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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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].


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.


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.


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].


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].


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].


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].


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.


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.


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).


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).


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.


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.


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).


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.


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.


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.


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.


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.


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.


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.


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.


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).


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.


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.


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).


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].


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.


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).


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.


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).


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.


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.


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.


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.