approximately 1, since the photons from hydrogen recombination will tend to have lower energies than those in the rest of the ionising background. While this would cause a decrease in temperatures, the effect is degenerate with our free parameter for the background spectral slope, so modelling this effect is outside the scope of this work."}
{"text": "We assume that there is negligible heating by HeII reionisation before z=4 [2016MNRAS.460.1885U]. If Helium reionisation is a highly extended process, then we would be underestimating the temperature, and overestimating the IGM cooling rate for any given reionisation history. With our parameterisation, this would bias our models to earlier reionisation scenarios (due to the flatter temperature gradient), with harder spectral slopes (due to the higher temperatures). The reionisation model in Meraxes assumes local absorption of ionising photons. Photons that would redshift below the ionisation threshold in a full radiative transfer model can still ionise in Meraxes. Since Meraxes is tuned to match the ionising emissivity measurements of [2013MNRAS.436.1023B], which were calculated based on radiative transfer models, J_21 could be overestimated by a small amount. This will not have a large effect during Hydrogen reionisation, as the size of HII regions are small enough to make local absorption a good approximation."}
{"text": "Furthermore, we find that temperature at all redshifts is insensitive to the value of J_21 after the region is reionised, as long as it is large enough to maintain a highly ionised IGM (Appendix B). We only vary the escape fraction (equation 10) to produce different reionisation scenarios, while keeping the same source model. This means that we ignore any degeneracy between our escape fraction parameters and source modelling with regards to the IGM thermal state. In particular the constraints we find due to the scatter in temperatures are likely optimistic, as the patchiness of reionisation will have a significant effect on the range of temperatures observed afterwards. Shock heating of high density regions as they collapse is also not modeled in this work, as we are primarily interested in the diffuse IGM. We only track the increase in temperatures from structure growth on the scale of our grid. This will exclude the ~ 10^5 K gas that exists in hydrodynamic simulations."}
{"text": "However, studies of IGM temperature have so far focused primarily on gas at or below the critical density, excluding shock heated gas in their analyses [2018arXiv181011683O]. Using the temperature evolution model described in section 2, we calculated the thermal and ionisation states of the same 10,000 randomly chosen voxels for 2750 Meraxes realisations, in order to obtain a wide range of density and ionising flux histories per model, as well as a wide range of global reionisation and thermal histories. We have also computed the evolution of one full box, to examine the topology of the temperature field. The model parameters used in the illustrative examples within this section are {f_5, beta, alpha} = {0.08, 1, 2} on the full 128^3 Meraxes box. This run was chosen as all the correlations between reionisation timing, density and temperature of reionisation are clearly shown in its results. However, this is not our highest likelihood model, based on observational data."}
{"text": "Thermal history of 3 ~ 800kpc^3 voxels in Meraxes, showing the effect of density history and ionisation timing on the thermal state. Top panel: Density contrast vs redshift. Middle panel: Temperature vs redshift. Bottom panel: Integrated thermal history, showing the total amount of energy injected by photo-ionisations per unit mass. Temperature and overdensity of a full 100 x 100 x 0.8 Mpc slice of the example model run with parameters {f_5, beta, alpha} = {0.08, 1, 2} at redshifts 4(bottom), 5(middle) and 6(top). An anti-correlation between temperature and density can be observed towards the end of reionisation (z=6), with very hot voids. This state then decays, forming a tighter positive correlation between T and delta. 100 x 100 x 0.8 Mpc redshift of reionisation slice (left) compared to the temperature just after the region ionises (right), showing an inverse correlation between them, with early reionisation corresponding to low reionsiation temperature. As the ionisation fronts speed up in the cosmic voids, the gas is ionised to a hotter temperature."}
{"text": "A few examples of thermal histories output by our model are given in Figure 1. Each voxel will experience a sudden rise in temperature when it is ionised, dominated by photo-ionisation heating. Afterwards, the voxel cools on a cosmological timescale at a rate determined mainly by the ratio of photo-heating and recombination cooling at ionisation equilibrium, as well as adiabatic cooling and inverse compton cooling off the CMB. Density evolution will modulate the temperature, but the previous density history of a voxel will have little effect on its thermal asymptote [2016MNRAS.456...47M]. However, the previous density history will have a substantial effect on the integrated photo-heating, u. Each voxel approches its thermal asymptote within a redshift interval Delta z is approximately equal to 1-3 of its reionisation, creating a distribution in temperatures in the whole box dependent on the inhomogeneous reionisation history. Figure 2 shows a 128^2 voxel slice of the temperature model at selected redshifts between 6 and 4."}
{"text": "It can be seen that shortly after reionisation, at z = 6, the high density regions reach temperatures of T is approximately equal to 2 x 10^4 K, as they have recombination rates high enough to allow continuous photo-heating of the gas. The larger voids also reach similar temperatures, as they reionise last due to the “inside-out\" nature of the EoR in our models, and hence have the least time to cool. The coolest regions are the low density regions in close proximity to high density regions, which are reionised early by stars in the nearby dense filament, and cool over time as their recombination rates are not high enough to maintain high levels of photo-heating. Long after reionisation, at z=4, the hotter low density regions cool so that temperature is closely correlated with density. The ionisation topology matches that of previous works modeling inhomogeneous reionisation [2008ApJ...689L..81T, 2012MNRAS.421.1969R, 2018MNRAS.477.5501K, 2014ApJ...788..175L, 2018arXiv181011683O]."}
{"text": "Comparing Figure 2 with the left panel of Figure 3, which show the redshifts of reionisation and temperatures within the same region, we see that shortly after reionisation there is a notable anti-correlation between temperature and redshift of reionisation. Over time this correlation diminishes, and the correlation between temperature and density becomes dominant. Reionisation temperature distributions in our grid Top panel: redshift of reionisation distribution. Middle: distribution of reionisation temperatures at the time of their reionisation. Bottom: reionisation temperature distributions for voxels reionising at specific redshifts, showing the increasing reionsation temperature as reionisation progesses. Note that these are the temperatures that voxels reionise to for the subset of voxels that reionise near a specific redshift, not the temperatures of all voxels at the same redshift."}
{"text": "In this section we present the reionisation temperatures in our fiducial model, using fits for the reionisation temperature provided by [2019ApJ...874..154D], to convert ionisation front velocities to reionisation temperatures. Using these fits allows us to include the correlations between temperature, ionisation history and the photon background in more detail; this reduces the number of free parameters we need to include. The temperature to which a region of the IGM is reionised to is inversely correlated with its redshift of reionisation, as shown in Figure 3. This anti-correlation results from the fact that the ionisation fronts speed up as they enter the low-density regions towards the end of the EoR, resulting in higher temperatures because there is less time for collisional cooling to take effect. Differences in simulated reionisation history, and to a lesser extent grid resolution, snapshot cadence, and algorithm to find ionisation front speed result in changes to the distribution."}
{"text": "Figure 4 shows the distribution of reionisation temperatures, compared to redshift of reionisation. As shown in the top panel, reionisation in this model occurs in the redshift range 6 is less than or approximately equal to z is less than or approximately equal to 12. The middle panel shows the full distribution of temperatures to which regions ionise. We find a similar range of reionisation temperatures as [2019ApJ...874..154D], between (15-25) x 10^4 K. The bottom panel splits up this distribution into regions that ionised at different times, showing that the temperature of the ionisation fronts increases as reionisation progresses. Lower spatial resolution, as well as our discrete timestep, likely smooths out the extreme ends of the distribution compared to [2019ApJ...874..154D], and results in a broader distribution of temperatures at any given redshift. However it is difficult to directly compare the distributions due to differences in reionisation history."}
{"text": "The excursion set formalism used to predict reionisation history in Meraxes is likely too crude to predict accurate ionisation front speeds on scales of individual voxels, as the spherical symmetry assumed by 21cmFAST effectively averages over many cells during the later stages of reionisation. However, since we recover a similar range of speeds and reionisation temperatures as [2019ApJ...874..154D], and the reionisation temperature increases as reionisation progresses, we consider this approach to be a valid approximation for testing the statistics of IGM temperature and more accurate than assuming a constant reionisation temperature for all voxels. Temperature density relation for 10,000 voxels in our model at redshifts 4 to 6, showing the large scatter in low density regions at early times, followed by a late time power law, with slope approaching gamma - 1 is approximately equal to 0.5 by redshift 4 for all densities. The solid black line shows mean temperature at binned denisties, and the dotted black lines show the 5th and 95th quantiles in each bin. The colours of each dot show the redshift at which the voxel ionised."}
{"text": "Figure 5 shows the temperature-density relation at various redshifts in our fiducial model. The temperature-density relation (TDR) is a powerful probe of the conditions in the IGM. The shape and scatter in the relation at various densities can reveal information about ionisation history and structure of the IGM during the EoR. A power law fit T=T_0(1+delta)^(gamma-1) is commonly used when characterising the thermal state of the IGM. However, this is only accurate for regions that ionised homogeneously or long before the measurement is taken. Restricting the study of temperature to a power law misses much of the information in the temperature density relation that can be used to constrain a patchy EoR [2018arXiv181011683O, 2019arXiv190704860W]. There is a wide distribution of temperatures in low density regions shortly after reionisation, as the temperature at low density is highly dependent on the redshift of ionisation at this time."}
{"text": "The large scatter lasts long after reionisation itself, halving approximately within a redshift interval Delta z is approximately equal to 1 after reionisation in most of our models. Long after reionisation, regions of all densities cool to their asymptotic temperature, and the temperature density relation is well described by a power law T = T_0(delta + 1)^(gamma - 1), with a slope approaching gamma - 1 is approximately equal to 0.6 by redshift z=4. This is consistent with other inhomogeneous reionisation models and analytic calculations of the thermal asymptote [1997MNRAS.292...27H, 2016MNRAS.456...47M]. High density regions do not show much variance in their temperatures, as their reionisation temperatures tend to be much closer to their early-reionisation asymptote. As a result high density regions settle much more quickly into the late time power-law. Furthermore, dense regions tend to ionise earlier, so any scatter at the high end of the temperature density relation will likely have disappeared by the time of measurement."}
{"text": "In agreement with other inhomogeneous reionisation models [2008ApJ...689L..81T, 2012MNRAS.421.1969R, 2018MNRAS.477.5501K], we find that the large scatter in low density regions shortly after reionisation is highly correlated with the redshift of ionisation of the region (shown in the colours in Figure 5). The size of this scatter, and its correlation with z_r, is what causes the changes in the T-delta slope. The scatter in temperatures can be a powerful probe of the patchiness of reionisation, as it shows differences in reionisation redshift between different regions of the low-density IGM, allowing us to quantify the patchiness of reionisation, as well as estimate how long ago reionisation occurred as the scatter diminishes (see section 4.1). Once every region has reached its thermal asymptote, and the TDR settles into a power law, the thermal memory of reionisation has been lost, as regions that ionised at different times approach the same temperature, based on their density."}
{"text": "[2008ApJ...689L..81T, 2009ApJ...701...94F] and [2012MNRAS.421.1969R] note an inversion of the temperature-density relation, with gamma-1~-0.2, at low densities shortly after reionisation, meaning the lowest density regions are hotter on average than mean density regions at the end of the EoR. This inversion is due to the lowest density regions ionising last, hence having less time to cool, as well as ionising to higher temperatures due to faster ionisation front speeds. In the above model, we find this inversion towards the end of reionisation, lasting until z is approximately equal to 5 as there are many hot low-density regions that have recently ionised, and have yet to cool towards the asymptotic power-law relation. The average slope of the TDR is highly dependent on reionisation history and spectral slope, as they alter the strength of the correlations between density, redshift of reionisation, and temperature. As a result, inversion in the TDR is not observed in all of our models, although the slope will always be at a minimum towards the end of the EoR."}
{"text": "In this section we investigate how the distribution of temperatures in the IGM can be used to probe reionisation. We have run a suite of realisations of our model, with different escape fractions and background spectral slopes (see section 2.4), controlling the timing and duration of reionisation, as well as the temperature of reionisation and subsequent cooling rates. In order to simulate earlier and later reionisation scenarios, we vary the escape fraction normalisation and redshift scaling (equation 10) in Meraxes. A higher (lower) escape fraction results in more (less) ionising photons escaping galaxies, and therefore an earlier (later) reionisation, and a colder (hotter) IGM at a fixed redshift, while thermal memory of reionisation still exists. Models with different escape fractions will tend towards the same temperature at late times, as all regions approach their thermal asymptote. The effects of the escape fraction parameters on global redshift of reionisation (defined as when the global neutral fraction is 10 percent) can be seen in Figure 6."}
{"text": "Reionisation history also has an effect on reionisation temperatures, by changing the speed of ionisation fronts in the IGM. Figure 7 shows the temperature at mean density, it's standard deviation, and the energy injected from photoionisations at z=4.5 versus the model's global redshift of reionisation (where the mass-weighted neutral fraction falls below 0.1) for varying spectral slopes. As noted in section 3.3, both the mean and spread of temperature are maximised shortly after the bulk of reionisation occurs. The mean temperature will decrease towards an asymptote dependent on the background spectrum, and the scatter will decrease towards zero. A harder spectral slope will impart more energy to the IGM on average per ionising photon, increasing the ratio of the photoheating rate to the ionisation rate. As a result, the thermal asymptote of each voxel becomes hotter. The reionisation temperature also increases, however this can be limited by collisional cooling if the ionisation front passes through the IGM slowly (see section 3.2 and [2019ApJ...874..154D])."}
{"text": "Changes in temperature due to reionisation timing and those due to background spectrum are difficult to differentiate using temperature measurements alone. However, mean temperature and scatter in temperature have different correlations with the timing of reionisation and background spectrum, and will evolve at different rates over time. As a result, observations of mean and scatter in IGM temperature at multiple redshifts can be used to break the degeneracy between the timing of reionisation and the background spectrum, offering tighter constraints on the redshift of reionisation. The integrated photo-ionisation energy at mean density, u_0, can be used to further tighten constraints. Unlike temperature, an earlier reionisation increases the photo-ionisation energy at mean density, u_0, since residual photo-heating that occurs after reionisation will have been occurring for longer. Because injected energy and temperature have opposite correlations with redshift of reionisation, their observations can be used together to simultaneously constrain the background spectral slope and the timing of reionisation [2016MNRAS.463.2335N, 2019ApJ...872..101B]."}
{"text": "In order to explore how temperature observations constrain the EoR, we perform mock observations on our simulation. We create mock observations on the model discussed in section 3 of temperature at mean density T_0, scatter of temperature at mean density sigma(T_0), and injected photo-ionisation energy at mean density u_0 at redshifts 4.5, 5.0 and 5.5, similar to the redshifts of the temperature measurements from [2019ApJ...872..101B], which are 4.2,4.6, and 5.0. T_0 and u_0 are derived from T and u by binning their respective distributions around mean density Delta = 0 +/- 0.1 and averaging. We use 0.125 dex as a 1 sigma measurement error, of similar size to the largest uncertainties given in [2019ApJ...872..101B]. By comparing the mock observations to our series of models, we then estimate the timing of reionisation and background spectral slope, to see how well the input parameters can be recovered."}
{"text": "We estimate the likelihood of each model assuming Gaussian errors, based on the true values from one model. The likelihoods of each of our models, compared to these mock observations from our model (with parameters {f_5, beta, alpha} = {0.08, 1.00, 2.00}, and redshift of reionization is approximately equal to 6.84), are shown in Figure 8. It is important to note that we do not create mock Lyman alpha spectra, due to the low resolution of our simulations. Here, “mock observations\" refers to the summary statistics of the IGM thermal state, that we generate from one of our models with some assumed error margin. These statistics correspond to the temperature and energy measurements attained from the analysis of Lyman alpha spectra, for example those published in [2011MNRAS.410.1096B, 2018arXiv180804367W] and [2019ApJ...872..101B]."}
{"text": "We recover a strong peak in alpha, and as seen in the contours of the beta versus f_5 panel, the highest likelihood models are those with the same redshift of reionization as the true model. However, we cannot recover our two escape fraction parameters independently with this sample, as our observables are more sensitive to the timing of reionisation than the duration of it. We will require more precise observations, across a wider range of redshifts to begin to distinguish these scenarios using the scatter in temperature. A more extended reionisation will have a wider distribution of temperatures, from a wider distribution of reionisation times. Contours of equal likelihood of our models when compared to each observable separately at redshifts 4.5, 5 and 5.5 with 0.125 dex errors, showing the degeneracies of each thermal statistic in redshift of reionization and alpha. Left panel: mean temperature at mean density. Middle panel: standard deviation of temperature at mean density. Right panel: photo-ionisation energy at mean density."}
{"text": "We next present the constraints from each observable separately. The different correlations of temperature at mean density, its scatter, and injected energy with redshift of reionisation and background spectral slope allow us to constrain these reionisation parameters simultaneously. A similar result was demonstrated by [2019ApJ...872..101B], using the integrated thermal history to break the degeneracy between reionisation timing and initial temperatures. Figure 9 illustrates this for the {f_5, beta, alpha} = {0.08, 1.00, 2.00} model, showing the constraints from mock observations of mean temperature, scatter and photo-heating separately on the redshift of reionisation and background spectrum. While each observable alone is degenerate between the timing of reionisation and the background spectrum, their degeneracies differ in magnitude and direction, allowing us to perform this analysis. We have applied this analysis to each of our models and present the precision achievable for recovery of reionisation redshift and spectral slope in Figure 10."}
{"text": "We can recover the redshift of reionisation in our model within a redshift interval Delta z is approximately equal to 1 and spectral slopes within a slope interval Delta alpha is approximately equal to 2 to 95% confidence, using an error margin of 0.125 dex for temperature and injected energy observations. As discussed in section 4.1, our mock observations with errors corresponding to existing datasets were unable to independently recover escape fraction normalisation and scaling. We now examine a much more optimistic dataset from possible future observations, where temperatures at mean density, scatters, and injected energies are known within a 1 sigma error of 0.05 dex at 9 evenly spaced redshifts between 4 and 6. We show the results for this case in Figure 11 for the parameter set {f_5, beta, alpha} = {0.08, 1.00, 2.00} and Figure 12 for all models. The recovery of parameters is much more precise in this scenario."}
{"text": "With such an extensive dataset we can recover the redshift of reionisation within a redshift interval Delta z is approximately equal to 0.5 and background spectral slope within a slope interval Delta alpha is approximately equal to 0.5 also to 95% confidence. This example is also closer to recovering the escape fraction normalisation and scaling independently. These mock measurements of the scatter in temperatures disfavour reionisation scenarios that are too extended or too sudden, however there is still a significant degeneracy between these two recovered parameters. Considering that this is a very optimistic dataset, recovering the duration of reionisation from its thermal state will likely require a more detailed analysis. In the last section, we demonstrated how IGM thermal state observables constrain the nature of the EoR using mock observations of our suite of models. In this section, we apply this process to recent observations of the thermal and ionisation history of the universe, in order to constrain our model parameters."}
{"text": "We constrain against measurements of temperature at mean density from [2019ApJ...872..101B], and electron optical depth measurements from [2018arXiv180706209P]. Temperature measurements from [2011MNRAS.410.1096B] and [2018arXiv180804367W] were also consdidered, but model likelihoods on these datasets will not be presented in this paper. The former dataset produces similar but looser constraints on reionisation, whereas we are unable to match temperatures from the latter dataset due to the sudden increase in temperatures at z=5. Figure 13 shows the observations utilised, and maximum likelihood models based on each temperature dataset. Electron Optical depth measurements place constraints on the redshift of reionisation, while temperature measurements constrain both the timing of reionisation and the background slope. We restrict our attention to temperature at mean density, T_0, and electron optical depth, tau_e. No measurements currently exist for scatter in temperatures, so we are unable to use this observable for our EoR constraints, as in our mock examples."}
{"text": "Regarding u_0, we are unable to reliably relate the integrated thermal history in the optically thin models that produce this measurement in [2019ApJ...872..101B], with the thermal histories in our patchy reionisation models. A patchy reionisation effectively has a much harder spectrum within ionisation fronts, reducing the effective spectral slope by approximately 3 due to all ionising photons being absorbed within the front. This creates a hotter reionisation, but most importantly, permanently offsets the injected energy by a certain amount compared to an optically thin model, because u_0 is a time-integrated statistic. Since we cannot model how u_0 affects the small scale Lyman alpha power spectrum in our patchy reionisation models, we do not include u_0 in our fiducial constraints. We have ignored temperature measurements at redshifts z<4 to minimise confusion resulting from the beginning of HeII reionisation."}
{"text": "If a substantial amount of HeII ionisation has occurred at the redshift of measurement, this could be confused with a hotter post HI reionisation IGM with a flatter or positive evolution. This would result in a bias towards models where the overall cooling rate is suppressed, either due to a harder ionising spectrum or earlier reionisation, where the gas is closer to its thermal asymptote and would show a flatter evolution. Given the strong degeneracy between escape fraction parameters, we instead show constraints on alpha and the redshift of reionisation, z_reion. Figure 14 shows our constraints on these parameters based on the measurements from [2019ApJ...872..101B] and [2018arXiv180706209P]. We find a strong degeneracy between z_reion and alpha where T_0 alone is considered. Using tau_e to break the degeneracy results in a late reionisation redshift of reionization equals 6.8 with an uncertainty of +0.5 / -0.8 and a soft ionising background alpha equals 2.8 with an uncertainty of +1.2 / -1.0."}
{"text": "In order to match temperature observations at z>4 as well as observations of electron optical depth, our simulations favour a softer UV spectrum than assumed in other works. This may result from tension between the observations, with temperature observations favouring an earlier reionisation than electron optical depth measurements. This is certainly the case when we restrict the background spectral slope to ranges supported by stellar population synthesis models, with 0.5 < alpha < 2.5, given by the red shaded region in figure 14 (see [2016MNRAS.460.1885U] and [2019ApJ...874..154D] for discussions of possible background spectral slopes) which tightens our reionisation timing constraints to redshift of reionization equals 6.9 with an uncertainty of +0.4 / -0.5. However many models without this restriction, with alpha < 2.5 and a slightly earlier reionisation redshift of reionization is approximately equal to 7 are within 1 sigma uncertainty of our results. Since the duration of reionisation also has an effect on temperatures via the ionisation front speed (see section 3.2, [2019ApJ...874..154D]), models with harder spectra require slower reionisation histories in order to agree with both temperature and CMB measurements [2019ApJ...872..101B]."}
{"text": "As a result constraining reionisation duration will result in tighter constraints on spectral slope. We also note that spectral slopes alpha < 0.5 are ruled out at 2 sigma, as these spectra produce temperatures that are too high compared to observations, even when reionisation occurs relatively early. Using an inhomogeneous reionisation model, we have probed the full distribution of IGM temperatures, and its correlations with structure growth, the ionising background and patchy reionisation. We have begun to show how these correlations can be used to characterise the EoR, placing simultaneous constraints on the timing of reionisation and the background spectrum. We recover thermal behaviours from other inhomogeneous reionisation models [2012MNRAS.421.1969R, 2008ApJ...689L..81T, 2017ApJ...847...63O, 2018MNRAS.477.5501K, 2009ApJ...701...94F, 2018arXiv181011683O], where shortly after reionisation, there is a large scatter in the low-density end of the temperature-density relation, and a strong correlation between temperature and redshift of ionisation."}
{"text": "By redshift z = 4, the temperature correlation shifts towards density, creating a power law temperature density relation, leaving no memory of the redshift of reionisation in the low-density IGM. The large initial scatter in the temperature density relation is highly correlated with the redshift of reionisation of the region, differentiating between regions near the cosmic filaments, which reionise early, and those in large voids, ionising later. Temperature measurements taken while the low-density scatter still exists contain information concerning when a region reionised, and the mean and scatter of multiple measurements can be used to constrain the reionisation history. However interpretations of these measurements will be highly dependent on the nature of the ionising sources, and the structure of the gas in the region. Performing mock observations of the mean and scatter of the temperature density relation at different redshifts illustrates the potential for constraints on the EoR."}
{"text": "Using uncertainties similar to those for recent temperature measurements [2019ApJ...872..101B, 2018arXiv180804367W], we can recover the redshift of reionisation from our mock observations to 1 sigma within a redshift interval Delta z_reion is approximately equal to 0.5 and background spectral slopes within a slope interval Delta alpha is approximately equal to 1. Comparing our suite of models to electron optical depth and temperature measurements, our modeling favours a reionisation history that finishes around redshift of reionization equals 6.8 with an uncertainty of +0.5 / -0.8 and a UV background with a power-law spectral index of alpha equals 2.8 with an uncertainty of +1.2 / -1.0 (1 sigma uncertainties) between 912 A ~and 228 A. If we restrict our models to those with spectral slopes consistent with population II stellar sysnthesis models (0.5 < alpha < 2.5), the redshift of reionisation is restricted further to redshift of reionization equals 6.9 with an uncertainty of +0.4 / -0.5."}
{"text": "Knowledge of the distribution and history of temperatures within the IGM in addition to temperature at mean density will greatly improve our understanding of the EoR. while the timing of reionisation is probed by mean temperature, as discussed in section 4.1, an estimate of the scatter in temperatures between different lines of sight from multiple quasar spectra, or by the large scale features of the Lyman alpha forest [2018arXiv181011683O, 2019arXiv190704860W], would begin to offer information about the duration and patchiness of reionisation. This is because the distribution of temperatures shortly after reionisation is closely related to the distribution of reionisation redshifts within a volume (see Figure 5). This is especially true for low density gas, where the distribution of temperatures is widest. One way to further probe the temperature density relation could involve the cross-correlation of temperature measurements with the galaxy field. In this manner, information could be gained on the correlation of temperatures with density at various scales throughout reionisation."}
{"text": "From the temperature-density plots in this work, we would expect to see the correlation on small scales flattening, or even inverting, shortly after reionisation. This section explores the effects of numerical factors in our model. The grid resolution of Meraxes will be investigated, as well as the parameters used in our DE solver, namely the convergence threshold that we use to determine the timestep throughout the model. For computational reasons, all of model runs were performed using 128^3 grids in Meraxes. However to ensure inhomogeneities below this scale do not greatly affect our results, we examine results from one run on a 256^3 grid. As shown in Figure A1, while the overall clumping factor has increased, the temperatures and photo-heating energy at mean density are largely unaffected. This is due to the fact that we follow the gas at the mean density of each voxel, rather than the voxel as a whole."}
{"text": "This will produce a very similar temperature-density relation regardless of grid resolution; The distribution of densities will change, but the temperature at any particular density will remain the same. We have altered the convergence conditions in our differential equation solver to test for convergence. We change the conversion threshold between the absolute value of the difference between the electron abundance at iteration k+1 and k, |(X tilde)_e,k+1 - (X tilde)_e,k|, is less than 10^-8 and 10^-4. The results of these changes for an individual voxel that ionised at z=10 are presented in Figure A2. The weakest threshold gives a maximum difference in temperatures of is approximately equal to 2 %, and our fiducial threshold of 10^-6 is negligibly different from the strictest thresholds. We are therefore confident that our choice of differential equation solver parameters does not affect our results."}
{"text": "Previous simulations have found little dependence of the long term thermal state on the amplitude of the ionising background, as long as it is strong enough to maintain an ionised IGM [1997MNRAS.292...27H, 2009ApJ...701...94F]. This result is verified in our model, as we can see no change in the long term thermal state when we artificially increase or decrease the amplitude of the ionising background post-reionisation, keeping our other parameters constant. The ionisation rate in a voxel is directly proportional to the amplitude, however the number of ionisations that actually occur is limited by the recombination rate, which is negligibly changed for all highly ionised states. As a result the long term cooling is largely unaffected at most densities. Figure B1 shows the mean temperature at mean density, a third of mean density, and three times mean density, for the three amplitudes tested. It is important to note that the ionising flux amplitude has little effect on temperature only when there is enough ionising flux to maintain the ionised state in a region."}
{"text": "If the amount of ionising flux is low enough such that it is comparable to or lower than the recombination rate, there will be a significant drop in temperature as the gas recombines. Furthermore, the long term temperatures will decrease, due to the ionisation rate falling below the recombination rate for a fully ionised state; this causes the ionisation equilibrium state to shift to a more neutral state, lowering the rate of ionisations and recombinations, and therefore the photo-heating rate near equilibrium, as the cooling rate is now limited by ionisations, rather than recombinations. In our simulation, there is enough ionising flux with the fiducial values from Meraxes to maintain a highly ionised state in the vast majority of the simulated volume, so a significant drop in temperature is observed only for highly dense regions. Voxels at mean density will only show a 5% decrease in temperatures when the ionising flux is decreased by a factor of 10. Differences in temperature will also diminish over time, as the gas cools to its thermal asymptote."}
{"text": "Regions near early galaxies that have their star formation suppressed or move between voxels can also show this behaviour, however in this case the temperature drop is also usually very short-lived, as nearby HII bubbles expand to re-heat the voxel, washing out any memory of previous ionisation events."}
{"text": "We present a new analysis of high-redshift UV observations using a semi-analytic galaxy formation model, and provide self-consistent predictions of the infrared excess (IRX) - β relations and cosmic star formation rate density. We combine the Charlot & Fall dust attenuation model with the MERAXES semi-analytic model, and explore three different parametrisations for the dust optical depths, linked to star formation rate, dust-to-gas ratio and gas column density respectively. A Bayesian approach is employed to statistically calibrate model free parameters including star formation efficiency, mass loading factor, dust optical depths and reddening slope directly against UV luminosity functions and colour-magnitude relations at z ~ 4 - 7. The best-fit models show excellent agreement with the observations. We calculate IRX using energy balance arguments, and find that the large intrinsic scatter in the IRX - β plane correlates with specific star formation rate. Additionally, the difference among the three dust models suggests at least a factor of two systematic uncertainty in the dust-corrected star formation rate when using the Meurer IRX - β relation at z >= 4."}
{"text": "One fundamental question in astronomy is to understand the buildup of stars and galaxies from baryonic matter in the early Universe. During this epoch, observations focus mainly on rest-frame UV properties due to cosmic redshift. These include measurements of UV luminosity functions (LFs) [2010A&A...523A..74V, 2015ApJ...803...34B, 2017ApJ...835..113L, 2018arXiv180707580B, 2018PASJ...70S..10O], and UV continuum slope to UV magnitude relations [2012ApJ...756..164F, 2014ApJ...793..115B, 2014MNRAS.440.3714R], which are also known as the colour-magnitude relations (CMRs). The UV luminosity is a tracer of star formation since most UV photons are emitted by young stars. However, star formation can be heavily obscured by the interstellar dust. One commonly adopted approach to perform dust corrections at high redshifts is to infer the infrared excess (IRX) from the observed UV slopes using a relation calibrated by [1999ApJ...521...64M] [e.g. 2015ApJ...803...34B, 2015ApJ...813...21M, 2016MNRAS.462..235L]. However, the [1999ApJ...521...64M] relation is calibrated against local starburst galaxies, and observations of far infrared data is rather challenging at high redshifts."}
{"text": "Recent observations at z >= 3 show large scatter in the IRX - β relation [2015Natur.522..455C, 2016A&A...587A.122A, 2016ApJ...833...72B, 2017ApJ...845...41B, 2017MNRAS.472..483F, 2018MNRAS.479.4355K]. For instance, the observed IRX by [2016ApJ...833...72B] is much lower than the [1999ApJ...521...64M] relation, while [2018MNRAS.479.4355K] suggest that the IRX - β relation does not evolve with redshift. These observations motivate investigation of the IRX - β at high redshifts from theoretical models. Theoretical studies of dust extinction require intrinsic galaxy properties as input, and one approach is to postprocess the output of a hydrodynamical simulation. This method has been implemented in [2017ApJ...840...15S] and [2018MNRAS.474.1718N] to investigate the origin of the IRX - β relation. At z >= 5, the IRX - β relation has been studied by [2016MNRAS.462.3130M], [2017MNRAS.470.3006C] and [2019MNRAS.487.1844M]. However, their results suggest different extinction curves. [2017MNRAS.470.3006C] pointed out that the reason for the disagreement could be due to systematics associated with different simulations."}
{"text": "Semi-analytic models are another popular approach for studying galaxy formation [e.g. 2011MNRAS.413..101G, 2015MNRAS.453.4337S, 2016ApJS..222...22C, 2016MNRAS.462.3854L, 2018MNRAS.479....2C, 2018MNRAS.481.3573L, 2019arXiv190101906C]. Semi-analytic models solve a system of differential equations that govern the mass accretion and transition of several key baryonic components of galaxies such as gas and stellar mass. Their construction is relatively simple, and hence they are computationally efficient. These models also introduce several free parameters to describe the unknown efficiency or strength of certain physics processes. These parameters bring flexibility, and allow the exploration of different galaxy formation scenarios, which is very useful for identifying which galaxy processes regulate certain observations. This work utilises MERAXES to predict intrinsic galaxy properties, and combines it with a simple and flexible dust attenuation model. The dust optical depths are calculated empirically using relevant galaxy properties. By taking full advantage of the fast computational speed, we carry out a Bayesian analysis on all the model free parameters, and use UV LFs and CMRs as constraints, which are the most fundamental observables at high redshift."}
{"text": "The MERAXES semi-analytic model is the backbone of the present work. It extends the models of [2006MNRAS.365...11C] and [2011MNRAS.413..101G] to high redshifts, and is modified to run on high cadence halo merge trees with a delayed supernova feedback scheme. It also implements gas infall, radiative cooling, star formation, supernova feedback, metal enrichment, and reionisation feedback. The active galactic nuclei (AGN) feedback of the model is later introduced by [2017MNRAS.472.2009Q]. This work also applies several updates to the model, aiming to improve the predicted gas phase metallicity. We utilise the halo merger trees of the Tiamat N-body simulation [2016MNRAS.459.3025P, 2017MNRAS.472.3659P]. The simulation contains 2160³ particles in a (67.8 h⁻¹)^3 Mpc³ box, with mass resolution m_p = 2.64 × 10⁶ h⁻¹ Msun. Halos and friends-of-friends groups are identified using SUBFIND [2001MNRAS.328..726S]. The high cadence of the simulation is critical to this study since UV magnitudes are sensitive to starbursts in the recent 100 Myr."}
{"text": "Since this work requires evaluating the model many times, and does not focus on ionising structures, we adopt homogeneous reionisation feedback [2000ApJ...542..535G] instead of using 21cmfast [2007ApJ...669..663M]. Both approaches are described in [2016MNRAS.462..250M] and found to have almost the same predictions on global galaxy properties such as the stellar mass function up to z ≈ 5. However, the homogeneous prescription is more computationally efficient. Our model assumes that gas undergoes shock heating and forms a quasi-static hot halo when it is accreted by the host dark matter halo. The gas can cool and form a cold disk, which then becomes fuel for star formation. Following the disk stability argument of [1996MNRAS.281..475K], our model assumes that gas can only form stars when its mass is greater than a critical mass, which is a function of the halo's maximum circular velocity V_max and the disk scale radius r_disk. The mass of new formed stars is then proportional to the star formation efficiency α_SF and the excess gas mass, divided by the disk's dynamical time."}
{"text": "We update the supernova feedback model with a different treatment of supernova energy, and a different parametrisation of mass loading factor and energy coupling efficiency. Our original model is a modified version of [2011MNRAS.413..101G], taking into account the high cadence of our halo merger trees. The effect of supernova feedback is to transfer the gas in the cold disk to the hot halo. The amount of mass that is reheated is determined by a two-case equation: it is estimated by the mass loading factor argument, and reduced if the energy injected by supernova is smaller than the underlying energy increase of the hot halo. Moreover, if the injected energy is greater than what is required for reheating, materials can be further ejected from the hot halo. The ejected mass is subtracted from the hot gas and put into a separated component. The injected supernova energy plays an important role in this model, calculated as an integral over the star formation history weighted by the energy release rate of a simple stellar population."}
{"text": "While our original model uses an analytic fit to estimate the energy release rate from supernovae, this work generates it using STARBURST99 [1999ApJS..123....3L, 2005ApJ...621..695V, 2010ApJS..189..309L, 2014ApJS..212...14L] with metallicity dependence, assuming a Kroupa IMF [2002Sci...295...82K]. This treatment provides more reasonable and self-consistent estimates of the supernova energy. To evaluate the integral, MERAXES tracks the mass of new formed stars and their metals in four previous snapshots. The mass loading factor η and energy coupling efficiency ϵ are given by a broken power law based on the FIRE simulations [2014MNRAS.445..581H, 2015MNRAS.454.2691M]. This form is primarily motivated by its impact on metallicity, as previous studies found that explicit redshift-dependent models can lead to evolution of the mass metallicity relation [2016MNRAS.461.1760H, 2018MNRAS.481..954C]. We set the redshift dependence of reheating α_reheat = 2 and assume no redshift dependence on the energy coupling efficiency (α_eject = 0), leaving η₀ and ϵ₀ as free parameters."}
{"text": "We also apply STARBURST99 to the mass recycling and metal enrichment. The mass of materials produced by type-II supernova and released into the ISM is obtained by an integral over the star formation history, weighted by the stellar yield. This quantity depends on the IMF and varies with different elements. We generate the table of yields using STARBURST99, including metallicity dependence and assuming a Kroupa IMF [2002Sci...295...82K]. This age-dependent mass recycling scheme is more realistic than the commonly adopted constant recycling fraction, particularly at high redshift. The ejected gas can be transferred back to the hot gas halo via reincorporation. We employ the model proposed by [2013MNRAS.431.3373H] where the reincorporation timescale is inversely proportional to the virial mass of the halo. We also force this timescale to be smaller than the halo dynamic time. This model provides a better fit of stellar mass functions against observations at z <= 3 [2013MNRAS.431.3373H]. Reincorporation is more efficient in our model relative to [2013MNRAS.431.3373H] at high redshifts, particularly for low mass halos."}
{"text": "We implement the dust model proposed by [2000ApJ...539..718C]. This model's transmission function accounts for the relative stars-dust geometry of different stellar populations. Photons from young stars are absorbed by an additional component from the surrounding molecular cloud, which is assumed to have a lifetime of 10 Myr [2000ApJ...539..718C, 2008MNRAS.388.1595D]. Older stars' light is only absorbed by diffuse ISM dust. The attenuation is described by optical depths for the birth cloud and ISM, which vary between galaxies. We explore three different parametrisations: M-SFR, M-DTG, and M-GCD, linked to star formation rate (SFR), dust-to-gas (DTG) ratio, and gas column density (GCD) respectively. These properties are indirectly related to dust; for example, one dust production channel from supernova ejecta is proportional to the SFR [2018PhR...780....1D]. Since M-DTG and M-GCD primarily depend on gas density, they are expected to yield similar results. The dependence of dust optical depths on SFR is motivated by observations that more UV luminous galaxies have redder UV continuum slopes [2012ApJ...756..164F, 2014ApJ...793..115B, 2014MNRAS.440.3714R]."}
{"text": "The M-SFR model parameterizes the dust optical depth as a function of SFR, redshift, and wavelength, with five free parameters. For all three parametrisations, we include an exponential redshift dependence factor to fit the model against multiple redshifts, motivated by the work of [2019MNRAS.483.2983Y]. In the literature, dust optical depths are often linked to gas column density, converted using the DTG ratio [2007MNRAS.375....2D, 2011MNRAS.413..101G, 2012MNRAS.423.1992S, 2019MNRAS.483.2983Y]. The M-DTG model expresses optical depths as a function of cold gas metallicity, mass, and disk radius, with five free parameters. We also propose the M-GCD model, which is independent of metallicity. In MERAXES, we assume metals are first fully mixed with cold gas, but in reality, this may take time. Thus, the M-GCD model parameterizes optical depths as a function of cold gas mass and disk radius, with a power law scaling on cold gas mass instead of metallicity. The computation of galaxy SEDs follows standard stellar population synthesis, integrating the star formation history, SSP luminosity, and the ISM transmission function."}
{"text": "We generate the SSP luminosity using STARBURST99 [1999ApJS..123....3L, 2005ApJ...621..695V, 2010ApJS..189..309L, 2014ApJS..212...14L], assuming a metallicity range from Z = 0.001 to Z = 0.040 and a Kroupa IMF [2002Sci...295...82K]. Nebular continuum emissions are also added. To compute UV magnitudes, we apply a tophat filter centred at 1600 Å with a width of 100 Å. UV slopes are obtained by a linear fit using five of the ten windows proposed by [1994ApJ...429..582C] for computational speed. This treatment introduces negligible errors. We also make a numeric approximation to accelerate the SED evaluation by first computing the intrinsic luminosity in necessary filters and then applying the dust transmission using the central wavelength. This approximation has a negligible effect on the results. An essential part of this work is to determine the free parameters in both the galaxy formation and dust attenuation models. We carry out a Bayesian analysis on these parameters, using observed UV LFs and CMRs at z ~ 4 - 7 as constraints."}
{"text": "A key goal of a Bayesian analysis is to estimate the posterior distribution of model parameters. The MCMC method has been applied in several studies [2013MNRAS.431.3373H, 2013MNRAS.428.2001M, 2015MNRAS.451.2663H], but it has several drawbacks, including difficulties in determining convergence and handling multimodal parameter spaces [doi:10.1080/01621459.1996.10476956, Neal1996]. In this work, we use the multimodal nested sampling introduced by [2009MNRAS.398.1601F] to achieve higher sampling efficiency and more stable results. This algorithm is a competitive alternative to MCMC methods. The nested sampling was designed to evaluate the Bayesian evidence [2004AIPC..735..395S], but its output can also be used to estimate posterior distributions. No burn-in phase is required, and the stopping criterion is based on an estimated error of the Bayesian evidence. The algorithm's efficiency is improved by using existing sample points to approximate iso-likelihood surfaces as hyper ellipsoids and includes a special treatment for multimodal problems by using a clustering algorithm to detect and split multiple modes [2007MNRAS.378.1365S]."}
{"text": "The Bayesian posterior distribution is comprised of the likelihood and prior distributions. We construct the log-likelihood as a chi-squared sum over LF and CMR data points. Observational data of LFs and CMRs are taken from [2015ApJ...803...34B] and [2014ApJ...793..115B] respectively. We convert the Hubble constant from h = 0.7 to h = 0.678 for consistency. Due to the limited size of the simulation box, the model is unable to probe the full range of the LFs and CMRs. Therefore, we drop bins if the expected number of galaxies is less than five for the LF and twenty for the CMR. We focus on four galaxy formation parameters: star formation efficiency, critical mass normalisation, mass loading factor, and supernova energy coupling efficiency, with uniform logarithmic priors. Each of the three dust models has five free parameters with uniform linear priors. The prior ranges are chosen based on experiments to improve sampling efficiency. We utilise a modified version of the open-source Python package nestle, coupled with the MERAXES Python interface MHysa. We set the number of active points to 300 for the sampler."}
{"text": "For the three different dust models, we obtain 5,000 - 6,000 sample points from the nested sampling algorithm. The point with the highest posterior distribution value is chosen as the best-fit result. The three models all fit the observational data extremely well. All parameters are well constrained for the M-DTG and M-GCD models, while the mass loading factor η₀ is less constrained for the M-SFR model. An interesting finding is that the derived galaxy formation parameters preferred by these three dust models are quite different. M-DTG and M-GCD suggest similar mass loading and supernova energy coupling efficiency, but M-DTG shows evidence of a more active star formation scenario. M-SFR requires much smaller supernova energy coupling efficiency. The variation among the posterior distributions implies that these parameters fit the data in a complex way and the constraints depend on the assumptions used to model the dust attenuation. We find similar correlations among the parameters of the supernova feedback, dust relation scaling, and reddening slope. The supernova energy coupling efficiency is positively and inversely correlated with γ and the reddening slope n, respectively."}
{"text": "The intrinsic LFs of the best-fit M-SFR is roughly a factor of two higher than for the other two models. The supernova coupling efficiency of the best-fit M-SFR model is much smaller, which is likely the main reason for the difference in the intrinsic LFs. The number density at a fixed UV magnitude decreases with an increasing mass loading factor η₀. While higher energy coupling efficiency ϵ₀ decreases the LFs, the effect is more significant at the bright end, as it allows more gas to be reheated in galaxies hosted by more massive halos. The shape of both the LFs and CMRs are quite sensitive to the dust parameter γ. The effective UV optical depth is a function of γ and the optical depth normalisations. The effective optical depth should be degenerate with the intrinsic UV LFs, which are primarily controlled by the supernova feedback parameters. The observed UV continuum slope β depends on the reddening curve. The cold gas is more metal enriched in the best-fit M-DTG than in M-GCD. The normalisation of the critical mass Σ_SF is the primary driver for this difference."}
{"text": "By simultaneously fitting our models to the observed UV LFs and CMRs, we can estimate the infrared luminosity F_IR and the infrared excess (IRX) using energy balance arguments. The resulting IRX - β relations for galaxies with stellar mass greater than 10⁸ Msun are shown in Figure \ref{plot_IRX}. Our results cover the observations from [2018MNRAS.479.4355K] and [2017ApJ...845...41B]. The [1999ApJ...521...64M] relation is frequently used to correct dust extinction at high redshifts [2014MNRAS.444.2960D, 2015ApJ...803...34B, 2015ApJ...813...21M, 2016MNRAS.462..235L, 2018PASJ...70S..11H]. The best-fit M-SFR predicts higher IRX than the [1999ApJ...521...64M] relation at a fixed β, while the other two models suggest lower IRX. This implies that a direct application of the local relation at high redshifts may lead to systematic errors. The best-fit models have quite different reddening slopes 'n': M-SFR has the shallowest slope, while M-DTG and M-GCD have much steeper slopes. This difference is directly reflected on the IRX - β plane."}
{"text": "Similar disagreements in the reddening slope can be found in other studies. For example, [2017MNRAS.470.3006C] suggest n = -0.55, which is more consistent with our best-fit M-SFR model. On the other hand, [2016MNRAS.462.3130M] reproduce observed LFs and CMRs using a steeper, SMC-like extinction curve, similar to our best-fit M-DTG and M-GCD models. Since all our models can well reproduce observed LFs and CMRs, we cannot draw any firm conclusions on the reddening slope and treat this as a systematic uncertainty. Observations at z >= 3 show considerable scatter in the IRX - β plane [2015Natur.522..455C, 2016A&A...587A.122A, 2016ApJ...833...72B, 2017ApJ...845...41B, 2017MNRAS.472..483F, 2018MNRAS.479.4355K], which might be explained by the large intrinsic scatter in our predicted relations. Low IRX galaxies vanish in the best-fit M-SFR model due to the nature of our star formation prescription. In the M-SFR model, the dust optical depths of galaxies with zero SFR are also zero, resulting in the disappearance of the IRX. This unrealistic feature shows the limitations of this model."}
{"text": "The IRX - β relations at z ~ 5 as functions of stellar mass and sSFR show that massive galaxies form a tight correlation between IRX and β in the high IRX and red β regions. The trend that more massive galaxies have higher IRX is also observed by [2016A&A...587A.122A] and [2017MNRAS.472..483F]. However, we also find several larger stellar mass galaxies which have lower IRX and redder β, which might explain some of the outliers detected by [2017ApJ...845...41B]. The scatter of the IRX - β relation is tightly correlated with sSFR. At a fixed IRX, redder galaxies typically have lower sSFR, consistent with other theoretical studies [2017MNRAS.472.2315P, 2017ApJ...840...15S, 2018MNRAS.474.1718N, 2019arXiv190101747C]. Dust corrections are typically required for the conversion between UV luminosity and SFR. The [1999ApJ...521...64M] relation is widely used, though it is calibrated against local galaxies. The dust extinction predicted by our models is rather different from this relation. We directly present the predicted SFRs, and the difference among the three models allows us to estimate the systematic uncertainties."}
{"text": "We compare our predicted cosmic SFRD with [2015ApJ...803...34B], whose estimations are based on the CMRs of [2014ApJ...793..115B] and the [1999ApJ...521...64M] relation. The comparison quantifies the systematic errors of using the [1999ApJ...521...64M] relation. Our models suggest bluer intrinsic UV continuum slopes than the one used in [1999ApJ...521...64M]. The best-fit results of M-DTG and M-GCD have shallower IRX - β relations. Thus, compared with the [1999ApJ...521...64M] relation, the dust extinction in these two models is stronger for bluer galaxies but weaker for redder galaxies. On the other hand, the dust attenuation is stronger for all galaxies in the best-fit M-SFR. The cosmic SFRD of the best-fit M-DTG and M-GCD are consistent with those of [2015ApJ...803...34B], while the results of the best-fit M-SFR is roughly a factor of two higher. We also compare our results with [2018MNRAS.475.2891D], whose dust-corrected SFRs are derived from the energy balance SED-fitting code MAGPHYS [2008MNRAS.388.1595D]. Better consistency is found between their measurements and our best-fit models of M-DTG and M-GCD."}
{"text": "This work investigates the IRX - β relation and cosmic SFRD at z ~ 4 - 7 by combining the MERAXES semi-analytic galaxy formation model [2016MNRAS.462..250M, 2017MNRAS.472.2009Q] and the [2000ApJ...539..718C] dust attenuation model. The supernova feedback model of MERAXES is updated using results from previous studies [2015MNRAS.454.2691M, 2016MNRAS.461.1760H, 2018MNRAS.479....2C]. We introduce three different parametrisations of the dust optical depths (M-SFR, M-DTG, M-GCD). We adopt a Bayesian approach, calibrating these parameters against the UV LFs of [2015ApJ...803...34B] and CMRs of [2014ApJ...793..115B] at z ~ 4 - 7. The posterior distribution is estimated using multimodal nested sampling [2009MNRAS.398.1601F]. We find that these observations can be fit extremely well by all three dust models. However, the preferred parameter ranges are quite different among the models. Our analysis indicates that the combination of the LFs and CMRs can put strong constraints on a given dust attenuation model. The differences in our results are due to the different assumptions of the dust models."}
{"text": "Using energy balance arguments, we estimate the IRX for each model galaxy. We find that the predicted IRX - β relations are quite different from the [1999ApJ...521...64M] relation, and contain large intrinsic scatter, which might explain the current discrepancy among several high redshift observations [2015Natur.522..455C, 2016A&A...587A.122A, 2016ApJ...833...72B, 2017ApJ...845...41B, 2017MNRAS.472..483F, 2018MNRAS.479.4355K]. We also confirm the correlation between the intrinsic scatter and sSFR, consistent with other theoretical studies [2017MNRAS.472.2315P, 2017ApJ...840...15S, 2018MNRAS.474.1718N, 2019arXiv190101747C]. Secondly, we present model predictions for the cosmic SFRD, and compare these with observations [2015ApJ...803...34B, 2018MNRAS.475.2891D]. The difference among the three dust models implies at least a factor of two systematic uncertainty in the observed SFRD when corrected using the Meurer IRX - β relation. This work has simultaneously constrained the free parameters of a semi-analytic model and dust parameters using UV properties. This approach is particularly useful for studies at high redshifts where UV properties are the most robust observables. This work could be further improved by explicitly modelling the dust evolution."}
{"text": "We implemented Population III (Pop. III) star formation in mini-halos within the Meraxes semi-analytic galaxy formation and reionisation model, run on top of a N-body simulation with a side length of 10 per h comoving Megaparsecs with 2048^3 particles resolving all dark matter halos down to the mini-halos (approximately 10^5 solar masses). Our modelling includes the chemical evolution of the IGM, with metals released through supernova-driven bubbles that expand according to the Sedov-Taylor model. We found that SN-driven metal bubbles are generally small, with radii typically of 150 comoving kiloparsecs at redshift z = 6. Hence, the majority of the first galaxies are likely enriched by their own star formation. However, as reionization progresses, the feedback effects from the UV background become more pronounced, leading to a halt in star formation in low-mass galaxies, after which external chemical enrichment becomes more relevant. We explore the sensitivity of the star formation rate density and stellar mass functions on the unknown values of free parameters."}
{"text": "We also discuss the observability of Pop. III dominated systems with JWST, finding that the inclusion of Pop. III galaxies can have a significant effect on the total UV luminosity function at redshift z = 12 - 16. Our results support the idea that the excess of bright galaxies detected with JWST might be explained by the presence of bright top-heavy Pop. III dominated galaxies without requiring an increased star formation efficiency. The first episodes of star formation likely occurred at redshift 30-40 inside low-mass (10^5-7 solar masses) halos with a pristine chemical composition (metal-free or extremely metal-poor). These environments were responsible for the chemical enrichment of the intergalactic medium (IGM) leading to the Pop. III/Pop II transition at redshift 15-10. However, due to the low mass and the high-redshift, the study of Pop. III star formation in mini-halos is challenging both in terms of observations and simulations [Klessen2023]."}
{"text": "Even with the launch of JWST, we do not have confirmed observations of Pop III stars and only a few potential candidates [Welch2022, Maiolino2023]. As pointed out by [Trussler2023], a direct detection of a Pop. III galaxies will be extremely challenging as, in the best-case scenario, hundreds of hours of integration time are needed in order to detect an unlensed Pop. III system with 5-sigma confidence. A complementary tool to direct observation could be the redshifted 21cm global signal whose depth might be determined by the radiation emitted from Pop. III stars and early accreting black holes during the Cosmic Dawn [among the most recent works see Mebane2018, Mirocha2018, Mebane2020, Munoz2022, GesseyJones2022, Magg2022, Ventura2023, Hegde2023]. So far, there is no detection confirmed of the 21cm redshifted line, however, a large number of facilities aiming to the observation of the 21cm global signal and power spectrum are already operating or becoming operative in this decade."}
{"text": "There are a number of Pop. III star formation simulations at different scales. Hydrodynamical simulations that follow the cooling of gas in a single pristine or very metal-poor cloud suggest that the inefficient cooling due to the lack of metals might favour an initial mass function (IMF) that is shifted to larger masses [e.g.][Bromm1999, Hirano2014, Stacy2016, Chon2021]; however, there is no general consensus (e.g. [Wollenberg2020, Jaura2022, Prole2022] predict IMF shifted to lower masses). Simulations at larger scales (>=1 cMpc) are instead used to follow the global evolution of Pop. III stars with redshift and their impact on the cosmic metal enrichment and reionization. In the last decade, many of these simulations have been performed both with hydrodynamical and semi-analytical codes. At the same time we also need to consider a volume large enough in order to have a statistically significant sample of the Universe. However, to satisfy both requirements of large volumes and high-resolution is impossible and thus all the semi-analytical and hydrodynamical simulations have to make compromise in one of the two directions."}
{"text": "In this work, we chose to use the semi-analytical model of galaxy formation Meraxes ([Mutch2016], M16 hereafter) within a simulation that allows us to resolve all the mini-halos down to a few 10^5 solar masses in a simulation of L = 10 Mpc per h. As so, in this paper we ran Meraxes on top of a N-body simulation of L = 10 Mpc. The size of this simulation is not large enough to be representative of the Universe (we will miss the most massive galaxies). However, the scales are large enough to investigate the impact of the main physical processes on the Pop. III star formation. We incorporated a number of new physical processes that are relevant to Pop. III star formation in mini-halos including: (i) molecular hydrogen cooling functions for mini-halos, (ii) baryon-dark matter streaming velocities, (iii) photo-dissociation of H2 molecules from the Lyman-Werner background and (iv) the chemical evolution of the intergalactic medium."}
{"text": "This latter effect has been implemented assuming that metals are released through supernova explosions and within a bubble that expands accordingly to the Sedov-Taylor model (the approach is very similar to the analytical calculation shown in [FL2003]). We found that these bubbles are generally small and that they roughly agree with the previous estimate by [Trenti2009], with typical radii of 150 ckpc at redshift z = 6. The implementation of both internal and external metal enrichment allows us to understand whether a galaxy will form Pop. III or Pop. II stars and thus quantify the impact of Pop. III galaxies on the total luminosity function at redshift z >= 5. We assumed that the Pop. III star formation occurs in an instantaneous burst at a random Delta t from the end of the snapshot. Considering an instantaneous rather than a continuous star formation makes some of the Pop. III dominated systems significantly brighter, hence at high-redshift the brightest systems are likely to host Pop. III stars."}
{"text": "The semi-analytical model Meraxes was first developed by [Mutch2016] (hereafter M16), [Qin2017, Qiu2019] in order to study galaxy formation and growth through the Epoch of Reionization. Despite the variety of physical processes included in Meraxes assumes that all the galaxies form in a previously chemically enriched Universe and inside atomic cooling halos. Such an approximation does not allow us to study the first episodes of star formation that mostly occurred in mini-halos when the Universe did not have any metals. The version of Meraxes presented in this work allows us to compute the physics of the first episodes of star formation from the initial molecular cooling of the gas to the external metal enrichment from the supernova feedback. As in the previous work, Meraxes is coupled to the reionization so that all the radiative backgrounds are computed in a self-consistent way from the galaxy properties. This has been done by implementing a modified version of 21cmFAST ([Mesinger2011]) that includes the local ionizing UV background from [Sobacchi2014] and the X-ray heating ([Balu2023])."}
{"text": "In this version, we also included the Lyman-Werner background. The updates to Meraxes for Pop. III necessitate high mass and spatial resolution. For this purpose, we introduce L10_N2048 (hereafter L10) from the Genesis suite of dark matter only N-body simulations. L10 is a periodic cubical simulation of side 10 per h Mpc and consists of 2048^3 dark matter particles of mass m_p = 9.935 x 10^3 per h solar masses resulting in a halo mass resolution of ~ 3.18 x 10^5 per h solar masses (based on a minimum of 32 particles per halo). The simulation, run using the SWIFT [Schaller2018] cosmological code, evolves these dark matter particles from redshift z = 99 down to z = 5. The halos were identified using the friends-of-friends phase space halo-finder VELOCIraptor [VR] and the merger trees were constructed using TREEFROG [treefrog]."}
{"text": "We note that the mass resolution achieved in this simulation allows us to resolve all the mini-halos below redshift z ~ 30 and is the highest resolution on which Meraxes has been run. The output trees of the N-body simulation used in this work are available on Zenodo at [balu2024]. The first process in order to enable star formation is the cooling of the gas. For dark matter halos with virial temperature T_vir >= 10^4 K, the main coolant is the atomic hydrogen, while in mini-halos (10^3 K <= T_vir < 10^4 K), the cooling occurs via roto-vibrational transitions of molecular hydrogen [e.g.][Tegmark1997]. For the details on how the cooling of the gas is implemented in Meraxes, we refer the reader to M16; in this section, we only highlight the main differences between the atomic and the molecular cooling. As in M16, we compute the ratio of the specific thermal energy to the cooling rate per unit volume: t_cool(r) = (1.5 * mu_bar * m_p * k * T) / (rho_hot(r) * Lambda(T, f_H2))."}
{"text": "M16 included only atomic cooling halos. Thus they set the mean molecular weight assuming a fully ionized gas and the cooling function from [Sutherland1993]. For mini-halos we instead set the mean molecular weight for a fully neutral gas and implement the molecular hydrogen cooling functions from [Galli1998]. This choice is valid as long as we assume that the cooling inside mini-halos occurs only due to H2. This may not be valid as, if a mini-halo is chemically enriched with metals by a nearby halo, metals are much more effective in the cooling of the gas [e.g.][Nebrin2023]. However, this enrichment is almost ineffective at redshift z > 10. The molecular cooling function depends on the gas density of the halo and on the molecular hydrogen fraction f_H2. For the latter we assumed a fixed value of 0.1%, which is consistent with results from [Nebrin2023] for halos of virial temperature of approximately 5x10^3 K at redshift z = 15-20."}
{"text": "As a first approximation, gas in a mini-halo can start to cool down the gas once it reaches the virial temperature of approximately 10^3 K. This requirement would correspond to a minimum virial mass of M_min,H2 = 2.5 x 10^5 * (26 / (1+z)) solar masses [Visbal2015]. However, there are a number of effects that can decrease the amount of molecular hydrogen present in the halo, reducing the cooling efficiency and ultimately increasing the minimum virial mass of a halo capable of cooling. A non-radiative process that can delay the gas cooling in very low-mass halos is the streaming velocity between baryons and dark matter ([Tseliakhovich2010]). This effect is a consequence of the different decoupling of baryons and dark matter particles from photons that results in a velocity difference between the two species. The presence of a relative motion between baryons and dark matter particles will make it harder for baryons to fall into the potential wells of dark matter halos, delaying the accretion and, hence, the cooling of the gas in mini-halos."}
{"text": "The main outcome of this physical process is to delay the very first episodes of star formation around redshift z ~ 40. Throughout this work, we implemented the effect of the streaming velocities as per other semi-analytical models based on a fitting function found by [Fialkov2012], which is calibrated to reproduce the results of the hydrodynamical simulations of [Greif2011] and [Stacy2011]: V_cool,H2 = (a^2 + (b*v_bc)^2)^0.5, where a = 3.714 km/s and b = 4.015 km/s. This equation provides the minimum circular velocity that a halo needs to have in order to have enough H2 to cool down the gas. This can be easily converted into a virial mass. In this work we fixed the streaming velocity v_bc(z) = sigma_bc(z) and we assumed this value for the entire box. Once the first mini-halos are forming stars, the effect of the streaming velocities becomes widely subdominant compared to the photo-dissociation of the Lyman-Werner background."}
{"text": "A self-consistent model of star formation in mini-halos must consider the photo-dissociation of H2 from UV photons in the Lyman-Werner (LW) band ([11.2 - 13.6] eV). LW photons destroy H2 and thus prevent mini-halos gas from cooling ([Haiman2006]). We implement this effect by changing the minimum mass for molecular cooling using the fitting from [Visbal2015]: M_crit,MC = M_cool,H2 * [1 + 22.87 * J_LW^0.47]. This critical mass only applies to minihalos which are below the atomic cooling halo mass threshold. J_LW is the LW flux that reaches the minihalo. LW photons have a mean free path of ~ 100Mpc, so each minihalo will be affected even by distant galaxies that formed at higher redshift. Thus, we modelled the LW background by integrating contributions across the cosmic history. As for all the radiative backgrounds in Meraxes, we follow an excursion-set formalism ([Furlanetto2004]) which counts the number of photons in a certain band in spheres of radius R."}
{"text": "At each of these locations, we compute the LW emissivity using the spectral energy distributions from [Barkana2005]. We assume that LW photons are absorbed only at resonant frequencies. Under these approximations, we can compute the LW emissivity smoothed over R at redshift z and location x for sources emitted at redshift z' as an integral over the star formation rate density for both Pop. III and Pop. II stars. This sum accounts for the resonances in the Lyman series. Given the large mean free path of LW photons, we must also account for distant galaxies at higher redshift z' > z with the redshifted spectrum. The sum of these two effects causes the peculiar shape of the LW spectrum. Following [Barkana2005] we account for all the Lyman resonances with n <= 23. Finally, we need to convert the emissivity into a flux following ([Qin2020])."}
{"text": "The approach described above differs from the one in 21cmFAST only for the computation of the SFRD. In [Qin2020], the SFRD is estimated from the density field and the collapsed fraction, while in this work, it is computed directly from Meraxes, which tracks the formation of each galaxy and its entire star formation history. Together with the LW background, the main radiative feedback that suppresses star formation is the UV photo-ionization. We used the same prescriptions as in M16, which consists of reducing the baryon content through a baryon fraction modifier that stops the gas infall. In difference from the LW feedback, the UV photo-ionization is relevant only during reionization (redshift z <= 10), and it also affects atomic cooling halos as massive as ~ 10^9.5 solar masses. However, given that the volume of our simulation (L = 10 cMpc) is much smaller than the mean-free path of LW photons, each halo is losing the contribution of the most distant sources, thus neglecting the self-shielding should partially counterbalance the loss of the LW background from distant galaxies."}
{"text": "Once stars start to form in the Universe, they also explode as supernovae, releasing metals. Most of these will stay inside the same galaxy, contributing to the chemical enrichment of the galaxy itself. This process is commonly known as \"genetic\" enrichment. However, some of the metals escape their parent galaxy. In this case, they will pollute the nearby IGM, and if later a galaxy forms in a region where the IGM was enriched, the new galaxy will be pre-enriched with metals. This latter mechanism is referred to as \"external\" metal enrichment [e.g.][Pallottini2014, Smith2015, Hartwig2018, Visbal2020, Yamaguchi2023]. Keeping track of the metallicity evolution of the Universe is crucial in order to put constraints on when the Pop. III/II transition occurred. We account for both processes, and we are able to follow the metallicity evolution of the IGM. Firstly, we choose a critical metallicity Z_crit = 10^-4 solar metallicity as the threshold value below which a galaxy will form Pop. III stars."}
{"text": "All new galaxies, unless externally polluted, will accrete pristine gas (without any metals) onto the hot gas reservoir. This gas, once it cools, will provide the reservoir for the star formation. Hence, a galaxy that is not externally polluted will always form Pop. III stars for the first time. At each snapshot, we compute the metallicity of the cold gas reservoir from the amount of metals released by earlier supernovae and if this is higher than Z_crit, the galaxy will form Pop. II stars, otherwise it will form Pop. III. While internal enrichment is the main mechanism that drives the Pop.III/II transition, some galaxies can be externally enriched through supernova winds originating in a nearby galaxy. Once several supernovae in a galaxy go off, they will form a \"super-bubble\" that will expand outside the galaxy escaping the binding energy of the dark matter halo."}
{"text": "We followed the expansion in time of this \"metal bubble\" using the analytic approximation in [Dijkstra2014]: the bubble radius r_bubble(t) equals (Delta E_SN / (m_p * n_gas))^0.2 * t^0.4. All quantities that appear in this equation are computed in Meraxes. Delta E_SN is the total supernova energy released at a certain snapshot. n_gas is the number density of the gas to which the bubble has expanded, and t is the time since the explosion occurred. We assume that all the supernova events will occur in the middle of the snapshot. Note that since Meraxes accounts for both contemporaneous and delayed supernova feedback, each galaxy has several bubbles associated with the same star formation episode. However, we consider only the largest of these bubbles so that each galaxy has only one associated bubble. Having calculated the bubble size, we can predict if a nearby galaxy will accrete pristine or enriched gas."}
{"text": "In order to reduce the computational cost, we avoid computing the distance between all the pairs of galaxies and instead use a grid-based approach. We build a high-resolution grid with 128^3 cells. For each cell, we compute the average metallicity Z_IGM,i as the ratio between the sum of the metals ejected by all galaxies inside the cell and the total gas in the cell. We only let the galaxies with a bubble radius r_bubble >= 3 * R_vir contribute. For each cell, we compute the volume fraction filled with metals (the metal filling factor), summing the volume of the largest bubble surrounding each galaxy within the pixel and dividing by the cell volume. At the beginning of each snapshot, we assign the probability p for external metal enrichment to each galaxy inside the cell. This probability will be given by the metal filling factor. We assign a random number m between 0 and 1 to each newly formed galaxy, and when m <= p is satisfied, we label that galaxy as externally enriched."}
{"text": "Furthermore, when a galaxy experiences a star formation episode, we enforce the probability p = 1 (in this latter case, we know that this galaxy will be inside its own metal bubble and thus cannot accrete pristine gas). With this latter condition and internal enrichment, we effectively stop Pop. III star formation inside a galaxy after the first supernova episode. The main limitation of this technique is that we are not accounting for the overlap of the bubbles and thus are overestimating the metal-filling factor and underestimating the metallicity of those galaxies that are polluted from more than one galaxy. However, given the small size of the bubbles, this is not a major factor, especially prior to reionization. The model shows the bubble growth over time from a typical radius of ~ 30 ckpc at redshift z = 20 to ~ 150 ckpc at redshift z = 5. These values are consistent with the results shown in [Trenti2009]."}
{"text": "A galaxy that already formed stars or a galaxy that formed in a region enriched with metals so that its metallicity is larger than Z_crit = 10^-4 solar metallicity will form Pop. II stars. We adopted the same prescription and parameters for Pop. II star formation as described in M16 and [Qiu2019]. The uncertainty around the properties of Pop. III stars motivated us to include Pop. III star formation in a flexible way so that it is easy and fast to investigate the impact of Pop. III stars changing a few parameters. In particular, once a galaxy reaches a mass of cold gas larger than a critical value, this galaxy will convert the cold gas into stars according to the star formation efficiency. Since we are now considering two different stellar populations, we adopted two different free parameters, both for the star formation efficiency alpha_SF,III and for the critical surface density Sigma_crit,III."}
{"text": "Recent full hydrodynamical simulations that follow the collapse of a pristine gas cloud until a Pop. III star is formed [e.g.][Hirano2014, Stacy2016, Chon2021], suggest that the Pop. III IMF is shifted to larger masses as a result of less fragmentation due to inefficient cooling. Within this work, we adopted the IMFs from [Raiter2010], while for Pop. II stars, we assumed a [Kroupa2001] IMF. For the fiducial model, we chose a Salpeter IMF with a mass between 1 and 500 solar masses. The choice of the IMF is crucial as it determines many properties of the stellar population, including what fraction of stars will explode as supernovae and, hence, the amount of energy and metals injected into the IGM. Since the focus of this work is on the first galaxies formed during the Cosmic Dawn, we do not explore parameters describing the UV ionizing and X-ray radiation (e.g. escape fraction), and we will take the same fiducial values as in the previous works."}
{"text": "The fate of a zero-metallicity star is quite uncertain. Here, we adopt a simplified picture of the final fate of a Pop. III star depends only on its initial mass ([Heger2002]). For masses below 8 solar masses, there will be no SN event. If stellar mass is in [8,40] solar masses it will explode as a core-collapse SN (CCSN) leaving a remnant, if stellar mass is in [140,260] solar masses there will be a pair-instability SN (PISN) leaving no remnant and if stellar mass is in [40,140] solar masses or stellar mass > 260 solar masses stars collapse directly into a black hole (BH) with negligible feedback. While we use the technique of [Qiu2019] for Pop. II stars with precomputed tables assuming a Kroupa IMF ([Kroupa2001]), for Pop. III supernova feedback we estimated the amount of SN energy and metal yields with an analytic calculation as in M16."}
{"text": "The total energy provided by Pop. III supernovae explosions at the snapshot j is the sum of delayed contributions from core-collapse supernovae and contemporaneous contributions from pair-instability supernovae. These are computed by integrating the chosen IMF over the correct mass limits. Assuming that all-star formation occurred in the middle of the snapshot, the mass limits for CCSN are computed from the lifetimes for Pop. III stars using [Schaerer2002] assuming no mass loss and zero metallicity. We highlight that a zero metallicity star with a mass between 140 and 260 solar masses has a lifetime smaller than the time separation between two consecutive snapshots in meraxes; hence, it will explode as a PISN in the same snapshot in which it forms. For CCSN, instead, we keep track of the star formation history over the last 17 snapshots, which correspond to >= 40 Myr, after which all stars with mass >= 8 solar masses will already be exploded."}
{"text": "We also update the amount of ejected gas and metals from Pop. III stars. These are taken from [Heger2010] assuming non-mixing and a supernova explosion of 1.2 x 10^51 erg. In all the previous Meraxes works, all the stellar mass locked up in remnants (neutron stars and BHs) was neglected as it was recycled into the gas mass budget of the galaxy. We decided to drop this approximation for Pop III stars as they are likely to leave more massive remnants. Firstly, we need to consider the BHs that formed after a \"failed SN scenario\" typical of a star with an initial mass between 40 and 140 solar masses and greater than 260 solar masses. Finally, we need to account for the BH remnants that are left after a CCSN. Meraxes, does not evolve the remnants (via accretion), as the main focus of this work is Pop. III stars. However, the impact of the first accreting BHs on the formation of the supermassive black holes might be important even at high-redshift ([Ventura2023])."}
{"text": "In order to investigate the observability of the first Pop. III galaxies we implement spectral energy distributions (SED) for Pop. III stars. We use SEDs from [Raiter2010] that have been computed for the IMFs listed in Table 2 assuming that star formation occurs in an instantaneous burst. These SEDs also include the nebular continuum emission and the UV ionizing properties. To compute the luminosity of galaxies at a specific wavelength, we used the model introduced by [Qiu2019] (see also [Mutch2023]), and we extended it to Pop. III galaxies. Having the Pop. III SEDs, we can compute the luminosity of a Pop. III galaxy at time t as an integral over its star formation history, modulated by the luminosity of a stellar population per unit mass and a dust transmission function. For the latter term, we refer the reader to [Qiu2019] while the luminosity per unit mass for each Pop. III IMF has been taken from [Raiter2010]."}
{"text": "This calculation is nearly identical to [Qiu2019], with the difference being that we do not have the metallicity dependence because Pop. III stars SEDs are defined with a zero metallicity. In this framework, we assume that the star formation occurs continuously throughout the snapshot. While this is a good approximation for Pop. II stars, Pop. III star formation is expected to occur in a single burst because of the feedback from Pop. III stars are likely to prevent continuous star formation. For this reason, we expanded the calculation of the luminosity of Pop. III galaxies assuming that new stars form instantaneously at a specific time. As we will discuss in Section 4, instantaneous (instead of continuous) Pop. III star formation has an impact on the estimated luminosity function of galaxies hosting Pop. III stars. This is because Pop. III stars have lifetimes that can be shorter than the duration of the snapshot."}
{"text": "Hence, when we consider continuous star formation, we average the star formation over the entire snapshot, leading to lower luminosity with a higher duty cycle. When we instead consider Pop. III stars to form in a single burst, if this burst will occur toward the end of the snapshot the galaxy will appear much brighter when it is observed in that snapshot. In order to account for instantaneous star formation, we assumed that a Pop. III star formation episode in a galaxy can occur at random Delta t within the snapshot duration prior to the end of the snapshot. For the detailed evaluation of the UV luminosity function accounting for the stochasticity in the time at which the burst of star formation occurs in different galaxies, we refer the reader to Appendix B."}
{"text": "To explore the Pop. III contributions to the cosmic star formation history, we ran two simulations on the L10 box, one with all the updates described in Section 2 adopting the fiducial parameters and one without the new physics that we labelled as \"NoMini\". Given that there are no observational constraints on Pop. III, the choice of a fiducial model is arbitrary. The one adopted in this work has both a low star formation efficiency and a Salpeter-like IMF, which will result in a relatively small global impact of Pop. III star formation compared to Pop. II. The stellar mass function at different redshifts accounts for all, only Pop. III dominated, and only Pop. II dominated galaxies. We classified a galaxy as Pop. III or Pop. II dominated based on which population is brighter in the UV band. The new updates on Meraxes mostly affect the lower end of the SMF with a larger impact at high-redshift."}
{"text": "This reflects the star formation in mini-halos (we are now considering molecular cooling), which is dominant at redshift z >= 15 before the Lyman-Werner background becomes strong enough to photodissociate all the molecular hydrogen. The low-mass peak of the SMF is dominated by Pop. III systems and the more massive one by Pop. II. This bimodality of the SMF could have an impact on the faint end of the luminosity function at redshift z ~ 10. The low mass of Pop. III systems is mainly a consequence of both the shorter lifetimes of Pop. III stars (given their larger mass) and the lower SF efficiency, but also suggests that most of the Pop. III star formation must occur in mini-halos. The halo mass function for Pop. III and Pop. II star-forming halos is shown at several redshifts. The dashed line corresponds to the limit of atomic cooling (virial temperature T_vir = 10^4 K)."}
{"text": "Given the small size of the box, we have only a few atomic cooling halos at redshift z ~ 20, so all star-forming systems are mini-halos (and are mostly Pop. III). At lower redshift, the peak of the distribution shifts to higher masses and the impact of Pop. II increases. Finally, Pop. III stars mostly form in mini-halos. This is because the more massive halos are more likely to have already experienced star formation and so will be internally chemically enriched. The total star formation rate density (SFRD) as a function of redshift for both the fiducial and the NoMini model is also analyzed. In the case of the fiducial model, we also show the Pop. III (Pop. II) contribution in the upper (lower) panel. Mini-halos have an appreciable impact on the SFRD only up to redshift z >= 20, while at lower redshift, most star formation occurs in atomic cooling halos."}
{"text": "We see that accounting for Pop. III star formation in mini-halos is crucial during the Cosmic Dawn because Pop. III stars dominate the global star formation history at redshift z >= 20 and are still relevant up to redshift z = 18. The Pop. III SFRD flattens at redshift z ~ 18 and starts to decrease at redshift z ~ 10. The early flattening occurs due to the build-up of the Lyman-Werner background that affects Pop. III star formation in minihalos. The sharp drop at redshift z <= 10 is mostly caused by the photoionizing feedback from reionization that also affects the atomic cooling halos. The feedback from reionization also mildly affects Pop. II. Compared to reionization, the chemical enrichment of the IGM is a much slower process due to the lower velocity of the expansion of the metal bubbles."}
{"text": "As already found in previous works [e.g.][Visbal2020, Yamaguchi2023], the impact of external metal enrichment is subdominant compared to internal metal enrichment. However, external enrichment might still be important for low-mass halos that do not form stars until redshift z ~ 10. The redshift evolution of the average metallicity of the box is shown. As expected, the average metallicity increases monotonically. It crosses the critical value at redshift z ~ 11 and at the end of the simulation is ~ 5 x 10^-3 solar metallicity. The redshift evolution of the IGM metallicity is in very good agreement with [Yamaguchi2023], especially for their \"bursty\" models, which is the one that most closely resembles the star formation in Meraxes. However, the average metallicity of the IGM does not completely inform us of the average metallicity of the galaxies since, when averaging through the entire box, we are considering voids that have no galaxies and hence zero IGM metallicity."}
{"text": "For this reason, we computed the average metallicity only through cells that have at least one metal bubble (meaning that there must be at least one galaxy that formed stars). The average metallicity, in this case, is much higher, and it is always above the critical value. This suggests that once the first galaxies form, the ejection of metals from Pop. III is quite effective in the nearby regions, allowing a fast Pop. III/II transition in those cells where star formation already occurred. The lower panels instead show the fraction of the IGM that reached the critical metallicity. Considering the entire box, less than 1% of the volume gets enriched above the critical metallicity by redshift z ~ 5. This result is fairly consistent with [Visbal2020] and [Yamaguchi2023] (~ 1% by z = 6)."}
{"text": "These small differences are likely due to differences in the star formation models and in the choice of parameters, such as the star formation efficiency. If we focus only on the regions with at least one galaxy that formed stars, we find larger filling factors, and by the end of the simulation, those pixels are all completely enriched. This final result reflects our choice of pixel size that is designed to be similar to the average volume of the metal bubble at redshift z ~ 5. The halo mass function for the externally and internally metal enriched halos at several redshifts is also analyzed. While most halos get internally enriched by their own star formation, at redshift z = 5 halos with virial masses <= 10^7.5 solar masses get their metals mostly from a nearby supernova bubble. This picture reflects the fact that low-mass halos during reionization are not able to form stars because of the LW and photo-ionizing feedback."}
{"text": "Hence, those objects can be chemically enriched only from an external source. In conclusion, when looking at the global evolution of star formation, the effect of the external metal enrichment is quite negligible as it is important only for low-mass halos at low redshift that will hardly form stars due to the radiative feedback effects. We verified this by running a simulation without external metal enrichment. There are no appreciable differences between the two models except at redshift z <= 8 when the dashed line is slightly larger (about 0.1 dex difference). The results in previous sections were obtained adopting quite conservative assumptions for Pop. III stars given the very low SF efficiency and the Salpeter-like IMF. In the following sections, we explore the four main free parameters that regulate Pop. III star formation in Meraxes: the Pop. III star formation efficient, the critical metallicity for Pop.III/II transition, the critical surface density of cold gas for Pop. III star formation to occur and the IMF."}
{"text": "The star formation efficiency determines the conversion of the cold gas into stars and is the free parameter with the largest impact on the Pop. III global SFRD and SMF. This parameter is largely unconstrained, with some simulations supporting very low values (10^-4 - 10^-3, [Skinner2020]) and others suggesting higher values ([Fukushima2020]). We ran two simulations keeping all the Pop. III free parameters unchanged except for the star formation efficiency, which we boosted by one order of magnitude and to a very high value. Pop. III galaxies become more massive as the star formation efficiency increases, erasing the \"double peak\" feature in the total SMF. For the model with equal Pop. II and Pop. III efficiency, the peak of the Pop. III SMF is still shifted to the left by half dex compared to the Pop. II. This is because, despite having the same star formation efficiency, Pop. III galaxies mostly form in mini-halos."}
{"text": "The star formation efficiency also regulates the Pop. III/II transition as it directly correlates with the SFRD. For a high efficiency, the SFRD is dominated by Pop. III up to redshift z ~ 15 compared to the fiducial model where Pop. II SF becomes larger than Pop. III at redshift z > 20. The Pop. II SFRD does not significantly change between the three models, and so the change in the Pop. III SFRD also affects the total SFRD. All the models converge at redshift z ~ 13 when even with the highest efficiency the total SFRD is entirely dominated by the Pop. II contributions. The critical metallicity defines the metallicity at which there is a change in the IMF. There is currently no consensus on the value of Z_crit, with two competing models that assume the fragmentation driven by either the carbon and oxygen line or the dust cooling. The first class of models determine a Z_crit ~ 10^-2 - 10^-3 solar metallicity while the seconds give a lower value (~ 10^-6 solar metallicity)."}
{"text": "Some studies also argue that the value of Z_crit evolves with redshift due to the effect of the CMB ([Chon2022]). Following simulations in the literature ([Schneider2006, Visbal2020]), in this work we adopted an intermediate value Z_crit = 10^-4 solar metallicity as the fiducial value, hereafter we will also show results for the two extreme values of 10^-2 and 10^-6 solar metallicity. The SMF between the fiducial model and Z_crit = 10^-6 solar metallicity does not change. This is because, in the overdense regions where there is star formation, the metallicity becomes larger than 10^-4 solar metallicity very quickly so that changing Z_crit to 10^-6 solar metallicity does not further accelerate the Pop. III/II transition. However, considering a higher value changes the total SMF as we end up with many more Pop. III stars. The high-mass tail of Pop. III SMF extends up to 10^7.5 solar masses at redshift z = 5 when Z_crit = 10^-2 solar metallicity."}
{"text": "The combined effect of Pop. III and Pop. II makes the total SMF computed from the simulation with Z_crit = 10^-2 solar metallicity single peaked as the high-mass peak coming from Pop. II stars are washed out even at redshift z = 5 so that the total SMF peaks at stellar mass ~ 10^4 solar masses at redshift z = 10 - 5 with a high-mass tail that extends up to 10^9 solar masses. The critical metallicity also has a strong impact on the evolution of the SFRD as it affects both the internal and external enrichment. While decreasing the value of Z_crit from the fiducial value only mildly decreases the Pop. III SFRD without altering the total result, choosing Z_crit = 10^-2 solar metallicity strongly changes the SFRD history at redshift z <= 18. The Pop. III SFRD increases by 1-2 orders of magnitude while the Pop. II decreases by the same amount."}
{"text": "Increasing the Pop. III star formation and simultaneously decreasing the Pop. II impacts on the total SFRD. Since Pop. III stars form less efficiently we predict a lower total SFRD compared to the fiducial model. Overall the critical metallicity heavily impacts both the SFRD and SMF during the Cosmic Dawn and the Epoch of Reionization and affects when the universe transitions from being Pop. III dominated Pop. II. In order to trigger the star formation in a galaxy, our model requires the gas density in the disk to be above a certain threshold. We decided to duplicate this free parameter so that we have one for Pop. III and one for Pop. II. While keeping the Pop. II parameter fixed, we explore the extreme case of a Pop. III critical surface density of 0, which is equivalent to assuming that Pop. III stars start to form as soon as the cooling of the gas begins."}
{"text": "This choice results in a larger abundance of low-mass Pop. III systems at high-redshift. However, since the main changes in the Pop. III SF are in low-mass halos, setting the critical surface density to 0 does not significantly change the SFRD history. Overall, this free parameter is the one with the smallest impact on the star formation history, as it only impacts the low-end of the stellar mass function at high-redshift for which there are no observational constraints. The last parameter we explore is the IMF of Pop. III stars. Our fiducial model is quite similar to the Pop. II IMF as we assume a Salpeter IMF that favours the formation of low-mass stars. We consider two log-normal IMFs labelled logA and logE as in [Tumlinson2006]. For these IMFs we have spectral energy distributions (from [Raiter2010]) which will be used in Section 4."}
{"text": "The IMF logA is centred at M = 10 solar masses, which enhances the probability of a Pop. III stars ending its life as a core-collapse SN. logE is centred at even a higher mass (M = 60 solar masses), so we expect most of the stars with very short lifetimes to end their lives by collapsing into a black hole without any supernova explosion. Compared to the Salpeter IMF, both log-normal IMFs do not have many low mass stars (mass < 8 solar masses). Decreasing the lifetime of Pop. III stars make the Pop. III SMF shift to lower masses, increasing the separation between the two peaks of the total SMF. The difference between the fiducial model and one adopting the logA IMF is less than one dex. However, in the logE IMF model, most of the stars die in the same snapshot in which they form. This effect strongly prevents the build-up of Pop. III systems."}
{"text": "There are no significant differences in the SFRD from adopting different IMFs, except for the first few snapshots of our simulation where the star formation is mildly reduced in the logE model. This result comes from the stronger feedback typical of the more top-heavy IMF, and it has a stronger impact at redshift z >= 24 when Pop. III star formation is dominating. Unconstrained Pop. III free parameters in our model have an impact on the redshift evolution of the SMF and SFRD. However, our model predicts a consistent number density of Pop. III dominated systems with stellar masses between 10^3 - 10^5 solar masses. Here we will explore the UV luminosity of these systems using the model described in Section 2.6 focusing on the luminosity functions at very high-redshift. Given the same total stellar mass, Pop. III systems have larger luminosities compared to Pop. II galaxies, but shine for shorter times."}
{"text": "We show the evolution in the first 10Myr of the SED of a Pop. III galaxy that forms 10^5 solar masses of Pop. III stars at redshift z = 8 and the absolute UV magnitude at different times since the star formation burst. The black horizontal line corresponds to the magnitude computed assuming a continuous star formation throughout the snapshot. For reference, we also show the magnitude of a Pop. II galaxy forming the same amount of Pop. II stars. Firstly, we notice that Pop. III galaxies with continuous star formation and a log-normal IMF are one magnitude brighter than Pop. II galaxies with the same SFR. Once we focus on the instantaneous star formation model for Pop. III stars, the brightness of the galaxy can be boosted (or reduced) by several magnitudes depending on the time since the burst at which we are observing the system [see also Trussler2023]. Even when we consider a Salpeter IMF, the brightness of a Pop. III galaxy changes ~ 2 mags in ~ 10Myr."}
{"text": "This change is more dramatic for the log-normal IMFs (especially for the logE IMF where in 10 Myr the change in absolute magnitude is approximately 7 mags). The large difference between the instantaneous and continuous star formation models for a single Pop. III galaxy will reflect in the entire population and potentially lead to a higher number density of extremely bright Pop. III galaxies. As a result of instantaneous Pop. III star formation, there are chances to observe these galaxies at a time when their luminosities are higher than what is given by the continuous scenario. When looking at the total luminosity function we see a much significant Pop. III contribution to the number density of galaxies around an absolute magnitude of approximately -16 when assuming a LogE IMF for their star formation. Given their larger brightness, a population of Pop. III galaxies with a top-heavy IMF has been suggested as a possible explanation for the abundance of bright galaxies at redshift z > 10."}
{"text": "Without invoking any exotic physics or a revision of the standard LambdaCDM model of cosmology, other possible explanations are a combination of increased star formation efficiencies at high-redshift and reduced feedback [Qin2023], bursty star formation [Sun2023], cosmic variance [Shen2023] and a modified LambdaCDM power spectrum [Parashari2023, Padmanabhan2023]. Here, we show the predicted UV luminosity functions at several redshifts. Results for different IMFs and different star formation efficiencies are summarized, where all the other Pop. III parameters are taken as in the fiducial model. For all the models considered below, our total luminosity function agrees with early JWST observations at redshift z <= 12 (except for the points at an absolute magnitude < -19 where we do not have galaxies in Meraxes). With our fiducial parameters, both with the Salpeter and with the logA IMF, we find that Pop. III systems are not the brightest galaxies at the redshift considered (absolute magnitude >= -14)."}
{"text": "However, when we consider a log-normal IMF with a characteristic mass of 60 solar masses, Pop. III galaxies become significantly brighter and at redshift z = 12 and 16 when some of the brightest systems (absolute magnitude ~ -16) are Pop. III dominated. Even though most of the Pop. III galaxies are still very faint (well below the sensitivity of JWST). This result may indicate that Pop. III dominated galaxies are present at redshift z > 12. This result becomes more robust when considering a Pop. III star formation efficiency equal to the Pop. II efficiency. The bright end of the total and Pop. III dominated galaxy UVLF shifts of 1-2 magnitudes (depending on the IMF) at redshift z = 16 and 12. At redshift z <= 11, there is no or little difference in the total UVLF with different star formation efficiency even though Pop. III dominated galaxies are still ~ 1 mag brighter."}
{"text": "Models with a Salpeter or a log-normal IMF centered at 10 solar masses predict that the bright end of the UVLF at redshift z = 16 is impacted by Pop. III dominated systems while at redshift z <= 12 none or very few of the brightest galaxies are Pop. III dominated. Overall, the abundance of bright galaxies at redshift z >= 12 is better explained by the model with the logE Pop. III IMF and a Pop. III star formation efficiency equal to the Pop. II efficiency. For this model at redshift z >= 12 we find Pop. III dominated galaxies with an absolute magnitude of approximately -18 and at redshift z = 16 all the brightest galaxies (absolute magnitude <= -16) are Pop. III dominated. We compared our results with [Trinca2023], and found a good agreement at redshift z <= 12 and absolute magnitude less than or approximately equal to -16.5 for all the models considered."}
{"text": "The main differences are that at redshift z = 9, we do not have any galaxy with an absolute magnitude of approximately -20, and their model has a steeper evolution predicting many more faint galaxies. At redshift z = 16 only models with high Pop. III star formation efficiency and a log-normal IMF reproduce their results. Even though the total UVLF are similar, their Pop. III contribution is significantly lower, especially when compared to the models with high Pop. III star formation efficiency. The main differences in the model that can explain the different results are (i) the homogeneous feedback and (ii) the Pop. III luminosity calculation. In their model, both the radiative feedback and the chemical enrichment are homogeneous; this might overestimate the suppression of Pop. III systems at redshift z ~ 10-20. Regarding the second point, our model accounts for the fact that a Pop. III galaxies might be observed immediately after they formed stars."}
{"text": "Without accounting for this effect, our Pop. III galaxies would have similar luminosity to those predicted by [Trinca2023]. The main limitation of our results is that, given the small size of the simulation, we intrinsically miss the brightest galaxies. Larger simulation volumes will allow us to be conclusive, but this result suggests that if Pop. III stars are still forming at redshift z >= 10-12, and they have a top-heavy IMF, they do not require increased star formation efficiencies to outshine the Pop. II systems. As Pop. III dominated galaxies become much more rare at redshift z <~ 10, this scenario allows us to increase the abundance of bright galaxies only at redshift z > 10 without boosting the bright end of the UV luminosity function at lower redshift hence we achieve a good agreement with early JWST observations from [Donnan2023, Harikane2023] and [Perez2023]."}
{"text": "In this paper, we studied Pop. III star formation in mini-halos with an updated version of the Meraxes semi-analytic model of galaxy formation that includes Lyman-Werner background and the streaming velocities. We also implemented external metal enrichment following the growth of the supernova bubbles according to the Sedov-Taylor model. We computed the bubble size distribution function and found that our results agree with [Trenti2009] (most bubbles are smaller than 150 per h ckpc at z = 6 and have a typical size of 100-200 ckpc at z = 5) hence most halos get self-enriched rather than externally polluted. Only low-mass halos (virial mass <= 10^7.5 solar masses) at redshift z < 10 are more likely to get their metals from the IGM. This is a consequence of the small size of the supernova bubbles that results in a small filling factor (0.1% at z = 12 and less than 1% at z = 5)."}
{"text": "The free parameters allow us to explore the global properties of Pop. III dominated galaxies. We ran this model on top of a dark matter-only N-body simulation able to resolve all the mini-halos down to ~ 3 x 10^5 solar masses at redshift z <= 30. We explored the impact on the SMF and SFRD of the main free parameters of our model. All models converge at redshift z <~ 10. However, Pop. III star formation efficiency and IMF lead to differences at high-redshift. Finally, we investigated the SED evolution of a Pop. III dominated galaxy for different IMFs. The shorter lifetime of a Pop. III galaxy motivated us to use an instantaneous star formation model when computing the luminosity function. We computed the total and the Pop. III galaxy UV luminosity functions and compared these to the early JWST results in order to study whether the excess of bright galaxies at high-redshift could be explained by a population of Pop. III dominated galaxies."}
{"text": "Having explored different IMFs and star formation efficiencies, our model predicts, for a log-normal IMF with a characteristic mass of 60 solar masses and a Pop. III star formation efficiency comparable to the Pop. II, most of the brightest galaxies at redshift z >= 12 and all at redshift z = 16 (absolute magnitude = - 18) are Pop. III dominated. Adopting a smaller characteristic mass or a Salpeter IMF, Pop. III dominated systems still have an impact on the bright end of the UVLF, but only at redshift z = 16. In conclusion, this work supports the scenario for which top-heavy Pop. III dominated galaxies might explain the abundance of bright JWST galaxies at redshift z >= 12 without requiring very high star formation efficiencies or extremely weak feedback at high-redshift. In this appendix, we discuss the extent to which our approximation on the external metal enrichment based on the filling factor is appropriate and when it fails."}
{"text": "Since we are avoiding computing all the pairs of distance, there might be some galaxies for which we are not getting a correct enrichment. For this reason, we computed in post-processing the distance between all the pairs of galaxies throughout the entire simulation and we counted how many galaxies in Meraxes are marked as externally metal enriched (pristine) even if they are outside (inside) a metal bubble. We repeated this computation for several grid resolutions: N = 16, 32, 64, 128 and 256. Hereafter, we will call \"false pristine galaxies\" those galaxies that lie inside a metal bubble (and so should be enriched) but in Meraxes are labelled as pristine and \"false enriched galaxies\" those galaxies that are not reached by any bubble but in Meraxes are labelled as enriched. At lower resolution, the percentage of the false pristine galaxies increases from 4% at N = 128 to 7% at N = 16."}
{"text": "This happens since, as the pixel becomes bigger, the assumption of the galaxies randomly distributed inside each pixel is no longer valid as the clustering becomes much more important. However, when we use a very fine grid (N = 256), the mass fraction of false enriched galaxies dramatically increases at redshift z <= 10. This happens because by redshift z = 10, the typical bubble size becomes larger than the pixel volume, and so we lose all the contribution that overflows outside the pixel. The mass percentage of false enriched galaxies instead is only mildly affected by different resolutions (always below 2%). We then compute the absolute value of the difference between the mass percentage of the false pristine and the false enriched galaxies. This quantity tells us if, statistically, we are reproducing the correct global enrichment of the Universe. We can see that having a high-resolution grid significantly improves the quality of our results."}
{"text": "For N = 128, this difference is always below 2%, and at redshift z < 12 is approximately 0%. This tells us that for a high-resolution grid, globally, we are getting the correct enrichment of the Universe as the mass percentage of false pristine and false enriched galaxies cancels out. This agreement is almost perfect during the EoR, while during the Cosmic Dawn we are underestimating the metal enrichment of ~ 1-2%. Finally, we are also showing the sum between the false enriched and pristine galaxies. This quantity instead tells us what is the mass percentage of galaxies for which we are getting a wrong estimation of the enrichment. Increasing the resolution improves our result, which, for N = 128, peaks at ~ 4% during the Cosmic Dawn. In conclusion, our model for N = 128, while reducing the computational cost, still gives an excellent agreement on global enrichment and a very good agreement on the enrichment of single galaxies."}
{"text": "In this case we assumed that the probability p of each galaxy to be enriched is equal to the metal filling factor multiplied by the two-point correlation function. We also note that at the scales of the metal bubbles (< 1 comoving Mpc) we need to use the non linear bias as the linear case would give an underestimation of one order of magnitude ([Dijkstra2008]). The mass percentage of false pristine and false enriched both peak at 4-5% with the percentage of false pristine galaxies decreasing at higher resolution and the percentage of false enriched galaxies increasing at higher resolution. Accounting for the clustering and using a low-resolution grid still allows us to get an excellent agreement on the statistical properties but, compared to the model adopted in this work, it doubles the mass percentage of the galaxies for which we are getting a wrong prediction. This final check further confirms that the model for the external metal enrichment that we are adopting in this work, is the best one."}
{"text": "In this appendix, we discuss how to evaluate the UV luminosity function of Pop. III galaxies assuming instantaneous star formation. Due to the stochasticity involved in the process of star formation, the burst might occur at any time within a snapshot for a galaxy, resulting in different luminosities when observed. We refer to Delta t as the time delay of the star formation burst happening relative to the end of our snapshot, and draw its value from a random uniform distribution between zero and the snapshot duration. One can then evaluate the luminosity of this galaxy, repeat the exercise for all targets after assigning them different Delta t, and calculate their probability distribution as a function of UV magnitude (i.e. the UV luminosity function). To achieve a more efficient computation, we instead sample Delta t in fine steps. Then we calculate the UV magnitudes of each galaxy for given Delta t_i and evaluate the corresponding luminosity function at the condition of fixed Delta t."}
{"text": "Finally, the luminosity function is obtained by summing all conditional probability distributions as the sum over all conditional luminosity functions multiplied by the probability of each time delay. Note that the probability of each conditional luminosity function is simply calculated based on the size of the time step relative to the total snapshot duration."}
{"text": "The highly neutral inter-galactic medium (IGM) during the Epoch of Reionization (EoR) is expected to suppress Lyα emission with damping-wing absorption, causing nearly no Lyα detection from star-forming galaxies at redshift z is approximately 8. However, spectroscopic observations of the 4 brightest galaxies (H-band magnitude is approximately 25) at these redshifts do reveal prominent Lyα line, suggesting locally ionised IGM. In this paper, we explore the Lyα IGM transmission and environment of bright galaxies during the EoR using the Meraxes semi-analytic model. We find brighter galaxies to be less affected by damping-wing absorption as they are effective at ionizing surrounding neutral hydrogen. Specifically, the brightest sources (H-band magnitude is less than or approximately equal to 25.5) lie in the largest ionized regions in our simulation, and have low attenuation of their Lyα from the IGM (optical depth is less than 1). Fainter galaxies (25.5 mag is less than H-band magnitude is less than 27.5 mag) have transmission that depends on UV luminosity, leading to a lower incidence of Lyα detection at fainter magnitudes. This luminosity-dependent attenuation explains why Lyα has only been observed in the brightest galaxies at redshift z is approximately 8."}
{"text": "Follow-up observations have revealed counterparts in the vicinity of these confirmed redshift z is approximately 8 Lyα emitters. The environments of our modelled analogues agree with these observations in the number of nearby galaxies, which is a good indicator of whether Lyα can be detected among fainter galaxies. At the current observational limit, galaxies with greater than or equal to 2 to 5 neighbours within a 2 arcminute by 2 arcminute area are approximately 2 to 3 times more likely to show Lyα emission. JWST will discover an order of magnitude more neighbours, revealing greater than or approximately equal to 50 galaxies in the largest ionizing bubbles and facilitating direct study of reionization morphology. The transmission of Lyman-α (Lyα) photons has played a significant role in observational studies of reionization due to its highly resonant nature in neutral hydrogen, which provides a direct probe of the ionization state of the intergalactic medium (IGM). Toward the end of reionization, the large-scale neutral hydrogen distribution has been studied with the Lyα forest along the line of sight towards bright background quasars."}
{"text": "For instance, by counting the zero-flux pixels on quasar spectra, [McGreer2015MNRAS.447..499M] concludes that the average neutral hydrogen fraction at redshift z~5.9 should be lower than 6 -- 11 per cent. However, individual sight-lines seem to suggest that large chunks (greater than 160 cMpc) of residual neutral hydrogen still exist even at redshift z<6, requiring late reionization and/or that the underlying accountable sources possess unusual ionizing properties. Damping-wing absorption of Lyα emission lines of quasars also facilitates estimates of the neutral hydrogen fraction during the epoch of reionization (EoR). This is done by directly comparing the observed flux to the intrinsic flux inferred from low-redshift analogues using continuum and metal lines. For instance, among some of the 9 quasars discovered at redshift z>7 to date, high-quality spectra have enabled direct measurement of the neutral hydrogen, ranging from a neutral fraction of approximately 10% to 80%."}
{"text": "High-redshift star-forming galaxies that have detectable Lyα emission are referred to as Lyα emitting galaxies (LAEs). The incidence of LAEs has also been used to determine the neutral fraction. This is because Lyα detection during the EoR could provide evidence for whether galaxies sit in large ionized bubbles, so that their Lyα photons are redshifted deep into the damping wing, and are therefore less attenuated by the intergalactic neutral hydrogen. As the Universe becomes more neutral, observations have shown a rapidly decreasing fraction of LAEs among Lyman break galaxies (LBGs) from redshift z=6 to 8. However, despite the increasing neutral fraction in the high-redshift Universe, prominent Lyα lines in some of the brightest sources have been observed even out to redshift z is approximately 9 with a much higher detection rate of Lyα emission than expected."}
{"text": "In particular, the 4 most luminous galaxies (H-band magnitude is approximately 25) in CANDELS have all been spectroscopically confirmed by Keck as LAEs. In contrast, when targeting relatively fainter galaxies, no Lyα emission was detected at redshift z is approximately 8 while the probability of detecting Lyα was found to be less than 2% and less than 15% at redshifts of approximately 7.5 and 7, respectively. Similarly, more recent larger spectroscopic samples of Lyα emission among high-redshift, bright galaxies find the probability of detecting Lyα varying between 20% and 50% at redshifts from 6 to 9. Apart from possibly having higher intrinsic Lyα emission due to recent star formation, these brightest galaxies are likely located in more overdense regions, and may be surrounded by a larger number of star-forming galaxies producing a more transparent IGM."}
{"text": "In this work, we use a semi-analytic galaxy-formation model to explore the Lyα IGM transmission properties and environment of bright galaxies during the EoR. We focus on both the brightest galaxies, which are analogous to those observed at redshift z is approximately 8, as well as relatively fainter galaxies, including those that can be considered promising candidates for the James Webb Space Telescope (JWST). Our semi-analytic model (SAM) follows a number of astrophysical processes of galaxy formation and self-consistently calculates photon-heating feedback from reionzation as well as recombination in ionized regions. The model has been shown to successfully reproduce a large number of observables including galaxy and quasar UV luminosity functions in addition to the inferred EoR history from the comic microwave background (CMB). This paper is organized as follows. We provide a brief review of our model as well as the newly implemented calculation of Lyα damping-wing absorption in Section 2."}
{"text": "We present our results including the strategy for hunting LAEs in Section 3 before concluding in Section 4. In this work, we set the cosmological parameters based on the Planck 2015 results. We use the Meraxes SAM from the DRAGONS program, which is coupled to a parent N-body simulation providing dark matter halo properties from redshift z=35 to 2. With a mass resolution of approximately 4x10^6 solar masses and a box size of 100cMpc, we are able to properly sample low-mass halos down to the atomic cooling threshold and capture massive galaxies of approximately 7x10^11 solar masses at redshift z=8. These allow us to resolve faint galaxies that are responsible for reionization and study galaxies as bright as M_1600 of approximately -22 mag at redshift z=11 or an H-band magnitude of 24.5 mag at redshift z=8."}
{"text": "Meraxes evaluates the accretion and cooling of gas, stellar evolution and feedback, growth of supermassive blackholes and their impact on galaxy formation, as well as other environmental influences such as mergers and photo-heating from reionization. We also consider dust attenuation and forward model the observed galaxy and quasar UV magnitudes. These allow us to adjust our model parameters in order to match the predicted observables with existing measurements during the EoR. In this work, we use the galaxy catalogue generated by the fiducial model presented in [Qin2017a]. We assume all star-forming galaxies during the EoR are effective at producing Lyα photons and their detectability in Lyα is solely determined by neutral hydrogen present along the line of sight. To evaluate the IGM ionization state, Meraxes couples its UV ionizing photon source model with 21cmFAST."}
{"text": "We divide the simulation volume into 512^3 cells having an equal length of 0.195 cMpc. With an excursion-set algorithm, we compare the ionizing photon budget to the number of present neutral hydrogen atoms and estimate the neutral hydrogen fraction in each cell. The model used in this work has a predicted EoR history consistent with the latest Planck results. It is predominately driven by UV ionizing photons emitted by stars in faint galaxies with supermassive blackholes having an insignificant contribution to the overall reionization. The only regions of ionizing background dominated by luminous AGN are in their immediate environment. The ionization field at redshift z=8 has a volume-averaged neutral hydrogen fraction of 0.86. We see reionization (anti-)correlates with underlying densities and brighter galaxies, in general, are located in larger ionized bubbles. We also confirm that, in these star-forming galaxies, the central supermassive black holes have a negligible role in ionizing the surrounding IGM."}
{"text": "We compute the Lyα optical depth in each cell based on the equation: tau_alpha = L * n_H,0 * x_HI * Delta * (1+z)^2 * sigma_alpha, where L, n_H,0 and Delta are the pixel length, the cosmic mean of the comoving hydrogen number density and its local overdensity in each cell, while sigma_alpha corresponds to the Lyα scattering cross section in neutral hydrogen redwards of the line centre with c and Lambda representing the speed of light and the decay constant for the Lyα resonance. From these two equations, we see that damping-wing absorption increases towards higher redshifts and drops significantly at distances further from the line center. Therefore, we ignore damping-wing absorption at distances longer than our box length (100cMpc) and estimate the total optical depth as the sum of the optical depth in each cell along a sight-line. Here, the optical depth in the i-th cell away from the source along a sight-line where Lyα has shifted to a new wavelength is calculated with the velocity offset of the intrinsic Lyα line and the Hubble parameter at that redshift."}
{"text": "Note that, for each bright galaxy, we randomly select 500 sight-lines and estimate the bubble size and total damping-wing optical depth as well as their associated uncertainties by taking the median and [16, 84] percentiles. There are an increasing number of observed LAEs presenting a velocity offset between the Lyα emission peak and the systemic redshift up to approximately 1000 km/s, as well as a possible correlation showing higher velocity offset with increasing galaxy UV luminosities. This could increase the Lyα transmission in the IGM for brighter galaxies. However, when splitting low-redshift LAEs by their UV magnitudes, we see the opposite with more luminous galaxies showing a lower fraction of LAEs, possibly due to a reduced Lyα escape fraction in deeper gravitational potentials. As current measurements are still inconclusive and limited by the small LAE sample, particularly at higher redshifts, we do not consider the intrinsic line intensity, offset or escape fraction of Lyα."}
{"text": "Since the targets in this work are those mostly sitting in large ionized bubbles, we also expect them to be less affected by the velocity offset. Based on these, we treat the detectability of a LAE governed primarily by its IGM transmission. It is worth noting that fully ionized regions do not contribute to the total damping-wing optical depth. However, to account for resonant absorption by residual neutral hydrogen inside the ionized region, we follow previous work and assume all flux bluer than the circular velocity of the host halo becomes attenuated. This leads to a factor of 2 further reduction to the Lyα transmission so that the transmission T is equal to exp(-tau_total) which equals 0.5 * exp(-tau_D). This results in an optical depth inside ionized regions of approximately 0.69. In this work, we consider galaxies with a total optical depth larger (or lower) than 1 as highly attenuated (or transparent) LAEs subject to damping-wing absorption in the IGM."}
{"text": "The 4 modelled galaxies presented demonstrate some of the characteristic Lyα IGM transmission properties among bright LBGs during the EoR. They also clearly present the real and substantial variations in Lyα detectability within a quite modest range of luminosities (factors of a few). In this section, we use the whole modelled high-redshift galaxy population to quantify how reionization impacts Lyα transmission, and provide guidance for searching for ionized bubbles in the heart of the cosmic reionization epoch. At a given redshift the damping wing optical depth, on average, decreases if the LAE sits inside larger ionized bubbles. Such a transmission-bubble size correlation becomes obvious when the mean density and neutral hydrogen fraction are substituted in the optical depth equation. However, as overdense regions are typically the first to become ionized, we also expect to see a positive correlation between the Lyα transmitted fluxes and large-scale overdensities. This is shown in analysis where we also observe a much larger scatter compared to the transmission-bubble size relation."}
{"text": "When focusing on currently observable galaxies (i.e. H-band magnitude < 27.5), we see that the obscured LAEs are on average located in ionized regions smaller than approximately 7cMpc at redshift z=8 and with an overdensity of less than or approximately equal to 1. The relation between galaxy UV luminosity and Lyα transmission is also explored. In general, brighter galaxies possess higher Lyα transmission as their UV ionizing luminosities are more effective at ionizing the surrounding IGM and therefore creating larger ionized bubbles. However, we also see a bimodal distribution in this relation. After separating galaxies according to their luminosities in each ionized bubble, we find that the two peaks originate from different galaxy populations. Central galaxies, defined as the brightest galaxy in each bubble, dominate the local ionizing photon budget and therefore have lower damping-wing optical depth with increasing luminosities."}
{"text": "However, most galaxies brighter than an H-band magnitude of approximately 25.5 have a similar level of damping-wing absorption and all of them are transparent in Lyα. This is consistent with the 4 observed bright LBGs showing strong Lyα emission and suggests that the brightest, color-selected LBGs are likely to reside in large ionized regions as predicted by generic inside-out models of reionization. On the other hand, fainter satellite galaxies have their ionized bubble size mostly set by the central galaxies. Therefore, we see a horizontal offset towards lower luminosity from the median transmission-luminosity relation of central galaxies to that of the satellites. Comparing between the two galaxy populations, we see that galaxies fainter than an H-band magnitude of approximately 27.5 can only be detected in Lyα when they share the same ionized bubble as another brighter one."}
{"text": "Despite being more than one magnitude fainter than the brightest galaxy in our simulation, another example galaxy possesses a much higher Lyα transmission rate as its high overdensity environment leads to a great number of bright galaxies contributing to the local ionizing photon budget, which pushes the ionizing front much further. Compared to those dominating their UV background alone, galaxies with neighbours in their ionized regions are more likely to reside in high-density regions, and are less obscured by the Lyα damping-wing absorption. To illustrate this in more detail, we select mock (central) galaxies brighter than an H-band magnitude of 27.5 and plot their Lyα transmission fluxes as a function of the number of neighbours. We see a positive correlation between transmission and the number of neighbours -- galaxies with an increasing number of neighbours are more likely to have their surrounding gas ionized to a great distance, and therefore their Lyα emission is less obscured."}
{"text": "It is worth noting that, as transparent LAEs are located in bubbles with a radius of greater than or approximately equal to 7cMpc (larger than the FoV in the mock image), their neighbouring galaxies are also likely to be observable in Lyα. On average, greater than or approximately equal to 4 LAEs can be found in those highly ionized regions. The majority of modelled galaxies with an H-band magnitude of less than or approximately equal to 26 have bright neighbours within a WFC3 FoV. This agrees with preliminary results from an environmental study of 3 confirmed redshift z is approximately 8 LAEs -- up to 6 LBGs brighter than an H-band magnitude of approximately 27.5 were revealed in each of their HST WFC3 images. Finding more of these objects will help understand their properties and impact during the EoR, as well as to infer the ionizing bubble size and to quantify the morphology of reionization. Therefore, in this subsection, we further explore the strategy to search for LAEs during the EoR."}
{"text": "We present the cumulative number density, for all central galaxies with a varying number of bright neighbours as well as for those classified as transparent LAEs. The fraction of modelled LBGs with detectable Lyα emission, p(Lyα), is an informative quantity. Not only can it place constraints on the neutral hydrogen fraction, in a blind survey of Lyα emission among known high-redshift LBGs, p(Lyα) is also an indicator of the detection rate. We find that the success rate for finding LAEs among LBGs regardless of their environment is 100% when targeting the brightest galaxies (i.e. H-band magnitude less than or approximately equal to 25.5). This rate drops significantly towards the fainter end (e.g. 20-30% at H-band magnitude between 26 and 27.5). Considering only LBGs surrounded by bright neighbours can increase the detectability. For instance, at the current observing limit, we find that following up galaxies with at least 2 neighbours can boost the detectability up to 40%."}
{"text": "This number rises to nearly 60% when focusing on galaxies with at least 5 neighbours. However, only less than or approximately equal to 25% of galaxies brighter than an H-band magnitude of 26 have at least 5 neighbours. Therefore, we conclude an optimal survey strategy for finding LAEs is to follow up with spectroscopy all LBGs brighter than an H-band magnitude of 26 while only focusing on fainter ones with at least 2 neighbours. In the coming decade, JWST will allow study of galaxies at magnitudes much fainter than the current limit. To model this we reconsider the detection threshold to be an H-band magnitude of 30, and search for neighbouring galaxies that will be detectable by JWST. For simplicity, we use the same field of view as the mock HST WFC3 survey but assume reduced photometric uncertainties and consider a redshift depth of 0.35. We see the number of neighbours increases by a factor of approximately 10 and that, on average, at least 25 galaxies with an H-band magnitude less than 30 are found in the area surrounding transparent LAEs."}
{"text": "Consequently, we will need to target galaxies with many more neighbours to see an influence of neighbours on the damping-wing optical depth, since having at least 10 neighbours is nearly identical to having at least 0. We find a number of approximately 50 neighbours is optimal in order to reach a detection rate of >50% at an H-band magnitude of less than or approximately equal to 27. At even fainter magnitudes, the Lyα emission from most galaxies will be highly attenuated by damping-wing absorption. In this work, we study Lyα transmission in the IGM by forward-modelling the damping-wing absorption using Meraxes, a coupled galaxy formation and reionization SAM that is consistent with the measured high-redshift LBG luminosity functions and EoR history inferred from Planck. As more luminous galaxies (and their neighbours) are able to ionize surrounding inter-galactic hydrogen to a much larger radius than fainter galaxies, we find the inter-galactic Lyα absorption becomes weaker towards brighter galaxies."}
{"text": "We assume the detectability of Lyα to be determined by the damping-wing optical depth and define LBGs with a total Lyα optical depth less than 1 to be transparent LAEs. Our model shows that transparent LAEs will be found in ionized bubbles that are at least 7cMpc in size at redshift z=8 (where the global neutral hydrogen fraction is predicted to be approximately 86%). In particular, we find that all modelled LBGs with an H-band magnitude of less than or approximately equal to 25.5 are detectable LAEs. This is consistent with the high detection rate of Lyα emission in recent spectroscopic follow-up of the 4 brightest galaxies at redshift z is approximately 8. These results, in addition to the more recent findings of redshift z is approximately 8 LAEs indicate very high LAE fractions among luminous galaxies beyond redshift z is approximately 6."}
{"text": "This is in contrast to measurements of fainter galaxies in deep fields or using less-massive lensed galaxies, which show a significant drop of the probability of detecting Lyα from redshift z=6 to 8. Our simulation suggests that the combination of these measurements at both high and low luminosity provides evidence for massive LAEs being likely to reside in large ionized bubbles. We also find that reionization is more advanced around galaxies in high-density regions compared to those that are isolated, with galaxies having a larger number of bright neighbours being more likely to reside in large ionized bubbles, leading to Lyα emission that is less attenuated by the IGM. This not only provides evidence that overdensity plays an important role in driving reionization, but can also motivate searching for LAEs in high-density environments during reionization."}
{"text": "Transparent LAEs, on average, are located in overdense regions and are found to possess at least 2 (25) neighbouring galaxies brighter than an H-band magnitude of approximately 27.5 (30) within mock images of a 2 arcminute by 2 arcminute field of view. As their neighbours are also within the same ionized bubbles, they are also likely to be observable in Lyα. We find that while nearly 70--80% of redshift z=8 galaxies with an H-band magnitude between 26 and 27.5 experience strong damping-wing absorption, targeting those surrounded by bright neighbours can significantly increase the incidence of Lyα emission. For example, at the current observational limit, 40% galaxies with more than 1 neighbour would be considered detectable LAEs. This number increases to 60% when focusing on galaxies with at least 5 neighbours. Finally, we predict that upcoming JWST observations are likely to reveal a factor of 10 more neighbouring galaxies."}
{"text": "With such a large sample size, we find that targeting galaxies with approximately 50 neighbours will yield a success rate of more than 50% for finding LAEs among LBGs during the EoR. These large samples from JWST will provide insights into the morphology and scale sizes of the ionized regions, and their development and growth with redshift through the EoR, that is just not possible with HST."}
{"text": "We predict the 21-cm global signal and power spectra during the Epoch of Reionisation using the MERAXES semi-analytic galaxy formation and reionisation model, updated to include X-ray heating and thermal evolution of the intergalactic medium. Studying the formation and evolution of galaxies together with the reionisation of cosmic hydrogen using semi-analytic models (such as MERAXES) requires N-body simulations within large volumes and high mass resolutions. For this, we use a simulation of side-length 210 h⁻¹ Mpc with 4320³ particles resolving dark matter haloes to masses of 5×10⁸ h⁻¹ Msun. To reach the mass resolution of atomically cooled galaxies, thought to be the dominant population contributing to reionisation, at z=20 of ~2×10⁷ h⁻¹ Msun, we augment this simulation using the DFOREST Monte-Carlo merger tree algorithm (achieving an effective particle count of ~10¹²). Using this augmented simulation we explore the impact of mass resolution on the predicted reionisation history as well as the impact of X-ray heating on the 21-cm global signal and the 21-cm power spectra."}
{"text": "We also explore the cosmic variance of 21-cm statistics within 70³ h⁻³ Mpc³ sub-volumes. We find that the midpoint of reionisation varies by a change in redshift of approximately 0.8 and that the cosmic variance on the power spectrum is underestimated by a factor of 2-4 at k-values of approximately 0.1-0.4 Mpc⁻¹ due to the non-Gaussian nature of the 21-cm signal. To our knowledge, this work represents the first model of both reionisation and galaxy formation which resolves low-mass atomically cooled galaxies while simultaneously sampling sufficiently large scales necessary for exploring the effects of X-rays in the early Universe. The formation of the first luminous objects during the cosmic dawn resulted in the ionisation of the cosmic neutral hydrogen gas, rendering the intergalactic medium (IGM) transparent to UV photons. This period, termed the Epoch of Reionisation (EoR), constitutes the last major phase change of hydrogen in the Universe and had an impact on subsequent galaxy formation and evolution [BarkanaReview]."}
{"text": "A promising probe of this period is the 21-cm hyperfine spin-flip transition of neutral hydrogen which is sensitive to the evolution of the thermal and ionisation states of the IGM [BibleReview]. A number of low-frequency radio telescope arrays are in operation or are planned to detect this signal. Current instruments (MWA, LOFAR, HERA) aim to detect the signal statistically via the 21-cm power spectrum (21-cm PS) [StuartReview]. While a detection has not yet been made, in recent years there has been significant progress in lowering the available upper limits [LOFAR_limits, MWA_limits, HERA_limits]. In addition, the evolution of the all-sky averaged 21-cm global signal (21-cm GS) is being sought with experiments such as EDGES [edges] and SARAS [SARAS3]. In the near future, the Square Kilometre Array (SKA) will provide an unprecedented ability to place observational constraints on the physics of this era by enabling the production of detailed 3-D 21-cm maps showing the distribution and evolution of the cosmic neutral hydrogen [SKAmain]."}
{"text": "For interpreting current and future observations it is important that realistic simulations of the early Universe are available and many authors have contributed to this effort [GnedinMadau]. Simulations of the EoR are made challenging by the large range of scales involved. The main drivers controlling the ionisation and thermal states of the neutral hydrogen are respectively the intense UV and X-ray photons from star-forming galaxies [EoRbook]. X-ray photons have mean-free paths of the order of 10s - 100s of Mpc in the high-redshift Universe, while the typical individual ionized hydrogen bubble sizes are ~10 - 15 Mpc [Stu2004, Furlanetto2006]. It has also been shown that simulation volumes of sidelength greater than or equal to 100 h⁻¹ Mpc are needed for convergent reionisation histories [Iliev2014] while greater than or equal to 200 h⁻¹ Mpc are needed for convergent 21-cm power spectra [Kim2016, Kaur2020]. These considerations necessitate simulations capable of resolving structures from a few Mpc in volumes of greater than or equal to 100s Mpc on a side."}
{"text": "At the same time, realistic EoR modelling requires the ability to resolve haloes down to at least the hydrogen cooling limit corresponding to a halo virial temperature of about 10⁴ K and virial mass, which is proportional to the virial temperature over one plus redshift, to the 3/2 power [BarkanaReview]. These so-called atomically cooled haloes provide sites where gas efficiently cools via atomic line transitions to form stars. Thus, to realistically simulate a representative volume of the early Universe, one requires large simulation volumes as well as sufficiently high mass resolutions. Several techniques have been developed to simulate the EoR [GnedinMadau]. Semi-numerical simulations (e.g. [Simfast21, 21cmFAST, Maity2022]) typically associate ionising photon sources with the density peaks of evolved Gaussian random fields. As these models do not require running computationally expensive N-body simulations, they are able to achieve very large volumes [Greig2022c] as well as efficiently explore the available parameter space [CMMC]. Their main drawback is the absence of detailed physics which self-consistently models a realistic galaxy population."}
{"text": "Achieving high resolution in large-volume hydrodynamical simulations is computationally expensive [CROC1, CoDaI, SPHINX, THESAN]. However, the computational overhead associated with hydrodynamical simulations precludes their use in parameter exploration. Semi-analytic models (SAMs) of galaxy formation (e.g. [GalForm, Galacticus, SAGE, SAG, SHARK]) typically take merger trees from comparatively cheaper dark matter-only N-body simulations and evolve key baryonic components which describe the physical processes involved in galaxy formation, growth and evolution using simple but physically motivated prescriptions [SomervilleReview]. Importantly, being based on N-body trees, the galaxies retain their association with the large-scale structure. These galaxy SAMs then provide a realistic galaxy population at a fraction of the cost of full hydrodynamical simulations. Coupling a galaxy SAM with a semi-numerical reionisation code can provide the best of both worlds: large-volume simulations of reionisation with a self-consistent, realistic population of galaxies. In this work, we use MERAXES, developed as part of the DRAGONS program, which couples a galaxy SAM model designed for galaxies in the high-redshift Universe during the EoR with the semi-numerical code 21cmFAST for simulating the reionisation process [Dragons3, RSAGE, Visbal2020, Astraeus]."}
{"text": "Additionally, for the first time, we implement the evolution of the neutral hydrogen gas spin temperature into MERAXES, taking into account heating by X-ray photons. We run our updated MERAXES on a new dark matter-only N-body simulation which has a volume of 210³ h⁻³ Mpc³ with 4320³ particles. This is the largest volume on which MERAXES has been deployed (previously 67.8³ h⁻³ Mpc³; [Dragons19]). To achieve sufficient mass resolution (atomic cooling limit at z=20 of ~2×10⁷ h⁻¹ Msun) within our simulations we use DFOREST -- a Monte Carlo algorithm-based code introduced in [DARKFOREST]. This provides a unique dataset modelling both individual galaxy formation and evolution during reionisation in volumes large enough for exploring the effects of X-rays on the 21-cm signal from the cosmic dawn and the EoR. Importantly, this is the first time such a large volume coupled reionisation and galaxy SAM has been performed to study the 21-cm signal into the cosmic dawn. With our large volume, we are able to explore the impact of cosmic variance across the 21-cm statistics."}
{"text": "We use the L210_N4320 (hereafter L210) box of the GENESIS suite of N-body simulations. This simulation is 210 h⁻¹ Mpc on a side and consists of 4320³ dark matter particles of mass m_p = 9.95 × 10⁶ h⁻¹ Msun. The halo mass resolution is ~5 × 10⁸ h⁻¹ Msun based on a minimum of 50 particles. The simulation was evolved from z=99 down to z=5 using the SWIFT code [SWIFT] and the haloes were identified via friends-of-friends by the VELOCIraptor halo-finder [VELOCIRAPTOR]. Halo catalogues are saved over 120 snapshots evenly distributed in dynamical time between redshifts 30 and 5. The merger trees were generated using TREEFROG [TREEFROG]. To increase the mass resolution of the L210 simulation from ~5 × 10⁸ h⁻¹ Msun to the atomic hydrogen cooling limit at z=20 (~2×10⁷ h⁻¹ Msun) we augment it by extending the merger trees to lower mass haloes. This is achieved using DFOREST [DARKFOREST], a Monte-Carlo (MC) based algorithm. We call this new simulation L210_AUG."}
{"text": "DFOREST uses an updated prescription of [Benson2016] for augmenting merger trees and works on what are termed 'simple branches' -- merger tree branches that are composed of a halo and all of its immediate progenitors. To add new haloes to the existing merger trees new simple branches are generated using the algorithm outlined in [Parkinson2008] which employs a conditional mass function, with extra parametrisation derived from the Extended Press Schechter theory [EPS3, EPS2, EPS1]. These new MC branches, by construction, have a higher mass resolution than the N-body trees. Building on the methods employed in [Benson2016], the new branches are used to augment the existing N-body merger tree. For this we first define a mass threshold, M_cut, which serves as a dynamic boundary between the N-body and MC halo populations in the final augmented merger tree. The final augmented merger tree with these MC branches grafted onto it will thus have both N-body as well as MC haloes with the M_cut serving as the barrier separating them."}
{"text": "DFOREST determines the positions and assigns velocities to the newly added MC haloes. We apply the non-linear halo bias prescription from [Ahn2015] on the input dark matter density field from L210 to generate a halo density field. This is normalised and used as a one-dimensional probability distribution from which the MC haloes are assigned their positions by random sampling. We performed a convergence test to determine the resolution providing the best performance and use 512³ cells for our calculations. This method is used to assign positions to every new MC that is not a progenitor of another MC halo. The evolution of the MC haloes' position with time is based on their peculiar velocity field, using the linear continuity equation where the divergence of the peculiar velocity field is related to the difference in the halo density field at two different times. The halo density field uses the linear halo bias from [Tinker2010]. We run a number of tests to ensure that the MC haloes are introduced without compromising the accuracy of the underlying L210 simulation."}
{"text": "We use the MERAXES [Dragons3] SAM which was specifically designed to study the interplay and feedback between galaxy formation and evolution, and reionisation. Since its introduction MERAXES has undergone several updates including AGN feedback [Dragons10] and updates to supernova feedback, recycling and chemical enrichment of the ISM, and reincorporation of the ejected gas [Dragons19]. MERAXES includes detailed, physically motivated prescriptions for processes including baryonic infall, radiative cooling, star formation, supernova feedback, mass recycling, metal enrichment of the interstellar medium (ISM), and reincorporation of gas. At each snapshot, the baryonic content of a dark matter halo increases up to a fraction of the virial mass in the form of pristine primordial gas. This fraction is determined by the universal baryon fraction and a baryon fraction modifier which couples the feedback of reionisation to galaxy formation. This newly acquired baryonic gas is deposited into a shock-heated hot-gas reservoir. A fraction of this hot gas cools radiatively to a much colder gas cloud, which then participates in star formation following the [Kauffmann1996] model."}
{"text": "To model reionisation and investigate the role of photoionisation feedback on the high-z galaxies, MERAXES includes a modified version of 21cmFAST [21cmFAST, 21cmFASTv3]. In MERAXES the density and velocity fields come directly from the N-body simulations while the stellar mass grids are computed realistically by MERAXES making use of the full galaxy properties. We extend the reionisation calculations of MERAXES to additionally follow the evolution of the spin temperature, T_S, of neutral hydrogen by incorporating the heating and ionisation of the IGM by X-rays following the same approach taken within 21cmFAST. The ionisation state of the IGM is determined directly from the stellar mass grids following the excursion-set formalism [Furlanetto2004]. A simulation cell is flagged as ionised if the number of stellar baryons multiplied by the average number of ionising photons per baryon and the escape fraction is greater than or equal to the total number of baryons in the same volume, accounting for recombinations and secondary ionisations by X-ray photons. We account for recombinations inside Lyman limit systems via a sub-grid prescription [Sobacchi2014]."}
{"text": "The 21-cm signal depends upon the spin temperature T_S, which is sensitive to the thermal state of the IGM influenced by X-ray photons. Its inverse is a weighted average of the inverse temperatures of the CMB, colour, and gas kinetic temperatures, with weights determined by the Wouthuysen-Field (WF) coupling constant [Wouthuysen1952, Field1958] and the collisional coupling coefficient. Following 21cmFAST, we compute the gas kinetic temperature T_K and the ionised fraction. The thermal evolution of the gas incorporates contributions from Compton heating, adiabatic cooling/heating, and changes in internal energy. These calculations depend on the angle-averaged specific X-ray intensity, which is computed by integrating the comoving X-ray specific emissivity back along the light-cone. We relate the X-ray emissivity to the star formation rate density (SFRD) computed directly from MERAXES. This differs from 21cmFAST, where SFRD is calculated from the density field and collapse fraction. The X-ray emission is characterized by three free parameters: the soft-band X-ray luminosity per SFR (L(X<2keV)/SFR), a threshold energy E₀, and a power-law index α_X."}
{"text": "The 21-cm brightness temperature field depends on the ionization, density, velocity, and spin temperature fields. Below redshift z~25, the signal reflects three broad periods [PritchardReview]: 1. WF coupling (Lyman-alpha pumping), which drives the signal into absorption. 2. X-ray heating, where the IGM is heated and the signal shows an emission feature. 3. Reionisation, where the signal goes to zero. Most studies focus on the post-heating regime assuming the spin temperature is much greater than the CMB temperature, an assumption that breaks down in the Dark Ages and Epoch of Heating. The main drivers of heating are X-ray photons [Furlanetto2006, McQuinn2012]. Large-scale simulations with low mass resolution are unable to simulate the effects of X-rays since the build-up of the stellar mass is delayed. We use MERAXES combined with our augmented N-body simulations for calculations of the full brightness temperature field including contributions from heating, the spin temperature, recombinations, and peculiar velocities. This allows for a more complete picture of the early Universe's thermal history."}
{"text": "SAMs contain many free parameters that require calibration against existing observations. MERAXES involves two sets of calibrations: one for galaxy formation parameters and another for reionisation calculations. We calibrate the L210_AUG simulation by varying a subset of MERAXES input parameters related to star formation efficiency, critical mass, mass loading, supernova energy coupling, and dust scaling. We use the same parameter values for all of our simulations. Following [Dragons19], we calibrate against observed luminosity functions (LFs) and stellar mass functions (SMFs) at z~5-8, using data from [Bouwens2015, Bouwens2021] and [Song2016, Stefanon2021]. We re-calibrated the dust parameter which governs how dust optical depth scales with cold gas metallicity, as our larger simulation volume allowed us to extend calibrations to brighter LFs than were previously available. The second calibration set is for reionisation. The photon budget is influenced by the escape fraction (f_esc), which is poorly constrained. We use a prescription where f_esc evolves with redshift, skewed towards higher redshifts where smaller galaxies with shallower potentials allow more photons to escape."}
{"text": "We tune the escape fraction parameters (normalization and redshift scaling) so that our reionisation history matches measured constraints on the IGM neutral fractions and the integrated optical depth of CMB photons (τ_e) from scattering off free electrons from [Planck2018]. In this section, we demonstrate the full reionisation model from our L210_AUG simulation. We focus on comparing the impact of the missing low-mass haloes from the L210 simulation to illustrate the importance of mass resolution. We note that our model does not include smaller galaxies in molecularly cooled 'mini-haloes', which likely contain PopIII stars, so the appearance of features in this work will be delayed relative to simulations which include them [Yuxiang2020, Yuxiang2021, EmanueleMaria_pop3_1]. The missing small halos in L210 delay the build-up of cosmic stellar mass, and consequently any physical property dependent on it. The L210_AUG simulation, however, includes a realistic galaxy population capable of producing the whole X-ray background, allowing us to present the first large-scale simulation of the thermal and ionisation history incorporating realistic galaxy formation down to the atomic cooling limit."}
{"text": "The L210_AUG box starts to reionise much earlier than L210 owing to the introduction of low-mass galaxies found only in Monte-Carlo haloes. However, the fiducial L210_AUG and L210 simulations both finish reionisation at approximately the same redshift. There are two main reasons for this. Firstly, towards the end of the EoR, reionisation is primarily maintained by larger mass haloes (which are accurately simulated across both simulations) while the lower mass galaxies are more relevant at earlier times. Secondly, the impact of inhomogeneous recombination is different in the two simulations. Since small galaxies, which initiate reionisation in L210_AUG are short-lived, the cosmic gas recombines until sufficiently big galaxies have had time to form and produce enough ionising photons to complete reionisation. To check this, we ran two additional simulations where we turned off inhomogeneous recombinations. Turning off this process results in the augmented simulation reionising much earlier than the un-augmented one, as expected. Ionization field slices show that at a fixed neutral fraction, the L210_AUG simulation has smaller ionized regions, as they are driven by lower stellar mass galaxies at an earlier cosmic time."}
{"text": "The 21-cm global signal for L210_AUG and L210 shows that the augmented simulation has a similar but broader absorption feature, occurring earlier in redshift. This highlights the importance of including low-mass haloes. By including them, the Lyman-alpha and X-ray backgrounds build up at earlier times. The Lyman-alpha background couples the spin temperature to the much lower gas kinetic temperature, resulting in the broader and earlier absorption. The delayed but sudden formation of sources in L210 results in a comparatively rapid build-up of stellar mass and radiation backgrounds. The spherically-averaged 3-D 21-cm power spectrum at fixed spatial scales (k~0.1 and 1 Mpc⁻¹) shows a qualitatively similar evolution for both simulations, but the delayed formation of stellar mass in L210 causes considerable differences in the timing of the peaks. The Lyman-alpha-coupling peak in L210 is delayed by a redshift difference of about 3 relative to L210_AUG. Below z~7, when X-rays have initiated heating and reionisation is underway, the power in both simulations becomes similar."}
{"text": "Even though the large-scale 21-cm power is expected to have three peaks corresponding to Lyman-alpha-pumping, X-ray heating, and reionisation epochs [Pritchard2007, MesingerXRay], we observe only two peaks. The Epoch of Heating peak, expected at z~12 for L210_AUG, is masked by the Lyman-alpha peak, merging into one broad peak due to the timing and build-up of the backgrounds. On the other hand, the small-scale (k~1 Mpc⁻¹) power is characterised by two peaks corresponding to a combined Lyman-alpha-pumping and heating, and an EoR peak [Yuxiang2020]. On small scales, the impact of the Epoch of Heating is harder to disentangle as it primarily impacts larger scales due to the larger mean free path of X-ray photons. The large volume of our simulations enables the exploration of the effects of X-rays on the EoR morphology with a full source population. We vary the X-ray luminosity per SFR, keeping other parameters fixed, considering values from 3.16 × 10³⁸ to 3.16 × 10⁴² erg s⁻¹ Msun⁻¹ yr to encompass a plausible range [Fialkov2017, GreigCMMC2]."}
{"text": "Recent results from HERA have ruled out many 'cold reionisation' models corresponding to low X-ray luminosity [HERA_limits], making our lowest luminosity model an unlikely scenario, though useful for developing intuition. The ionisation photon budget is dominated by UV photons, with X-rays contributing at most 10-15 per cent in extreme models [MesingerXRay]. We find that X-rays can hasten reionisation, in agreement with other studies. The 21-cm brightness temperature light cone slices show a delayed but rapid evolution for the lower-resolution L210 simulation. For the low-luminosity model, the signal remains in absorption across our full redshift range, whereas for the high-luminosity model it is mostly in emission. As shown by the global signal, X-ray photons heat the cosmic gas. Lower X-ray luminosity results in colder gas and a stronger absorption dip. Higher X-ray luminosity leads to a hotter IGM, causing the signal to go into emission at z less than or equal to 17 and a merging of the Lyman-alpha-pumping and heating epochs."}
{"text": "Like the global signal, the shape and amplitude of the 21-cm power spectrum (PS) are strongly affected by X-ray luminosity, meaning accurate PS measurements have great constraining power [HERA_limits]. At large scales, the low X-ray luminosity model has the highest power for most epochs due to large temperature contrasts from the cold IGM, and the heating and reionisation peaks merge. The fiducial simulation shows the three expected peaks, with power peaking at z~16. The high luminosity model has less power during all epochs due to reduced temperature contrast. On small scales, the high luminosity model has clearly differentiated Lyman-alpha and heating peaks, with the heating peak merging with the reionisation peak due to the extended Epoch of Heating. Measurement of any statistical signal from a finite volume of the Universe introduces an inherent uncertainty termed cosmic variance. We explore the cosmic variance of the 21-cm signal by dividing each augmented simulation into 27 equal sub-volumes of side 70 h⁻¹ Mpc. Each sub-volume is larger than typical ionised regions and comparable to many state-of-the-art simulations [CROC3, BLUETIDES, SpringelTNG, CODA, THESAN, Dragons19]."}
{"text": "We find the range in redshift for reionisation histories among sub-volumes at a neutral fraction of approximately 0.5 is a change in redshift of about 0.8. We see the same trend among the simulations, except features in the high-luminosity simulation occur earlier. For the 21-cm global signal, the fractional change in brightness temperature is higher than in the neutral fraction. During the Epoch of Heating, the scatter in brightness temperature is driven by variations in spin temperature, while during reionisation the scatter in the neutral fraction dominates. The scatter in the 21-cm power spectrum increases for decreasing k-value (larger scales) and decreasing redshift. This is due to sample variance, since there are fewer modes at large scales to average over. At low redshifts, most of the 21-cm emission comes from sparse, isolated neutral patches, leading to considerable scatter. The power spectrum quantifies the variance in amplitudes of a random field. A purely Gaussian-random field is fully specified by its power spectrum [PeeblesLSS]. However, higher-order statistics are required to capture information for non-Gaussian fields."}
{"text": "The 21-cm field is non-Gaussian, especially on small scales and during the final stages of the EoR. Initially, it traces the underlying matter-density field which is Gaussian on large scales. However, once the complex 3D morphology of the radiation fields (ionisation, X-ray or Lyman-alpha) impacts the signal, the statistics deviate from Gaussianity [StuartReview]. Hence the cosmic variance of the 21-cm power spectrum will be larger than the Poisson sampling error. We explore the impact of non-Gaussianity on this uncertainty. The full error-covariance matrix of the PS includes a trispectrum component arising from non-Gaussianity [Mondal2016]. Studies often assume the field is Gaussian and ignore this term. Any deviation from the Gaussian expectation measured from our 27 sub-volumes must occur as a result of non-Gaussianity. We compute the ratio of the measured cosmic variance to the theoretical Gaussian expectation. For a Gaussian field, this ratio is unity. We find similar trends among all simulations, though we caution we may over-predict variance due to our sub-volume size being slightly smaller than needed for convergence."}
{"text": "The ratio of measured-to-theoretical variance increases from small to large k-values, implying large scales are more Gaussian. Our results agree qualitatively with [Mondal2015, Mondal2016], who show that non-Gaussianity grows as reionisation progresses. During early stages (80% neutral), non-Gaussianity's contribution to variance is comparable to the Gaussian term for k between 0.1 and 0.4 Mpc⁻¹. As reionisation progresses (30% neutral), this ratio becomes 2-4 for the same scales. Our model's transition to non-Gaussianity appears to occur earlier than in [Mondal2016], likely due to detailed physics including spin temperature fluctuations. Our results show that assuming the 21-cm field is Gaussian underestimates cosmic variance in ~100 Mpc boxes by a factor of ~2 on scales relevant to current and upcoming telescopes. This paper introduced an updated MERAXES model including X-ray heating and thermal evolution. We utilized a new, large-volume N-body simulation (L=210 h⁻¹ Mpc) and performed Monte-Carlo augmentation to resolve all atomically cooled haloes out to z=20, creating a unique dataset for exploring galaxy formation physics and its impact on the EoR."}
{"text": "We found that including Monte-Carlo haloes significantly impacts the build-up of stellar mass and consequently reionisation, which commences earlier and is more gradual. Lyman-alpha-coupling and X-ray heating also occur earlier in the higher-resolution simulation. The timing and duration of the 21-cm power spectrum peaks are also different. These results underscore the need for both large volume and sufficient mass resolution for EoR simulations. The large volume and implementation of thermal evolution in MERAXES enables exploration of X-ray luminosity's impact on heating. In agreement with semi-numerical studies [MesingerXRay, GreigCMMC2], we show that while X-rays' impact on reionisation history is minimal, their effect on both the 21-cm global signal and power spectrum is appreciable. Observations of the 21-cm PS will thus provide constraints on the X-ray properties of early sources. We explored the scatter in reionisation history and the 21-cm global signal within 27 sub-volumes of side 70 h⁻¹ Mpc. As previously described in [Mondal2016], we find that non-Gaussianity contributes significantly to the variance of the 21-cm PS on all scales, increasing towards smaller scales."}
{"text": "This work is the first study of the error-variance of the 21-cm power spectrum at high redshifts in a model that also includes both a model of galaxy formation and spin temperature fluctuations. We find that the assumption of Gaussianity for the 21-cm field results in underestimating the cosmic variance of the 21-cm power spectrum by a factor of greater than or equal to 2 for the scales relevant for the SKA (k~0.1-0.5 Mpc⁻¹)."}
{"text": "Correlations between black holes and their host galaxies provide insight into what drives black hole--host co-evolution. We use the Meraxes semi-analytic model to investigate the growth of black holes and their host galaxies from high redshift to the present day. Our modelling finds no significant evolution in the black hole--bulge and black hole--total stellar mass relations out to a redshift of 8. The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. In our modelling the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. We find that black hole growth is dominated by instability-driven or secular quasar-mode growth and not by merger-driven growth at all redshifts. Our model also predicts that disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation, in agreement with recent observations and hydrodynamical simulations."}
{"text": "Extensive low-redshift studies reveal a complex interplay between galaxies and the supermassive black holes that reside at their centres, with clear correlations observed between black hole mass and host bulge mass, total stellar mass, velocity dispersion and luminosity [e.g.][Magorrian1998, Gebhardt2000, Merritt2001, Tremaine2002, Marconi2003, Haring2004, Bentz2009, Kormendy2013, Reines2015]; see the review by [Heckman2014]. These tight correlations suggest a co-evolution between galaxies and supermassive black holes, which may be causal, due to feedback from the active galactic nucleus [AGN; e.g.][Silk1998, Matteo2005, Bower2006, Ciotti2010] or the efficiency with which the galaxy can fuel the black hole [e.g.][Hopkins2010, Cen2015, AnglesAlcazar2017], or coincidental, simply due to mergers causing both black hole and galaxy growth [e.g.][Haehnelt2000, Croton2006b, Peng2007, Gaskell2011, Jahnke2011]. To understand what drives black hole--host co-evolution, it is necessary to study how these correlations change with redshift."}
{"text": "Observing high-redshift black hole--host correlations is fraught with difficulties. Host galaxies are hard to detect since they are often completely outshined by the AGN light, particularly in the rest-frame optical where common stellar mass estimators can be used [e.g.][Zibetti2009, Taylor2011]. Subtracting the quasar light has resulted in host detections out to redshift z is approximately equal to 2 [Jahnke2009, Mechtley2016], but is yet to be successful for detecting the highest redshift quasars at redshift z is approximately equal to 6 [Mechtley2012]. For these quasars, host masses are often estimated using the widths of observed submillimeter and millimeter emission lines, such as the [CII] 158 micron and CO (6--5) lines [e.g.][Wang2013]. However, dynamical masses determined from emission line widths are highly dependent on the assumptions made, such as the gas-disc geometries and inclination angles [e.g.][Valiante2014]. In fact, inclination angle assumptions can change the determined black hole mass to bulge mass ratio measurements by roughly 3 orders of magnitude [Wang2013]."}
{"text": "In addition, the emission regions may not trace the spatial distribution of the stellar component of the galaxy, meaning that these dynamical masses may not be representative of the total stellar mass [Narayanan2009]. Determining the black hole masses of high-z quasars is also difficult, with emission-line based estimators relying on calibrations at low redshift. Where these observations are unavailable, Eddington accretion rates are instead often assumed to estimate the black hole mass [as in e.g.][Wang2013, Willott2017], which also leads to large uncertainties. High-redshift studies of the black hole--host mass relations are thus very uncertain. With this in mind, high redshift observations find black holes that are more massive than expected by the local relation, where the canonical black hole--bulge mass ratio is 10 to the power of (-2.31 +/- 0.05) for a bulge mass of 10^11 solar masses [Kormendy2013]."}
{"text": "For example, ALMA observations of five redshift z is approximately equal to 6 quasar hosts show black hole to dynamical mass ratios ranging from 10 to the power of -1.9 to 10 to the power of -1.5 [Wang2013]. Similar studies at redshift z is approximately equal to 4--7 [e.g.][Maiolino2007, Riechers2008, Venemans2012] also give estimates for individual quasars of a black hole mass to dynamical mass ratio greater than or approximately equal to 10 to the power of -2, which is significantly larger than the local value if dynamical masses and bulge masses are assumed to be roughly equivalent. This suggests a faster evolution of the first supermassive black holes relative to their host galaxies [Valiante2014], which could potentially be a result of super-Eddington accretion [Volonteri2015]. The high observed black hole mass to dynamical mass ratio relation at high redshift could, however, be a result of selection effects [Lauer2007, Schulze2011, Schulze2014, DeGraf2015, Willott2017]."}
{"text": "[Willott2017] suggest that since only the most massive z>6 black holes are observed, if the relation has a wide dispersion then one would expect to see a higher value due to the Lauer bias [Lauer2007]: since the luminosity function falls off rapidly at high masses, the most massive black holes occur more often as outliers in galaxies of smaller masses than as typical black holes in the most massive galaxies. Indeed, [Willott2017] found that black holes with mass less than 10^9 solar masses at redshift z>6 fall below the black hole mass--dynamical mass relation for low redshift galaxies, in contrast to the opposite being true for higher mass black holes. Similarly, [Schulze2014] claim that selection effects are the reason for the observed evolution of the black hole mass--bulge mass relation; on applying a fitting method to correct for selection effects, they find no statistical evidence for a cosmological evolution in the black hole mass--bulge mass relation."}
{"text": "A lack of evolution in the black hole--host relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016], which observes very little evolution in the black hole mass--stellar mass relation from redshift z=0 to 5, and BlueTides [Huang2018], which finds a black hole mass--stellar mass relation at redshift z=8 that is consistent with the local [Kormendy2013] relation. [DeGraf2015], on the other hand, found that the relation evolves slightly for redshift z greater than or equal to 1 for the highest mass black holes, with a steeper slope at the high-mass end at higher redshifts, making selection effects important. The more statistical study of [Schindler2016] found that the ratio of the black hole to stellar mass density is constant within the uncertainties from redshift z=0 to 5, with a slight decrease in the ratio at redshifts between 3 and 5; this is also consistent with no cosmological evolution in the black hole mass--stellar mass relation."}
{"text": "In this work we explore the evolution of the black hole--host relations with the Meraxes semi-analytic model [Mutch2016]. Meraxes is designed specifically to study galaxy formation and evolution at high redshifts, making it ideal for studying the evolution of black holes and their host galaxies. In this work we use Meraxes, a semi-analytic model designed to study galaxy evolution at high redshifts [Mutch2016]. Using the properties of dark matter halos from an N-body simulation, Meraxes analytically models the physics involved in galaxy formation and evolution. We run Meraxes on the collisionless N-body simulations Tiamat and Tiamat-125-HR [Poole2016, Poole2017]. Tiamat is ideal for studying high redshifts, with a high mass and temporal resolution. Tiamat runs from redshift z=35 to z=1.8, with a box size of (67.8 per h Mpc)^3, 2160^3 particles of mass 2.64x10^6 per h solar masses, and a high cadence of 11.1 Myr per output snapshot at redshift z>5."}
{"text": "Tiamat-125-HR is a low-redshift counterpart to Tiamat, running from redshift z=35 to z=0 with the same temporal resolution, but with a lower mass resolution (1080^3 particles of mass 1.33x10^8 per h solar masses) and larger box size of (125 per h Mpc)^3, more suited for low-redshift studies. Throughout this work, we use the higher resolution Tiamat at high-redshifts, and Tiamat-125-HR for redshift z<2, unless otherwise specified. Meraxes assumes that galaxies reside in the centre of dark matter haloes produced by the N-body simulation. Using the properties of these haloes, Meraxes analytically models the baryonic physics involved in galaxy formation and evolution, such as gas cooling, star formation, black hole growth, and supernova and black hole feedback. These analytical prescriptions involve a range of free parameters, which must be calibrated using observations such as the stellar mass function."}
{"text": "In Meraxes, stars in galaxies reside in three components: an exponential disc, a spheroidal merger-driven bulge and a disc-like instability-driven bulge. Bulges grow through both galaxy-galaxy mergers and disc-instabilities. In Meraxes, we assume that galaxy mergers with merger ratio greater than 0.01 trigger a burst of star formation, by causing shocks and turbulence in the cold gas of the parent galaxy. The galaxy will also accumulate the mass of the secondary galaxy. We assume that the dominant mass component of the primary galaxy will regulate where these stars produced by the burst and the secondary's mass will be deposited. If the primary is dominated by a discy component, the mass is added to the instability-driven bulge. Otherwise, we assume that the new stars will accumulate in shells around the spheroidal merger-driven bulge. In major mergers, where the merger ratio is greater than 0.1 or 0.3, we assume that the stellar disc and instability-driven bulges are destroyed, with all stars placed into the merger-driven bulge."}
{"text": "In our model we assume that the galaxy discs are thin, with an exponential surface density and flat rotation curve. Such discs become unstable if the disc mass is greater than the disc velocity squared times the scale radius divided by the gravitational constant, which equals the critical mass [Efstathiou1982, Mo1998]. Here, we take the disc mass as the combined mass of both gas and stars in the disc, and the disc velocity and scale radius as the mass-weighted velocity and scale radius of the stellar and gas discs. If such a disc instability occurs, Meraxes returns the disc to stability by transferring the unstable mass of stars from the disc to the instability-driven bulge. The Meraxes black hole model was introduced in Q17, and updated to include instability-driven growth in M19. In Meraxes, black holes are seeded in every newly-formed galaxy, with a seed mass of 10^4 solar masses. Black holes then grow by accretion of both hot and cold gas, through the radio- and quasar modes, respectively."}
{"text": "We also assume that black holes grow in galaxy mergers, with the black holes in each galaxy merging together. Black holes accrete hot gas from the static hot gas reservoir around the galaxy, at a fraction of the Bondi-Hoyle accretion rate. We consider this fraction a free parameter, which adjusts the efficiency of radio-mode black hole growth [Croton2016]. This accretion is limited by the amount of hot gas in the reservoir and the Eddington limit. A fraction of this accretion mass is radiated away and so during one snapshot, black holes grow through the radio-mode by the remaining mass. We include the effects of radio-mode AGN feedback by assuming that a fraction of the radiated energy is coupled to the surrounding gas, adiabatically heating a mass which is subtracted from the cooling flow, regulating the accretion of new gas onto the black hole [Croton2006a, Croton2016]. This AGN feedback has no significant effect on the results of Tiamat at redshift z greater than or equal to 2."}
{"text": "Black holes accrete cold gas from the galaxy, when triggered by either a galaxy-galaxy merger or a disc instability. During such an event, the black hole mass grows by a certain amount, where the virial velocity and a free parameter adjust the growth efficiency. For merger-triggered growth, we take the efficiency parameter to be proportional to the merger ratio. For instability driven growth, we consider two separate free parameters. During the quasar mode, black holes are assumed to accrete at the Eddington rate, and thus the mass accreted by the black hole during one simulation snapshot is limited. This can result in the mass being accreted over multiple simulation snapshots. We incorporate quasar-mode AGN feedback by considering the energy injected into the gas during a simulation time-step. We assume that this energy generates a wind that heats the cold disc gas and transfers it to the hot gas reservoir, depleting the supply of cold gas available for the black hole to accrete. If sufficient energy is injected by the quasar, this wind can also eject the hot gas."}
{"text": "We calculate the bolometric luminosities of each black hole in the model following the Q17 method, which assumes Eddington luminosity for all accreting black holes, and self-consistently calculates the duty cycle. We consider the luminosities from both the quasar- and radio-modes of accretion. At high-redshifts the contribution from the radio-mode is negligible. At the lowest redshifts (redshift z less than or equal to 2), the radio-mode becomes a more significant growth mechanism for the most massive black holes, and so their luminosities are enhanced slightly by the addition of the radio-mode luminosity. We convert from bolometric to B-band luminosities using the [Hopkins2007] bolometric correction, and then assume a continuum slope of 0.44 to convert to UV luminosities. We also account for obscuration due to quasar orientation, by scaling the UV luminosity function by a factor related to the opening angle of quasar radiation. In our model we assume a constant opening angle, for simplicity, which is a free parameter in our model."}
{"text": "In M19 we calibrated the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8, and the black hole--bulge mass relation at redshift z=0. Using this model, we find that the black hole mass function and quasar luminosity functions are much larger than predicted by the observations. In addition, we note that [Shankar2016] find significant selection biases in the black hole--bulge mass relation---a topic of recent debate [see e.g.][Kormendy2019]. Due to the M19 predictions and this potential bias, we assume that the [Shankar2009] redshift z=0 black hole mass function is a less biased indicator of the local black hole population, and retune the model here to better reproduce the black hole observations. Note that we use the same parameter values for Tiamat and Tiamat-125-HR, and use both simulations to tune the model: Tiamat for matching redshift z greater than or equal to 2 observations and Tiamat-125-HR for redshift z<2."}
{"text": "We find that our results from the two simulations are generally consistent at redshift z is approximately equal to 2, with broad qualitative agreement at higher redshifts. We calibrate the free parameters in the model to match the observed stellar mass functions at redshift z=0--8, the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0, and the quasar X-ray luminosity functions from redshift z=5 to 2. Since [Shankar2016] find that the observed black hole--bulge mass relation is biased to high black hole masses, we also require our model to not over-predict this relation, however we do not otherwise tune to it. We note that our best models produce black hole--host mass relations lower than the observations, consistent with the expectations of [Shankar2009], and have steeper slopes. We find that these criteria are met by a range of free parameter values for the merger-driven black hole growth efficiency, and the definition of a major merger."}
{"text": "We note that all of these parameter sets produce very similar results. As a further check of the black hole population, we plot the black hole accretion rate density as a function of redshift for models with these different merger-driven black hole growth efficiencies. We find that the models with lower efficiencies give black hole accretion histories in approximate agreement with the observations. The larger efficiencies overproduce measurements of the black hole accretion rate density [e.g.][Delvecchio2014]. The opening angle of AGN radiation, theta, adjusts the normalization of the UV luminosity function. We tune this to match the observations, finding a preferred theta of 70 degrees, corresponding to an observable fraction of UV quasars of 18 per cent. We show the quasar X-ray luminosity functions at redshift z=5--0, with X-ray luminosities calculated using the [Hopkins2007] bolometric to X-ray correction."}
{"text": "At redshift z=2 the model and the observations agree remarkably well. At redshift z>2 the model over-predicts the observed quasar X-ray luminosity function at intermediate luminosities, by up to ~0.7 dex at redshift z=4, while at redshift z<2 the model under-predicts the luminosity function at these luminosities. Our model shows better agreement with the observations than previous versions of Meraxes. While the observations show a slight increase in the X-ray quasar luminosity functions from redshift z=4 to 2, the model predicts a slight decrease. In fact, we cannot find a combination of black hole parameters that results in a redshift evolution that matches that of the observed X-ray quasar luminosity function at redshift z>2. However, the key quantity of black hole accretion rate density is predicted by the model to peak at redshift z=2 as observed."}
{"text": "In addition to published uncertainties in the observations, it may also be the case that at higher redshifts X-ray AGN are more likely to be obscured, which is consistent with evidence from a range of X-ray observations [Treister2006, Vito2014, Buchner2015]. Thus we argue that the inability of our model to match the redshift evolution of the X-ray quasar luminosity function may not represent a significant concern. We show the quasar UV luminosity functions at redshift z=5--0. We find that, as with the X-ray luminosity function, the UV luminosity function decreases from redshift z=5 to 0, though it agrees well with observations at redshift z>2. At redshift z<2, however, we note that the faint-end of the UV luminosity function becomes flat, and by redshift z<1 there is a significant disagreement with the observations, with the model producing too many luminous quasars."}
{"text": "The black hole accretion rate density becomes significantly higher than the observations at redshift z<1, consistent with the quasar luminosities being overestimated at these redshifts. This excess black hole accretion is most likely a result of the model missing important physics required for modelling low-redshift galaxy evolution, particularly in the quenching of massive galaxies, or due to the simplifications assumed in the model such as a constant black hole accretion efficiency. However, as the overall accretion rate density at these redshifts is low, this will not have a significant impact on the black hole mass, an integrated quantity. Thus, while the redshift z<1 black hole accretion rates are overestimated, the black hole mass function and black hole--host mass relations are reliable at low redshifts. Indeed, we find that assuming a lower Eddington ratio significantly improves the match between the model and observed UV luminosity functions at redshift z<1."}
{"text": "However, this causes the model to no longer match the observations at higher redshifts. Thus, some evolving Eddington ratio is necessary for Meraxes to accurately reproduce the redshift z<1 quasar UV luminosity function. We now use the model described to explore black hole growth. We investigate the redshift evolution of the black hole--host scaling relations. To investigate the redshift evolution of the black hole--bulge and black hole--total stellar mass relations we first perform linear least squares fits to the relations at a range of redshifts. We only include galaxies with mass > 10^9.5 solar masses in our fits, so that they are not biased by the large number of low-mass galaxies. Both relations have a slope and normalization that increase with redshift from redshift z=0 to 2, with much weaker evolution for redshift z>2."}
{"text": "Relative to the scatter in the relations, we see minimal evolution in both the black hole--bulge and black hole--total stellar mass relations from redshift z=0 to 6. This lack of evolution in the black hole--host mass relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016] and BlueTides [Huang2018]. We find that our black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. While the black hole mass has a slightly stronger relationship with the bulge stellar mass, the black hole and total stellar mass are still tightly correlated. The scatter in the relations is slightly larger than the 0.28 dex observed by [Kormendy2013] locally. However, they are very consistent with those from the BlueTides simulation at high redshift."}
{"text": "The scatter decreases with increasing stellar mass. The median black hole mass to total stellar mass ratio as a function of redshift for galaxies with black hole mass > 10^6 solar masses shows no statistically-significant evolution out to redshift z is approximately equal to 8. This is consistent with current high redshift observations; when selection effects are accounted for, the observations at high redshift are consistent with no cosmological evolution in these relations [Schulze2014]. Our model predicts no significant evolution in the black hole--host mass relations, with the scatter in the relations decreasing at the highest redshifts. This indicates that there is a connection between the growth of black holes and their host galaxies. Indeed, our model includes joint triggering of star formation and black hole growth during galaxy mergers, and black hole feedback which regulates star formation, meaning that the co-evolution of black holes and galaxies is implicit in our model."}
{"text": "This is not consistent with the scenario proposed by [Peng2007] and [Jahnke2011], for example, where the black hole and galaxy growth is uncorrelated and the relationships are generated naturally within a merger driven galaxy evolution framework, due to a central-limit-like tendency. The median black hole mass to total stellar mass ratio as a function of redshift with galaxies split into black hole mass bins shows that lower mass black holes have lower mass ratios than higher mass black holes. This will lead to a notable selection bias, since when observing the most massive black holes, the measured ratio will be higher than that of the entire population. This is generally expected for any sample selected by black hole mass or luminosity where the scatter in the relation is large [e.g.][Lauer2007]. Finally, we note an interesting effect of changing the parameter controlling the black hole efficiency for converting mass to energy."}
{"text": "For a higher efficiency, the median black hole--stellar mass ratio decreases at redshifts z greater than or approximately equal to 6, instead of remaining constant with redshift. We investigate the cause of this high-redshift decrease in the black hole--host relation by considering the Eddington limit. Increasing the efficiency from 0.06 to 0.2 decreases the Eddington limit. This results in many black holes having Eddington-limited growth at the highest redshifts (redshift z greater than or approximately equal to 6), which is not the case for the lower efficiency model. This causes black holes to grow slower than their host galaxies at high redshifts, resulting in a decreased black hole--stellar mass ratio. Observing the high-redshift black hole--stellar mass relation may therefore probe the Eddington limit and the efficiency of black holes in converting mass to energy."}
{"text": "We consider the cumulative fraction of black hole mass formed through each of the mechanisms in our model: black hole seeding, merger-driven quasar-mode accretion, instability-driven quasar-mode accretion, radio-mode accretion and black hole--black hole coalescence in galaxy mergers. The merger-driven growth mode becomes more important at low redshifts, at both low- and high-black hole masses. On average, instabilities grow the majority of mass in black holes at all redshifts, except for galaxies with black hole mass > 10^9 solar masses at redshift z is approximately equal to 0, whose black hole growth becomes dominated by galaxy mergers. Radio-mode growth slowly increases in significance with redshift, yet still has only contributed to a small proportion of the total black hole mass by redshift z=0, except at the highest masses. Note that we consider growth from disc instabilities that are triggered by earlier galaxy mergers as growth via the instability-driven mode."}
{"text": "We also consider the instantaneous growth fractions of black hole mass formed through each mechanism as a function of redshift. As discussed, the model produces unreliable black hole accretion rates at redshift z<1, and so we only consider these black hole growth rates at redshift z>1. The instability-driven growth mode is the dominant growth mechanism, on average, at all redshifts, regardless of black hole mass. The merger-driven quasar mode and black hole--black hole coalescence mode are sub-dominant at all redshifts. The radio-mode grows more mass at low redshift and in the most massive galaxies, with the percentage of total instantaneous black hole growth from this mode increasing from only 0.1 per cent at redshift z=5 to almost 5 per cent at redshift z is approximately equal to 1. Our finding that mergers are not the dominant mechanism for growing black holes is in agreement with a range of observations."}
{"text": "For example, [Koss2010] find that only 25 per cent of local, moderate luminosity X-ray AGN show signs of mergers, though the fraction is much higher for luminous AGN [Hong2015]. From redshift z from approximately 0.3 to 1.0, [Cisternas2010] find that the vast majority (>85 per cent) of X-ray selected AGN do not show signs of mergers, suggesting that the bulk of their black hole accretion has been triggered by some other mechanism. This is also consistent with the findings of [Georgakakis2009], [Villforth2018], [Schawinski2012], [Mechtley2016], [DelMoro2015] and [Marian2019] for AGN at various redshifts. Our result that disc instabilities cause the majority of black hole growth is also consistent with predictions from other simulations. In the GALFORM semi-analytic model, [Fanidakis2011] found that the growth of black holes is dominated by accretion due to disc instabilities."}
{"text": "Using an updated GALFORM model, [Griffin2019] found that accretion of hot gas dominates the growth of black holes at redshift z<2, with disc-instabilities dominant at higher redshifts. [Hirschmann2012] found that instability-driven black hole growth was required to reproduce AGN downsizing, and that while major mergers are the dominant trigger for luminous AGN, especially at high redshift, disc instabilities cause the majority of black hole growth in moderately luminous Seyfert galaxies at low redshift. [Menci2014] find that in their semi-analytic model disc instabilities can provide enough black hole accretion to reproduce the observed AGN luminosity functions up to redshift z is approximately equal to 4.5, but are not likely to be dominant for the highest luminosity AGN or at the highest redshifts. In contrast, [Shirakata2018] find that the primary trigger of AGN at redshift z less than or equal to 4 in their semi-analytic model is mergers."}
{"text": "The hydrodynamical simulation Horizon-AGN found that only ~35 per cent of black hole mass in local massive galaxies is directly attributable to merging, with the majority of black hole growth instead growing via secular processes [Martin2018]. The Magneticum Pathfinder Simulation also found that merger events are not the dominant fuelling mechanism for black holes in redshift z=0--2, with merger fractions less than 20 per cent, except for very luminous quasars at redshift z is approximately equal to 2 [Steinborn2018]. Finally, we comment on the effect of the efficiency parameters for merger-driven and instability-driven black hole growth in the model. We find the instability-driven efficiency from tuning the model, whereas the merger-driven efficiency is less constrained, with several values producing reasonable model results. Having a merger growth efficiency that is twice, six times or even 18 times larger than the instability-driven growth efficiency may have an effect on the conclusions outlined above."}
{"text": "We find, as expected, that models with larger merger efficiencies result in more merger-driven growth. For a merger efficiency twice the instability efficiency, the instability-driven mode still dominates at redshift z=2, while for a six times larger efficiency, the merger-driven mode begins to dominate at the highest black hole masses. For the model with an 18 times larger merger efficiency, the merger-driven mode contributes even more black hole growth, but is still not the dominant growth mode for black holes with mass between 10^6 and 10^9 solar masses. Thus, while the efficiency parameter for merger-driven growth has some effect on the relative distributions of the instability-driven and merger-driven growth modes, the instability-driven mode is still dominant for the majority of black holes, even if the merger growth efficiency is as much as 18 times larger than the secular growth efficiency."}
{"text": "A popular explanation for the black hole--host correlations is that major mergers drive the growth of both black holes and bulges [e.g.][Haehnelt2000, Croton2006b]. If this were the case, one would expect that black holes would only correlate with galaxy properties directly related to the merger process, such as bulge mass, and not, for example, total stellar mass. [Simmons2017] consider a sample of 101 disc-dominated AGN hosts from the SDSS, which they assume must have a major merger-free history since redshift z is approximately equal to 2. They found that these galaxies lie on the typical black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation. This indicates that the substantial and ongoing black hole growth in these merger-free disc galaxies must be due to a process other than major mergers, and that major mergers cannot be the primary mechanism behind the black hole--host correlations."}
{"text": "We plot the black hole mass--total stellar mass and black hole mass--bulge mass relation for disc-dominated and bulge-dominated galaxies at redshift z=0. Our simulated disc galaxies lie on the black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation, as they have small bulges relative to their black hole mass. This is consistent with the [Simmons2017] observations, and the results from the Horizon-AGN hydrodynamical simulation [Martin2018]. However, we see a less significant offset, which occurs at lower black hole masses than [Simmons2017] and [Martin2018], since the black holes in our disc-dominated galaxies are less massive in comparison. [Mutlu-Pakdil2017] also find no dependence of the black hole mass--total stellar mass relation on galaxy type in the Illustris hydrodynamical simulation. [Martin2018] suggest that major mergers therefore cannot be primarily responsible for feeding black holes."}
{"text": "This is consistent with our finding that the instability-driven mode is the dominant growth mechanism for black holes. We use the Meraxes semi-analytic model to investigate the evolution of black holes and their relations to their host galaxies. We find the following key predictions of our model: There is minimal statistically-significant evolution in the black hole--bulge and black hole--total stellar mass relations out to high redshifts (redshift z is approximately equal to 8). The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. This indicates that the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. Higher mass black holes have higher black hole--total stellar mass ratios, leading to a significant selection effect in measurements of this ratio when observing only the most massive black holes."}
{"text": "The instability-driven or secular quasar-mode growth is the dominant growth mechanism for black holes at all redshifts. The contribution from merger-driven quasar-mode growth only becomes significant at low redshift for black holes with mass greater than or approximately equal to 10^9 solar masses. Disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation. Our simulation is limited in making predictions for the highest redshift quasars at redshift z=6--7 due to the simulation box size and resolution. In future work we will run Meraxes on larger N-body simulations in order to make predictions for these objects. We calibrate the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8 and the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0. The black hole mass functions produced by Tiamat and Tiamat-125-HR are converged at redshift z=2 for black holes with mass > 10^7.1 solar masses [see Marshall2019]."}
{"text": "We therefore focus on matching the observed black hole mass functions at masses > 10^7.1 solar masses. While the [Shankar2009] and [Davis2014] relations are different, particularly at black hole mass ~ 10^8.5 solar masses, they are similar relative to the freedom we have in adjusting our model black hole mass function, and so when calibrating we found the most reasonable fit to both. In the model stellar mass function, we also plot the Meraxes stellar mass function produced when AGN feedback is switched off. This shows that AGN feedback has no effect on galaxies in Tiamat at redshift z greater than or equal to 2, but suppresses the growth of the most massive galaxies at lower redshifts as seen in Tiamat-125-HR. Throughout this work, we use the higher resolution Tiamat simulation at redshift z greater than or equal to 2, and Tiamat-125-HR for redshift z<2, where Tiamat is unavailable."}
{"text": "We find that the results discussed in this paper are generally consistent between the two simulations at redshift z is approximately equal to 2. However, one notable result is that the best-fitting black hole--stellar mass relations change rapidly between redshift z=2 (using Tiamat) and z=1 (using Tiamat-125-HR). To verify that this jump is not purely a result of the simulation change, we show the best-fitting relations from redshift z=6--0 using Tiamat-125-HR. The Tiamat-125-HR simulation shows similar results to those found using Tiamat at redshift z greater than or equal to 2, with a slightly milder but still relatively rapid evolution from redshift z=2 to z=1. The qualitative result of the evolution being insignificant relative to the scatter in the relation still holds. Thus, while the change in simulation slightly amplifies the rapid change in the black hole--stellar mass relations from redshift z=2 to z=1, this does not change our conclusions."}
{"text": "We also note that where the black hole mass functions are converged, the black hole--stellar mass relations are in good agreement between the two simulations."}
{"text": "The hyperfine 21-cm transition of neutral hydrogen from the early Universe (z>5) is a sensitive probe of the formation and evolution of the first luminous sources[cite: 1007]. Using the Fisher matrix formalism we explore the complex and degenerate high-dimensional parameter space associated with the high-z sources of this era and forecast quantitative constraints from a future 21-cm power spectrum (21-cm PS) detection[cite: 1008]. This is achieved using Meraxes, a coupled semi-analytic galaxy formation model and reionisation simulation, applied to an N-body halo merger tree with a statistically complete population of all atomically cooled galaxies out to z~20[cite: 1009]. Our mock observation assumes a 21-cm detection spanning z in [5, 24] from a 1000 h mock observation with the forthcoming Square Kilometre Array and is calibrated with respect to ultraviolet luminosity functions (UV LFs) at z in [5, 10], the optical depth of CMB photons to Thompson scattering from Planck, and various constraints on the IGM neutral fraction at z > 5[cite: 1010]."}
{"text": "In this work, we focus on the X-ray luminosity, ionising UV photon escape fraction, star formation and supernova feedback of the first galaxies[cite: 1011]. We demonstrate that it is possible to recover 5 of the 8 parameters describing these properties with better than 50 per cent precision using just the 21-cm PS[cite: 1012]. By combining with UV LFs, we are able to improve our forecast, with 5 of the 8 parameters constrained to better than 10 per cent (and all below 50 per cent)[cite: 1013]."}
{"text": "Following recombination, the early Universe entered the cosmic Dark Ages characterised by a neutral intergalactic medium (IGM) and the absence of luminous sources[cite: 1014]. The formation of the first stars and galaxies ushered in the era of the Cosmic Dawn[cite: 1015]. The intense ionising ultraviolet (UV) radiation, characteristic of the young and massive stars, as well as X-rays (possibly from high-mass X-ray binaries, e.g. [MesingerXRay]) impacted the thermal and ionisation state of the IGM[cite: 1016]. This period was brought to its conclusion in the Epoch of Reionisation (EoR) when the UV photons ionised the neutral hydrogen rendering it transparent to UV photons[cite: 1017]. Considerable effort has been expended in the last few decades to unravel the complex physics of this period (see [EoRbook] and references therein)[cite: 1018]. The forbidden 21-cm hyperfine transition signal is well-suited for this purpose because of its extreme sensitivity to the formation and evolution of the first stars and galaxies (z <~ 30) as well as the various feedback mechanisms in the early Universe[cite: 1019]."}
{"text": "Though the ultimate goal of 21-cm interferometric experiments is to map the tomography of the IGM as a function of frequency (redshift) the first set of observations will be statistical in nature[cite: 1020]. The 21-cm signal is observed as a brightness temperature against a background source (which is almost always assumed to be the cosmic microwave background (CMB) radiation; e.g. [BibleReview, StuartReview, PritchardReview])[cite: 1021]. The 21-cm power spectrum (21-cm PS) quantifies the fluctuations in the brightness temperature of the 21-cm signal across the sky[cite: 1022]. Though a detection has yet to be made, current experiments such as the Murchison Widefield Array (MWA; [MWA_main]), LOw Frequency ARray (LOFAR; [LOFAR_main]), Hydrogen Epoch of Reionization Array (HERA; [HERA_main]) have already begun setting upper limits on the 21-cm PS (see [LOFAR_limits, MWA_limits, HERA_limits])[cite: 1023]. The upcoming Square Kilometre Array (SKA; [SKA_main]) will revolutionise 21-cm EoR cosmology with its unprecedented sensitivity[cite: 1024]."}
{"text": "The amplitude and shape of the 21-cm PS are extremely sensitive to the thermal and ionisation state of the IGM [cite: 1025] and hence the astrophysics of early galaxy formation and evolution[cite: 1025, 1025]. It is therefore imperative that realistic and efficient models (see [GnedinMadau] for a recent review) are available to interpret current and upcoming observations[cite: 1026]. Despite significant progress in this direction, there is considerable uncertainty about the properties of the underlying source populations of these models[cite: 1027]. In this paper, we ask: What can we learn about the underlying physical processes driving reionisation from a successful detection of the 21-cm PS? Simulating reionisation requires large volumes (>=200 h^-1 Mpc according to [Iliev2014, Kaur2020] for convergent reionisation and 21-cm statistics)[cite: 1028]. As a result, a number of models have been developed to make large-scale but computationally efficient realisations of the early Universe (e.g. [Battaglia2013, GRIZZLY, Simfast, SCRIPT, 21cmFASTv3])[cite: 1030]."}
{"text": "To investigate the utility of the 21-cm PS as a probe of galaxy formation, MCMC methods have been utilised to place constraints on the parameterised properties (e.g. UV and X-ray) of population II & III star-forming galaxies (e.g. [CMMC1, CMMC2, Park2019, Yuxiang_tale1, Yuxiang_tale2, Maity_2022, Bevins_2023])[cite: 1031]. In this work, we use Meraxes [Dragons3] - a semi-analytic model (SAM) of galaxy formation (see [SomervilleReview] for a recent review) and evolution self-consistently coupled to a reionisation model - to forecast constraints on astrophysical properties of the early galaxies[cite: 1032]. Unlike semi-numerical models (for example, [21cmFAST], [SCRIPT]), which focus on population-averaged quantities (i.e. these models generally have no galaxies), Meraxes provides a realistic population of galaxies as sources of photons[cite: 1033]. Meraxes incorporates a detailed, physically motivated galaxy formation and evolution model that includes baryonic infall, gas cooling, star formation, supernova feedback, active galactic nuclei feedback, galaxy mergers, etc[cite: 1034]."}
{"text": "By efficiently coupling the reionisation of the IGM via a modified version of 21cmFAST [21cmFAST, 21cmFASTv3] and an underlying galaxy population sourced from a dark matter only N-body simulation, Meraxes is thus well-suited to explore the underlying parameter space of the complex astrophysics of this era[cite: 1035]. We deploy Meraxes on a 210 h^-1 Mpc cosmological simulation which resolves all the atomically cooled galaxies down from z~20[cite: 1036]. The large volume and high mass resolution of our simulation make an MCMC analysis using Meraxes prohibitively expensive computationally[cite: 1037]. Using a Fisher matrix analysis, we forecast the constraints on a total of 8 astrophysical parameters in our model that directly control the X-ray luminosity, UV escape fraction, star formation rates and supernova feedback of the galaxies of the high-z Universe[cite: 1039]. Focusing on the upcoming SKA1-low, we forecast constraints from the 21-cm PS before exploring the improvements available when combining information from the UV LFs[cite: 1040]."}
{"text": "We use the L210_N4320 dark matter-only N-body simulation of the Genesis suite of simulations (Power et al. in prep)[cite: 1047]. Containing 4320^3 particles in a 210^3 h^-3 Mpc^3 volume, the simulation has a mass resolution of ~5x10^8 h^-1 M_sun[cite: 1048]. L210_N4320 was run with the SWIFT [SWIFT] cosmological code, using the VELOCIraptor [VELOCIRAPTOR] halo identifier and merger trees generated using TreeFrog [TREEFROG][cite: 1049]. The simulation consists of 120 snapshots between redshifts 30 and 5[cite: 1050]. In order to resolve haloes down to the atomic cooling limit at z=20, the L210_N4320 simulation was augmented using the Monte-Carlo algorithm-based code dforest [DARKFOREST] achieving an effective halo mass resolution of ~2 x 10^7 h^-1 M_sun (genpsim of [Balu2022]) [cite: 1050]. dforest achieves this by sampling from a conditional mass function based on the extended Press-Schechter theory [EPS1, EPS2, EPS3] that has been modified to match the halo mass functions from N-body simulations[cite: 1051]."}
{"text": "Meraxes [Dragons3] contains detailed and physically motivated prescriptions for galaxy formation and evolution[cite: 1063]. These include, for example, gas infall into dark matter haloes from the IGM followed by its radiative cooling and subsequent star formation, as well as eventual supernova feedback and metal enrichment of the ISM[cite: 1064]. Active galactic Nuclei (AGN) feedback from central black holes of the galaxies was implemented in [Dragons10] and calculations of the galaxies' UV luminosity in [Dragons19][cite: 1065]. In addition, Meraxes also has a coupled treatment of reionisation based on the 21cmFAST semi-numerical code ([21cmFAST, 21cmFASTv3]; see section 2.3 for more details)[cite: 1066]. At every snapshot, the baryonic content of a dark matter halo increases by (1-f_mod)*f_b*M_vir, where f_b is the baryonic fraction and f_mod is the baryon fraction modifier - set by the local IGM ionisation state from the previous snapshot - coupling galaxy growth to the ionisation state of the IGM[cite: 1069]."}
{"text": "Star formation in Meraxes follows the disc stability argument of [Kauffmann1996], wherein gas participates in star formation when the cold-gas mass is higher than a critical mass given by Equation 7[cite: 1071]. The new stellar mass, Delta_M_star, formed in the time-step Delta_t is given by Equation 8, where alpha_SF is the star formation efficiency[cite: 1072]. In this work, both Sigma_SF and alpha_SF are free parameters in our astrophysical model[cite: 1073]. The primary impact of SNe feedback is to heat the gas reservoirs of the halo resulting in the transfer of the gas from the cold to the hot gas reservoirs and in extreme cases the removal of the gas from the hot halo[cite: 1077]. Our implementation, modified from [Guo2011] to take advantage of our high cadence merger trees [Dragons19], is based on energy conservation[cite: 1078]. The total stellar mass going SNe at a particular snapshot of the simulation depends on both the current and previous star formation[cite: 1079]. To account for this, we track the stars formed in the present and four previous snapshots[cite: 1080]."}
{"text": "Following [Dragons19], the supernova energy coupling efficiency (epsilon) and mass loading factor (eta) are implemented as functions of halo circular velocity and redshift, as shown in Equations 12 and 13[cite: 1085]. These are controlled by two free normalization parameters, epsilon_0 and eta_0, respectively[cite: 1086]. We forecast the fractional uncertainty on both epsilon_0 and eta_0[cite: 1087]. The fraction of ionising photons escaping into the IGM from galaxies plays an important role in regulating the ionisation fraction and morphology[cite: 1088]. Following [Dragons3] we employ an escape fraction (f_esc) prescription for galaxies that is solely redshift dependent ([though see e.g.][Kimm2017, Yeh2023])[cite: 1090]. This results in an f_esc that is skewed towards higher z, motivated by two factors: it is easier for photons to escape the shallower potential wells of high-z galaxies, and early galaxies have less dust attenuation[cite: 1091, 1092, 1093]. The escape fraction is given by Equation 14, and we allow both the normalisation (f_esc,0) and redshift scaling (alpha_esc) to be free parameters[cite: 1094]."}
{"text": "The thermal evolution and ionisation state of the IGM follows 21cmFAST [21cmFAST, 21cmFASTv3], modified to take advantage of our realistic galaxy population[cite: 1095]. We divide our simulation into 1024^3 voxels corresponding to a cell dimension of ~0.21 h^-1 Mpc[cite: 1098]. The thermal state of a neutral hydrogen cloud is characterised by the spin temperature T_S. Even though T_S is influenced by both UV and X-ray photons, the latter has a considerably more pronounced impact (e.g. [MesingerXRay]) and is computed via Equation 15[cite: 1101]. We compute the comoving X-ray emissivity as shown in Equation 17, where L'_X/SFR is the specific X-ray luminosity per SFR[cite: 1107]. This is one of the free parameters of our model and has units [erg s^-1 M_sun^-1 yr]. We impose a lower limit E_0, another free parameter, which is motivated by the absorption of low-energy X-rays within the galaxy itself[cite: 1110]."}
{"text": "We compute the ionisation (x_HII) grid by employing an excursion-set formalism [Furlanetto2004] by comparing the total number of ionising photons to the combined number of neutral atoms and recombinations within spheres of decreasing radii[cite: 1112]. Grid voxels inside a sphere are deemed to be ionised if Equation 19 is satisfied[cite: 1113]. The number of stellar baryons is inferred from the stellar mass that is dependent on the star formation histories of all star-forming galaxies[cite: 1117]. We compute a baryon modifier, f_mod, for each galaxy based on their local neutral hydrogen value, enabling us to couple a galaxy's growth to its local IGM ionisation state[cite: 1118]. In the next snapshot, the amount of fresh gas accreting onto the galaxy is modulated by f_mod which is calculated following [Sobacchi2013] based on the 'filtering mass'[cite: 1119]. In this manner, by coupling galaxy growth to the local ionisation state as well as the local UV ionising background, Meraxes enables a self-consistent reionisation scenario[cite: 1121]."}
{"text": "The genpsim simulation from [Balu2022] was calibrated against existing observables including UV LFs from [Bouwens2015] and [Bouwens2021], and stellar mass functions from [Song2016] and [Stefanon2021][cite: 1127]. The reionisation history was calibrated using the Thomson scattering optical depth of free electrons to CMB photons from the [Planck2018][cite: 1128]. Figure 2 shows the dimensionless 21-cm PS from our fiducial model[cite: 1129]. The grey-shaded region represents the sensitivity for a 1000 h observation with the upcoming SKA1-low[cite: 1130]. We use the 'moderate' foreground removal case from [Pober2014] effectively ignoring all the k-modes falling within the 21-cm foreground wedge (setting a k_min=0.16 Mpc^-1)[cite: 1131]. The k_max=1.4 Mpc^-1 is set by a combination of the spatial scales resolved by SKA1-low and scales we trust not to be dominated by the Poisson noise of the sources[cite: 1132]."}
{"text": "The sensitivity of a radio interferometer to the 21-cm PS can be divided into two components: thermal noise and sample (cosmic) variance[cite: 1143]. The total noise power is given by adding these two in quadrature[cite: 1144]. We focus on a future observation of the 21-cm PS by the SKA1-low[cite: 1146]. We only include the stations in the 'Central Area', resulting in 296 stations, and calculate the sensitivity using the 21cmSense python package [Pober2013, Pober2014][cite: 1148]. We assume a total of 1080 hours of observation and a sky temperature dominated by galactic synchrotron emission [T_Sky][cite: 1149]. We combine partially coherent baselines to improve power spectrum sensitivity and use the `moderate` foreground removal scenario of 21cmSense wherein we avoid the modes that are contained within the foreground wedge [Datta2010][cite: 1151]. As we ignore the modes that fall within the foreground wedge, we are limited to k_min = 0.16 Mpc^-1 for our analysis[cite: 1152]."}
{"text": "In addition to exploring constraints from the 21-cm PS we also consider the improvements achievable with a joint analysis with the UV LFs[cite: 1156]. Here, we adopt the parameterisation for the UV optical depth that depends on the dust-to-gas ratio [Charlot2000] of the galaxies[cite: 1158]. The model differentiates between a short-lived birth cloud of the stars as well as the interstellar medium (ISM) of the galaxy[cite: 1159]. The free parameters of Meraxes have been calibrated [Dragons19, Balu2022] to their fiducial values against infrared excess (IRX)-beta, UV LFs, and stellar mass functions at z>5[cite: 1161]. The blue curves in Fig. 3 are the UV LFs from our calibrated simulation[cite: 1162]. The error bars are determined by multiplying our simulated UV LF data by the corresponding fractional uncertainty on each data point from the [Bouwens2021] observational data[cite: 1163]. In addition to the 21-cm PS, we thus have 6 UV LFs from z in [5, 10][cite: 1164]."}
{"text": "To place quantitative constraints on the model parameters we use the Fisher information matrix ([Tegmark1997, Albrecht2009])[cite: 1165]. For any set of observations, the Fisher matrix provides the best possible constraints on the parameters of an assumed model[cite: 1166]. An implicit assumption is that the errors on these parameters are Gaussian and that the observational data points are statistically independent[cite: 1167]. In this limit, by the Cramer-Rao theorem, the covariance matrix of the parameters is given by the inverse of the Fisher matrix[cite: 1168]. Another relevant property of the Fisher matrices is their additive nature enabling one to do joint analyses of a different set of observations by adding the corresponding Fisher matrices together[cite: 1170]. For the present work, we compute the Fisher matrix as shown in Equation 24, where the summation is over all k-modes and z-bins[cite: 1173]. Fisher matrices are thus sensitive to the derivatives of the 21-cm PS, with a larger value indicating increased sensitivity and tighter constraining power[cite: 1174]. Parameters with a similar structure for the derivatives, as a function of k, will be degenerate [Pober2014][cite: 1176]."}
{"text": "We obtain tight constraints (<~10 per cent) for the X-ray parameters (luminosity L_X/SFR & minimum X-ray photon energy escaping galaxies E_0), escape fraction normalisation (f_esc,0) and star formation efficiency (alpha_SF) while the SNe ejection efficiency (epsilon_0) is constrained to ~25 per cent[cite: 1204]. On the other hand, the critical mass normalisation (Sigma_SF) and the efficiency of SNe reheating (eta_0) remain relatively unconstrained with ~234 per cent and ~117 per cent fractional 1-sigma uncertainties respectively[cite: 1205]. The relatively poor constraints on Sigma_SF and eta_0 are primarily because these parameters have negligible impact on the 21-cm PS[cite: 1206]. The 21-cm signal is very sensitive to the amount and energy of the X-ray photons in the early Universe[cite: 1208]. The 21-cm PS, therefore, provides tight constraints on the X-ray parameters, E_0 (~11 per cent) and L_X/SFR (~10^-2 per cent), in our model[cite: 1209]."}
{"text": "We next add in the Fisher matrix corresponding to the UV LFs from 6 redshifts in [5,10][cite: 1220]. As the UV LFs functions are sensitive to parameters that do not have a pronounced impact on the ionisation morphology, the addition of the UV LFs into the analysis helps improve the overall constraints on the astrophysical model [Park2019][cite: 1221]. Figure 5 shows the constraints from the joint analysis of the 21-cm PS and UV LFs[cite: 1226]. This results in significant improvements in Sigma_SF (from ~234 to ~40 per cent) and eta_0 (from ~117 to ~8 per cent) for the joint case of both the 21-cm PS and the UV LFs as the degeneracies between stellar properties and escape fraction can be weakened[cite: 1230]. This then translates into improvements in other parameters[cite: 1231]. The relatively larger improvement in Sigma_SF compared to alpha_SF following the inclusion of information from the UV LFs stems from the breaking of parameter degeneracies[cite: 1231]."}
{"text": "X-rays can contribute to the ionisation of the local IGM of a galaxy leading to photoionisation regulation of the amount of neutral gas available for accretion onto the galaxy and hence subsequent star formation[cite: 1243]. Thus increasing L_X/SFR can be compensated by a decrease in the SNe feedback and/or the ionising UV escape fraction[cite: 1244]. The amount of cold gas available for star formation is influenced by the SNe ejection efficiency which sets the amount of gas removed from the galaxy[cite: 1249]. An increase in f_esc therefore should be accompanied by a decrease in the SNe feedback[cite: 1250]. The strong correlation between alpha_SF and SNe reheat efficiency eta_0 is expected as they are two of the parameters impacting the stellar mass in a galaxy[cite: 1258]. On the other hand, the correlation between alpha_SF and the critical mass normalisation Sigma_SF is surprisingly weak given Equation 8[cite: 1259]. This is because of the relatively small value of Sigma_SF[cite: 1260]."}
{"text": "Using the semi-analytic galaxy formation model Meraxes we perform a Fisher matrix analysis to forecast the constraints on physical properties of galaxy formation and reionisation that will be available from future 21-cm PS observations[cite: 1264]. We focused on 8 free parameters in our model that directly impact the X-ray luminosity, UV escape fraction, star formation rate and SNe feedback of the galaxies[cite: 1267]. We constructed a mock observation of the 21-cm PS, focusing on a 1000 hr observation with the forthcoming SKA1-low[cite: 1268]. Using the Fisher matrix formalism, we find that 4 (5) out of the 8 parameters can be constrained to within <~10 (<~50) per cent using the 21-cm PS alone from the EoR[cite: 1270]. Specifically, we forecast tight constraints on our X-ray parameters, star formation efficiency, and the normalisation of the UV escape fraction of the early galaxies[cite: 1271, 1272]. On the other hand, SNe feedback parameters remain largely unconstrained reflecting that the 21-cm PS is relatively insensitive to them[cite: 1273]."}
{"text": "The complex astrophysics of the early galaxy formation and evolution is captured in the degeneracies and correlations among the model parameters[cite: 1274]. To improve the overall constraining power of our analysis we added the Fisher matrix corresponding to the UV LFs from redshifts z in [5, 10][cite: 1276]. This results in an improvement in all of our parameter forecasts, most notably the critical mass normalisation Sigma_SF and the SNe reheat efficiency eta_0[cite: 1277]. This is not surprising as these parameters primarily control the stellar mass content of the galaxies to which the UV LFs are very sensitive[cite: 1278]. Incorporating the UV LFs into the analyses results in 5 of our parameters being constrained to <~10 per cent and all 8 of them being to within <~50 per cent[cite: 1279]. Our forecasts illustrate that detailed observations of reionisation with the SKA will be valuable in constraining the astrophysics of the early galaxies[cite: 1280]."}
{"text": "This research was supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project #CE170100013[cite: 1283]. Part of this work was performed on the OzSTAR national facility at the Swinburne University of Technology[cite: 1284]. The OzSTAR program partially receives funding from the Astronomy National Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by the Australian Government[cite: 1285]. This research also made use of resources from the National Computational Infrastructure (NCI Australia), another NCRIS-enabled capability supported by the Australian Government[cite: 1286]. This research relies heavily on the python [PYTHON] open source community, in particular, numpy [NUMPY], matplotlib [MATPLOTLIB], scipy [SCIPY], h5py, jupyter [Jupyter], and pandas [Pandas][cite: 1287]. The data underlying this article will be shared on reasonable request to the corresponding author[cite: 1288]."}
{"text": "In this section, we show the derivatives of our primary statistics i.e. the 21-cm PS (Fig. A1)[cite: 1289]. These derivatives are computed by perturbing the genpsim simulation about the fiducial model, one parameter at a time[cite: 1290]. These are then used to compute the Fisher matrix (see equation 24)[cite: 1291]. Parameters corresponding to similarly shaped derivatives will be degenerate. Figure A1 shows these derivatives weighted by the noise powers[cite: 1292]. This section shows the analysis using only the UV LFs[cite: 1295]. Figure B1 shows the derivatives of the UV LFs, computed by perturbing the genpsim simulation about the fiducial model[cite: 1296]. We do not vary the X-ray parameters, L_X/SFR and E_0, for the UV LFs analysis as they do not have an impact on the UV LFs[cite: 1297]. In Figure B2 we show the forecasted constraints from the UV LFs Fisher matrix[cite: 1299]."}
{"text": "Correlations between black holes and their host galaxies provide insight into what drives black hole--host co-evolution. We use the Meraxes semi-analytic model to investigate the growth of black holes and their host galaxies from high redshift to the present day. Our modelling finds no significant evolution in the black hole--bulge and black hole--total stellar mass relations out to a redshift of 8. The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. In our modelling the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. We find that black hole growth is dominated by instability-driven or secular quasar-mode growth and not by merger-driven growth at all redshifts. Our model also predicts that disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation, in agreement with recent observations and hydrodynamical simulations."}
{"text": "Extensive low-redshift studies reveal a complex interplay between galaxies and the supermassive black holes that reside at their centres, with clear correlations observed between black hole mass and host bulge mass, total stellar mass, velocity dispersion and luminosity [e.g.][Magorrian1998, Gebhardt2000, Merritt2001, Tremaine2002, Marconi2003, Haring2004, Bentz2009, Kormendy2013, Reines2015]; see the review by [Heckman2014]. These tight correlations suggest a co-evolution between galaxies and supermassive black holes, which may be causal, due to feedback from the active galactic nucleus [AGN; e.g.][Silk1998, Matteo2005, Bower2006, Ciotti2010] or the efficiency with which the galaxy can fuel the black hole [e.g.][Hopkins2010, Cen2015, AnglesAlcazar2017], or coincidental, simply due to mergers causing both black hole and galaxy growth [e.g.][Haehnelt2000, Croton2006b, Peng2007, Gaskell2011, Jahnke2011]. To understand what drives black hole--host co-evolution, it is necessary to study how these correlations change with redshift."}
{"text": "Observing high-redshift black hole--host correlations is fraught with difficulties. Host galaxies are hard to detect since they are often completely outshined by the AGN light, particularly in the rest-frame optical where common stellar mass estimators can be used [e.g.][Zibetti2009, Taylor2011]. Subtracting the quasar light has resulted in host detections out to redshift z is approximately equal to 2 [Jahnke2009, Mechtley2016], but is yet to be successful for detecting the highest redshift quasars at redshift z is approximately equal to 6 [Mechtley2012]. For these quasars, host masses are often estimated using the widths of observed submillimeter and millimeter emission lines, such as the [CII] 158 micron and CO (6--5) lines [e.g.][Wang2013]. However, dynamical masses determined from emission line widths are highly dependent on the assumptions made, such as the gas-disc geometries and inclination angles [e.g.][Valiante2014]. In fact, inclination angle assumptions can change the determined black hole mass to bulge mass ratio measurements by roughly 3 orders of magnitude [Wang2013]."}
{"text": "In addition, the emission regions may not trace the spatial distribution of the stellar component of the galaxy, meaning that these dynamical masses may not be representative of the total stellar mass [Narayanan2009]. Determining the black hole masses of high-z quasars is also difficult, with emission-line based estimators relying on calibrations at low redshift. Where these observations are unavailable, Eddington accretion rates are instead often assumed to estimate the black hole mass [as in e.g.][Wang2013, Willott2017], which also leads to large uncertainties. High-redshift studies of the black hole--host mass relations are thus very uncertain. With this in mind, high redshift observations find black holes that are more massive than expected by the local relation, where the canonical black hole--bulge mass ratio is 10 to the power of (-2.31 +/- 0.05) for a bulge mass of 10^11 solar masses [Kormendy2013]."}
{"text": "For example, ALMA observations of five redshift z is approximately equal to 6 quasar hosts show black hole to dynamical mass ratios ranging from 10 to the power of -1.9 to 10 to the power of -1.5 [Wang2013]. Similar studies at redshift z is approximately equal to 4--7 [e.g.][Maiolino2007, Riechers2008, Venemans2012] also give estimates for individual quasars of a black hole mass to dynamical mass ratio greater than or approximately equal to 10 to the power of -2, which is significantly larger than the local value if dynamical masses and bulge masses are assumed to be roughly equivalent. This suggests a faster evolution of the first supermassive black holes relative to their host galaxies [Valiante2014], which could potentially be a result of super-Eddington accretion [Volonteri2015]. The high observed black hole mass to dynamical mass ratio relation at high redshift could, however, be a result of selection effects [Lauer2007, Schulze2011, Schulze2014, DeGraf2015, Willott2017]."}
{"text": "[Willott2017] suggest that since only the most massive z>6 black holes are observed, if the relation has a wide dispersion then one would expect to see a higher value due to the Lauer bias [Lauer2007]: since the luminosity function falls off rapidly at high masses, the most massive black holes occur more often as outliers in galaxies of smaller masses than as typical black holes in the most massive galaxies. Indeed, [Willott2017] found that black holes with mass less than 10^9 solar masses at redshift z>6 fall below the black hole mass--dynamical mass relation for low redshift galaxies, in contrast to the opposite being true for higher mass black holes. Similarly, [Schulze2014] claim that selection effects are the reason for the observed evolution of the black hole mass--bulge mass relation; on applying a fitting method to correct for selection effects, they find no statistical evidence for a cosmological evolution in the black hole mass--bulge mass relation."}
{"text": "A lack of evolution in the black hole--host relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016], which observes very little evolution in the black hole mass--stellar mass relation from redshift z=0 to 5, and BlueTides [Huang2018], which finds a black hole mass--stellar mass relation at redshift z=8 that is consistent with the local [Kormendy2013] relation. [DeGraf2015], on the other hand, found that the relation evolves slightly for redshift z greater than or equal to 1 for the highest mass black holes, with a steeper slope at the high-mass end at higher redshifts, making selection effects important. The more statistical study of [Schindler2016] found that the ratio of the black hole to stellar mass density is constant within the uncertainties from redshift z=0 to 5, with a slight decrease in the ratio at redshifts between 3 and 5; this is also consistent with no cosmological evolution in the black hole mass--stellar mass relation."}
{"text": "In this work we explore the evolution of the black hole--host relations with the Meraxes semi-analytic model [Mutch2016]. Meraxes is designed specifically to study galaxy formation and evolution at high redshifts, making it ideal for studying the evolution of black holes and their host galaxies. The outline of the paper is as follows. We give a brief overview of Meraxes in Section 2, and detail the calibration procedure in Section 3. We then investigate the evolution of black holes in the model in Section 4, and conclude in Section 5. Throughout this work, we adopt the [Planck2015] cosmological parameters. In this work we use Meraxes, a semi-analytic model designed to study galaxy evolution at high redshifts [Mutch2016]. Using the properties of dark matter halos from an N-body simulation, Meraxes analytically models the physics involved in galaxy formation and evolution."}
{"text": "We run Meraxes on the collisionless N-body simulations Tiamat and Tiamat-125-HR [Poole2016, Poole2017]. Tiamat is ideal for studying high redshifts, with a high mass and temporal resolution. Tiamat runs from redshift z=35 to z=1.8, with a box size of (67.8 per h Mpc)^3, 2160^3 particles of mass 2.64x10^6 per h solar masses, and a high cadence of 11.1 Myr per output snapshot at redshift z>5. Tiamat-125-HR is a low-redshift counterpart to Tiamat, running from redshift z=35 to z=0 with the same temporal resolution, but with a lower mass resolution (1080^3 particles of mass 1.33x10^8 per h solar masses) and larger box size of (125 per h Mpc)^3, more suited for low-redshift studies. For a detailed description of these simulations, see [Poole2016] and [Poole2017]."}
{"text": "Throughout this work, we use the higher resolution Tiamat at high-redshifts, and Tiamat-125-HR for redshift z<2, unless otherwise specified. Meraxes assumes that galaxies reside in the centre of dark matter haloes produced by the N-body simulation. Using the properties of these haloes, Meraxes analytically models the baryonic physics involved in galaxy formation and evolution, such as gas cooling, star formation, black hole growth, and supernova and black hole feedback. These analytical prescriptions involve a range of free parameters, which must be calibrated using observations such as the stellar mass function. The model outputs a range of properties for each galaxy in the simulation, including the mass of hot gas, cold gas and stars, its star formation rate, and the mass of its central black hole. For a full description of the processes modelled in Meraxes, see [Mutch2016], [Qin2017] (herein Q17) and [Marshall2019] (herein M19)."}
{"text": "In Meraxes, stars in galaxies reside in three components: an exponential disc, a spheroidal merger-driven bulge and a disc-like instability-driven bulge. Bulges grow through both galaxy-galaxy mergers and disc-instabilities. A full description of this model is given in M19, with a brief summary outlined below. In Meraxes, we assume that galaxy mergers with merger ratio greater than 0.01 trigger a burst of star formation, by causing shocks and turbulence in the cold gas of the parent galaxy. The galaxy will also accumulate the mass of the secondary galaxy. We assume that the dominant mass component of the primary galaxy will regulate where these stars produced by the burst and the secondary's mass will be deposited. If the primary is dominated by a discy component, the mass will be deposited in the plane of the disc and so it is added to the instability-driven bulge. Otherwise, we assume that the new stars will accumulate in shells around the spheroidal merger-driven bulge."}
{"text": "In major mergers, where the merger ratio is greater than 0.1 or 0.3, we assume that the stellar disc and instability-driven bulges are destroyed, with all stars placed into the merger-driven bulge. In our model we assume that the galaxy discs are thin, with an exponential surface density and flat rotation curve. Such discs become unstable if the disc mass is greater than the disc velocity squared times the scale radius divided by the gravitational constant, which equals the critical mass [Efstathiou1982, Mo1998]. Here, we take the disc mass as the combined mass of both gas and stars in the disc, and the disc velocity and scale radius as the mass-weighted velocity and scale radius of the stellar and gas discs. If such a disc instability occurs, Meraxes returns the disc to stability by transferring the unstable mass of stars from the disc to the instability-driven bulge."}
{"text": "The Meraxes black hole model was introduced in Q17, and updated to include instability-driven growth in M19. We summarize the model below, however the interested reader is encouraged to refer to Q17 for the full details. In Meraxes, black holes are seeded in every newly-formed galaxy, with a seed mass of 10^4 solar masses. Black holes then grow by accretion of both hot and cold gas, through the radio- and quasar modes, respectively. We also assume that black holes grow in galaxy mergers, with the black holes in each galaxy merging together. Black holes accrete hot gas from the static hot gas reservoir around the galaxy, at a fraction of the Bondi-Hoyle accretion rate. We consider this fraction a free parameter, which adjusts the efficiency of radio-mode black hole growth [Croton2016]. This accretion is limited by the amount of hot gas in the reservoir and the Eddington limit."}
{"text": "A fraction of this accretion mass is radiated away and so during one snapshot, black holes grow through the radio-mode by the remaining mass. We include the effects of radio-mode AGN feedback by assuming that a fraction of the radiated energy is coupled to the surrounding gas, adiabatically heating a mass which is subtracted from the cooling flow, regulating the accretion of new gas onto the black hole [Croton2006a, Croton2016]. This AGN feedback has no significant effect on the results of Tiamat at redshift z greater than or equal to 2, suppressing the growth of only the most massive galaxies in Tiamat-125-HR at lower redshifts. Black holes accrete cold gas from the galaxy, when triggered by either a galaxy-galaxy merger or a disc instability. During such an event, the black hole mass grows by a certain amount, where the virial velocity and a free parameter adjust the growth efficiency."}
{"text": "For merger-triggered growth, we take the efficiency parameter to be proportional to the merger ratio. For instability driven growth, we consider two separate free parameters. During the quasar mode, black holes are assumed to accrete at the Eddington rate, and thus the mass accreted by the black hole during one simulation snapshot is limited. This can result in the mass being accreted over multiple simulation snapshots. We incorporate quasar-mode AGN feedback by considering the energy injected into the gas during a simulation time-step. We assume that this energy generates a wind that heats the cold disc gas and transfers it to the hot gas reservoir, depleting the supply of cold gas available for the black hole to accrete. If sufficient energy is injected by the quasar, this wind can also eject the hot gas."}
{"text": "We calculate the bolometric luminosities of each black hole in the model following the Q17 method, which assumes Eddington luminosity for all accreting black holes, and self-consistently calculates the duty cycle. We consider the luminosities from both the quasar- and radio-modes of accretion. At high-redshifts the contribution from the radio-mode is negligible. At the lowest redshifts (redshift z less than or equal to 2), the radio-mode becomes a more significant growth mechanism for the most massive black holes, and so their luminosities are enhanced slightly by the addition of the radio-mode luminosity. We convert from bolometric to B-band luminosities using the [Hopkins2007] bolometric correction, and then assume a continuum slope of 0.44 to convert to UV luminosities. We also account for obscuration due to quasar orientation, by scaling the UV luminosity function by a factor related to the opening angle of quasar radiation."}
{"text": "In our model we assume a constant opening angle, for simplicity, which is a free parameter in our model; this simply adjusts the normalisation of our UV luminosity functions. In M19 we calibrated the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8, and the black hole--bulge mass relation at redshift z=0. Using this model, we find that the black hole mass function and quasar luminosity functions are much larger than predicted by the observations. In addition, we note that [Shankar2016] find significant selection biases in the black hole--bulge mass relation---a topic of recent debate [see e.g.][Kormendy2019]. Due to the M19 predictions and this potential bias, we assume that the [Shankar2009] redshift z=0 black hole mass function is a less biased indicator of the local black hole population, and retune the model here to better reproduce the black hole observations."}
{"text": "Note that we use the same parameter values for Tiamat and Tiamat-125-HR, and use both simulations to tune the model: Tiamat for matching redshift z greater than or equal to 2 observations and Tiamat-125-HR for redshift z<2. We find that our results from the two simulations are generally consistent at redshift z is approximately equal to 2, with broad qualitative agreement at higher redshifts, and so we can reliably use the Tiamat-125-HR simulation at redshift z<2 where Tiamat is unavailable. We calibrate the free parameters in the model to match the observed stellar mass functions at redshift z=0--8, the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0, and the quasar X-ray luminosity functions from redshift z=5 to 2. Since [Shankar2016] find that the observed black hole--bulge mass relation is biased to high black hole masses, we also require our model to not over-predict this relation, however we do not otherwise tune to it."}
{"text": "We note that our best models produce black hole--host mass relations lower than the observations, consistent with the expectations of [Shankar2009], and have steeper slopes. We find that these criteria are met by a range of free parameter values for the merger-driven black hole growth efficiency, and the definition of a major merger. We note that all of these parameter sets produce very similar results, so unless otherwise specified we only show the model results for one case hereafter. As a further check of the black hole population, we plot the black hole accretion rate density as a function of redshift for models with these different merger-driven black hole growth efficiencies. We find that the models with lower efficiencies give black hole accretion histories in approximate agreement with the observations. The larger efficiencies overproduce measurements of the black hole accretion rate density [e.g.][Delvecchio2014]."}
{"text": "The opening angle of AGN radiation, theta, adjusts the normalization of the UV luminosity function. We tune this to match the observations, finding a preferred theta of 70 degrees, corresponding to an observable fraction of UV quasars of 18 per cent. We show the quasar X-ray luminosity functions at redshift z=5--0, with X-ray luminosities calculated using the [Hopkins2007] bolometric to X-ray correction. At redshift z=2 the model and the observations agree remarkably well. At redshift z>2 the model over-predicts the observed quasar X-ray luminosity function at intermediate luminosities, by up to ~0.7 dex at redshift z=4, while at redshift z<2 the model under-predicts the luminosity function at these luminosities. Our model shows better agreement with the observations than previous versions of Meraxes. While the observations show a slight increase in the X-ray quasar luminosity functions from redshift z=4 to 2, the model predicts a slight decrease."}
{"text": "In fact, we cannot find a combination of black hole parameters that results in a redshift evolution that matches that of the observed X-ray quasar luminosity function at redshift z>2. However, the key quantity of black hole accretion rate density is predicted by the model to peak at redshift z=2 as observed. In addition to published uncertainties in the observations, it may also be the case that at higher redshifts X-ray AGN are more likely to be obscured, which is consistent with evidence from a range of X-ray observations [Treister2006, Vito2014, Buchner2015]. Thus we argue that the inability of our model to match the redshift evolution of the X-ray quasar luminosity function may not represent a significant concern. We show the quasar UV luminosity functions at redshift z=5--0. We find that, as with the X-ray luminosity function, the UV luminosity function decreases from redshift z=5 to 0, though it agrees well with observations at redshift z>2."}
{"text": "At redshift z<2, however, we note that the faint-end of the UV luminosity function becomes flat, and by redshift z<1 there is a significant disagreement with the observations, with the model producing too many luminous quasars. The black hole accretion rate density becomes significantly higher than the observations at redshift z<1, consistent with the quasar luminosities being overestimated at these redshifts. This excess black hole accretion is most likely a result of the model missing important physics required for modelling low-redshift galaxy evolution, particularly in the quenching of massive galaxies, or due to the simplifications assumed in the model such as a constant black hole accretion efficiency. However, as the overall accretion rate density at these redshifts is low, this will not have a significant impact on the black hole mass, an integrated quantity. Thus, while the redshift z<1 black hole accretion rates are overestimated, the black hole mass function and black hole--host mass relations are reliable at low redshifts."}
{"text": "We now use the model described in Sections 2 and 3 to explore black hole growth. We investigate the redshift evolution of the black hole--host scaling relations. We then consider the relative contributions of the different black hole growth modes, and we consider the black hole--host scaling relations in galaxies of different morphologies. To investigate the redshift evolution of the black hole--bulge and black hole--total stellar mass relations we first perform linear least squares fits to the relations: log(M_BH / M_sun) = alpha * log(M / M_sun) + beta, for the total stellar mass and bulge mass at a range of redshifts. We only include galaxies with mass M > 10^9.5 solar masses in our fits, so that they are not biased by the large number of low-mass galaxies. Both relations have a slope and normalization that increase with redshift from redshift z=0 to 2, with much weaker evolution for redshift z>2."}
{"text": "Relative to the scatter in the relations, we see minimal evolution in both the black hole--bulge and black hole--total stellar mass relations from redshift z=0 to 6. This lack of evolution in the black hole--host mass relations is consistent with the findings of cosmological hydrodynamical simulations such as Horizon-AGN [Volonteri2016] and BlueTides [Huang2018]. We find that our black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. While the black hole mass has a slightly stronger relationship with the bulge stellar mass, the black hole and total stellar mass are still tightly correlated. The scatter in the relations is slightly larger than the 0.28 dex observed by [Kormendy2013] locally. However, they are very consistent with those from the BlueTides simulation at high redshift."}
{"text": "The scatter decreases with increasing stellar mass---including only galaxies with stellar/bulge mass greater than 10^10 or 10^10.5 solar masses reduces the scatter. The median black hole mass to total stellar mass ratio as a function of redshift for galaxies with black hole mass > 10^6 solar masses shows no statistically-significant evolution out to redshift z is approximately equal to 8. This is consistent with current high redshift observations; when selection effects are accounted for, the observations at high redshift are consistent with no cosmological evolution in these relations [Schulze2014]. Our model predicts no significant evolution in the black hole--host mass relations, with the scatter in the relations decreasing at the highest redshifts. This indicates that there is a connection between the growth of black holes and their host galaxies. Indeed, our model includes joint triggering of star formation and black hole growth during galaxy mergers, and black hole feedback which regulates star formation, meaning that the co-evolution of black holes and galaxies is implicit in our model."}
{"text": "This is not consistent with the scenario proposed by [Peng2007] and [Jahnke2011], for example, where the black hole and galaxy growth is uncorrelated and the relationships are generated naturally within a merger driven galaxy evolution framework, due to a central-limit-like tendency. The median black hole mass to total stellar mass ratio as a function of redshift with galaxies split into black hole mass bins shows that lower mass black holes have lower mass ratios than higher mass black holes. For example, at high redshifts (redshift z>2), the median ratio for black holes with mass between 10^7 and 10^8 solar masses is higher than those with mass between 10^6 and 10^7 solar masses by ~0.25 dex, with that for black holes with mass > 10^8 solar masses being a further ~0.25 dex higher. This will lead to a notable selection bias, since when observing the most massive black holes, the measured ratio will be higher than that of the entire population."}
{"text": "This is generally expected for any sample selected by black hole mass or luminosity where the scatter in the relation is large [e.g.][Lauer2007]. Finally, we note an interesting effect of changing the parameter controlling the black hole efficiency for converting mass to energy. The median black hole--stellar mass ratio for our best model is compared to a run with a higher efficiency, with all other parameters unchanged. For the higher efficiency, the median black hole--stellar mass ratio decreases at redshifts z greater than or approximately equal to 6, instead of remaining constant with redshift. This effect is not seen by adjusting any of the other black hole parameters we tune in the model. We investigate the cause of this high-redshift decrease in the black hole--host relation by considering the Eddington limit. Increasing the efficiency from 0.06 to 0.2 decreases the Eddington limit."}
{"text": "This results in many black holes having Eddington-limited growth at the highest redshifts (redshift z greater than or approximately equal to 6), which is not the case for the lower efficiency model. This causes black holes to grow slower than their host galaxies at high redshifts, resulting in a decreased black hole--stellar mass ratio. Observing the high-redshift black hole--stellar mass relation may therefore probe the Eddington limit and the efficiency of black holes in converting mass to energy. We consider the cumulative fraction of black hole mass formed through each of the mechanisms in our model: black hole seeding, merger-driven quasar-mode accretion, instability-driven quasar-mode accretion, radio-mode accretion and black hole--black hole coalescence in galaxy mergers. The merger-driven growth mode becomes more important at low redshifts, at both low- and high-black hole masses. On average, instabilities grow the majority of mass in black holes at all redshifts, except for galaxies with black hole mass > 10^9 solar masses at redshift z is approximately equal to 0, whose black hole growth becomes dominated by galaxy mergers."}
{"text": "Radio-mode growth slowly increases in significance with redshift, yet still has only contributed to a small proportion of the total black hole mass by redshift z=0, except at the highest masses; this is discussed in Q17. Note that we consider growth from disc instabilities that are triggered by earlier galaxy mergers as growth via the instability-driven mode, and do not treat them in a more detailed manner as in [IzquierdoVillalba2019], for example. We also consider the instantaneous growth fractions of black hole mass formed through each mechanism as a function of redshift. Here we take the `instantaneous' fraction to be the fraction of growth caused by a mechanism between the specified redshift and the simulation snapshot immediately preceding it. As discussed, the model produces unreliable black hole accretion rates at redshift z<1, and so we only consider these black hole growth rates at redshift z>1."}
{"text": "The instability-driven growth mode is the dominant growth mechanism, on average, at all redshifts, regardless of black hole mass. The merger-driven quasar mode and black hole--black hole coalescence mode are sub-dominant at all redshifts. The radio-mode grows more mass at low redshift and in the most massive galaxies, with the percentage of total instantaneous black hole growth from this mode increasing from only 0.1 per cent at redshift z=5 to almost 5 per cent at redshift z is approximately equal to 1. Our finding that mergers are not the dominant mechanism for growing black holes is in agreement with a range of observations. For example, [Koss2010] find that only 25 per cent of local (redshift z<0.05), moderate luminosity X-ray AGN show signs of mergers, though the fraction is much higher for luminous AGN [Hong2015]. From redshift z from approximately 0.3 to 1.0, [Cisternas2010] find that the vast majority (>85 per cent) of X-ray selected AGN do not show signs of mergers, suggesting that the bulk of their black hole accretion has been triggered by some other mechanism."}
{"text": "This is also consistent with the findings of [Georgakakis2009] who claim that a large fraction of AGN at redshift z is approximately equal to 1 are triggered by processes other than major mergers, as do [Villforth2018] at redshift z is approximately equal to 0.9, and [Schawinski2012], [Mechtley2016], [DelMoro2015] and [Marian2019] for AGN at redshift z is approximately equal to 2. Our result that disc instabilities cause the majority of black hole growth is also consistent with predictions from other simulations. In the GALFORM semi-analytic model, [Fanidakis2011] found that the growth of black holes is dominated by accretion due to disc instabilities, with the fraction of mass in black holes produced by disc instabilities more than an order of magnitude larger than that produced by mergers, at all redshifts. Using an updated GALFORM model, [Griffin2019] found that accretion of hot gas dominates the growth of black holes at redshift z<2, with disc-instabilities dominant at higher redshifts."}
{"text": "[Hirschmann2012] found that instability-driven black hole growth was required to reproduce AGN downsizing, and that while major mergers are the dominant trigger for luminous AGN, especially at high redshift, disc instabilities cause the majority of black hole growth in moderately luminous Seyfert galaxies at low redshift. [Menci2014] find that in their semi-analytic model disc instabilities can provide enough black hole accretion to reproduce the observed AGN luminosity functions up to redshift z is approximately equal to 4.5, but are not likely to be dominant for the highest luminosity AGN or at the highest redshifts. In contrast, [Shirakata2018] find that the primary trigger of AGN at redshift z less than or equal to 4 in their semi-analytic model is mergers, while disc instabilities are essential for fuelling moderate luminosity AGN at higher redshifts. The hydrodynamical simulation Horizon-AGN found that only ~35 per cent of black hole mass in local massive galaxies is directly attributable to merging, with the majority of black hole growth instead growing via secular processes [Martin2018]."}
{"text": "The Magneticum Pathfinder Simulation also found that merger events are not the dominant fuelling mechanism for black holes in redshift z=0--2, with merger fractions less than 20 per cent, except for very luminous quasars at redshift z is approximately equal to 2 [Steinborn2018]. Finally, we comment on the effect of the efficiency parameters for merger-driven and instability-driven black hole growth in the model. We find the instability-driven efficiency from tuning the model, whereas the merger-driven efficiency is less constrained, with several values producing reasonable model results. Having a merger growth efficiency that is twice, six times or even 18 times larger than the instability-driven growth efficiency may have an effect on the conclusions outlined above. We find, as expected, that models with larger merger efficiencies result in more merger-driven growth. For a merger efficiency twice the instability efficiency, the instability-driven mode still dominates at redshift z=2, while for a six times larger efficiency, the merger-driven mode begins to dominate at the highest black hole masses."}
{"text": "For the model with an 18 times larger merger efficiency, the merger-driven mode contributes even more black hole growth, but is still not the dominant growth mode for black holes with mass between 10^6 and 10^9 solar masses. Thus, while the efficiency parameter for merger-driven growth has some effect on the relative distributions of the instability-driven and merger-driven growth modes, the instability-driven mode is still dominant for the majority of black holes, even if the merger growth efficiency is as much as 18 times larger than the secular growth efficiency. A popular explanation for the black hole--host correlations is that major mergers drive the growth of both black holes and bulges [e.g.][Haehnelt2000, Croton2006b]. If this were the case, one would expect that black holes would only correlate with galaxy properties directly related to the merger process, such as bulge mass, and not, for example, total stellar mass."}
{"text": "[Simmons2017] consider a sample of 101 disc-dominated AGN hosts from the SDSS, which they assume must have a major merger-free history since redshift z is approximately equal to 2. They found that these galaxies lie on the typical black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation. This indicates that the substantial and ongoing black hole growth in these merger-free disc galaxies must be due to a process other than major mergers, and that major mergers cannot be the primary mechanism behind the black hole--host correlations. We plot the black hole mass--total stellar mass and black hole mass--bulge mass relation for disc-dominated and bulge-dominated galaxies at redshift z=0. Our simulated disc galaxies lie on the black hole mass--total stellar mass relation, but lie offset to the left of the black hole mass--bulge mass relation, as they have small bulges relative to their black hole mass."}
{"text": "This is consistent with the [Simmons2017] observations, and the results from the Horizon-AGN hydrodynamical simulation [Martin2018]. However, we see a less significant offset, which occurs at lower black hole masses than [Simmons2017] and [Martin2018], since the black holes in our disc-dominated galaxies are less massive in comparison. [Mutlu-Pakdil2017] also find no dependence of the black hole mass--total stellar mass relation on galaxy type in the Illustris hydrodynamical simulation. [Martin2018] suggest that major mergers therefore cannot be primarily responsible for feeding black holes, otherwise major-merger free disc galaxies should have less massive black holes than are observed and simulated. This is consistent with our finding that the instability-driven mode is the dominant growth mechanism for black holes. We use the Meraxes semi-analytic model to investigate the evolution of black holes and their relations to their host galaxies."}
{"text": "We find the following key predictions of our model: There is minimal statistically-significant evolution in the black hole--bulge and black hole--total stellar mass relations out to high redshifts (redshift z is approximately equal to 8). The black hole--total stellar mass relation has similar but slightly larger scatter than the black hole--bulge relation, with the scatter in both decreasing with increasing redshift. This indicates that the growth of galaxies, bulges and black holes are all tightly related, even at the highest redshifts. Higher mass black holes have higher black hole--total stellar mass ratios, leading to a significant selection effect in measurements of this ratio when observing only the most massive black holes. The instability-driven or secular quasar-mode growth is the dominant growth mechanism for black holes at all redshifts. The contribution from merger-driven quasar-mode growth only becomes significant at low redshift for black holes with mass greater than or approximately equal to 10^9 solar masses."}
{"text": "Disc-dominated galaxies lie on the black hole--total stellar mass relation, but lie offset from the black hole--bulge mass relation. Our simulation is limited in making predictions for the highest redshift quasars at redshift z=6--7 due to the simulation box size and resolution. In future work we will run Meraxes on larger N-body simulations in order to make predictions for these objects. We calibrate the free parameters in Meraxes to match the observed stellar mass functions at redshift z=0--8 and the [Shankar2009] and [Davis2014] black hole mass function at redshift z=0. The black hole mass functions produced by Tiamat and Tiamat-125-HR are converged at redshift z=2 for black holes with mass > 10^7.1 solar masses [see Marshall2019], with Tiamat-125-HR producing more low-mass black holes. We therefore focus on matching the observed black hole mass functions at masses > 10^7.1 solar masses."}
{"text": "While the [Shankar2009] and [Davis2014] relations are different, particularly at black hole mass ~ 10^8.5 solar masses, they are similar relative to the freedom we have in adjusting our model black hole mass function, and so when calibrating we found the most reasonable fit to both. In the model stellar mass function, we also plot the Meraxes stellar mass function produced when AGN feedback is switched off. This shows that AGN feedback has no effect on galaxies in Tiamat at redshift z greater than or equal to 2, but suppresses the growth of the most massive galaxies at lower redshifts as seen in Tiamat-125-HR. Throughout this work, we use the higher resolution Tiamat simulation at redshift z greater than or equal to 2, and Tiamat-125-HR for redshift z<2, where Tiamat is unavailable. We find that the results discussed in this paper are generally consistent between the two simulations at redshift z is approximately equal to 2."}
{"text": "However, one notable result is that the best-fitting black hole--stellar mass relations change rapidly between redshift z=2 (using Tiamat) and z=1 (using Tiamat-125-HR). To verify that this jump is not purely a result of the simulation change, we show the best-fitting relations from redshift z=6--0 using Tiamat-125-HR. The Tiamat-125-HR simulation shows similar results to those found using Tiamat at redshift z greater than or equal to 2, with a slightly milder but still relatively rapid evolution from redshift z=2 to z=1. The qualitative result of the evolution being insignificant relative to the scatter in the relation still holds. Thus, while the change in simulation slightly amplifies the rapid change in the black hole--stellar mass relations from redshift z=2 to z=1, this does not change our conclusions. We also note that where the black hole mass functions are converged, the black hole--stellar mass relations are in good agreement between the two simulations."}
{"text": "We implemented Population III (Pop. III) star formation in mini-halos within the Meraxes semi-analytic galaxy formation and reionisation model, run on top of a N-body simulation with a side length of 10 per h comoving Megaparsecs with 2048^3 particles resolving all dark matter halos down to the mini-halos (approximately 10^5 solar masses). Our modelling includes the chemical evolution of the IGM, with metals released through supernova-driven bubbles that expand according to the Sedov-Taylor model. We found that SN-driven metal bubbles are generally small, with radii typically of 150 comoving kiloparsecs at redshift z = 6. Hence, the majority of the first galaxies are likely enriched by their own star formation. However, as reionization progresses, the feedback effects from the UV background become more pronounced, leading to a halt in star formation in low-mass galaxies, after which external chemical enrichment becomes more relevant. We explore the sensitivity of the star formation rate density and stellar mass functions on the unknown values of free parameters."}
{"text": "We also discuss the observability of Pop. III dominated systems with JWST, finding that the inclusion of Pop. III galaxies can have a significant effect on the total UV luminosity function at redshift z = 12 - 16. Our results support the idea that the excess of bright galaxies detected with JWST might be explained by the presence of bright top-heavy Pop. III dominated galaxies without requiring an increased star formation efficiency. The first episodes of star formation likely occurred at redshift 30-40 inside low-mass (10^5-7 solar masses) halos with a pristine chemical composition (metal-free or extremely metal-poor). These environments were responsible for the chemical enrichment of the intergalactic medium (IGM) leading to the Pop. III/Pop II transition at redshift 15-10. However, due to the low mass and the high-redshift, the study of Pop. III star formation in mini-halos is challenging both in terms of observations and simulations [Klessen2023]."}
{"text": "Even with the launch of JWST, we do not have confirmed observations of Pop III stars and only a few potential candidates [Welch2022, Maiolino2023]. As pointed out by [Trussler2023], a direct detection of a Pop. III galaxies will be extremely challenging as, in the best-case scenario, hundreds of hours of integration time are needed in order to detect an unlensed Pop. III system with 5-sigma confidence. A complementary tool to direct observation could be the redshifted 21cm global signal whose depth might be determined by the radiation emitted from Pop. III stars and early accreting black holes during the Cosmic Dawn [among the most recent works see Mebane2018, Mirocha2018, Mebane2020, Munoz2022, GesseyJones2022, Magg2022, Ventura2023, Hegde2023]. So far, there is no detection confirmed of the 21cm redshifted line, however, a large number of facilities aiming to the observation of the 21cm global signal and power spectrum are already operating or becoming operative in this decade."}
{"text": "There are a number of Pop. III star formation simulations at different scales. Hydrodynamical simulations that follow the cooling of gas in a single pristine or very metal-poor cloud suggest that the inefficient cooling due to the lack of metals might favour an initial mass function (IMF) that is shifted to larger masses [e.g.][Bromm1999, Hirano2014, Stacy2016, Chon2021]; however, there is no general consensus (e.g. [Wollenberg2020, Jaura2022, Prole2022] predict IMF shifted to lower masses). Simulations at larger scales (>=1 cMpc) are instead used to follow the global evolution of Pop. III stars with redshift and their impact on the cosmic metal enrichment and reionization. In the last decade, many of these simulations have been performed both with hydrodynamical and semi-analytical codes. At the same time we also need to consider a volume large enough in order to have a statistically significant sample of the Universe. However, to satisfy both requirements of large volumes and high-resolution is impossible and thus all the semi-analytical and hydrodynamical simulations have to make compromise in one of the two directions."}
{"text": "In this work, we chose to use the semi-analytical model of galaxy formation Meraxes ([Mutch2016], M16 hereafter) within a simulation that allows us to resolve all the mini-halos down to a few 10^5 solar masses in a simulation of L = 10 Mpc per h. As so, in this paper we ran Meraxes on top of a N-body simulation of L = 10 Mpc. The size of this simulation is not large enough to be representative of the Universe (we will miss the most massive galaxies). However, the scales are large enough to investigate the impact of the main physical processes on the Pop. III star formation. We incorporated a number of new physical processes that are relevant to Pop. III star formation in mini-halos including: (i) molecular hydrogen cooling functions for mini-halos, (ii) baryon-dark matter streaming velocities, (iii) photo-dissociation of H2 molecules from the Lyman-Werner background and (iv) the chemical evolution of the intergalactic medium."}
{"text": "This latter effect has been implemented assuming that metals are released through supernova explosions and within a bubble that expands accordingly to the Sedov-Taylor model (the approach is very similar to the analytical calculation shown in [FL2003]). We found that these bubbles are generally small and that they roughly agree with the previous estimate by [Trenti2009], with typical radii of 150 ckpc at redshift z = 6. The implementation of both internal and external metal enrichment allows us to understand whether a galaxy will form Pop. III or Pop. II stars and thus quantify the impact of Pop. III galaxies on the total luminosity function at redshift z >= 5. We assumed that the Pop. III star formation occurs in an instantaneous burst at a random Delta t from the end of the snapshot. Considering an instantaneous rather than a continuous star formation makes some of the Pop. III dominated systems significantly brighter, hence at high-redshift the brightest systems are likely to host Pop. III stars."}
{"text": "The semi-analytical model Meraxes was first developed by [Mutch2016] (hereafter M16), [Qin2017, Qiu2019] in order to study galaxy formation and growth through the Epoch of Reionization. Despite the variety of physical processes included in Meraxes assumes that all the galaxies form in a previously chemically enriched Universe and inside atomic cooling halos. Such an approximation does not allow us to study the first episodes of star formation that mostly occurred in mini-halos when the Universe did not have any metals. The version of Meraxes presented in this work allows us to compute the physics of the first episodes of star formation from the initial molecular cooling of the gas to the external metal enrichment from the supernova feedback. As in the previous work, Meraxes is coupled to the reionization so that all the radiative backgrounds are computed in a self-consistent way from the galaxy properties. This has been done by implementing a modified version of 21cmFAST ([Mesinger2011]) that includes the local ionizing UV background from [Sobacchi2014] and the X-ray heating ([Balu2023])."}
{"text": "In this version, we also included the Lyman-Werner background. The updates to Meraxes for Pop. III necessitate high mass and spatial resolution. For this purpose, we introduce L10_N2048 (hereafter L10) from the Genesis suite of dark matter only N-body simulations. L10 is a periodic cubical simulation of side 10 per h Mpc and consists of 2048^3 dark matter particles of mass m_p = 9.935 x 10^3 per h solar masses resulting in a halo mass resolution of ~ 3.18 x 10^5 per h solar masses (based on a minimum of 32 particles per halo). The simulation, run using the SWIFT [Schaller2018] cosmological code, evolves these dark matter particles from redshift z = 99 down to z = 5. The halos were identified using the friends-of-friends phase space halo-finder VELOCIraptor [VR] and the merger trees were constructed using TREEFROG [treefrog]."}
{"text": "We note that the mass resolution achieved in this simulation allows us to resolve all the mini-halos below redshift z ~ 30 and is the highest resolution on which Meraxes has been run. The output trees of the N-body simulation used in this work are available on Zenodo at [balu2024]. The first process in order to enable star formation is the cooling of the gas. For dark matter halos with virial temperature T_vir >= 10^4 K, the main coolant is the atomic hydrogen, while in mini-halos (10^3 K <= T_vir < 10^4 K), the cooling occurs via roto-vibrational transitions of molecular hydrogen [e.g.][Tegmark1997]. For the details on how the cooling of the gas is implemented in Meraxes, we refer the reader to M16; in this section, we only highlight the main differences between the atomic and the molecular cooling. As in M16, we compute the ratio of the specific thermal energy to the cooling rate per unit volume: t_cool(r) = (1.5 * mu_bar * m_p * k * T) / (rho_hot(r) * Lambda(T, f_H2))."}
{"text": "M16 included only atomic cooling halos. Thus they set the mean molecular weight assuming a fully ionized gas and the cooling function from [Sutherland1993]. For mini-halos we instead set the mean molecular weight for a fully neutral gas and implement the molecular hydrogen cooling functions from [Galli1998]. This choice is valid as long as we assume that the cooling inside mini-halos occurs only due to H2. This may not be valid as, if a mini-halo is chemically enriched with metals by a nearby halo, metals are much more effective in the cooling of the gas [e.g.][Nebrin2023]. However, this enrichment is almost ineffective at redshift z > 10. The molecular cooling function depends on the gas density of the halo and on the molecular hydrogen fraction f_H2. For the latter we assumed a fixed value of 0.1%, which is consistent with results from [Nebrin2023] for halos of virial temperature of approximately 5x10^3 K at redshift z = 15-20."}
{"text": "As a first approximation, gas in a mini-halo can start to cool down the gas once it reaches the virial temperature of approximately 10^3 K. This requirement would correspond to a minimum virial mass of M_min,H2 = 2.5 x 10^5 * (26 / (1+z)) solar masses [Visbal2015]. However, there are a number of effects that can decrease the amount of molecular hydrogen present in the halo, reducing the cooling efficiency and ultimately increasing the minimum virial mass of a halo capable of cooling. A non-radiative process that can delay the gas cooling in very low-mass halos is the streaming velocity between baryons and dark matter ([Tseliakhovich2010]). This effect is a consequence of the different decoupling of baryons and dark matter particles from photons that results in a velocity difference between the two species. The presence of a relative motion between baryons and dark matter particles will make it harder for baryons to fall into the potential wells of dark matter halos, delaying the accretion and, hence, the cooling of the gas in mini-halos."}
{"text": "The main outcome of this physical process is to delay the very first episodes of star formation around redshift z ~ 40. Throughout this work, we implemented the effect of the streaming velocities as per other semi-analytical models based on a fitting function found by [Fialkov2012], which is calibrated to reproduce the results of the hydrodynamical simulations of [Greif2011] and [Stacy2011]: V_cool,H2 = (a^2 + (b*v_bc)^2)^0.5, where a = 3.714 km/s and b = 4.015 km/s. This equation provides the minimum circular velocity that a halo needs to have in order to have enough H2 to cool down the gas. This can be easily converted into a virial mass. In this work we fixed the streaming velocity v_bc(z) = sigma_bc(z) and we assumed this value for the entire box. Once the first mini-halos are forming stars, the effect of the streaming velocities becomes widely subdominant compared to the photo-dissociation of the Lyman-Werner background."}
{"text": "A self-consistent model of star formation in mini-halos must consider the photo-dissociation of H2 from UV photons in the Lyman-Werner (LW) band ([11.2 - 13.6] eV). LW photons destroy H2 and thus prevent mini-halos gas from cooling ([Haiman2006]). We implement this effect by changing the minimum mass for molecular cooling using the fitting from [Visbal2015]: M_crit,MC = M_cool,H2 * [1 + 22.87 * J_LW^0.47]. This critical mass only applies to minihalos which are below the atomic cooling halo mass threshold. J_LW is the LW flux that reaches the minihalo. LW photons have a mean free path of ~ 100Mpc, so each minihalo will be affected even by distant galaxies that formed at higher redshift. Thus, we modelled the LW background by integrating contributions across the cosmic history. As for all the radiative backgrounds in Meraxes, we follow an excursion-set formalism ([Furlanetto2004]) which counts the number of photons in a certain band in spheres of radius R."}
{"text": "At each of these locations, we compute the LW emissivity using the spectral energy distributions from [Barkana2005]. We assume that LW photons are absorbed only at resonant frequencies. Under these approximations, we can compute the LW emissivity smoothed over R at redshift z and location x for sources emitted at redshift z' as an integral over the star formation rate density for both Pop. III and Pop. II stars. This sum accounts for the resonances in the Lyman series. Given the large mean free path of LW photons, we must also account for distant galaxies at higher redshift z' > z with the redshifted spectrum. The sum of these two effects causes the peculiar shape of the LW spectrum. Following [Barkana2005] we account for all the Lyman resonances with n <= 23. Finally, we need to convert the emissivity into a flux following ([Qin2020])."}
{"text": "The approach described above differs from the one in 21cmFAST only for the computation of the SFRD. In [Qin2020], the SFRD is estimated from the density field and the collapsed fraction, while in this work, it is computed directly from Meraxes, which tracks the formation of each galaxy and its entire star formation history. Together with the LW background, the main radiative feedback that suppresses star formation is the UV photo-ionization. We used the same prescriptions as in M16, which consists of reducing the baryon content through a baryon fraction modifier that stops the gas infall. In difference from the LW feedback, the UV photo-ionization is relevant only during reionization (redshift z <= 10), and it also affects atomic cooling halos as massive as ~ 10^9.5 solar masses. However, given that the volume of our simulation (L = 10 cMpc) is much smaller than the mean-free path of LW photons, each halo is losing the contribution of the most distant sources, thus neglecting the self-shielding should partially counterbalance the loss of the LW background from distant galaxies."}
{"text": "Once stars start to form in the Universe, they also explode as supernovae, releasing metals. Most of these will stay inside the same galaxy, contributing to the chemical enrichment of the galaxy itself. This process is commonly known as \"genetic\" enrichment. However, some of the metals escape their parent galaxy. In this case, they will pollute the nearby IGM, and if later a galaxy forms in a region where the IGM was enriched, the new galaxy will be pre-enriched with metals. This latter mechanism is referred to as \"external\" metal enrichment [e.g.][Pallottini2014, Smith2015, Hartwig2018, Visbal2020, Yamaguchi2023]. Keeping track of the metallicity evolution of the Universe is crucial in order to put constraints on when the Pop. III/II transition occurred. We account for both processes, and we are able to follow the metallicity evolution of the IGM. Firstly, we choose a critical metallicity Z_crit = 10^-4 solar metallicity as the threshold value below which a galaxy will form Pop. III stars."}
{"text": "All new galaxies, unless externally polluted, will accrete pristine gas (without any metals) onto the hot gas reservoir. This gas, once it cools, will provide the reservoir for the star formation. Hence, a galaxy that is not externally polluted will always form Pop. III stars for the first time. At each snapshot, we compute the metallicity of the cold gas reservoir from the amount of metals released by earlier supernovae and if this is higher than Z_crit, the galaxy will form Pop. II stars, otherwise it will form Pop. III. While internal enrichment is the main mechanism that drives the Pop.III/II transition, some galaxies can be externally enriched through supernova winds originating in a nearby galaxy. Once several supernovae in a galaxy go off, they will form a \"super-bubble\" that will expand outside the galaxy escaping the binding energy of the dark matter halo."}
{"text": "We followed the expansion in time of this \"metal bubble\" using the analytic approximation in [Dijkstra2014]: the bubble radius r_bubble(t) equals (Delta E_SN / (m_p * n_gas))^0.2 * t^0.4. All quantities that appear in this equation are computed in Meraxes. Delta E_SN is the total supernova energy released at a certain snapshot. n_gas is the number density of the gas to which the bubble has expanded, and t is the time since the explosion occurred. We assume that all the supernova events will occur in the middle of the snapshot. Note that since Meraxes accounts for both contemporaneous and delayed supernova feedback, each galaxy has several bubbles associated with the same star formation episode. However, we consider only the largest of these bubbles so that each galaxy has only one associated bubble. Having calculated the bubble size, we can predict if a nearby galaxy will accrete pristine or enriched gas."}
{"text": "In order to reduce the computational cost, we avoid computing the distance between all the pairs of galaxies and instead use a grid-based approach. We build a high-resolution grid with 128^3 cells. For each cell, we compute the average metallicity Z_IGM,i as the ratio between the sum of the metals ejected by all galaxies inside the cell and the total gas in the cell. We only let the galaxies with a bubble radius r_bubble >= 3 * R_vir contribute. For each cell, we compute the volume fraction filled with metals (the metal filling factor), summing the volume of the largest bubble surrounding each galaxy within the pixel and dividing by the cell volume. At the beginning of each snapshot, we assign the probability p for external metal enrichment to each galaxy inside the cell. This probability will be given by the metal filling factor. We assign a random number m between 0 and 1 to each newly formed galaxy, and when m <= p is satisfied, we label that galaxy as externally enriched."}
{"text": "Furthermore, when a galaxy experiences a star formation episode, we enforce the probability p = 1 (in this latter case, we know that this galaxy will be inside its own metal bubble and thus cannot accrete pristine gas). With this latter condition and internal enrichment, we effectively stop Pop. III star formation inside a galaxy after the first supernova episode. The main limitation of this technique is that we are not accounting for the overlap of the bubbles and thus are overestimating the metal-filling factor and underestimating the metallicity of those galaxies that are polluted from more than one galaxy. However, given the small size of the bubbles, this is not a major factor, especially prior to reionization. The model shows the bubble growth over time from a typical radius of ~ 30 ckpc at redshift z = 20 to ~ 150 ckpc at redshift z = 5. These values are consistent with the results shown in [Trenti2009]."}
{"text": "A galaxy that already formed stars or a galaxy that formed in a region enriched with metals so that its metallicity is larger than Z_crit = 10^-4 solar metallicity will form Pop. II stars. We adopted the same prescription and parameters for Pop. II star formation as described in M16 and [Qiu2019]. The uncertainty around the properties of Pop. III stars motivated us to include Pop. III star formation in a flexible way so that it is easy and fast to investigate the impact of Pop. III stars changing a few parameters. In particular, once a galaxy reaches a mass of cold gas larger than a critical value, this galaxy will convert the cold gas into stars according to the star formation efficiency. Since we are now considering two different stellar populations, we adopted two different free parameters, both for the star formation efficiency alpha_SF,III and for the critical surface density Sigma_crit,III."}
{"text": "Recent full hydrodynamical simulations that follow the collapse of a pristine gas cloud until a Pop. III star is formed [e.g.][Hirano2014, Stacy2016, Chon2021], suggest that the Pop. III IMF is shifted to larger masses as a result of less fragmentation due to inefficient cooling. Within this work, we adopted the IMFs from [Raiter2010], while for Pop. II stars, we assumed a [Kroupa2001] IMF. For the fiducial model, we chose a Salpeter IMF with a mass between 1 and 500 solar masses. The choice of the IMF is crucial as it determines many properties of the stellar population, including what fraction of stars will explode as supernovae and, hence, the amount of energy and metals injected into the IGM. Since the focus of this work is on the first galaxies formed during the Cosmic Dawn, we do not explore parameters describing the UV ionizing and X-ray radiation (e.g. escape fraction), and we will take the same fiducial values as in the previous works."}
{"text": "The fate of a zero-metallicity star is quite uncertain. Here, we adopt a simplified picture of the final fate of a Pop. III star depends only on its initial mass ([Heger2002]). For masses below 8 solar masses, there will be no SN event. If stellar mass is in [8,40] solar masses it will explode as a core-collapse SN (CCSN) leaving a remnant, if stellar mass is in [140,260] solar masses there will be a pair-instability SN (PISN) leaving no remnant and if stellar mass is in [40,140] solar masses or stellar mass > 260 solar masses stars collapse directly into a black hole (BH) with negligible feedback. While we use the technique of [Qiu2019] for Pop. II stars with precomputed tables assuming a Kroupa IMF ([Kroupa2001]), for Pop. III supernova feedback we estimated the amount of SN energy and metal yields with an analytic calculation as in M16."}
{"text": "The total energy provided by Pop. III supernovae explosions at the snapshot j is the sum of delayed contributions from core-collapse supernovae and contemporaneous contributions from pair-instability supernovae. These are computed by integrating the chosen IMF over the correct mass limits. Assuming that all-star formation occurred in the middle of the snapshot, the mass limits for CCSN are computed from the lifetimes for Pop. III stars using [Schaerer2002] assuming no mass loss and zero metallicity. We highlight that a zero metallicity star with a mass between 140 and 260 solar masses has a lifetime smaller than the time separation between two consecutive snapshots in meraxes; hence, it will explode as a PISN in the same snapshot in which it forms. For CCSN, instead, we keep track of the star formation history over the last 17 snapshots, which correspond to >= 40 Myr, after which all stars with mass >= 8 solar masses will already be exploded."}
{"text": "We also update the amount of ejected gas and metals from Pop. III stars. These are taken from [Heger2010] assuming non-mixing and a supernova explosion of 1.2 x 10^51 erg. In all the previous Meraxes works, all the stellar mass locked up in remnants (neutron stars and BHs) was neglected as it was recycled into the gas mass budget of the galaxy. We decided to drop this approximation for Pop III stars as they are likely to leave more massive remnants. Firstly, we need to consider the BHs that formed after a \"failed SN scenario\" typical of a star with an initial mass between 40 and 140 solar masses and greater than 260 solar masses. Finally, we need to account for the BH remnants that are left after a CCSN. Meraxes, does not evolve the remnants (via accretion), as the main focus of this work is Pop. III stars. However, the impact of the first accreting BHs on the formation of the supermassive black holes might be important even at high-redshift ([Ventura2023])."}
{"text": "In order to investigate the observability of the first Pop. III galaxies we implement spectral energy distributions (SED) for Pop. III stars. We use SEDs from [Raiter2010] that have been computed for the IMFs listed in Table 2 assuming that star formation occurs in an instantaneous burst. These SEDs also include the nebular continuum emission and the UV ionizing properties. To compute the luminosity of galaxies at a specific wavelength, we used the model introduced by [Qiu2019] (see also [Mutch2023]), and we extended it to Pop. III galaxies. Having the Pop. III SEDs, we can compute the luminosity of a Pop. III galaxy at time t as an integral over its star formation history, modulated by the luminosity of a stellar population per unit mass and a dust transmission function. For the latter term, we refer the reader to [Qiu2019] while the luminosity per unit mass for each Pop. III IMF has been taken from [Raiter2010]."}
{"text": "This calculation is nearly identical to [Qiu2019], with the difference being that we do not have the metallicity dependence because Pop. III stars SEDs are defined with a zero metallicity. In this framework, we assume that the star formation occurs continuously throughout the snapshot. While this is a good approximation for Pop. II stars, Pop. III star formation is expected to occur in a single burst because of the feedback from Pop. III stars are likely to prevent continuous star formation. For this reason, we expanded the calculation of the luminosity of Pop. III galaxies assuming that new stars form instantaneously at a specific time. As we will discuss in Section 4, instantaneous (instead of continuous) Pop. III star formation has an impact on the estimated luminosity function of galaxies hosting Pop. III stars. This is because Pop. III stars have lifetimes that can be shorter than the duration of the snapshot."}
{"text": "Hence, when we consider continuous star formation, we average the star formation over the entire snapshot, leading to lower luminosity with a higher duty cycle. When we instead consider Pop. III stars to form in a single burst, if this burst will occur toward the end of the snapshot the galaxy will appear much brighter when it is observed in that snapshot. In order to account for instantaneous star formation, we assumed that a Pop. III star formation episode in a galaxy can occur at random Delta t within the snapshot duration prior to the end of the snapshot. For the detailed evaluation of the UV luminosity function accounting for the stochasticity in the time at which the burst of star formation occurs in different galaxies, we refer the reader to Appendix B."}
{"text": "To explore the Pop. III contributions to the cosmic star formation history, we ran two simulations on the L10 box, one with all the updates described in Section 2 adopting the fiducial parameters and one without the new physics that we labelled as \"NoMini\". Given that there are no observational constraints on Pop. III, the choice of a fiducial model is arbitrary. The one adopted in this work has both a low star formation efficiency and a Salpeter-like IMF, which will result in a relatively small global impact of Pop. III star formation compared to Pop. II. The stellar mass function at different redshifts accounts for all (black), only Pop. III dominated (cyan), and only Pop. II dominated (red) galaxies. We classified a galaxy as Pop. III or Pop. II dominated based on which population is brighter in the UV band. The new updates on Meraxes mostly affect the lower end of the SMF with a larger impact at high-redshift."}
{"text": "This reflects the star formation in mini-halos (we are now considering molecular cooling), which is dominant at redshift z >= 15 before the Lyman-Werner background becomes strong enough to photodissociate all the molecular hydrogen. The low-mass peak of the SMF is dominated by Pop. III systems and the more massive one by Pop. II. This bimodality of the SMF could have an impact on the faint end of the luminosity function at redshift z ~ 10. The low mass of Pop. III systems is mainly a consequence of both the shorter lifetimes of Pop. III stars (given their larger mass) and the lower SF efficiency, but also suggests that most of the Pop. III star formation must occur in mini-halos. The halo mass function for Pop. III and Pop. II star-forming halos is shown at several redshifts. The dashed line corresponds to the limit of atomic cooling (virial temperature T_vir = 10^4 K)."}
{"text": "Given the small size of the box, we have only a few atomic cooling halos at redshift z ~ 20, so all star-forming systems are mini-halos (and are mostly Pop. III). At lower redshift, the peak of the distribution shifts to higher masses and the impact of Pop. II increases. Finally, Pop. III stars mostly form in mini-halos. This is because the more massive halos are more likely to have already experienced star formation and so will be internally chemically enriched. The total star formation rate density (SFRD) as a function of redshift for both the fiducial and the NoMini model is also analyzed. In the case of the fiducial model, we also show the Pop. III (Pop. II) contribution in the upper (lower) panel. Mini-halos have an appreciable impact on the SFRD only up to redshift z >= 20, while at lower redshift, most star formation occurs in atomic cooling halos."}
{"text": "We see that accounting for Pop. III star formation in mini-halos is crucial during the Cosmic Dawn because Pop. III stars dominate the global star formation history at redshift z >= 20 and are still relevant up to redshift z = 18. The Pop. III SFRD flattens at redshift z ~ 18 and starts to decrease at redshift z ~ 10. The early flattening occurs due to the build-up of the Lyman-Werner background that affects Pop. III star formation in minihalos. The sharp drop at redshift z <= 10 is mostly caused by the photoionizing feedback from reionization that also affects the atomic cooling halos. The feedback from reionization also mildly affects Pop. II as can be seen from the flattening of the red line at redshift z ~ 8 in the upper panel. Compared to reionization, the chemical enrichment of the IGM is a much slower process due to the lower velocity of the expansion of the metal bubbles."}
{"text": "As already found in previous works [e.g.][Visbal2020, Yamaguchi2023], the impact of external metal enrichment is subdominant compared to internal metal enrichment. However, external enrichment might still be important for low-mass halos that do not form stars until redshift z ~ 10. The top left panel of Fig. 5 shows the redshift evolution of the average metallicity of the box. As expected, the average metallicity increases monotonically. It crosses the critical value at redshift z ~ 11 and at the end of the simulation is ~ 5 x 10^-3 solar metallicity. The redshift evolution of the IGM metallicity is in very good agreement with [Yamaguchi2023], especially for their \"bursty\" models, which is the one that most closely resembles the star formation in Meraxes. However, the average metallicity of the IGM does not completely inform us of the average metallicity of the galaxies since, when averaging through the entire box, we are considering voids that have no galaxies and hence zero IGM metallicity."}
{"text": "For this reason, in the top right panel, we computed the black solid line, averaging only through cells that have at least one metal bubble (meaning that there must be at least one galaxy that formed stars). The average metallicity, in this case, is much higher, and it is always above the critical value. This suggests that once the first galaxies form, the ejection of metals from Pop. III is quite effective in the nearby regions, allowing a fast Pop. III/II transition in those cells where star formation already occurred. The lower panels instead show the fraction of the IGM that reached the critical metallicity. Considering the entire box (left panel), less than 1% of the volume gets enriched above Z_crit by redshift z ~ 5. This result is fairly consistent with [Visbal2020] and [Yamaguchi2023] (~ 1% by z = 6)."}
{"text": "These small differences are likely due to differences in the star formation models and in the choice of parameters, such as the star formation efficiency. If we focus only on the regions with at least one galaxy that formed stars, we find larger filling factors, and by the end of the simulation, those pixels are all completely enriched. This final result reflects our choice of pixel size that is designed to be similar to the average volume of the metal bubble at redshift z ~ 5. The halo mass function for the externally (black line) and internally (grey line) metal enriched halos at several redshifts is also analyzed. While most halos get internally enriched by their own star formation, at redshift z = 5 halos with virial masses M_vir <= 10^7.5 solar masses get their metals mostly from a nearby supernova bubble. This picture reflects the fact that low-mass halos during reionization are not able to form stars because of the LW and photo-ionizing feedback."}
{"text": "Hence, those objects can be chemically enriched only from an external source. In conclusion, when looking at the global evolution of star formation, the effect of the external metal enrichment is quite negligible as it is important only for low-mass halos at low redshift that will hardly form stars due to the radiative feedback effects. We verified this by running a simulation without external metal enrichment. There are no appreciable differences between the two models except at redshift z <= 8 when the dashed line is slightly larger (about 0.1 dex difference). The results in previous sections were obtained adopting quite conservative assumptions for Pop. III stars given the very low SF efficiency and the Salpeter-like IMF. In the following sections, we explore the four main free parameters that regulate Pop. III star formation in Meraxes listed in Table 1: the Pop. III star formation efficient, the critical metallicity for Pop.III/II transition, the critical surface density of cold gas for Pop. III star formation to occur and the IMF."}
{"text": "The star formation efficiency determines the conversion of the cold gas into stars and is the free parameter with the largest impact on the Pop. III global SFRD and SMF. This parameter is largely unconstrained, with some simulations supporting very low values (10^-4 - 10^-3, [Skinner2020]) and others suggesting higher values ([Fukushima2020]). We ran two simulations keeping all the Pop. III free parameters unchanged except for the star formation efficiency, which we boosted by one order of magnitude and to a very high value. Pop. III galaxies become more massive as the star formation efficiency increases, erasing the \"double peak\" feature in the total SMF. For the model with equal Pop. II and Pop. III efficiency, the peak of the Pop. III SMF is still shifted to the left by half dex compared to the Pop. II. This is because, despite having the same star formation efficiency, Pop. III galaxies mostly form in mini-halos."}
{"text": "The star formation efficiency also regulates the Pop. III/II transition as it directly correlates with the SFRD. For a high efficiency, the SFRD is dominated by Pop. III up to redshift z ~ 15 compared to the fiducial model where Pop. II SF becomes larger than Pop. III at redshift z > 20. The Pop. II SFRD does not significantly change between the three models, and so the change in the Pop. III SFRD also affects the total SFRD. All the models converge at redshift z ~ 13 when even with the highest efficiency the total SFRD is entirely dominated by the Pop. II contributions. The critical metallicity defines the metallicity at which there is a change in the IMF. There is currently no consensus on the value of Z_crit, with two competing models that assume the fragmentation driven by either the carbon and oxygen line or the dust cooling. The first class of models determine a Z_crit ~ 10^-2 - 10^-3 solar metallicity while the seconds give a lower value (~ 10^-6 solar metallicity)."}
{"text": "Some studies also argue that the value of Z_crit evolves with redshift due to the effect of the CMB ([Chon2022]). Following simulations in the literature ([Schneider2006, Visbal2020]), in this work we adopted an intermediate value Z_crit = 10^-4 solar metallicity as the fiducial value, hereafter we will also show results for the two extreme values of 10^-2 and 10^-6 solar metallicity. The SMF between the fiducial model and Z_crit = 10^-6 solar metallicity does not change. This is because, in the overdense regions where there is star formation, the metallicity becomes larger than 10^-4 solar metallicity very quickly so that changing Z_crit to 10^-6 solar metallicity does not further accelerate the Pop. III/II transition. However, considering a higher value changes the total SMF as we end up with many more Pop. III stars. The high-mass tail of Pop. III SMF extends up to 10^7.5 solar masses at redshift z = 5 when Z_crit = 10^-2 solar metallicity."}
{"text": "The combined effect of Pop. III and Pop. II makes the total SMF computed from the simulation with Z_crit = 10^-2 solar metallicity single peaked as the high-mass peak coming from Pop. II stars are washed out even at redshift z = 5 so that the total SMF peaks at stellar mass ~ 10^4 solar masses at redshift z = 10 - 5 with a high-mass tail that extends up to 10^9 solar masses. The critical metallicity also has a strong impact on the evolution of the SFRD as it affects both the internal and external enrichment. While decreasing the value of Z_crit from the fiducial value only mildly decreases the Pop. III SFRD without altering the total result, choosing Z_crit = 10^-2 solar metallicity strongly changes the SFRD history at redshift z <= 18. The Pop. III SFRD increases by 1-2 orders of magnitude while the Pop. II decreases by the same amount."}
{"text": "Increasing the Pop. III star formation and simultaneously decreasing the Pop. II impacts on the total SFRD. Since Pop. III stars form less efficiently we predict a lower total SFRD compared to the fiducial model. Overall the critical metallicity heavily impacts both the SFRD and SMF during the Cosmic Dawn and the Epoch of Reionization and affects when the universe transitions from being Pop. III dominated Pop. II. In order to trigger the star formation in a galaxy, our model requires the gas density in the disk to be above a certain threshold. We decided to duplicate this free parameter so that we have one for Pop. III and one for Pop. II. While keeping the Pop. II parameter fixed, we explore the extreme case of a Pop. III critical surface density of 0, which is equivalent to assuming that Pop. III stars start to form as soon as the cooling of the gas begins."}
{"text": "This choice results in a larger abundance of low-mass Pop. III systems at high-redshift. However, since the main changes in the Pop. III SF are in low-mass halos, setting the critical surface density to 0 does not significantly change the SFRD history. Overall, this free parameter is the one with the smallest impact on the star formation history, as it only impacts the low-end of the stellar mass function at high-redshift for which there are no observational constraints. The last parameter we explore is the IMF of Pop. III stars. Our fiducial model is quite similar to the Pop. II IMF as we assume a Salpeter IMF that favours the formation of low-mass stars. We consider two log-normal IMFs labelled logA and logE as in [Tumlinson2006]. For these IMFs we have spectral energy distributions (from [Raiter2010]) which will be used in Section 4."}
{"text": "The IMF logA is centred at M = 10 solar masses, which enhances the probability of a Pop. III stars ending its life as a core-collapse SN. logE is centred at even a higher mass (M = 60 solar masses), so we expect most of the stars with very short lifetimes to end their lives by collapsing into a black hole without any supernova explosion. Compared to the Salpeter IMF, both log-normal IMFs do not have many low mass stars (mass < 8 solar masses). Decreasing the lifetime of Pop. III stars make the Pop. III SMF shift to lower masses, increasing the separation between the two peaks of the total SMF. The difference between the fiducial model and one adopting the logA IMF is less than one dex. However, in the logE IMF model, most of the stars die in the same snapshot in which they form. This effect strongly prevents the build-up of Pop. III systems."}
{"text": "There are no significant differences in the SFRD from adopting different IMFs, except for the first few snapshots of our simulation where the star formation is mildly reduced in the logE model. This result comes from the stronger feedback typical of the more top-heavy IMF (a larger number of massive stars implies more supernovae), and it has a stronger impact at redshift z >= 24 when Pop. III star formation is dominating. Unconstrained Pop. III free parameters in our model have an impact on the redshift evolution of the SMF and SFRD. However, our model predicts a consistent number density of Pop. III dominated systems with stellar masses between 10^3 - 10^5 solar masses. Here we will explore the UV luminosity of these systems using the model described in Section 2.6 focusing on the luminosity functions at very high-redshift."}
{"text": "Given the same total stellar mass, Pop. III systems have larger luminosities compared to Pop. II galaxies, but shine for shorter times. We show the evolution in the first 10Myr of the SED of a Pop. III galaxy that forms 10^5 solar masses of Pop. III stars at redshift z = 8 and the absolute UV magnitude at different times since the star formation burst. Left, mid and right panels assume a Pop. III Salpeter, logA and logE IMF respectively. The black horizontal line corresponds to the magnitude computed assuming a continuous star formation throughout the snapshot. For reference, we also show the magnitude of a Pop. II galaxy forming the same amount of Pop. II stars (red dashed line). Firstly, we notice that Pop. III galaxies with continuous star formation and a log-normal IMF are one magnitude brighter than Pop. II galaxies with the same SFR (while there is no significant difference if Pop. III stars follow a Salpeter IMF)."}
{"text": "Once we focus on the instantaneous star formation model for Pop. III stars, the brightness of the galaxy can be boosted (or reduced) by several magnitudes depending on the time since the burst at which we are observing the system [see also Trussler2023]. Even when we consider a Salpeter IMF, the brightness of a Pop. III galaxy changes ~ 2 mags in ~ 10Myr. This change is more dramatic for the log-normal IMFs (especially for the logE IMF where in 10 Myr the change in absolute magnitude is approximately 7 mags). The large difference between the instantaneous and continuous star formation models for a single Pop. III galaxy will reflect in the entire population and potentially lead to a higher number density of extremely bright Pop. III galaxies. As a result of instantaneous Pop. III star formation, there are chances to observe these galaxies at a time when their luminosities are higher than what is given by the continuous scenario."}
{"text": "When looking at the total luminosity function we see a much significant Pop. III contribution to the number density of galaxies around an absolute magnitude of approximately -16 when assuming a LogE IMF for their star formation. Given their larger brightness, a population of Pop. III galaxies with a top-heavy IMF has been suggested as a possible explanation for the abundance of bright galaxies at redshift z > 10 [see, e.g. Trinca2023, Yung2023, Harikane2023]. Without invoking any exotic physics or a revision of the standard LambdaCDM model of cosmology, other possible explanations are a combination of increased star formation efficiencies at high-redshift and reduced feedback [Qin2023], bursty star formation [Sun2023], cosmic variance [Shen2023] and a modified LambdaCDM power spectrum [Parashari2023, Padmanabhan2023]."}
{"text": "Here, we show the predicted UV luminosity functions at several redshifts. Results for different IMFs and different star formation efficiencies are summarized, where all the other Pop. III parameters are taken as in the fiducial model. For all the models considered below, our total luminosity function agrees with early JWST observations at redshift z <= 12 (except for the points at an absolute magnitude < -19 where we do not have galaxies in Meraxes). With our fiducial parameters (dashed lines), both with the Salpeter and with the logA IMF, we find that Pop. III systems are not the brightest galaxies at the redshift considered (absolute magnitude >= -14). However, when we consider a log-normal IMF with a characteristic mass of 60 solar masses (lower row), Pop. III galaxies become significantly brighter and at redshift z = 12 and 16 when some of the brightest systems (absolute magnitude ~ -16) are Pop. III dominated."}
{"text": "This result may indicate that Pop. III dominated galaxies are present at redshift z > 12. This result becomes more robust when considering a Pop. III star formation efficiency equal to the Pop. II efficiency. The bright end of the total and Pop. III dominated galaxy UVLF shifts of 1-2 magnitudes (depending on the IMF) at redshift z = 16 and 12. At redshift z <= 11, there is no or little difference in the total UVLF with different star formation efficiency even though Pop. III dominated galaxies are still ~ 1 mag brighter. Models with a Salpeter or a log-normal IMF centered at 10 solar masses predict that the bright end of the UVLF at redshift z = 16 is impacted by Pop. III dominated systems while at redshift z <= 12 none or very few of the brightest galaxies are Pop. III dominated."}
{"text": "Overall, the abundance of bright galaxies at redshift z >= 12 is better explained by the model with the logE Pop. III IMF and a star formation efficiency equal to the Pop. II efficiency. For this model at redshift z >= 12 we find Pop. III dominated galaxies with an absolute magnitude of approximately -18 and at redshift z = 16 all the brightest galaxies (absolute magnitude <= -16) are Pop. III dominated. We compared our results with [Trinca2023], and found a good agreement at redshift z <= 12 and absolute magnitude less than or approximately equal to -16.5 for all the models considered. The main differences are that at redshift z = 9, we do not have any galaxy with an absolute magnitude of approximately -20, and their model has a steeper evolution predicting many more faint galaxies. At redshift z = 16 only models with a high Pop. III star formation efficiency and a log-normal IMF reproduce their results."}
{"text": "Even though the total UVLF are similar, their Pop. III contribution is significantly lower, especially when compared to the models with high Pop. III star formation efficiency. The main differences in the model that can explain the different results are (i) the homogeneous feedback and (ii) the Pop. III luminosity calculation. In their model, both the radiative feedback and the chemical enrichment are homogeneous; this might overestimate the suppression of Pop. III systems at redshift z ~ 10-20. Regarding the second point, our model accounts for the fact that a Pop. III galaxies might be observed immediately after they formed stars. Without accounting for this effect, our Pop. III galaxies would have similar luminosity to those predicted by [Trinca2023]. The main limitation of our results is that, given the small size of the simulation, we intrinsically miss the brightest galaxies. Larger simulation volumes will allow us to be conclusive, but this result suggests that if Pop. III stars are still forming at redshift z >= 10-12, and they have a top-heavy IMF, they do not require increased star formation efficiencies to outshine the Pop. II systems."}
{"text": "As Pop. III dominated galaxies become much more rare at redshift z <~ 10, this scenario allows us to increase the abundance of bright galaxies only at redshift z > 10 without boosting the bright end of the UV luminosity function at lower redshift hence we achieve a good agreement with early JWST observations from [Donnan2023, Harikane2023] and [Perez2023]. In this paper, we studied Pop. III star formation in mini-halos with an updated version of the Meraxes semi-analytic model of galaxy formation that includes Lyman-Werner background and the streaming velocities. We also implemented external metal enrichment following the growth of the supernova bubbles according to the Sedov-Taylor model. We computed the bubble size distribution function and found that our results agree with [Trenti2009] (most bubbles are smaller than 150 per h ckpc at z = 6 and have a typical size of 100-200 ckpc at z = 5) hence most halos get self-enriched rather than externally polluted."}
{"text": "Only low-mass halos (virial mass <= 10^7.5 solar masses) at redshift z < 10 are more likely to get their metals from the IGM. This is a consequence of the small size of the supernova bubbles that results in a small filling factor (0.1% at z = 12 and less than 1% at z = 5). The free parameters allow us to explore the global properties of Pop. III dominated galaxies. We ran this model on top of a dark matter-only N-body simulation able to resolve all the mini-halos down to ~ 3 x 10^5 solar masses at redshift z <= 30. We explored the impact on the SMF and SFRD of the main free parameters of our model. All models converge at redshift z <~ 10. However, Pop. III star formation efficiency and IMF lead to differences at high-redshift."}
{"text": "Finally, we investigated the SED evolution of a Pop. III dominated galaxy for different IMFs. The shorter lifetime of a Pop. III galaxy motivated us to use an instantaneous star formation model when computing the luminosity function. We computed the total and the Pop. III galaxy UV luminosity functions and compared these to the early JWST results in order to study whether the excess of bright galaxies at high-redshift could be explained by a population of Pop. III dominated galaxies. Having explored different IMFs and star formation efficiencies, our model predicts, for a log-normal IMF with a characteristic mass of 60 solar masses and a Pop. III star formation efficiency comparable to the Pop. II, most of the brightest galaxies at redshift z >= 12 and all at redshift z = 16 (absolute magnitude = - 18) are Pop. III dominated. Adopting a smaller characteristic mass or a Salpeter IMF, Pop. III dominated systems still have an impact on the bright end of the UVLF, but only at redshift z = 16."}
{"text": "In conclusion, this work supports the scenario for which top-heavy Pop. III dominated galaxies might explain the abundance of bright JWST galaxies at redshift z >= 12 without requiring very high star formation efficiencies or extremely weak feedback at high-redshift. In this appendix, we discuss the extent to which our approximation on the external metal enrichment based on the filling factor is appropriate and when it fails. Since we are avoiding computing all the pairs of distance, there might be some galaxies for which we are not getting a correct enrichment. For this reason, we computed in post-processing the distance between all the pairs of galaxies throughout the entire simulation and we counted how many galaxies in Meraxes are marked as externally metal enriched (pristine) even if they are outside (inside) a metal bubble. We repeated this computation for several grid resolutions: N = 16, 32, 64, 128 and 256."}
{"text": "Hereafter, we will call \"false pristine galaxies\" those galaxies that lie inside a metal bubble (and so should be enriched) but in Meraxes are labelled as pristine and \"false enriched galaxies\" those galaxies that are not reached by any bubble but in Meraxes are labelled as enriched. At lower resolution, the percentage of the false pristine galaxies increases from 4% at N = 128 to 7% at N = 16. This happens since, as the pixel becomes bigger, the assumption of the galaxies randomly distributed inside each pixel is no longer valid as the clustering becomes much more important. However, when we use a very fine grid (N = 256), the mass fraction of false enriched galaxies dramatically increases at redshift z <= 10. This happens because by redshift z = 10, the typical bubble size becomes larger than the pixel volume, and so we lose all the contribution that overflows outside the pixel."}
{"text": "The mass percentage of false enriched galaxies instead is only mildly affected by different resolutions (always below 2%). We then compute the absolute value of the difference between the mass percentage of the false pristine and the false enriched galaxies. This quantity tells us if, statistically, we are reproducing the correct global enrichment of the Universe. We can see that having a high-resolution grid significantly improves the quality of our results. For N = 128, this difference is always below 2%, and at redshift z < 12 is approximately 0%. This tells us that for a high-resolution grid, globally, we are getting the correct enrichment of the Universe as the mass percentage of false pristine and false enriched galaxies cancels out. This agreement is almost perfect during the EoR, while during the Cosmic Dawn we are underestimating the metal enrichment of ~ 1-2%."}
{"text": "Finally, we are also showing the sum between the false enriched and pristine galaxies. This quantity instead tells us what is the mass percentage of galaxies for which we are getting a wrong estimation of the enrichment. Increasing the resolution improves our result, which, for N = 128, peaks at ~ 4% during the Cosmic Dawn. In conclusion, our model for N = 128, while reducing the computational cost, still gives an excellent agreement on global enrichment and a very good agreement on the enrichment of single galaxies. We also assumed that the probability p of each galaxy to be enriched is equal to the metal filling factor multiplied by the two-point correlation function. In this case we get the best results using N = 16. The mass percentage of false pristine and false enriched both peak at 4-5% with the percentage of false pristine galaxies decreasing at higher resolution and the percentage of false enriched galaxies increasing at higher resolution."}
{"text": "Accounting for the clustering and using a low-resolution grid still allows us to get an excellent agreement on the statistical properties but, compared to the model adopted in this work, it doubles the mass percentage of the galaxies for which we are getting a wrong prediction. This final check further confirms that the model for the external metal enrichment that we are adopting in this work, is the best one. In this appendix, we discuss how to evaluate the UV luminosity function of Pop. III galaxies assuming instantaneous star formation. Due to the stochasticity involved in the process of star formation, the burst might occur at any time within a snapshot for a galaxy, resulting in different luminosities when observed. We refer to Delta t as the time delay of the star formation burst happening relative to the end of our snapshot, and draw its value from a random uniform distribution between zero and the snapshot duration."}
{"text": "One can then evaluate the luminosity of this galaxy, repeat the exercise for all targets after assigning them different Delta t, and calculate their probability distribution as a function of UV magnitude (i.e. the UV luminosity function). To achieve a more efficient computation, we instead sample Delta t in fine steps. Then we calculate the UV magnitudes of each galaxy for given Delta t_i and evaluate the corresponding luminosity function at the condition of fixed Delta t. Finally, the luminosity function is obtained by summing all conditional probability distributions as the sum over all conditional luminosity functions multiplied by the probability of each time delay. Note that the probability of each conditional luminosity function is simply calculated based on the size of the time step relative to the total snapshot duration."}
{"text": "Reionization morphology and intrinsic velocity offsets allow transmission of Lyman-α emission from JADES-GS-z13-1-LA. We investigate the detectability of Lyman-α (Lyα) emission from galaxies at the onset of cosmic reionization, aiming to understand the conditions necessary for detecting high-redshift sources like JADES-GS-z13-1-LA at a redshift of 13. By integrating galaxy formation models with detailed intergalactic medium (IGM) reionization simulations, we construct high-redshift galaxy catalogs to model intrinsic Lyα profiles and assess their transmission through the IGM. For a galaxy with a UV magnitude of about -18.5 like JADES-GS-z13-1-LA, our fiducial model predicts a Lyα transmission of approximately 13% and there is a probability of observing Lyα emission with an equivalent width greater than 40 Angstroms of up to 10%. We also explore how variations in the UV ionizing escape fraction, dependent on host halo mass, impact Lyα detectability. Our findings reveal that reionization morphology significantly influences detection chances -- models where reionization is driven by low-mass galaxies can boost the detection probability to as much as 12%, while those driven by massive galaxies tend to reduce ionized regions around faint emitters, limiting their detectability."}
{"text": "This study underscores the importance of reionization morphology in interpreting high-redshift Lyα observations. Lyman-α (Lyα) emission is expected to be heavily suppressed by neutral hydrogen in the intergalactic medium (IGM) [miraldaescide1998apj...501...15m]. As a result, detecting Lyα emitters (LAEs) in the early Universe is unanticipated and suggests enhanced production of ionizing and/or Lyman-α photons in the first galaxies [Stark2015MNRAS.454.1393S, Witten2024NatAs...8..384W]. The recently reported, stunning Lyα detection from JADES-GS-z13-1-LA [Witstok2024arXiv240816608W] with an equivalent width (EW) of 43 +15/-11 Angstroms from a redshift of 13, is therefore interpreted as measuring the onset of reionization. Possible mechanisms to increase the intrinsic Lyα emission include a young, metal-poor stellar population [miraldaescide1998apj...501...15m, Schaerer2003A&A...397..527S] and the presence of an active galactic nucleus (AGN) [ouchi2018pasj...70s..13o, Sobral2018MNRAS.477.2817S]. However, clustered environments can also boost observability when a large ionized region is hollowed out by a cluster of galaxies [qin2022mnras.510.3858q, leonova2022mnras.515.5790l]."}
{"text": "Furthermore, outflows within the interstellar medium can shift the intrinsic Lyα line redwards, allowing the emission to penetrate deeper into the damping wing and significantly reducing its cross section before hitting the neutral IGM [Dijkstra2011MNRAS.414.2139D]. Recent advancements with JWST have substantially expanded the sample of high-redshift LAEs (see e.g., [Witstok2024A&A...682A..40W], [Tang2024arXiv240801507T, jones2024jadesmeasuringreionizationproperties] and references therein). With improved statistics to refine the modelling of Lyα profiles [mason2018apj...856....2m], this work aims to quantify the detectability of Lyα emission from a redshift of 13. By integrating IGM reionization simulations with semi-analytic galaxy-formation models, we use galaxies with realistic UV properties to infer their Lyα line profiles and to self-consistently compute the morphology of neutral hydrogen during the Epoch of Reionization (EoR). Our findings suggest up to a 10% chance of observing a Lyα equivalent width greater than 40 Angstroms in a galaxy with a UV magnitude of about -18.5 like JADES-GS-z13-1-LA [Witstok2024arXiv240816608W], increasing to 12% when varying reionization morphologies are further considered."}
{"text": "After briefly summarizing our model in the next section, we present the results in Section 3 and conclude in Section 4. In this work, we apply the cosmological parameters from Planck 2018 (Omega_m = 0.312, Omega_b = 0.0490, Omega_Lambda = 0.688, h = 0.675, sigma_8 = 0.815, n_s = 0.968; [Planck2020A&A...641A...6P]). We model galaxy formation and reionization using the Meraxes semi-analytic model [Mutch2016MNRAS.463.3556M, Qin2017a, Balu2023MNRAS.520.3368B], applied to dark matter halo merger trees that resolve all atomic-cooling halos at redshift less than or equal to 20 within a cosmological volume of 210 h-inverse cMpc per side. The model implements various astrophysical processes to generate a statistically representative sample of high-redshift galaxies, including accretion and cooling of the gaseous reservoir, evolution and feedback of the stellar component and AGN, merger and suppression of the satellite companions, and photoheating during the EoR. The UV and X-ray emissivities are channeled to 21cmFAST [Mesinger2011MNRAS.411..955M, Murray2020JOSS....5.2582M] to assess the ionization and thermal status of the IGM."}
{"text": "Slides of overdensity and neutral hydrogen fraction at a redshift of 13 (projected over a depth of 7cMpc, larger than most ionized bubbles) for three models with different contributions of galaxies to the ionizing budget based on their host halo masses. The upper right zoom-in insets show galaxies brighter than a UV magnitude of -17 mag as star symbols, with their size representing galaxy brightness. The lower right inset displays the globally averaged reionization histories for these three models (indicating CMB optical depth and reionization timing) along with 70 additional models with varying ionizing escape fractions. These models are broadly consistent with observational results that are based on dark pixel measurements (black; [McGreer2015MNRAS.447..499M, Jin2023ApJ...942...59J]), damping-wing absorption in quasar spectra (orange; [Banados2018Natur.553..473B, Greig2017, Greig2019, Greig2022, Davies2018, Wang2020ApJ...896...23W, Zhu2024MNRAS.533L..49Z]), equivalent width measurements (green; [Mason2019MNRAS.485.3947M, Jung2020ApJ...904..144J, Whitler2020MNRAS.495.3602W, Bolan2022MNRAS.517.3263B]), luminosity functions or clustering of Lyα emitters (purple; [Inoue2018PASJ...70...55I, Morales2021ApJ...919..120M, ouchi2018pasj...70s..13o, wold2022apj...927...36w]), and CMB polarization ([Planck2020A&A...641A...6P, qin2020mnras.499..550q])."}
{"text": "Summary of models used in this work. M_10 denotes the base-10 logarithm of (M_vir / 10^10 Solar masses). Our fiducial model [Qin2023MNRAS.526.1324Q] is calibrated to reproduce well-established galaxy UV luminosity functions measured by HST (e.g. [Finkelstein2015ApJ...810...71F, Oesch2016ApJ...819..129O, Atek2018MNRAS.479.5184A, Ishigaki2018ApJ...854...73I, Bhatawdekar2019MNRAS.486.3805B, Bouwens2021AJ....162...47B, Bouwens2023MNRAS.523.1036B]) and has shown consistency with recent JWST result up to at least redshift of about 13 (e.g. [Donnan2023MNRAS.518.6011D, finkelstein2022ApJ...940L..55F, Harikane2023ApJS..265....5H, Naidu2022ApJ...940L..14N, PG2023arXiv230202429P, Willott2024ApJ...966...74W]). Assuming a UV ionizing photon escape fraction (f_esc) of 15%, the resulting reionization history aligns with measurements at redshifts between 5 and about 10 (e.g. [McGreer2015MNRAS.447..499M, Banados2018Natur.553..473B, ouchi2018pasj...70s..13o, Wang2020ApJ...896...23W, Jung2020ApJ...904..144J, Whitler2020MNRAS.495.3602W, Morales2021ApJ...919..120M, Greig2022, wold2022apj...927...36w, Jin2023ApJ...942...59J, Zhu2024MNRAS.533L..49Z]). For detailed information on our model and its calibration, we direct interested readers to the referenced publications."}
{"text": "To explore different reionization morphologies at a redshift of 13, we parameterize the escape fraction (f_esc) as a function of the host halo mass (M_vir), following the approach of [Park2019MNRAS.484..933P] with the formula: f_esc = min[1, f_esc,10 * (M_vir / 10^10 Solar masses)^alpha_esc], where f_esc,10 and alpha_esc represent the normalization and scaling index, respectively, and are considered as free parameters in this study. The escape fraction is also capped at 100% in all models. It is important to note that f_esc remains highly uncertain, both in observations available at low redshift (e.g., [Steidel2018ApJ...869..123S, Naidu2018MNRAS.478..791N, Fletcher2019ApJ...878...87F, Izotov2021MNRAS.503.1734I, Pahl2021arXiv210402081P]) and in detailed reionization simulations (e.g., [ma2020mnras.498.2001m, Kostyuk2023MNRAS.521.3077K, Choustikov2024MNRAS.529.3751C]), with some simulations suggesting increased f_esc in less massive galaxies [Paardekooper2015MNRAS.451.2544P, Xu2016ApJ...833...84X, Kostyuk2023MNRAS.521.3077K]. This aligns with expectations that it is easier for supernovae to evacuate low column density channels from shallower gravitational potentials, which allows ionizing photons to escape."}
{"text": "Within a Bayesian framework, our systematic exploration of escape fraction variations with halo mass also indicates that current constraints favor larger f_esc in lower-mass galaxies (i.e. a negative value of alpha_esc; [mutch2024mnras.527.7924m]). We conduct 234 simulations by varying the two ionizing free parameters within the range of f_esc,10 in (0, 0.45] and alpha_esc in [-1.5,1.0]. For this work, we only consider 73 of these simulations, which meet the criteria of having a cosmic microwave background (CMB) optical depth consistent with Planck measurements (i.e. tau_e between 0.05 and 0.065; [Planck2020A&A...641A...6P, qin2020mnras.499..550q]) and reaching a globally averaged neutral fraction of 1% after z_re=6.8 (broadly consistent with various observations, e.g., [Banados2018Natur.553..473B, Whitler2020MNRAS.495.3602W, Morales2021ApJ...919..120M, Jin2023ApJ...942...59J]; see their reionization histories in the lower-right panel of Fig. 1). Although these simulations exhibit similar reionization histories, they show significant variations in the spatial distribution of neutral hydrogen. We use these simulations to investigate how reionization morphology affects the detectability of Lyα emission in the highly neutral universe at a redshift of 13."}
{"text": "Fig. 1 highlights three example models: (i) Fiducial with f_esc=0.15; (ii) Democratic with f_esc,10=0.05 and alpha_esc=-0.4; and (iii) Oligarchic with f_esc,10=0.45 and alpha_esc=0.9, are summarized in Table 1. There are notable differences in reionization morphology between these models. Compared to the Fiducial model, Democratic allows less-massive galaxies to emit more ionizing photons into the IGM and, due to the higher abundance of low-mass galaxies at high redshifts, Democratic features a greater number of small-sized ionized bubbles at a redshift of 13. Additionally, overdense regions can expand their surrounding HII regions with the aid of clustered low-mass galaxies. This model aligns most closely with the escape fraction constraints from [mutch2024mnras.527.7924m]. In contrast, the Oligarchic model, which relies on galaxies with well-established stellar mass to ionize the IGM, shows delayed reionization due to the scarcity of these massive contributors in the early stages of the EoR. Furthermore, the brightness of the first galaxies is sensitive to the ionization history and can be significantly influenced by local photoheating feedback."}
{"text": "The globally averaged neutral fraction also evolves differently between these models: Democratic shows a more extended and slowly evolving neutral fraction, while Oligarchic exhibits a narrower and more rapid evolution compared to the Fiducial model. Despite these variations, the globally averaged neutral fraction (x_HI) at a redshift of 13 remains similar across models (all above 97%), with a CMB optical depth around tau_e = 0.06 and reionization concluding around z_re = 6. We model the Lyα profile (F_alpha) before damping-wing absorption as a truncated normal distribution with respect to velocity (v): F_alpha follows a normal distribution with a mean of v_alpha and variance related to v_alpha squared, for velocity (v) greater than the circular velocity of the host halo (v_circ), and 0 otherwise (see Fig. 1 in [mason2018apj...856....2m] for examples). Here, the full width at half maximum of the profile is assumed to be v_alpha, and emission blueward of the circular velocity of the host halo (v_circ) is considered completely absorbed by residual neutral hydrogen within ionized bubbles."}
{"text": "To model the Lyα damping-wing transmission, we follow [mason2018apj...856....2m] and sample the intrinsic Lyα line offset (v_alpha) and equivalent width (EW) with slight modifications to their originally proposed distributions. [mason2018apj...856....2m] created an empirical model for the v_alpha–M_UV relation by first converting UV magnitude to halo mass using the following relation [mason2015]: the base-10 log of (M_vir/10^10 Solar masses) = gamma * (M_UV - M_UV,c) +1.75, where M_UV,c = -20 - 0.26z and gamma = -0.7 for galaxies brighter than M_UV,c and -0.3 for fainter galaxies. [mason2018apj...856....2m] then used measurements of LAEs, primarily from post-reionization (redshift of about 2–3, based on Keck; e.g., [Erb2014ApJ...795...33E]), to fit Lyα line offset using a log-normal distribution with a variable mean that depends on the host halo mass yielding a distribution where the parameters (m, c, sigma) = (0.32, 1.78, 0.24)."}
{"text": "The top panel of Fig. 2 shows this low-redshift sample in grey and plots their fitted mean v_alpha against UV magnitude, indicated the long dash-dotted curve. The top panel of Fig. 2 also presents the resulting predicted mean v_alpha-M_UV relation at redshifts of about 7 and 13, along with the latest LAE measurements from JWST (see [Witstok2024A&A...682A..40W, Tang2024arXiv240801507T] and references therein), including the new redshift of 13 detection by [Witstok2024arXiv240816608W]. In their analysis [mason2018apj...856....2m] noted negligible differences in the v_alpha-M_vir distribution between the low-redshift sample and the observations at redshift greater than 6 that were available at the time (e.g., [Stark2017MNRAS.464..469S]), and therefore modelled a mean v_alpha–M_vir relation that does not evolve with redshift. However, newer data indicates that the redshift-independent v_alpha–M_vir relation requires revision to better fit the current LAE sample at higher redshifts. Indeed, if the relation between v_alpha and halo mass were driven by the depth of the gravitational potential well we would expect an offset at fixed halo mass that increased towards higher redshift."}
{"text": "Therefore, we propose increasing the intercept by 0.3 (to a value of c=2.08), and show the new fit for a redshift of about 13 in the top panel of Fig. 2 for comparison. In addition to the original fit proposed by [mason2018apj...856....2m] and this new fit with a larger c, we also explore a larger variance of sigma = 0.34, which corresponds to the standard deviation of the high-redshift sample shown in the panel. Although this choice is somewhat arbitrary, it aims to account for the increased scatter observed in the new high-redshift data. We refer to these three models as M18, Fiducial, and LargeScatter and summarize them in Table 1. As shown in the bottom panel of Fig. 2, much more observational data for the EW of high-redshift LAEs has become available since the study by [deboer2017pasp..129d5001d], whose sample was used by [mason2018apj...856....2m] to fit an exponential distribution (see also [Oyarzun2017ApJ...843..133O]) for redshift of about 6 LAEs."}
{"text": "The fit for the exponential distribution used parameters (EW_c, j, k, M_UV,c) = (31, 12, 4, -20.25). This fit was motivated by splitting the LAE sample into brighter than a UV magnitude of -21 mag, fainter than -20 mag, and in-between, as well as by providing a smooth transition between M_UV = -21 and -20 mag. Since this work focuses on much fainter luminosities, we adopt a new fit with (EW_c, j, k, M_UV,c) = (100, 80, 1, -19) for the Fiducial and LargeScatter models. As illustrated in the panel, our new fit agrees better with LAEs of higher redshifts and fainter luminosities while remaining comparable to [mason2018apj...856....2m] at the bright end. Lyα velocity offset (v_alpha) and equivalent width (EW) as a function of UV magnitude. Observational data are categorized by redshift ranges: redshift of 2 to 3 (from [mason2018apj...856....2m] and references therein), redshift of 6 to 11 (from [Witstok2024A&A...682A..40W], [Tang2024arXiv240801507T] and references therein), and redshift of 13 ([Witstok2024arXiv240816608W])."}
{"text": "At a redshift of 13 the open and filled stars respectively represent the observed and predicted intrinsic values following spectral fitting including Lyα and IGM and DLA transmission ([Witstok2024arXiv240816608W]). In the top panel, the curves represent the mean velocity offset v_alpha of the original log-normal distribution fitted by [mason2018apj...856....2m] for LAEs at redshifts of about 2, 7, and 13, along with our newly proposed fit. The dark and light shaded regions indicate the variance reported by [mason2018apj...856....2m] and the one further explored in this work. The scale parameter of the fitted exponential distributions for EW is shown in the bottom panel. Notably, recent measurements of the Lyα forest indicate that reionization may have occurred later than a redshift of 6, with significant fluctuations in the photoionizing background during these early times [nasir2020mnras.494.3080n, qin2021mnras.506.2390q, bosman2022mnras.514...55b, Gaikwad2023MNRAS.525.4093G, Davies2024ApJ...965..134D]. Therefore, these newly observed LAEs from JWST might be attenuated, as the damping-wing transmissions (T) at their redshifts are likely lower than 100%."}
{"text": "Consequently EWs sampled from the aforementioned fits might still be lower than the intrinsic values. To account for this, for each simulation we use the redshift = 6 snapshot to de-absorb the sampled EWs at higher redshifts. Dropping the assumption of transmission at a redshift of about 6 being 1 means that models with varying EoR endings but sharing the same transmission at higher redshifts will predict different LAE detectabilities, thus breaking degeneracy in reionization modeling. For each galaxy, we perform 500 random realizations with each drawing (i) an intrinsic velocity offset from the log-normal distribution; (ii) an EW based on the exponential distribution; and (iii) a line of sight in the IGM to obtain skews of the local density (Delta) and neutral fraction (x_HI), which also allows us to measure size of the ionized region (R_HII). We then compute the damping-wing optical depth outside the HII region using an integral over distance (l) [miraldaescide1998apj...501...15m]. Finally, the Lyα damping-wing transmission (T) is calculated and the observed EW is simply EW_obs(z) = EW * T(z) / T(z=6)."}
{"text": "Our results are summarized in Fig. 3, which shows the probability that a galaxy with a UV magnitude of about -19.5, -18.5, or -17.5 is located in an ionized region larger than R_HII (left panels) or has an observed Lyα emission greater than EW_obs (right panels). In the top panels, we compare the models M18, Fiducial and LargeScatter, which share the same UV ionizing fraction but differ in their Lyα modelling. As reionization morphology does not change between these models, they share the same bubble size distribution as shown in the upper left panel. We observe that fainter galaxies generally reside in smaller ionized regions but can sometimes be found in larger HII bubbles (up to about 8cMpc) when clustered around brighter neighbours. This is illustrated in the zoom-in insets of Fig. 1 and also studied by [qin2022mnras.510.3858q] in more detail. On the other hand, the Lyα detectability predictions differ among M18, Fiducial and LargeScatter. For galaxies with UV luminosities similar to JADES-GS-z13-1-LA (about -18.5 mag), our Fiducial model predicts a median Lyα transmission of around 13%."}
{"text": "When further restricting the modelled galaxies to those with the observed EWs of at least about 40 Angstroms -- matching that of the detected LAE -- we find a detectability rate of up to 10%. The detectability of LAEs with a given EW decreases at lower luminosities (i.e. UV magnitude between -18 and -17), as most reside in smaller ionized regions and suffer from a reduced median transmission of only 4% due to damping-wing absorption. On the other hand, despite having a higher median transmission of 24%, galaxies brighter than a UV magnitude of about -19 mag still show the same maximum detectability of 10% because their sampled EWs in Fiducial are preferentially lower (see the bottom panel of Fig. 2). Comparing Fiducial and LargeScatter, we see that increasing the variance when sampling the velocity offset results in a minor decrease in detectability. This small difference illustrates that our results are not qualitatively dependent on the assumed scatter. Our revised fit increases the probability of detection relative to the fit of M18 [mason2018apj...856....2m]."}
{"text": "However, should the v_alpha distribution indeed follow M18, there is still approximately a 5% chance of detecting LAEs brighter than an EW of about 30 Angstroms at these high redshifts. We further probe the impact of reionization morphology on Lyα detectability in the bottom panels of Fig. 3. The three example models shown in Fig. 1 -- Fiducial, Democratic and Oligarchic -- are highlighted. Our findings indicate that, at this early universe, reionization driven by high(low)-mass galaxies leads to smaller(larger) ionized regions around faint galaxies (UV magnitude greater than about -19). However, as bright galaxies tend to reside in overdense regions, boosting the ionizing fraction of galaxies either smaller or larger than a virial mass of 10^10 solar masses can advance their local ionization. As a result, uncertainties in ionized bubble size and observed Lyα equivalent width distributions become significantly larger when reionization is driven by galaxies with varying characteristic masses."}
{"text": "Assuming all morphologies share an equal likelihood when compared to existing reionization constraints, we illustrate the range of possible detectabilities using the shaded region in the lower-right panel of Fig. 3, encapsulating the distributions across all 73 models with varying f_esc, for a UV magnitude between -19 and -18. While most reionization morphologies reduce the likelihood of detecting JADES-GS-z13-1-LA (as low as 3%), models with characteristics similar to Democratic and having low-mass galaxies to drive reionization, can increase the detection probability to around 12%. Probability that a galaxy in three UV magnitude bins is located in an ionized region larger than R_HII (left panels) or has an observed Lyα emission greater than EW_obs (right panels). The top panels compare different Lyα sampling models (M18, Fiducial and LargeScatter) while the bottom panels assess the impact of reionization morphology (Fiducial, Democratic and Oligarchic). In the lower-right panel, the shaded region encapsulate the EW_obs distribution across all 73 models used in this work for UV magnitude between -19 and -18."}
{"text": "Tabulated in the upper left panel are the median Lyα transmissions, T_bar, for all redshift=13 galaxies in the Fiducial model within each of the UV magnitude bins. Correspondingly, the range of T_bar for all 73 varying-f_esc models is listed in the lower left panel. In this study, we explored the detectability of Lyα emission from galaxies during the onset of reionization. By integrating galaxy formation models with detailed IGM reionization simulations, we constructed high-redshift galaxy catalogues that are statistically representative of the real Universe. These catalogues enable us to empirically model Lyα profiles for galaxies at a redshift of 13, considering key intrinsic properties like velocity offset and equivalent width (EW). Our results indicate that while Lyα emission is attenuated by neutral hydrogen in the IGM, specific conditions such as large ionized regions around clustered galaxies and highly redshifted intrinsic emission can enable the detection of LAEs, even at these early cosmic epochs."}
{"text": "For a galaxy as bright as JADES-GS-z13-1-LA [Witstok2024arXiv240816608W], with a UV magnitude of approximately -18.5, we estimate a Lyα transmission of about 13%. Additionally, under fiducial conditions there is a roughly 10% probability of detecting its Lyα emission with an EW of about 40 Angstroms, matching that of JADES-GS-z13-1-LA. Reionization morphology plays a crucial role in shaping Lyα visibility. Our analysis shows that when reionization is driven by low-mass galaxies (e.g., the Democratic model), the probability of detecting JADES-GS-z13-1-LA-like LAEs can increase to as high as 12%. In contrast, reionization driven by massive galaxies tends to shrink ionized regions around fainter galaxies, further limiting their detectability. We find that fainter galaxies, which generally reside in smaller ionized regions, experience stronger damping-wing absorption and lower Lyα transmission. Conversely, brighter galaxies, despite having larger ionized regions and higher transmission, remain constrained by their lower intrinsic EWs, limiting their overall detectability."}
{"text": "Our modeling indicates that around 1 in 10 galaxies is expected to be observed in Lyα, even at these very high redshifts. At the time of writing there are about 15 Lyman-break candidates with a redshift between 12 and 14 and a UV magnitude between -19 and -18 (see Fig. 2 of [Carniani2024arXiv240518485C] and references therein). Of these candididates, JADES-GS-z13-1-LA [Witstok2024arXiv240816608W] is the only galaxy observed as a LAE, with another two spectroscopically confirmed galaxies showing no sign of Lyα [Curtis-Lake2023NatAs...7..622C]. This work highlights the complexities in detecting Lyα emission from the early Universe and underscores the importance of considering both galaxy properties and reionization morphology when interpreting these high-redshift observations. As the sample of LAEs identified by JWST continues to grow, this study offers valuable insights into the conditions required for early Lyα emission detection and their implications for the onset of cosmic reionization. The data underlying this article will be shared on reasonable request to the corresponding author."}
{"text": "Simulating Population (Pop.) III star formation in mini-halos in a large cosmological simulation is an extremely challenging task but it is crucial to estimate its impact on the 21cm power spectrum. In this work, we develop a framework within the semi-analytical code MERAXES to estimate the radiative backgrounds from Pop. III stars needed for the computation of the 21cm signal. We computed the 21cm global signal and power spectrum for different Pop. III models varying star formation efficiency, initial mass function (IMF) and specific X-ray luminosity per unit of star formation (Lx/SFR). In all the models considered, we find Pop. III stars have little to no impact on the reionization history but significantly affect the thermal state of the intergalactic medium (IGM) due to the strong injection of X-ray photons from their remnants that heat the neutral IGM at redshift of 15 or greater. This is reflected not only on the 21cm sky-averaged global signal during the Cosmic Dawn but also on the 21cm power spectrum at redshift of 10 or less where models with strong Pop. III X-ray emission have larger power than models with no or mild Pop. III X-ray emission. We estimate observational uncertainties on the power spectrum using 21CMSENSE and find that models where Pop. III stars have a stronger X-ray emission than Pop. II are distinguishable from models with no or mild Pop. III X-ray emission with 1000 hours observations of the upcoming SKA1-low."}
{"text": "When and where did Population III (Pop. III) stars form? What role did they play in the Cosmic Dawn and Epoch of Reionization (EoR)? And what is the best way to detect them? These questions remain open as no definitive observation of a mini-halo or Pop. III star has been reported. Up to the present day, we are relying on several cosmological simulations that investigate gas cooling and star formation in metal-free mini-halos (mass of around 10^5 to 10^7 solar masses). To gain insight, small size and high-resolution hydrodynamical simulations have been performed [e.g. Greif2011, Hirano2018, Chon2021, Chon2022, Toyouchi2023, Sadanari2024] that suggest that metal-free (or poor) mini-halos favour the formation of Pop. III stars with a more top-heavy Initial Mass Function (IMF) and with lower star formation efficiencies than observed today. It is also thought that Pop. III star formation might occur down to the end of the EoR at redshift less than approximately 6 in pristine metal free pockets of gas [e.g. Venditti2023]. The variety and complexity of the processes involved in Pop. III star formation and the resolution required to keep track of the evolution of the gas particles, limits the size of these hydrodynamical simulations to ~ 100 kpc. In order to mitigate this problem, semi-analytical models that account for Pop. III star formation have been developed [e.g. Visbal2020,Hegde2023,Boyuan2024]. These models allow a statistical study of Pop. III star formation in mini-halos out to scales of ~ 10 Mpc."}
{"text": "While these volumes start to investigate the chemical enrichment of the intergalactic medium (IGM) and the Pop. III/II transition, they are still too small to study the EoR as volumes of at least ~ 200 Mpc are required ([Iliev2014, Kaur2020, Balu2023]). Observations and models are converging on a scenario where the Universe was completely ionized by redshift of ~ 5.3 [e.g. Fan2006, Ouchi2010, McGreer2015, Qin2021, Bosman2022,Qin2024] with reionization likely driven by low-mass halos [e.g. Kuhlen2012, Qin2021b, Saxena2024, Mutch2024]. However, the impact of Pop. III stars and mini-halos on the EoR is unclear. Pop. III stars are likely to be the dominant contribution to the total star formation rate density (SFRD) at redshift greater than 15-20 and, if their IMF is more top-heavy than the present day one, Pop. III could significantly contribute to the heating and the ionization of the IGM which determines the evolution and shape of the 21cm signal [e.g. Qin2020, Jones2022, Sartorio2023]. The 21cm signal represents our most promising tool to put constraints on the thermal state of the IGM during the Cosmic Dawn and EoR. Even though no confirmed detection has been reported so far, the first upper limits on the 21cm power spectrum obtained with HERA phase I strongly disfavour cold reionization scenarios ([Hera2023]). While individual bubbles will be too small to be detected, it is possible to directly detect the EoR at z of approximately 10 by stacking redshifted 21-cm spectra centered on known galaxies [Geil2017]. In the last few years, the impact of Pop."}
{"text": "III stars on the 21cm signal has been studied using both analytical and semi-analytical models [e.g. Cohen2017, Chatterjee2020, Mebane2020]. However these models either did not compute reionization (e.g. [magg2022, Hegde2023, Hector2024]), focusing only on the absorption trough of the 21cm signal occurring at redshift of around 13-20, or used a very simple analytical approach to compute reionization (e.g.[Ventura2023]). On the other hand, [Cohen2017], [Qin2021] and [munoz2022] used a simple analytical model for modeling Pop. III star formation but computed the reionization self-consistently. In this work, we overcome these challenges using a realistic Pop. III star formation and mini-halo model ([Ventura2024]) developed within the semi-analytical model MERAXES designed to self-consistently couple galaxy formation and reionization. While in [Ventura2024] we ran this model on a small (L = 10 h-1 cMpc) and high-resolution box, here we extend it to a significantly larger volume simulation (L = 210 h-1 cMpc) enabling the study of cosmic reionization. Since at such large volumes we cannot directly resolve mini-halos, we implemented scaling relations between the SFRD and the dark matter density field calibrated on the results from the small and high-resolution box discussed in [Ventura2024]. With this new model we are able to accurately follow the evolution of the radiative backgrounds relevant to the EoR and 21cm signal (X-rays, Lyman-alpha, ionizing UV, Lyman-Werner) and to disentangle the contribution of Pop."}
{"text": "III star formation to the 21cm global signal and power spectrum. Pop. III stars are expected to have a stronger impact at redshift of 15 or greater where they dominate star formation and ionization. Differently from previous works who explored the differences in the 21cm signal at Cosmic Dawn due to various Pop. III models, here we focus our attention on the residual signature of Pop. III on the 21cm power spectrum at redshift of 10 or less where the sensitivity of SKA is expected to be significantly better and a detection is more plausible. To achieve this, it is crucial to model both Pop. III star formation and reionization in a self-consistent framework. This study allows us to assess under which conditions an early heating of the IGM from Pop. III stars leaves a detectable imprint on the 21cm power spectrum at redshift of 10 or less. This paper is structured as follows. In Section 2 we give a brief overview of Pop. III star formation in MERAXES. In Section 3 we present the scaling relation between the SFRD in mini-halos and the density field calibrated from the small and high-resolution box which is implemented in the large (210 h-1 cMpc)^3 box. In Section 4 we discuss the impact of different Pop. III star formation models on the 21cm power spectrum and in Section 5 we make forecasts on the observability of these power spectra with SKA. Finally, we summarize our main results and conclusions in Section 6."}
{"text": "Our simulations use the best-fit parameters from the [Planck16]: h = 0.6751, Omega_m = 0.3121, Omega_b = 0.0490, Omega_Lambda = 0.6879, sigma_8 = 0.8150, and n_s = 0.9653. MERAXES is a semi-analytical model (SAM) designed to study the interplay between galaxy formation and reionization ([Mutch2016, Qin2017, Qiu2019, Ventura2024]). MERAXES includes a number of free parameters that are calibrated against observations (see Tables 1 and 2). Values in Table 1 are calibrated against observed luminosity functions and stellar mass functions at redshift of around 5-8 while those in Table 2 are calibrated against constraints on the neutral hydrogen fraction, ionizing emissivity and the Thomson scattering optical depth tau_e from [Planck2020]. The most recent version of MERAXES ([Ventura2024], V24) includes Pop. III star formation and mini-halo physics. As shown in V24, the Pop. III parameters with the largest impact are the star formation efficiency alpha for Pop III and the shape of the IMF. The latter has a large impact on galaxy evolution as it determines the strength of the feedback and the emission properties of the Pop. III stellar population. In the following sections we quickly summarize the main features of MERAXES relevant for this work. Main free parameters for galaxy formation. Main free parameters for reionization. MERAXES post-processes the output of an N-body dark matter only simulation, reading the spatial and physical information of dark matter halos and computing the baryonic physics of galaxy formation."}
{"text": "In particular processes included are: (i) gas infall onto dark matter halos, (ii) radiative cooling of the infalling gas, (iii) star formation and (iv) supernova and AGN feedback. In V24 the cooling prescriptions were updated to account for H2 cooling (the main cooling channel in mini-halos) and a more detailed metal enrichment model to keep track of the metallicity of each gas reservoir in a halo (which is crucial to distinguish between Pop. III and Pop. II star formation episodes). We also account for the effects of both baryon-dark matter streaming velocity and H2 photo-dissociation by the Lyman-Werner background which increases the minimum mass of a mini-halo capable of hosting stars [e.g. Schauer2021]. Our model accounts for spatial variations only for the LW background, while for the relative velocity we assume a mean value throughout the entire box. For this work, we updated MERAXES by adding the effect of H2 self-shielding which counteracts the H2 photo-dissociation, increasing the Pop. III SFRD by up to one order of magnitude at redshift of around 10 (see e.g. [Feathers2024]). We discuss the details of the implementation and impact of H2 self-shielding in MERAXES in the Appendix A. We refer the reader to [Mutch2016] for a more detailed explanation of the main architecture of MERAXES, [Qiu2019] for the supernova model and V24 for the mini-halo model. The main free parameters that regulate the galaxy formation in MERAXES are summarized in Table 1."}
{"text": "The Pop. II related ones are taken from [Balu2023] where MERAXES was run on a cosmological volume of L = 210 h-1 cMpc resolving all atomic cooling halos and calibrated in order to match the observed UV luminosity functions at redshift of around 4-7 (the agreement holds up to redshift of around 13 as shown in [Qin2023]) and the stellar mass functions at redshift of around 5-8. Given the lack of observations of Pop. III stars, the Pop. III parameters are largely unconstrained. The fiducial values adopted in this work are taken from V24 and their values are suggested from hydrodynamical simulations [e.g. Chon2021]. Together with galaxy formation, MERAXES self-consistently computes the reionization and thermal evolution of the IGM using a modified version of the semi-numerical code 21cmFAST ([Mesinger2011]). In this work, we compute the backgrounds relevant for the computation of the 21cm signal: the UV ionizing, X-rays, Lyman-alpha and Lyman-Werner (LW). The first is crucial to study the evolution of the reionization, while the X-ray and the Lyman-alpha backgrounds determine the thermal state of the IGM. In particular the X-ray background is likely to be the dominant contribution to the heating of the IGM once the first galaxies form and the lyman-alpha background is responsible for the coupling between the kinetic and the spin temperature of the neutral hydrogen."}
{"text": "The LW background does not directly affect the IGM temperature, but determines whether or not mini-halos have enough molecular hydrogen to cool the gas and form Pop. III stars. Hereafter, we briefly summarize the key quantities that determine the evolution of these backgrounds. For a more detailed explanation on the implementations of these backgrounds, we refer the reader to [Balu2023] for the UV, Lyman-alpha and X-ray and to V24 for the LW. The ionizing background is mostly dependent on the SFRD, the average number of ionizing photons per stellar baryon N-gamma and the escape fraction of the UV photons f_esc. The second quantity is mostly determined by the IMF: for Pop. II stars we adopt a Kroupa IMF which leads to N-gamma of approximately 6000. Since the Pop. III IMF is a free parameter in our model, N-gamma for Pop III is computed from the IMF adopted using the Pop. III stellar spectra from ([Raiter2010]; N-gamma for Pop III of approximately 20000 - 70000). f_esc is tuned to reproduce the EoR histories in agreement with observations. As per [Balu2023], we adopt a redshift-dependent escape fraction defined as followed: The escape fraction is given by an equation where the escape fraction equals a baseline value multiplied by a factor related to redshift. X-ray emission is mostly associated with high mass X-ray binaries (HMXB) and its contribution is proportional to the SFRD."}
{"text": "In this work we use the widely adopted approximation for the comoving X-ray specific emissivity (erg s-1 Mpc-3) is proportional to Lx / SFR x SFRD. Finally, we need to account for the fact that only photons with an energy below 2 keV (soft X-rays) are able to heat the IGM. As a result the main free parameter that regulates X-ray emissivity is the soft X-ray luminosity per unit star formation L_X<2keV / SFR. For Pop. II stars, this quantity is estimated from theoretical studies of emission spectra of HMXBs in low metallicity environments [e.g. Fragos2013, Madau2017, Das2017, Qin2020,Kaur2022]. For Pop. III stars there are no observational constraints as this quantity depends on the unknown Pop. III IMF. Recently, [Sartorio2023] estimated the Lx / SFR for Pop. III stars and found that for more top-heavy IMFs this quantity can be up to two orders of magnitude higher than the Pop. II value. We highlight that in this work we separately compute the backgrounds from Pop. III and Pop. II stars due to the different spectra, properties and star formation rate density of the two distinct populations. Using the radiative backgrounds computed from the galaxy population in MERAXES, we can estimate the 21cm signal. We encourage the reader to see [FurlanettoRev], [Morales2010], [PritchardRev] and [LiuRev] for reviews on the topic. Hereafter we only summarize the key equations used in this work (see also [Balu2023])."}
{"text": "We start with the 21cm brightness temperature field (delta T_b) which measures the deviation of the spin temperature of the neutral hydrogen (Ts) from the cosmic background T-gamma (i.e. the CMB). This is given by the 21cm brightness temperature equation, which measures the deviation of the spin temperature of the neutral hydrogen from the cosmic background temperature. It depends on the neutral hydrogen fraction, density contrast, Hubble parameter, and the ratio of the spin temperature to the cosmic microwave background temperature. where tau at frequency nu0 is the optical depth at the 21cm transition frequency nu0, xH is the neutral hydrogen fraction, 1 + delta_nl is the density contrast in the dark matter field, H(z) is the Hubble parameter at the redshift z, and dv_r /dr is the radial derivative of the line-of-sight component of the peculiar velocity. Once the cosmological model ([Planck16]) and the velocity and density field (from the N-body simulation) are fixed, delta T_b is determined by the ionization and the spin temperature fields. The latter quantifies the population ratio of the two HI hyperfine energy levels and is sensitive to the thermal state (i.e. the kinetic temperature TK) of the gas as follows: The spin temperature is determined by a formula involving the cosmic microwave background temperature, kinetic temperature, and the Lyman-alpha and collisional coupling coefficients. where T-alpha is the colour temperature which we take equal to TK while x-alpha and x_c are the Lyman-alpha and collisional coupling coefficients, respectively."}
{"text": "These coefficients quantify the strength of the processes (resonant scattering of Lyman-alpha photons, [Wouthuysen1952], and collisions with free electrons) that drive the spin temperature towards the kinetic temperature (when x-alpha + x_c >> 1, Ts is approximately TK otherwise Ts is approximately T-gamma). TK is sensitive to the adiabatic cooling and to all the processes able to heat up (or cool) the IGM with the most dominant coming from the X-ray emission. Hence in this work we will consider only the X-ray heating neglecting the other source of heating such as primordial magnetic fields ([Minoda2019,Bera2020,Cruz2024a]), Lyman-alpha ([Ciardi2010,Reis2021,Mittal2021]), shocks ([Furlanetto2004,Gnedin2004,Ma2021]), cosmic rays ([Bera2023]), early accreting black holes ([Mebane2020, Ventura2023]) and decaying or annihilating dark matter ([Liu2018, Sun2023, Hou2024, Facchinetti2024]). Ultimately, the evolution of Ts during the Cosmic Dawn and the EoR is mostly determined by the Lyman-alpha (for the coupling between Ts and TK) and X-ray flux. Using Eq. 1 we can estimate both the all-sky averaged global signal and its fluctuations (i.e. the power spectrum). In this work we will often use the reduced power spectrum, unless otherwise stated. In this section, we present a novel approach that enables us to efficiently estimate the SFRD from mini-halos in a large box (that does not directly resolve these objects) using results from a small, high-resolution box."}
{"text": "In Table 3 we summarize the key parameters for both the small (L10) and large (L210) box. Our starting point is the small (L = 10 h-1 cMpc) high-resolution (halo mass resolution of M of approximately 4.7x 10^5 solar masses) simulation used in V24. When building a scaling relation between SFR and other physical quantity, the first obvious choice is the dark matter density field delta. For instance [Munoz2023] showed, as a first-order approximation, SFR scales as e to the power of delta_R where delta_R is the density field smoothed over a certain radius R and this relationship works quite well for delta of approximately 0 and large R (greater than or equal to 3Mpc). To link our SFR in mini-halos with the density field, we first compute density, delta(x, z), and SFR grids for both Pop. III, SFR for Pop III (x, z), and Pop. II, SFR for Pop II (x, z), in the L10 box using the same grid resolution used in [Balu2023] to compute reionization (L_pixel of approximately 0.3 cMpc) and accounting for the SFR within mini-halos. We highlight that our L_pixel is quite small compared to the smoothing radius R adopted by [Munoz2023], hence we expect a significant scatter in the above relation. We also split the contribution between Pop. III and Pop."}
{"text": "II stars (a chemically enriched mini-halo will form Pop. II stars). In the left panel of Fig. 1 we show our Pop. III SFR distribution as a function of the overdensity delta and with the grey line we highlight the SFR is proportional to e to the power of delta_R relation as in [Munoz2023]. Despite the significant scatter for the reasons outlined above (sigma of approximately 0.65), the analytical approximation agrees with our results. The results shown hereafter are obtained from our fiducial simulation in V24. We start by investigating the distribution function of log10(SFR) at a fixed overdensity delta and redshift log10(SFR(delta, z))) finding that it follows a Gaussian distribution (or lognormal in the linear space). We show results for log10(SFR for Pop III) and selected values of delta in the smaller panels in Fig. 1. Hence, we can write: A formula describing the distribution of star formation rates given overdensity and redshift, which follows a Gaussian form. where the normalization A, the mean log10(mean SFR) and the standard deviation sigma all depend on the overdensity and redshift. The normalization is defined as the ratio between the number of SF pixels and the total number of pixels. We found the best fit parameters for each delta (grouped in bins of width = 0.1) and snapshot of the simulation."}
{"text": "We tested whether the log10(SFR) distribution function is indeed Gaussian by conducting a K-S test. P-values are calculated for each cell with SFR > 0 and taking a predefined significance level of 0.05 below which the null hypothesis will be rejected. Results are shown in Fig. 2 for both SFR for Pop III and SFR for Pop II. P-values always exceed the significance level for both Pop. III (left panel) and Pop. II (right panel) SFR suggesting that the Gaussian distribution reproduces the distribution of star formation rates given overdensity and redshift both in the Pop. III and Pop. II cases. As expected, we see that there are far more Pop. III star forming pixels than Pop. II ones as mini-halos are more likely to form Pop. III stars. The next step is to study how the mean, standard deviation and normalization evolve with delta and z. In Fig. 3 we show the redshift evolution of these parameters for delta = 0.5 (black), 1.0 (grey), 1.5 (purple), 2.0 (red), 2.5 (green) and 3.0 (blue). mean SFR for Pop III exhibits an almost constant trend in redshift and a correlation with delta (higher delta results in higher mean SFR for Pop III). This demonstrates that mean SFR for Pop III is mostly determined by the number of Pop."}
{"text": "III star forming halos in a pixel, which is higher for more overdense regions. Since Pop. III star formation episodes in mini-halos are often the first episode of star formation experienced by a galaxy, it is not impacted by supernova feedback so the Pop. III SFR is almost constant at all redshift. This also explains why sigma is constant for all z and delta (sigma for Pop III of approximately 0.65). The parameter that is more sensitive to both delta and z is the normalization. For very overdense regions (delta greater than or equal to 2) it is almost one, meaning that almost all the overdense pixels host Pop. III SF mini-halos. For lower delta there is also an evolution in z as, with cosmic time, lower density regions will host a larger number of mini-halos above the minimum mass for star formation. We repeated the same analysis for Pop. II star forming pixels (see Fig. 4). In this case the evolution is more scattered as Pop. II star formation episodes are not the first star forming episodes within a galaxy and so will be affected by both mechanical and chemical feedback from the previous history of the galaxy. This is also demonstrated by the larger standard deviation (sigma for Pop II of approximately 0.8). The average value of mean SFR for Pop II is ~ 1 order of magnitude higher than for Pop. III."}
{"text": "This reflects the higher Pop. II star formation efficiency. Finally, A for Pop II is always smaller than A for Pop III showing that it is less likely for a mini-halo to form Pop. II stars. We test this parametrization on the small box by estimating the mini-halo contribution to the Pop. III and Pop. II SFRD from the matter density field. To do this, we read the density grid at each z and for each pixel assign a a value of Pop. III SFR drawn randomly from the distribution of star formation rate using delta of the pixel. We repeat the same procedure for SFR for Pop II adding the constraint that in order to have SFR for Pop II > 0 that pixel needs to already have experienced a Pop. III star formation episode. This latter condition ensures a more realistic enrichment model (a pixel cannot have Pop. II star formation if it has not previously hosted Pop. III star formation). We ran twenty different realizations and for each realization estimated the SFRD for Pop III and SFRD for Pop II and compared with results of the simulations. Results are shown in Fig. 5. In the upper panels we show the Pop. III (left) and Pop. II (right) SFRD from MERAXES output (black line) and from each realization using the method outlined above (cyan shaded lines)."}
{"text": "In the lower panels we show the ratio between the average of the 20 realizations and the true SFRD from MERAXES. All the realizations are in reasonable agreement with the data and the ratio is always lower than ~ 10% for both populations. This demonstrates the validity of the method outlined above. The main advantage of this method is that it allows estimation of the SFRD from mini-halos in a simulation where these are not directly resolved. Parametrizing SFRD with a Gaussian distribution enables us to account for stochastic star formation (different pixels with same delta can have different SFR), without losing the correlation with the matter density field (mean SFR, sigma and A all depend on delta). This method can be applied as long as the density field from both the low and the high resolution simulation share the same properties (mean, standard deviation) and it can be calibrated for any choice of parameters. We can now apply the methodology outlined in the previous section to the L210 box that can only resolve the atomic cooling halos by reading the density field and applying the distribution of star formation rate calibrated on different models. In Fig. 6 the mini-halo contribution to the Pop. III SFRD shows a good agreement between the two different simulations."}
{"text": "We highlight that our scaling relations do not explicitly depend on the Lyman-Werner background (except for the regions that are strongly irradiated by LW flux for which the distribution of star formation rate = 0). This implicitly assumes that both the L10 and L210 box have similar LW backgrounds. We verify this assumption by computing the average LW background and LW maps in both simulations (See Fig. 7 ). In the bottom right panel we show the redshift evolution of the LW background (in units of 10 to the power of -21 erg per second per square centimeter per Hertz per steradian) in the L10 (black line) and in the L210 box (red line). The two lines share similar trends showing that both simulations have a similar average LW background. The left and top right panels show the 2D projections of the LW field in the large and small box. These maps illustrate that the LW background is roughly uniform (as expected given that the mean free path of LW photons is ~ 100 Mpc). These plots demonstrate that the LW fields in the small and large box are indeed comparable showing that the estimation of the star formation in mini-halos with the scaling relations accounts for the radiative feedback. Differently from what has been done by [Hazlett2024] who calibrated a semi-analytical model to the Reinassance simulation in order to account for Pop."}
{"text": "III star formation by adding the previous star formation history to each atomic cooling galaxy resolved in the simulation, the methodology described in this section allows us to estimate only the total SFRD occurring in mini-halos within a certain pixel of the simulation. In this work we focus on three models of Pop. III star formation by varying three main parameters: the star formation efficiency, the IMF and the specific Pop. III X-ray luminosity per unit star formation while all the other free parameters (e.g. the escape fraction) are fixed at the fiducial value (see Tables 1 and 2). We chose to focus only on these three parameters since these have the strongest impact on both the evolution of the Pop. III SFRD and the amount of UV and X-ray photons emitted. The values chosen for the specific Pop. III X-ray luminosity per unit star formation are similar to those found in [Sartorio2023] for the different IMFs explored in their work. Hereafter, we analyze three different Pop. III models designed to have the minimum, intermediate and maximum impact from Pop. III star formation in mini-halos, each model is summarized in Table 4. The IMFs considered in this model are a Salpeter between 1 and 500 solar masses and a log-Normal IMF centered at 60 solar masses (see V24 for more details)."}
{"text": "We highlight that in our extreme Pop. III model we enhance star formation efficiency, Lx/SFR and the top-heaviness of the IMF at the same time. Each of these parameters has a different impact on the evolution of the 21cm signal (see Appendix B for a more detailed discussion of how each Pop. III parameter changes the evolution of the 21cm global signal and power spectrum). We can now estimate how different Pop. III star formation models in MERAXES affect the 21cm signal. We started by verifying that, after introducing the additional Pop. III contribution to the fiducial Pop. II only model ([Balu2023]) we still obtain reionization histories consistent with the observational constraints on the Thomson scattering optical depth tau_e (Fig. 6) and neutral hydrogen fraction (Fig. 7). The reionization histories from the models with Pop. III stars are only slightly modified and this negligible contribution comes from the secondary ionizations from X-rays. This is expected given that at z less than or equal to 15 the Pop. III SFRD is at least one order of magnitude lower than Pop. II and their main contribution is expected from the X-ray emission rather than the UV. We compute the sky-averaged 21cm global signal (see Fig. 8) without (black line) and with (grey, cyan and red line for weak, moderate and extreme Pop. III respectively) Pop."}
{"text": "III star formation. As expected, introducing a Pop. III population with the same X-ray properties as Pop. II ones (i.e. weak Pop. III), simply shifts the absorption through to earlier epochs in virtue of the stronger coupling at higher-z (see also [Ventura2023,Hegde2023]). However, if Pop. III stars have a stronger X-ray emission (i.e. moderate and extreme models) as suggested by [Sartorio2023], the absorption signal is quickly suppressed turning into an emission signal as early as redshift of around 18 for the extreme Pop. III model and at z of approximately 13 for the moderate Pop. III one. We note that a similar result has been found by a contemporaneous work by [Jones2025] who found an analogous variation in the timing (Delta-z of approximately 3) and depth (Delta-delta-T_b of approximately 50 mK) of the absorption trough when considering a stronger X-ray contribution from Pop. III stars (in their model the Lx/SFR is self-consistently modeled from the IMF so that the difference between their Int-0 and Sal model is of 2 orders of magnitudes.) As shown in Fig. 10 earlier coupling and heating from Pop. III impacts the 21cm power spectrum both at the large and small scales. The models considered here produce 21cm signals that are different not only during the coupling and heating epoch (redshift of around 10 - 20), but also at lower redshift when the reionization is in progress."}
{"text": "The impact is stronger at smaller scales where models with a stronger heating exhibit a larger power spectrum at redshift of around 7 - 10. This is of crucial importance as current and upcoming facilities are improving their observations at z less than or equal to 10 (see more discussion in Section 5). We compare our results with the ones in [munoz2022] who studied how different Pop. III parameters impact the 21cm signal using 21cmFAST. In the left panel of Fig. 10 the yellow and brown dashed lines are obtained by changing the specific Pop. III X-ray luminosity by a factor of 9. The global trends are similar with our models with stronger Pop. III X-ray emission (dashed yellow line and red/cyan lines) showing an earlier and weaker first peak compared to low X-ray models (dashed brown and grey lines). In their model, different Pop. III X-ray properties strongly impact the position and amplitude also of the second peak. In our models instead, the position of the second peak is only slightly anticipated in the strong X-ray models. This difference is likely due to the fact that our second peak occurs at much lower redshift (z of approximately 10) when most of the emission comes from Pop. II stars. Finally, differently from [munoz2022] at z of approximately 10 simulations with a stronger Pop."}
{"text": "III X-ray heating have a significantly larger power spectrum compared to weak X-ray models (a similar result has been found also by [Jones2025]). This analysis shows that Pop. III star formation not only impacts the 21cm global signal during the cosmic dawn as previously assessed [e.g. Qin2020, Jones2022, Ventura2023, Hegde2023, Hector2024] but also that an early (redshift of 15 or greater) heating of the IGM provided by this population leaves a strong signature on the power spectrum during the EoR (z less than or equal to 10). The impact on the power spectrum is stronger for models that have a large Pop. III X-ray emissivity (i.e. moderate and extreme Pop. III models) while models with a milder X-ray emission (i.e. weak Pop. III) have a stronger effect on the global signal. Ultimately, this tells us that the power spectrum during the EoR can be used to disentangle different heating models and potentially constrain the properties of Pop. III stars. We highlight that here we considered only the X-ray emission from stellar remnants. While there might be other sources that significantly heat the IGM at redshift of 15 or greater (see discussion at end of Section 2.3), the other effects are likely to be either subdominant, still related to Pop. III stars (e.g. cosmic rays) or dominant only at the dark-ages (e.g. dark matter annihilation)."}
{"text": "Finally, we note that in this work we did not include the effect of the X-ray feedback on Pop. III star formation. As noted by [Ricotti2016,Park2021], X-rays have both a positive and negative effect on Pop. III star formation as they heat the gas and increase the electron fraction. The heating makes gas accretion more difficult (hence delaying star formation) and free electrons promote the formation of H2 making the molecular cooling more efficient. In presence of a strong X-ray background this latter effect is dominant at 10 < z < 20 (see e.g. Fig. 9 in [Hegde2023]). Hence, including the X-ray feedback would likely increase the Pop. III SFRD making the impact of Pop. III stars even stronger than what predicted here especially for the moderate and extreme models. In the previous section we showed that an early heating of the IGM significantly affects the 21cm power spectrum during the EoR. Now we want to investigate how our models compare with the currently available upper limits and whether their differences will be observable with SKA. In this section we consider the power spectrum at z less than or equal to 10 as the current and upcoming interferometers are significantly less sensitive at higher redshift."}
{"text": "To better appreciate this, in Fig. 11 we show the power spectrum noise (mK squared) with SKA as a function of redshift at k of approximately 0.2 and 0.9 cMpc-1 assuming a 1000 hours (solid lines) and 180 hours (dashed lines) observations with SKA. At higher redshift the noise steadily increases and already at redshift of 10 or greater the noise is of the order of 10s to 100s mK squared with 1000 hours observation. Firstly, we compare our predictions with current upper limits from a number of facilities including MWA, LOFAR, GMRT, PAPER and HERA (we focus at z = 7 - 10 where most of the measurements have been taken). In Fig. 12 we show the 21cm power spectrum at z = 10, 9, 8 and 7 for all the four models together with the available upper limits (see label). All our models are below these upper limits. However, the moderate and extreme Pop. III models are closer to the current HERA constraints at z = 8 suggesting that soon these models can be either detected or ruled out. In our model the main effect of different Pop. III models is to change the timing and amplitude of the peaks in the 21cm power spectrum rather than introducing a specific feature."}
{"text": "We note that we did not account for spatial variations in the velocity acoustic oscillations (see Section 2.1) which would introduce wiggles in the power spectrum at scales k of approximately 0.1 Mpc-1 ([Hector2024]). While this effect can be important when focusing on the 21cm power spectrum during the coupling and heating epochs, these fluctuations are quickly washed out at z less than approximately 13 (see Fig. 13 and Section 6C in [Hector2024]). We next consider the upcoming SKA. In order to estimate the observability of the four models analyzed so far, we perform a similar analysis as in [Balu2023b] that we briefly summarize hereafter. The sensitivity of a radio interferometer is mostly regulated by the thermal noise and the cosmic variance with the former dominating the noise at small scales and the latter at large scales. The thermal noise is related to the bandwidths of the instrument, beam factor (see [Parsons2014]), the integration time of the mode k and the temperature of the system (given as the sum of the sky and receiver temperature) ([Morales2005,McQuinn2006,Parsons2012]). We can hence write the total noise by summing these two components: A formula for the inverse square of the total noise on the power spectrum, calculated by summing over individual noise components. By doing so, we are effectively assuming that the errors are Gaussian distributed, which is reasonable for the relevant scales in this work ([Qin2021,Prelogovic2023])."}
{"text": "Finally, a 21cm detection is heavily limited by the ability of removing the foregrounds. We used the python package 21CMSENSE ([Pober2013,Pober2014]) which, given the specifics of an interferometer, a mock 21cm power spectrum and an observational campaign, computes the interferometer sensitivity to the 21cm power spectrum under different assumptions of foreground removals. We used the assumption 'moderate' foreground removals and we focused on the first phase of SKA (i.e. SKA1-low), in particular we included the stations in the 'Central Area' of the SKA1-low, resulting in 296 stations of diameter 35m distributed across a circular area with 1.7 km diameter. We assumed two different observational campaigns: one of 180 hours (six hours per night for 30 days) and another of 1080 hours (six hours per night for 180 days). Additionally, we avoid the modes that are contained within the foreground wedge ([Datta2010]) so that effectively we are limited to k_min = 0.16 Mpc-1 for our analysis and k_max = 1.4 Mpc-1 (the latter arises from a combination of the spatial scales that are probed by the SKA1-low and the shot noise from our simulation). To quantify the detectability of a Pop. III model we compute by how many sigma its power spectrum differs from the one arising from the No Pop."}
{"text": "III model: An equation defining the detectability of a model, calculated as the difference between its power spectrum and a baseline model's power spectrum, divided by the combined uncertainty. where the subscript i refers to the Pop. III model considered and 0 to the No Pop. III model. To detect a Pop. III model the difference between its power spectrum and the No Pop. III one needs to be at least of 1-sigma otherwise the model is not detectable. In Fig. 13 we show the evolution in redshift of this quantity at k of approximately 0.2 (upper panel) and k of approximately 0.9 Mpc-1 (lower panel) for each Pop. III model and assuming 1080 (solid lines) and 180 (dashed lines) observation hours. The weak Pop. III model (grey line) is different from the No Pop. III one by less than 1-sigma both at the small and large scales even with an observation of 1080 hours. The moderate Pop. III model is several sigma away from the No Pop. III model at 7 < z < 10 both at the small and large scales with a 1080 hours observation while with a 180 hours the model is detectable only at the large scales where the difference is between 1 and 2 sigma. The extreme Pop."}
{"text": "III model is the one with the largest difference from the No Pop. III model being potentially detectable at both large and small scales even with a 180 hours observations. However, Finally, we highlight the differences between each Pop. III model by showing their power spectrum noise (shaded regions) assuming 180 and 1080 hours of observations in Fig. 14 and 15. Models with stronger X-ray contribution (red and cyan lines) have a power spectrum that differs from the models with no or mild Pop. III contribution (dark and light grey regions) by more than the observational uncertainty. The 1-sigma region of its power spectrum (pink shaded region) is above the models with no or mild Pop. III contribution at z = 7 and 8 for all the k-modes, at z = 9 at k less than approximately 0.7 Mpc-1 and at z = 10 only at the largest scales considered (k less than approximately 0.4 Mpc-1). With only 180 hours observations however, it is not possible to clearly distinguish between the intermediate and extreme Pop. III model (blue an pink shaded regions). At z = 6 it is not possible to distinguish any of these models since at this redshift the power spectrum is mostly determined by the ionization state of the IGM which is identical for all the four models considered."}
{"text": "The sensitivity greatly improves for an observational campaign of 1000 hours (Fig. 15). In this case, models accounting for Pop. III early heating which is stronger than Pop. II are clearly distinguishable from models with no or mild Pop. III contribution. At z = 10, 9 and 8, it is even possible to distinguish between intermediate and extreme Pop. III models at all scales within k_min and k_max, indicating that SKA observations of the 21cm power spectrum during the EoR are sensitive to the IGM heating occurred at redshift of 15 or greater. At z = 7, the difference between the various models are less evident but intermediate and extreme Pop. III models still fall outside the uncertainty regions of weak Pop. III and No Pop. III. This indicates that models with a harder Pop. III X-ray emission can be disentangled from models with no or mild Pop. III X-ray emission even at z = 7. Also [Jones2025] focused on the possibility of detecting difference Pop. III models using 21cm observations. In their analysis they included both REACH (sensitive to the 21cm global signal) and SKA-Low confirming that an observation of ~ 3000 hours with SKA-Low can constrain the Pop. III IMF due to their difference in the X-ray heating."}
{"text": "Finally, we highlight that the impact of Pop. III stars is visible on the power spectrum as long as their X-ray contribution is boosted compared to Pop. II. The differences between the weak Pop. III and the No Pop. III scenario are so small they will not be visible even with 1000 SKA hours. This demonstrates that an upcoming 21cm power spectrum detection will shed light on the properties of the first sources establishing their contribution to the heating of the IGM. In this work we investigated how the early (redshift of 15 or greater) heating of the IGM due to Pop. III stars impacts the 21cm power spectrum during the EoR (z less than or equal to 10) which will be observable by the SKA. We developed a framework of scaling relations between Pop. III star formation rate in mini-halos and the density field within the semi-analytical model MERAXES that allows us to account for the radiative contribution of mini-halos that cannot be directly resolved in a large (L = 210 h-1 cMpc) cosmological simulation. The scaling relations are calibrated on a smaller and higher resolution simulation able to resolve all the mini-halos. We then investigated three Pop. III models each with different IMF, star formation efficiency and specific X-ray luminosity."}
{"text": "This formalism is both based on realistic galaxy population and it provides an accurate estimation of the Pop. III backgrounds yielding a computation of the ionization and thermal state of the IGM which is crucial to obtain a reliable estimation of the 21cm signal and power spectrum during the EoR ( z less than approximately 10). The key results can be summarized as follows: 1. The inclusion of Pop. III stars does not significantly change the EoR history as their main contribution comes from the secondary ionizations from their X-ray emission. As a result, all the models that we considered give reionization histories consistent with the latest constraints on the neutral hydrogen fraction and the Thomson scattering optical depth. 2. As previously known, the evolution of the 21cm global signal during the Cosmic Dawn is significantly impacted by Pop. III stars. In a model where Pop. III and Pop. II have the same X-ray specific luminosity (weak Pop. III) the absorption through of the 21cm global signal is slightly deeper and occurs at higher-z. If instead Pop. III stars have a larger Lx / SFR, the signal is seen in emission at higher-z (z of ~14 for the intermediate Pop. III model and z of ~18 for the extreme Pop. III model)."}
{"text": "3. The heating from Pop. III stars significantly increases the 21cm power spectrum during the EoR both at large and small scales. This is more evident for models with an increased specific X-ray luminosity where the difference can be of more than a factor of 4 at z greater than or equal to 7. This shows that the 21cm power spectrum during the EoR is sensitive to the heating occurred at much higher redshift. 4. Focusing on a possible future detection of the 21cm power spectrum, we estimated the observational uncertainty of each model using the python package 21CMSENSE assuming an observational campaign with SKA1-low of 180 and 1080 hours respectively. We found that 180 hours are not enough to distinguish different Pop. III models but they already can confirm/exclude the presence of a stronger heating from Pop. III stars at high-z since their power spectra differs by more than 1-sigma from the No Pop. III model. However, using ~ 1000 hours of SKA, models with a stronger Pop. III contribution (stronger X-ray emission and/or higher Pop. III star formation efficiency) become clearly distinguishable at z greater than or equal to 7. This does not apply toward the end of the EoR (z less than or equal to 6) or for a model with the a lower Pop."}
{"text": "III X-ray emissivity (weak Pop. III). In the former case this is because at z of ~6 the power spectrum is mostly determined by the ionization state of the IGM (which is not impacted by Pop. III star formation in our models). When the Pop. III X-ray emissivity is the same as the Pop. II one, the 21cm power spectrum is only very mildly increased compared to the scenario without Pop. III stars. The power spectrum towards the end of the EoR (z less than or equal to 6) does not distinguish Pop. III models. We thank the anonymous referee for very constructive comments that help improve the quality of this paper. This research was supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D, project #CE170100013). This work was performed on the OzSTAR national facility at Swinburne University of Technology. OzSTAR is funded by Swinburne University of Technology and the National Collaborative Research Infrastructure Strategy (NCRIS). This research was also undertaken with the assistance of resources from the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government. SB acknowledges support from grant PID2022-138855NB-C32 funded by MICIU/AEI/10.13039/501100011033 and ERDF/EU, and project PPIT2024-31833, cofunded by EU--Ministerio de Hacienda y Funcion Publica--Fondos Europeos--Junta de Andalucia--Consejeria de Universidad, Investigacion e Innovacion."}
{"text": "YQ is supported by the ARC Discovery Early Career Researcher Award (DECRA) through fellowship #DE240101129. Finally, EMV thank A. Mesinger and J. B. Munoz for insightful discussions regarding the development of the scaling relation model and C. Power for assistance with the N-body simulation. The main data presented in this work have been analysed with the publicly available python package DRAGONS. The latest version of MERAXES is publicly available on GitHub. Further data and codes will be shared on reasonable request to the corresponding author. Many recent simulations [e.g. Nebrin2023,Hegde2023] have assessed the importance of incorporating H2 self-shielding in mini-halos as it significantly changes the minimum mass of mini-halos capable of cooling down the gas via molecular cooling. While this was not implemented in V24, for this work we now included it by updating M_crit, MC (Eq. 4 in V24) taking the fitting function found in [Kulkarni2021]: A formula defining the critical mass for molecular cooling, dependent on Lyman-Werner flux and streaming velocity. where a second formula defines the critical mass at z=20, and a third defines the redshift evolution power-law index. M_crit, MC is a function of the Lyman-Werner flux (J_LW) in 10 to the power of -21 erg per second per square centimeter and the rms streaming velocity at recombination (v_bc) in km per second."}
{"text": "This result is normalized to the minimum halo mass at z = 20 in absence of LW background and streaming velocity (M_z = 20)_0 and to typical values for LW background and streaming velocity (J_0 = 1, v_0 = 30). alpha_n and beta_n are free parameters calibrated to fit results of hydrodynamical simulations in [Kulkarni2021]. This fit accounts for the H2 self-shielding, so it makes the effect of the LW background on M_crit,MC less strong compared to what was previously assumed in V24 ([Visbal2015]). As shown in Fig. 14, accounting for self-shielding increases the Pop. III SFRD, especially when the Lyman-Werner background starts to build up. At z less than or equal to 15 the Pop. III SFRD when the H2 self-shield is considered (cyan dashed line) is ~ 1 order of magnitude higher than the no self-shield scenario (cyan solid). Similar results have been found by [Feathers2024]. While the 21cm power spectrum at z less than or equal to 10 is mostly sensitive to the amount of X-ray photons from Pop. III remnants, changing the star formation efficiency and the shape of the IMF impacts the 21cm signal evolution during the coupling and heating epochs."}
{"text": "In Fig. 15 and 16 we show the evolution of the 21cm global signal and power spectrum for the No Pop. III model (black line), Weak (grey line), Moderate (cyan line), high SFE (dashed grey line) and LogE (dashed red line) models. Compared to the Weak Pop. III model, increasing the Pop. III star formation efficiency, increases both the amount of Lyman-alpha and X-ray photons (they are both linked to SFR), hence the absorption trough shifts towards higher-z (Delta-z of ~1). Considering instead a top-heavy IMF, increases just the amount of Lyman-alpha photons hence the absorption trough becomes significantly deeper while still being at the same redshift compared to the weak Pop. III model. We note that this result is a consequence of the fact that we are considering the Lx/SFR and the shape of the IMF as two independent parameters. If, as shown in [Sartorio2023], the X-ray emissivity is linked to the shape of the IMF, the LogE model is not realistic as we would need to enhance the X-ray emissivity as well. We highlight that both the star formation efficiency and the shape of the IMF alone do not significantly affect neither the 21cm global signal nor the power spectrum at z less than or equal to 12 so a future 21cm detection with SKA-low likely will not help to constrain these parameters if they are not linked to a significantly stronger X-ray emissivity."}