Furthermore, when a galaxy experiences a star formation episode, we enforce the probability p = 1 (in this latter case, we know that this galaxy will be inside its own metal bubble and thus cannot accrete pristine gas). With this latter condition and internal enrichment, we effectively stop Pop. III star formation inside a galaxy after the first supernova episode. The main limitation of this technique is that we are not accounting for the overlap of the bubbles and thus are overestimating the metal-filling factor and underestimating the metallicity of those galaxies that are polluted from more than one galaxy. However, given the small size of the bubbles, this is not a major factor, especially prior to reionization. The model shows the bubble growth over time from a typical radius of ~ 30 ckpc at redshift z = 20 to ~ 150 ckpc at redshift z = 5. These values are consistent with the results shown in [Trenti2009].


A galaxy that already formed stars or a galaxy that formed in a region enriched with metals so that its metallicity is larger than Z_crit = 10^-4 solar metallicity will form Pop. II stars. We adopted the same prescription and parameters for Pop. II star formation as described in M16 and [Qiu2019]. The uncertainty around the properties of Pop. III stars motivated us to include Pop. III star formation in a flexible way so that it is easy and fast to investigate the impact of Pop. III stars changing a few parameters. In particular, once a galaxy reaches a mass of cold gas larger than a critical value, this galaxy will convert the cold gas into stars according to the star formation efficiency. Since we are now considering two different stellar populations, we adopted two different free parameters, both for the star formation efficiency alpha_SF,III and for the critical surface density Sigma_crit,III.


Recent full hydrodynamical simulations that follow the collapse of a pristine gas cloud until a Pop. III star is formed [e.g.][Hirano2014, Stacy2016, Chon2021], suggest that the Pop. III IMF is shifted to larger masses as a result of less fragmentation due to inefficient cooling. Within this work, we adopted the IMFs from [Raiter2010], while for Pop. II stars, we assumed a [Kroupa2001] IMF. For the fiducial model, we chose a Salpeter IMF with a mass between 1 and 500 solar masses. The choice of the IMF is crucial as it determines many properties of the stellar population, including what fraction of stars will explode as supernovae and, hence, the amount of energy and metals injected into the IGM. Since the focus of this work is on the first galaxies formed during the Cosmic Dawn, we do not explore parameters describing the UV ionizing and X-ray radiation (e.g. escape fraction), and we will take the same fiducial values as in the previous works.


The fate of a zero-metallicity star is quite uncertain. Here, we adopt a simplified picture of the final fate of a Pop. III star depends only on its initial mass ([Heger2002]). For masses below 8 solar masses, there will be no SN event. If stellar mass is in [8,40] solar masses it will explode as a core-collapse SN (CCSN) leaving a remnant, if stellar mass is in [140,260] solar masses there will be a pair-instability SN (PISN) leaving no remnant and if stellar mass is in [40,140] solar masses or stellar mass > 260 solar masses stars collapse directly into a black hole (BH) with negligible feedback. While we use the technique of [Qiu2019] for Pop. II stars with precomputed tables assuming a Kroupa IMF ([Kroupa2001]), for Pop. III supernova feedback we estimated the amount of SN energy and metal yields with an analytic calculation as in M16.


The total energy provided by Pop. III supernovae explosions at the snapshot j is the sum of delayed contributions from core-collapse supernovae and contemporaneous contributions from pair-instability supernovae. These are computed by integrating the chosen IMF over the correct mass limits. Assuming that all-star formation occurred in the middle of the snapshot, the mass limits for CCSN are computed from the lifetimes for Pop. III stars using [Schaerer2002] assuming no mass loss and zero metallicity. We highlight that a zero metallicity star with a mass between 140 and 260 solar masses has a lifetime smaller than the time separation between two consecutive snapshots in meraxes; hence, it will explode as a PISN in the same snapshot in which it forms. For CCSN, instead, we keep track of the star formation history over the last 17 snapshots, which correspond to >= 40 Myr, after which all stars with mass >= 8 solar masses will already be exploded.


We also update the amount of ejected gas and metals from Pop. III stars. These are taken from [Heger2010] assuming non-mixing and a supernova explosion of 1.2 x 10^51 erg. In all the previous Meraxes works, all the stellar mass locked up in remnants (neutron stars and BHs) was neglected as it was recycled into the gas mass budget of the galaxy. We decided to drop this approximation for Pop III stars as they are likely to leave more massive remnants. Firstly, we need to consider the BHs that formed after a "failed SN scenario" typical of a star with an initial mass between 40 and 140 solar masses and greater than 260 solar masses. Finally, we need to account for the BH remnants that are left after a CCSN. Meraxes, does not evolve the remnants (via accretion), as the main focus of this work is Pop. III stars. However, the impact of the first accreting BHs on the formation of the supermassive black holes might be important even at high-redshift ([Ventura2023]).


In order to investigate the observability of the first Pop. III galaxies we implement spectral energy distributions (SED) for Pop. III stars. We use SEDs from [Raiter2010] that have been computed for the IMFs listed in Table 2 assuming that star formation occurs in an instantaneous burst. These SEDs also include the nebular continuum emission and the UV ionizing properties. To compute the luminosity of galaxies at a specific wavelength, we used the model introduced by [Qiu2019] (see also [Mutch2023]), and we extended it to Pop. III galaxies. Having the Pop. III SEDs, we can compute the luminosity of a Pop. III galaxy at time t as an integral over its star formation history, modulated by the luminosity of a stellar population per unit mass and a dust transmission function. For the latter term, we refer the reader to [Qiu2019] while the luminosity per unit mass for each Pop. III IMF has been taken from [Raiter2010].


This calculation is nearly identical to [Qiu2019], with the difference being that we do not have the metallicity dependence because Pop. III stars SEDs are defined with a zero metallicity. In this framework, we assume that the star formation occurs continuously throughout the snapshot. While this is a good approximation for Pop. II stars, Pop. III star formation is expected to occur in a single burst because of the feedback from Pop. III stars are likely to prevent continuous star formation. For this reason, we expanded the calculation of the luminosity of Pop. III galaxies assuming that new stars form instantaneously at a specific time. As we will discuss in Section 4, instantaneous (instead of continuous) Pop. III star formation has an impact on the estimated luminosity function of galaxies hosting Pop. III stars. This is because Pop. III stars have lifetimes that can be shorter than the duration of the snapshot.


Hence, when we consider continuous star formation, we average the star formation over the entire snapshot, leading to lower luminosity with a higher duty cycle. When we instead consider Pop. III stars to form in a single burst, if this burst will occur toward the end of the snapshot the galaxy will appear much brighter when it is observed in that snapshot. In order to account for instantaneous star formation, we assumed that a Pop. III star formation episode in a galaxy can occur at random Delta t within the snapshot duration prior to the end of the snapshot. For the detailed evaluation of the UV luminosity function accounting for the stochasticity in the time at which the burst of star formation occurs in different galaxies, we refer the reader to Appendix B.


To explore the Pop. III contributions to the cosmic star formation history, we ran two simulations on the L10 box, one with all the updates described in Section 2 adopting the fiducial parameters and one without the new physics that we labelled as "NoMini". Given that there are no observational constraints on Pop. III, the choice of a fiducial model is arbitrary. The one adopted in this work has both a low star formation efficiency and a Salpeter-like IMF, which will result in a relatively small global impact of Pop. III star formation compared to Pop. II. The stellar mass function at different redshifts accounts for all (black), only Pop. III dominated (cyan), and only Pop. II dominated (red) galaxies. We classified a galaxy as Pop. III or Pop. II dominated based on which population is brighter in the UV band. The new updates on Meraxes mostly affect the lower end of the SMF with a larger impact at high-redshift.


This reflects the star formation in mini-halos (we are now considering molecular cooling), which is dominant at redshift z >= 15 before the Lyman-Werner background becomes strong enough to photodissociate all the molecular hydrogen. The low-mass peak of the SMF is dominated by Pop. III systems and the more massive one by Pop. II. This bimodality of the SMF could have an impact on the faint end of the luminosity function at redshift z ~ 10. The low mass of Pop. III systems is mainly a consequence of both the shorter lifetimes of Pop. III stars (given their larger mass) and the lower SF efficiency, but also suggests that most of the Pop. III star formation must occur in mini-halos. The halo mass function for Pop. III and Pop. II star-forming halos is shown at several redshifts. The dashed line corresponds to the limit of atomic cooling (virial temperature T_vir = 10^4 K).


Given the small size of the box, we have only a few atomic cooling halos at redshift z ~ 20, so all star-forming systems are mini-halos (and are mostly Pop. III). At lower redshift, the peak of the distribution shifts to higher masses and the impact of Pop. II increases. Finally, Pop. III stars mostly form in mini-halos. This is because the more massive halos are more likely to have already experienced star formation and so will be internally chemically enriched. The total star formation rate density (SFRD) as a function of redshift for both the fiducial and the NoMini model is also analyzed. In the case of the fiducial model, we also show the Pop. III (Pop. II) contribution in the upper (lower) panel. Mini-halos have an appreciable impact on the SFRD only up to redshift z >= 20, while at lower redshift, most star formation occurs in atomic cooling halos.


We see that accounting for Pop. III star formation in mini-halos is crucial during the Cosmic Dawn because Pop. III stars dominate the global star formation history at redshift z >= 20 and are still relevant up to redshift z = 18. The Pop. III SFRD flattens at redshift z ~ 18 and starts to decrease at redshift z ~ 10. The early flattening occurs due to the build-up of the Lyman-Werner background that affects Pop. III star formation in minihalos. The sharp drop at redshift z <= 10 is mostly caused by the photoionizing feedback from reionization that also affects the atomic cooling halos. The feedback from reionization also mildly affects Pop. II as can be seen from the flattening of the red line at redshift z ~ 8 in the upper panel. Compared to reionization, the chemical enrichment of the IGM is a much slower process due to the lower velocity of the expansion of the metal bubbles.


As already found in previous works [e.g.][Visbal2020, Yamaguchi2023], the impact of external metal enrichment is subdominant compared to internal metal enrichment. However, external enrichment might still be important for low-mass halos that do not form stars until redshift z ~ 10. The top left panel of Fig. 5 shows the redshift evolution of the average metallicity of the box. As expected, the average metallicity increases monotonically. It crosses the critical value at redshift z ~ 11 and at the end of the simulation is ~ 5 x 10^-3 solar metallicity. The redshift evolution of the IGM metallicity is in very good agreement with [Yamaguchi2023], especially for their "bursty" models, which is the one that most closely resembles the star formation in Meraxes. However, the average metallicity of the IGM does not completely inform us of the average metallicity of the galaxies since, when averaging through the entire box, we are considering voids that have no galaxies and hence zero IGM metallicity.


For this reason, in the top right panel, we computed the black solid line, averaging only through cells that have at least one metal bubble (meaning that there must be at least one galaxy that formed stars). The average metallicity, in this case, is much higher, and it is always above the critical value. This suggests that once the first galaxies form, the ejection of metals from Pop. III is quite effective in the nearby regions, allowing a fast Pop. III/II transition in those cells where star formation already occurred. The lower panels instead show the fraction of the IGM that reached the critical metallicity. Considering the entire box (left panel), less than 1% of the volume gets enriched above Z_crit by redshift z ~ 5. This result is fairly consistent with [Visbal2020] and [Yamaguchi2023] (~ 1% by z = 6).


These small differences are likely due to differences in the star formation models and in the choice of parameters, such as the star formation efficiency. If we focus only on the regions with at least one galaxy that formed stars, we find larger filling factors, and by the end of the simulation, those pixels are all completely enriched. This final result reflects our choice of pixel size that is designed to be similar to the average volume of the metal bubble at redshift z ~ 5. The halo mass function for the externally (black line) and internally (grey line) metal enriched halos at several redshifts is also analyzed. While most halos get internally enriched by their own star formation, at redshift z = 5 halos with virial masses M_vir <= 10^7.5 solar masses get their metals mostly from a nearby supernova bubble. This picture reflects the fact that low-mass halos during reionization are not able to form stars because of the LW and photo-ionizing feedback.


Hence, those objects can be chemically enriched only from an external source. In conclusion, when looking at the global evolution of star formation, the effect of the external metal enrichment is quite negligible as it is important only for low-mass halos at low redshift that will hardly form stars due to the radiative feedback effects. We verified this by running a simulation without external metal enrichment. There are no appreciable differences between the two models except at redshift z <= 8 when the dashed line is slightly larger (about 0.1 dex difference). The results in previous sections were obtained adopting quite conservative assumptions for Pop. III stars given the very low SF efficiency and the Salpeter-like IMF. In the following sections, we explore the four main free parameters that regulate Pop. III star formation in Meraxes listed in Table 1: the Pop. III star formation efficient, the critical metallicity for Pop.III/II transition, the critical surface density of cold gas for Pop. III star formation to occur and the IMF.


The star formation efficiency determines the conversion of the cold gas into stars and is the free parameter with the largest impact on the Pop. III global SFRD and SMF. This parameter is largely unconstrained, with some simulations supporting very low values (10^-4 - 10^-3, [Skinner2020]) and others suggesting higher values ([Fukushima2020]). We ran two simulations keeping all the Pop. III free parameters unchanged except for the star formation efficiency, which we boosted by one order of magnitude and to a very high value. Pop. III galaxies become more massive as the star formation efficiency increases, erasing the "double peak" feature in the total SMF. For the model with equal Pop. II and Pop. III efficiency, the peak of the Pop. III SMF is still shifted to the left by half dex compared to the Pop. II. This is because, despite having the same star formation efficiency, Pop. III galaxies mostly form in mini-halos.


The star formation efficiency also regulates the Pop. III/II transition as it directly correlates with the SFRD. For a high efficiency, the SFRD is dominated by Pop. III up to redshift z ~ 15 compared to the fiducial model where Pop. II SF becomes larger than Pop. III at redshift z > 20. The Pop. II SFRD does not significantly change between the three models, and so the change in the Pop. III SFRD also affects the total SFRD. All the models converge at redshift z ~ 13 when even with the highest efficiency the total SFRD is entirely dominated by the Pop. II contributions. The critical metallicity defines the metallicity at which there is a change in the IMF. There is currently no consensus on the value of Z_crit, with two competing models that assume the fragmentation driven by either the carbon and oxygen line or the dust cooling. The first class of models determine a Z_crit ~ 10^-2 - 10^-3 solar metallicity while the seconds give a lower value (~ 10^-6 solar metallicity).


Some studies also argue that the value of Z_crit evolves with redshift due to the effect of the CMB ([Chon2022]). Following simulations in the literature ([Schneider2006, Visbal2020]), in this work we adopted an intermediate value Z_crit = 10^-4 solar metallicity as the fiducial value, hereafter we will also show results for the two extreme values of 10^-2 and 10^-6 solar metallicity. The SMF between the fiducial model and Z_crit = 10^-6 solar metallicity does not change. This is because, in the overdense regions where there is star formation, the metallicity becomes larger than 10^-4 solar metallicity very quickly so that changing Z_crit to 10^-6 solar metallicity does not further accelerate the Pop. III/II transition. However, considering a higher value changes the total SMF as we end up with many more Pop. III stars. The high-mass tail of Pop. III SMF extends up to 10^7.5 solar masses at redshift z = 5 when Z_crit = 10^-2 solar metallicity.


The combined effect of Pop. III and Pop. II makes the total SMF computed from the simulation with Z_crit = 10^-2 solar metallicity single peaked as the high-mass peak coming from Pop. II stars are washed out even at redshift z = 5 so that the total SMF peaks at stellar mass ~ 10^4 solar masses at redshift z = 10 - 5 with a high-mass tail that extends up to 10^9 solar masses. The critical metallicity also has a strong impact on the evolution of the SFRD as it affects both the internal and external enrichment. While decreasing the value of Z_crit from the fiducial value only mildly decreases the Pop. III SFRD without altering the total result, choosing Z_crit = 10^-2 solar metallicity strongly changes the SFRD history at redshift z <= 18. The Pop. III SFRD increases by 1-2 orders of magnitude while the Pop. II decreases by the same amount.


Increasing the Pop. III star formation and simultaneously decreasing the Pop. II impacts on the total SFRD. Since Pop. III stars form less efficiently we predict a lower total SFRD compared to the fiducial model. Overall the critical metallicity heavily impacts both the SFRD and SMF during the Cosmic Dawn and the Epoch of Reionization and affects when the universe transitions from being Pop. III dominated Pop. II. In order to trigger the star formation in a galaxy, our model requires the gas density in the disk to be above a certain threshold. We decided to duplicate this free parameter so that we have one for Pop. III and one for Pop. II. While keeping the Pop. II parameter fixed, we explore the extreme case of a Pop. III critical surface density of 0, which is equivalent to assuming that Pop. III stars start to form as soon as the cooling of the gas begins.


This choice results in a larger abundance of low-mass Pop. III systems at high-redshift. However, since the main changes in the Pop. III SF are in low-mass halos, setting the critical surface density to 0 does not significantly change the SFRD history. Overall, this free parameter is the one with the smallest impact on the star formation history, as it only impacts the low-end of the stellar mass function at high-redshift for which there are no observational constraints. The last parameter we explore is the IMF of Pop. III stars. Our fiducial model is quite similar to the Pop. II IMF as we assume a Salpeter IMF that favours the formation of low-mass stars. We consider two log-normal IMFs labelled logA and logE as in [Tumlinson2006]. For these IMFs we have spectral energy distributions (from [Raiter2010]) which will be used in Section 4.


The IMF logA is centred at M = 10 solar masses, which enhances the probability of a Pop. III stars ending its life as a core-collapse SN. logE is centred at even a higher mass (M = 60 solar masses), so we expect most of the stars with very short lifetimes to end their lives by collapsing into a black hole without any supernova explosion. Compared to the Salpeter IMF, both log-normal IMFs do not have many low mass stars (mass < 8 solar masses). Decreasing the lifetime of Pop. III stars make the Pop. III SMF shift to lower masses, increasing the separation between the two peaks of the total SMF. The difference between the fiducial model and one adopting the logA IMF is less than one dex. However, in the logE IMF model, most of the stars die in the same snapshot in which they form. This effect strongly prevents the build-up of Pop. III systems.


There are no significant differences in the SFRD from adopting different IMFs, except for the first few snapshots of our simulation where the star formation is mildly reduced in the logE model. This result comes from the stronger feedback typical of the more top-heavy IMF (a larger number of massive stars implies more supernovae), and it has a stronger impact at redshift z >= 24 when Pop. III star formation is dominating. Unconstrained Pop. III free parameters in our model have an impact on the redshift evolution of the SMF and SFRD. However, our model predicts a consistent number density of Pop. III dominated systems with stellar masses between 10^3 - 10^5 solar masses. Here we will explore the UV luminosity of these systems using the model described in Section 2.6 focusing on the luminosity functions at very high-redshift.


Given the same total stellar mass, Pop. III systems have larger luminosities compared to Pop. II galaxies, but shine for shorter times. We show the evolution in the first 10Myr of the SED of a Pop. III galaxy that forms 10^5 solar masses of Pop. III stars at redshift z = 8 and the absolute UV magnitude at different times since the star formation burst. Left, mid and right panels assume a Pop. III Salpeter, logA and logE IMF respectively. The black horizontal line corresponds to the magnitude computed assuming a continuous star formation throughout the snapshot. For reference, we also show the magnitude of a Pop. II galaxy forming the same amount of Pop. II stars (red dashed line). Firstly, we notice that Pop. III galaxies with continuous star formation and a log-normal IMF are one magnitude brighter than Pop. II galaxies with the same SFR (while there is no significant difference if Pop. III stars follow a Salpeter IMF).


Once we focus on the instantaneous star formation model for Pop. III stars, the brightness of the galaxy can be boosted (or reduced) by several magnitudes depending on the time since the burst at which we are observing the system [see also Trussler2023]. Even when we consider a Salpeter IMF, the brightness of a Pop. III galaxy changes ~ 2 mags in ~ 10Myr. This change is more dramatic for the log-normal IMFs (especially for the logE IMF where in 10 Myr the change in absolute magnitude is approximately 7 mags). The large difference between the instantaneous and continuous star formation models for a single Pop. III galaxy will reflect in the entire population and potentially lead to a higher number density of extremely bright Pop. III galaxies. As a result of instantaneous Pop. III star formation, there are chances to observe these galaxies at a time when their luminosities are higher than what is given by the continuous scenario.


When looking at the total luminosity function we see a much significant Pop. III contribution to the number density of galaxies around an absolute magnitude of approximately -16 when assuming a LogE IMF for their star formation. Given their larger brightness, a population of Pop. III galaxies with a top-heavy IMF has been suggested as a possible explanation for the abundance of bright galaxies at redshift z > 10 [see, e.g. Trinca2023, Yung2023, Harikane2023]. Without invoking any exotic physics or a revision of the standard LambdaCDM model of cosmology, other possible explanations are a combination of increased star formation efficiencies at high-redshift and reduced feedback [Qin2023], bursty star formation [Sun2023], cosmic variance [Shen2023] and a modified LambdaCDM power spectrum [Parashari2023, Padmanabhan2023].


Here, we show the predicted UV luminosity functions at several redshifts. Results for different IMFs and different star formation efficiencies are summarized, where all the other Pop. III parameters are taken as in the fiducial model. For all the models considered below, our total luminosity function agrees with early JWST observations at redshift z <= 12 (except for the points at an absolute magnitude < -19 where we do not have galaxies in Meraxes). With our fiducial parameters (dashed lines), both with the Salpeter and with the logA IMF, we find that Pop. III systems are not the brightest galaxies at the redshift considered (absolute magnitude >= -14). However, when we consider a log-normal IMF with a characteristic mass of 60 solar masses (lower row), Pop. III galaxies become significantly brighter and at redshift z = 12 and 16 when some of the brightest systems (absolute magnitude ~ -16) are Pop. III dominated.


This result may indicate that Pop. III dominated galaxies are present at redshift z > 12. This result becomes more robust when considering a Pop. III star formation efficiency equal to the Pop. II efficiency. The bright end of the total and Pop. III dominated galaxy UVLF shifts of 1-2 magnitudes (depending on the IMF) at redshift z = 16 and 12. At redshift z <= 11, there is no or little difference in the total UVLF with different star formation efficiency even though Pop. III dominated galaxies are still ~ 1 mag brighter. Models with a Salpeter or a log-normal IMF centered at 10 solar masses predict that the bright end of the UVLF at redshift z = 16 is impacted by Pop. III dominated systems while at redshift z <= 12 none or very few of the brightest galaxies are Pop. III dominated.


Overall, the abundance of bright galaxies at redshift z >= 12 is better explained by the model with the logE Pop. III IMF and a star formation efficiency equal to the Pop. II efficiency. For this model at redshift z >= 12 we find Pop. III dominated galaxies with an absolute magnitude of approximately -18 and at redshift z = 16 all the brightest galaxies (absolute magnitude <= -16) are Pop. III dominated. We compared our results with [Trinca2023], and found a good agreement at redshift z <= 12 and absolute magnitude less than or approximately equal to -16.5 for all the models considered. The main differences are that at redshift z = 9, we do not have any galaxy with an absolute magnitude of approximately -20, and their model has a steeper evolution predicting many more faint galaxies. At redshift z = 16 only models with a high Pop. III star formation efficiency and a log-normal IMF reproduce their results.


Even though the total UVLF are similar, their Pop. III contribution is significantly lower, especially when compared to the models with high Pop. III star formation efficiency. The main differences in the model that can explain the different results are (i) the homogeneous feedback and (ii) the Pop. III luminosity calculation. In their model, both the radiative feedback and the chemical enrichment are homogeneous; this might overestimate the suppression of Pop. III systems at redshift z ~ 10-20. Regarding the second point, our model accounts for the fact that a Pop. III galaxies might be observed immediately after they formed stars. Without accounting for this effect, our Pop. III galaxies would have similar luminosity to those predicted by [Trinca2023]. The main limitation of our results is that, given the small size of the simulation, we intrinsically miss the brightest galaxies. Larger simulation volumes will allow us to be conclusive, but this result suggests that if Pop. III stars are still forming at redshift z >= 10-12, and they have a top-heavy IMF, they do not require increased star formation efficiencies to outshine the Pop. II systems.


As Pop. III dominated galaxies become much more rare at redshift z <~ 10, this scenario allows us to increase the abundance of bright galaxies only at redshift z > 10 without boosting the bright end of the UV luminosity function at lower redshift hence we achieve a good agreement with early JWST observations from [Donnan2023, Harikane2023] and [Perez2023]. In this paper, we studied Pop. III star formation in mini-halos with an updated version of the Meraxes semi-analytic model of galaxy formation that includes Lyman-Werner background and the streaming velocities. We also implemented external metal enrichment following the growth of the supernova bubbles according to the Sedov-Taylor model. We computed the bubble size distribution function and found that our results agree with [Trenti2009] (most bubbles are smaller than 150 per h ckpc at z = 6 and have a typical size of 100-200 ckpc at z = 5) hence most halos get self-enriched rather than externally polluted.


Only low-mass halos (virial mass <= 10^7.5 solar masses) at redshift z < 10 are more likely to get their metals from the IGM. This is a consequence of the small size of the supernova bubbles that results in a small filling factor (0.1% at z = 12 and less than 1% at z = 5). The free parameters allow us to explore the global properties of Pop. III dominated galaxies. We ran this model on top of a dark matter-only N-body simulation able to resolve all the mini-halos down to ~ 3 x 10^5 solar masses at redshift z <= 30. We explored the impact on the SMF and SFRD of the main free parameters of our model. All models converge at redshift z <~ 10. However, Pop. III star formation efficiency and IMF lead to differences at high-redshift.


Finally, we investigated the SED evolution of a Pop. III dominated galaxy for different IMFs. The shorter lifetime of a Pop. III galaxy motivated us to use an instantaneous star formation model when computing the luminosity function. We computed the total and the Pop. III galaxy UV luminosity functions and compared these to the early JWST results in order to study whether the excess of bright galaxies at high-redshift could be explained by a population of Pop. III dominated galaxies. Having explored different IMFs and star formation efficiencies, our model predicts, for a log-normal IMF with a characteristic mass of 60 solar masses and a Pop. III star formation efficiency comparable to the Pop. II, most of the brightest galaxies at redshift z >= 12 and all at redshift z = 16 (absolute magnitude = - 18) are Pop. III dominated. Adopting a smaller characteristic mass or a Salpeter IMF, Pop. III dominated systems still have an impact on the bright end of the UVLF, but only at redshift z = 16.


In conclusion, this work supports the scenario for which top-heavy Pop. III dominated galaxies might explain the abundance of bright JWST galaxies at redshift z >= 12 without requiring very high star formation efficiencies or extremely weak feedback at high-redshift. In this appendix, we discuss the extent to which our approximation on the external metal enrichment based on the filling factor is appropriate and when it fails. Since we are avoiding computing all the pairs of distance, there might be some galaxies for which we are not getting a correct enrichment. For this reason, we computed in post-processing the distance between all the pairs of galaxies throughout the entire simulation and we counted how many galaxies in Meraxes are marked as externally metal enriched (pristine) even if they are outside (inside) a metal bubble. We repeated this computation for several grid resolutions: N = 16, 32, 64, 128 and 256.


Hereafter, we will call "false pristine galaxies" those galaxies that lie inside a metal bubble (and so should be enriched) but in Meraxes are labelled as pristine and "false enriched galaxies" those galaxies that are not reached by any bubble but in Meraxes are labelled as enriched. At lower resolution, the percentage of the false pristine galaxies increases from 4% at N = 128 to 7% at N = 16. This happens since, as the pixel becomes bigger, the assumption of the galaxies randomly distributed inside each pixel is no longer valid as the clustering becomes much more important. However, when we use a very fine grid (N = 256), the mass fraction of false enriched galaxies dramatically increases at redshift z <= 10. This happens because by redshift z = 10, the typical bubble size becomes larger than the pixel volume, and so we lose all the contribution that overflows outside the pixel.


The mass percentage of false enriched galaxies instead is only mildly affected by different resolutions (always below 2%). We then compute the absolute value of the difference between the mass percentage of the false pristine and the false enriched galaxies. This quantity tells us if, statistically, we are reproducing the correct global enrichment of the Universe. We can see that having a high-resolution grid significantly improves the quality of our results. For N = 128, this difference is always below 2%, and at redshift z < 12 is approximately 0%. This tells us that for a high-resolution grid, globally, we are getting the correct enrichment of the Universe as the mass percentage of false pristine and false enriched galaxies cancels out. This agreement is almost perfect during the EoR, while during the Cosmic Dawn we are underestimating the metal enrichment of ~ 1-2%.


Finally, we are also showing the sum between the false enriched and pristine galaxies. This quantity instead tells us what is the mass percentage of galaxies for which we are getting a wrong estimation of the enrichment. Increasing the resolution improves our result, which, for N = 128, peaks at ~ 4% during the Cosmic Dawn. In conclusion, our model for N = 128, while reducing the computational cost, still gives an excellent agreement on global enrichment and a very good agreement on the enrichment of single galaxies. We also assumed that the probability p of each galaxy to be enriched is equal to the metal filling factor multiplied by the two-point correlation function. In this case we get the best results using N = 16. The mass percentage of false pristine and false enriched both peak at 4-5% with the percentage of false pristine galaxies decreasing at higher resolution and the percentage of false enriched galaxies increasing at higher resolution.


Accounting for the clustering and using a low-resolution grid still allows us to get an excellent agreement on the statistical properties but, compared to the model adopted in this work, it doubles the mass percentage of the galaxies for which we are getting a wrong prediction. This final check further confirms that the model for the external metal enrichment that we are adopting in this work, is the best one. In this appendix, we discuss how to evaluate the UV luminosity function of Pop. III galaxies assuming instantaneous star formation. Due to the stochasticity involved in the process of star formation, the burst might occur at any time within a snapshot for a galaxy, resulting in different luminosities when observed. We refer to Delta t as the time delay of the star formation burst happening relative to the end of our snapshot, and draw its value from a random uniform distribution between zero and the snapshot duration.


One can then evaluate the luminosity of this galaxy, repeat the exercise for all targets after assigning them different Delta t, and calculate their probability distribution as a function of UV magnitude (i.e. the UV luminosity function). To achieve a more efficient computation, we instead sample Delta t in fine steps. Then we calculate the UV magnitudes of each galaxy for given Delta t_i and evaluate the corresponding luminosity function at the condition of fixed Delta t. Finally, the luminosity function is obtained by summing all conditional probability distributions as the sum over all conditional luminosity functions multiplied by the probability of each time delay. Note that the probability of each conditional luminosity function is simply calculated based on the size of the time step relative to the total snapshot duration.


Reionization morphology and intrinsic velocity offsets allow transmission of Lyman-α emission from JADES-GS-z13-1-LA. We investigate the detectability of Lyman-α (Lyα) emission from galaxies at the onset of cosmic reionization, aiming to understand the conditions necessary for detecting high-redshift sources like JADES-GS-z13-1-LA at a redshift of 13. By integrating galaxy formation models with detailed intergalactic medium (IGM) reionization simulations, we construct high-redshift galaxy catalogs to model intrinsic Lyα profiles and assess their transmission through the IGM. For a galaxy with a UV magnitude of about -18.5 like JADES-GS-z13-1-LA, our fiducial model predicts a Lyα transmission of approximately 13% and there is a probability of observing Lyα emission with an equivalent width greater than 40 Angstroms of up to 10%. We also explore how variations in the UV ionizing escape fraction, dependent on host halo mass, impact Lyα detectability. Our findings reveal that reionization morphology significantly influences detection chances -- models where reionization is driven by low-mass galaxies can boost the detection probability to as much as 12%, while those driven by massive galaxies tend to reduce ionized regions around faint emitters, limiting their detectability.


This study underscores the importance of reionization morphology in interpreting high-redshift Lyα observations. Lyman-α (Lyα) emission is expected to be heavily suppressed by neutral hydrogen in the intergalactic medium (IGM) [miraldaescide1998apj...501...15m]. As a result, detecting Lyα emitters (LAEs) in the early Universe is unanticipated and suggests enhanced production of ionizing and/or Lyman-α photons in the first galaxies [Stark2015MNRAS.454.1393S, Witten2024NatAs...8..384W]. The recently reported, stunning Lyα detection from JADES-GS-z13-1-LA [Witstok2024arXiv240816608W] with an equivalent width (EW) of 43 +15/-11 Angstroms from a redshift of 13, is therefore interpreted as measuring the onset of reionization. Possible mechanisms to increase the intrinsic Lyα emission include a young, metal-poor stellar population [miraldaescide1998apj...501...15m, Schaerer2003A&A...397..527S] and the presence of an active galactic nucleus (AGN) [ouchi2018pasj...70s..13o, Sobral2018MNRAS.477.2817S]. However, clustered environments can also boost observability when a large ionized region is hollowed out by a cluster of galaxies [qin2022mnras.510.3858q, leonova2022mnras.515.5790l].


Furthermore, outflows within the interstellar medium can shift the intrinsic Lyα line redwards, allowing the emission to penetrate deeper into the damping wing and significantly reducing its cross section before hitting the neutral IGM [Dijkstra2011MNRAS.414.2139D]. Recent advancements with JWST have substantially expanded the sample of high-redshift LAEs (see e.g., [Witstok2024A&A...682A..40W], [Tang2024arXiv240801507T, jones2024jadesmeasuringreionizationproperties] and references therein). With improved statistics to refine the modelling of Lyα profiles [mason2018apj...856....2m], this work aims to quantify the detectability of Lyα emission from a redshift of 13. By integrating IGM reionization simulations with semi-analytic galaxy-formation models, we use galaxies with realistic UV properties to infer their Lyα line profiles and to self-consistently compute the morphology of neutral hydrogen during the Epoch of Reionization (EoR). Our findings suggest up to a 10% chance of observing a Lyα equivalent width greater than 40 Angstroms in a galaxy with a UV magnitude of about -18.5 like JADES-GS-z13-1-LA [Witstok2024arXiv240816608W], increasing to 12% when varying reionization morphologies are further considered.


After briefly summarizing our model in the next section, we present the results in Section 3 and conclude in Section 4. In this work, we apply the cosmological parameters from Planck 2018 (Omega_m = 0.312, Omega_b = 0.0490, Omega_Lambda = 0.688, h = 0.675, sigma_8 = 0.815, n_s = 0.968; [Planck2020A&A...641A...6P]). We model galaxy formation and reionization using the Meraxes semi-analytic model [Mutch2016MNRAS.463.3556M, Qin2017a, Balu2023MNRAS.520.3368B], applied to dark matter halo merger trees that resolve all atomic-cooling halos at redshift less than or equal to 20 within a cosmological volume of 210 h-inverse cMpc per side. The model implements various astrophysical processes to generate a statistically representative sample of high-redshift galaxies, including accretion and cooling of the gaseous reservoir, evolution and feedback of the stellar component and AGN, merger and suppression of the satellite companions, and photoheating during the EoR. The UV and X-ray emissivities are channeled to 21cmFAST [Mesinger2011MNRAS.411..955M, Murray2020JOSS....5.2582M] to assess the ionization and thermal status of the IGM.


Slides of overdensity and neutral hydrogen fraction at a redshift of 13 (projected over a depth of 7cMpc, larger than most ionized bubbles) for three models with different contributions of galaxies to the ionizing budget based on their host halo masses. The upper right zoom-in insets show galaxies brighter than a UV magnitude of -17 mag as star symbols, with their size representing galaxy brightness. The lower right inset displays the globally averaged reionization histories for these three models (indicating CMB optical depth and reionization timing) along with 70 additional models with varying ionizing escape fractions. These models are broadly consistent with observational results that are based on dark pixel measurements (black; [McGreer2015MNRAS.447..499M, Jin2023ApJ...942...59J]), damping-wing absorption in quasar spectra (orange; [Banados2018Natur.553..473B, Greig2017, Greig2019, Greig2022, Davies2018, Wang2020ApJ...896...23W, Zhu2024MNRAS.533L..49Z]), equivalent width measurements (green; [Mason2019MNRAS.485.3947M, Jung2020ApJ...904..144J, Whitler2020MNRAS.495.3602W, Bolan2022MNRAS.517.3263B]), luminosity functions or clustering of Lyα emitters (purple; [Inoue2018PASJ...70...55I, Morales2021ApJ...919..120M, ouchi2018pasj...70s..13o, wold2022apj...927...36w]), and CMB polarization ([Planck2020A&A...641A...6P, qin2020mnras.499..550q]).


Summary of models used in this work. M_10 denotes the base-10 logarithm of (M_vir / 10^10 Solar masses). Our fiducial model [Qin2023MNRAS.526.1324Q] is calibrated to reproduce well-established galaxy UV luminosity functions measured by HST (e.g. [Finkelstein2015ApJ...810...71F, Oesch2016ApJ...819..129O, Atek2018MNRAS.479.5184A, Ishigaki2018ApJ...854...73I, Bhatawdekar2019MNRAS.486.3805B, Bouwens2021AJ....162...47B, Bouwens2023MNRAS.523.1036B]) and has shown consistency with recent JWST result up to at least redshift of about 13 (e.g. [Donnan2023MNRAS.518.6011D, finkelstein2022ApJ...940L..55F, Harikane2023ApJS..265....5H, Naidu2022ApJ...940L..14N, PG2023arXiv230202429P, Willott2024ApJ...966...74W]). Assuming a UV ionizing photon escape fraction (f_esc) of 15%, the resulting reionization history aligns with measurements at redshifts between 5 and about 10 (e.g. [McGreer2015MNRAS.447..499M, Banados2018Natur.553..473B, ouchi2018pasj...70s..13o, Wang2020ApJ...896...23W, Jung2020ApJ...904..144J, Whitler2020MNRAS.495.3602W, Morales2021ApJ...919..120M, Greig2022, wold2022apj...927...36w, Jin2023ApJ...942...59J, Zhu2024MNRAS.533L..49Z]). For detailed information on our model and its calibration, we direct interested readers to the referenced publications.


To explore different reionization morphologies at a redshift of 13, we parameterize the escape fraction (f_esc) as a function of the host halo mass (M_vir), following the approach of [Park2019MNRAS.484..933P] with the formula: f_esc = min[1, f_esc,10 * (M_vir / 10^10 Solar masses)^alpha_esc], where f_esc,10 and alpha_esc represent the normalization and scaling index, respectively, and are considered as free parameters in this study. The escape fraction is also capped at 100% in all models. It is important to note that f_esc remains highly uncertain, both in observations available at low redshift (e.g., [Steidel2018ApJ...869..123S, Naidu2018MNRAS.478..791N, Fletcher2019ApJ...878...87F, Izotov2021MNRAS.503.1734I, Pahl2021arXiv210402081P]) and in detailed reionization simulations (e.g., [ma2020mnras.498.2001m, Kostyuk2023MNRAS.521.3077K, Choustikov2024MNRAS.529.3751C]), with some simulations suggesting increased f_esc in less massive galaxies [Paardekooper2015MNRAS.451.2544P, Xu2016ApJ...833...84X, Kostyuk2023MNRAS.521.3077K]. This aligns with expectations that it is easier for supernovae to evacuate low column density channels from shallower gravitational potentials, which allows ionizing photons to escape.


Within a Bayesian framework, our systematic exploration of escape fraction variations with halo mass also indicates that current constraints favor larger f_esc in lower-mass galaxies (i.e. a negative value of alpha_esc; [mutch2024mnras.527.7924m]). We conduct 234 simulations by varying the two ionizing free parameters within the range of f_esc,10 in (0, 0.45] and alpha_esc in [-1.5,1.0]. For this work, we only consider 73 of these simulations, which meet the criteria of having a cosmic microwave background (CMB) optical depth consistent with Planck measurements (i.e. tau_e between 0.05 and 0.065; [Planck2020A&A...641A...6P, qin2020mnras.499..550q]) and reaching a globally averaged neutral fraction of 1% after z_re=6.8 (broadly consistent with various observations, e.g., [Banados2018Natur.553..473B, Whitler2020MNRAS.495.3602W, Morales2021ApJ...919..120M, Jin2023ApJ...942...59J]; see their reionization histories in the lower-right panel of Fig. 1). Although these simulations exhibit similar reionization histories, they show significant variations in the spatial distribution of neutral hydrogen. We use these simulations to investigate how reionization morphology affects the detectability of Lyα emission in the highly neutral universe at a redshift of 13.


Fig. 1 highlights three example models: (i) Fiducial with f_esc=0.15; (ii) Democratic with f_esc,10=0.05 and alpha_esc=-0.4; and (iii) Oligarchic with f_esc,10=0.45 and alpha_esc=0.9, are summarized in Table 1. There are notable differences in reionization morphology between these models. Compared to the Fiducial model, Democratic allows less-massive galaxies to emit more ionizing photons into the IGM and, due to the higher abundance of low-mass galaxies at high redshifts, Democratic features a greater number of small-sized ionized bubbles at a redshift of 13. Additionally, overdense regions can expand their surrounding HII regions with the aid of clustered low-mass galaxies. This model aligns most closely with the escape fraction constraints from [mutch2024mnras.527.7924m]. In contrast, the Oligarchic model, which relies on galaxies with well-established stellar mass to ionize the IGM, shows delayed reionization due to the scarcity of these massive contributors in the early stages of the EoR. Furthermore, the brightness of the first galaxies is sensitive to the ionization history and can be significantly influenced by local photoheating feedback.


The globally averaged neutral fraction also evolves differently between these models: Democratic shows a more extended and slowly evolving neutral fraction, while Oligarchic exhibits a narrower and more rapid evolution compared to the Fiducial model. Despite these variations, the globally averaged neutral fraction (x_HI) at a redshift of 13 remains similar across models (all above 97%), with a CMB optical depth around tau_e = 0.06 and reionization concluding around z_re = 6. We model the Lyα profile (F_alpha) before damping-wing absorption as a truncated normal distribution with respect to velocity (v): F_alpha follows a normal distribution with a mean of v_alpha and variance related to v_alpha squared, for velocity (v) greater than the circular velocity of the host halo (v_circ), and 0 otherwise (see Fig. 1 in [mason2018apj...856....2m] for examples). Here, the full width at half maximum of the profile is assumed to be v_alpha, and emission blueward of the circular velocity of the host halo (v_circ) is considered completely absorbed by residual neutral hydrogen within ionized bubbles.


To model the Lyα damping-wing transmission, we follow [mason2018apj...856....2m] and sample the intrinsic Lyα line offset (v_alpha) and equivalent width (EW) with slight modifications to their originally proposed distributions. [mason2018apj...856....2m] created an empirical model for the v_alpha–M_UV relation by first converting UV magnitude to halo mass using the following relation [mason2015]: the base-10 log of (M_vir/10^10 Solar masses) = gamma * (M_UV - M_UV,c) +1.75, where M_UV,c = -20 - 0.26z and gamma = -0.7 for galaxies brighter than M_UV,c and -0.3 for fainter galaxies. [mason2018apj...856....2m] then used measurements of LAEs, primarily from post-reionization (redshift of about 2–3, based on Keck; e.g., [Erb2014ApJ...795...33E]), to fit Lyα line offset using a log-normal distribution with a variable mean that depends on the host halo mass yielding a distribution where the parameters (m, c, sigma) = (0.32, 1.78, 0.24).


The top panel of Fig. 2 shows this low-redshift sample in grey and plots their fitted mean v_alpha against UV magnitude, indicated the long dash-dotted curve. The top panel of Fig. 2 also presents the resulting predicted mean v_alpha-M_UV relation at redshifts of about 7 and 13, along with the latest LAE measurements from JWST (see [Witstok2024A&A...682A..40W, Tang2024arXiv240801507T] and references therein), including the new redshift of 13 detection by [Witstok2024arXiv240816608W]. In their analysis [mason2018apj...856....2m] noted negligible differences in the v_alpha-M_vir distribution between the low-redshift sample and the observations at redshift greater than 6 that were available at the time (e.g., [Stark2017MNRAS.464..469S]), and therefore modelled a mean v_alpha–M_vir relation that does not evolve with redshift. However, newer data indicates that the redshift-independent v_alpha–M_vir relation requires revision to better fit the current LAE sample at higher redshifts. Indeed, if the relation between v_alpha and halo mass were driven by the depth of the gravitational potential well we would expect an offset at fixed halo mass that increased towards higher redshift.


Therefore, we propose increasing the intercept by 0.3 (to a value of c=2.08), and show the new fit for a redshift of about 13 in the top panel of Fig. 2 for comparison. In addition to the original fit proposed by [mason2018apj...856....2m] and this new fit with a larger c, we also explore a larger variance of sigma = 0.34, which corresponds to the standard deviation of the high-redshift sample shown in the panel. Although this choice is somewhat arbitrary, it aims to account for the increased scatter observed in the new high-redshift data. We refer to these three models as M18, Fiducial, and LargeScatter and summarize them in Table 1. As shown in the bottom panel of Fig. 2, much more observational data for the EW of high-redshift LAEs has become available since the study by [deboer2017pasp..129d5001d], whose sample was used by [mason2018apj...856....2m] to fit an exponential distribution (see also [Oyarzun2017ApJ...843..133O]) for redshift of about 6 LAEs.


The fit for the exponential distribution used parameters (EW_c, j, k, M_UV,c) = (31, 12, 4, -20.25). This fit was motivated by splitting the LAE sample into brighter than a UV magnitude of -21 mag, fainter than -20 mag, and in-between, as well as by providing a smooth transition between M_UV = -21 and -20 mag. Since this work focuses on much fainter luminosities, we adopt a new fit with (EW_c, j, k, M_UV,c) = (100, 80, 1, -19) for the Fiducial and LargeScatter models. As illustrated in the panel, our new fit agrees better with LAEs of higher redshifts and fainter luminosities while remaining comparable to [mason2018apj...856....2m] at the bright end. Lyα velocity offset (v_alpha) and equivalent width (EW) as a function of UV magnitude. Observational data are categorized by redshift ranges: redshift of 2 to 3 (from [mason2018apj...856....2m] and references therein), redshift of 6 to 11 (from [Witstok2024A&A...682A..40W], [Tang2024arXiv240801507T] and references therein), and redshift of 13 ([Witstok2024arXiv240816608W]).


At a redshift of 13 the open and filled stars respectively represent the observed and predicted intrinsic values following spectral fitting including Lyα and IGM and DLA transmission ([Witstok2024arXiv240816608W]). In the top panel, the curves represent the mean velocity offset v_alpha of the original log-normal distribution fitted by [mason2018apj...856....2m] for LAEs at redshifts of about 2, 7, and 13, along with our newly proposed fit. The dark and light shaded regions indicate the variance reported by [mason2018apj...856....2m] and the one further explored in this work. The scale parameter of the fitted exponential distributions for EW is shown in the bottom panel. Notably, recent measurements of the Lyα forest indicate that reionization may have occurred later than a redshift of 6, with significant fluctuations in the photoionizing background during these early times [nasir2020mnras.494.3080n, qin2021mnras.506.2390q, bosman2022mnras.514...55b, Gaikwad2023MNRAS.525.4093G, Davies2024ApJ...965..134D]. Therefore, these newly observed LAEs from JWST might be attenuated, as the damping-wing transmissions (T) at their redshifts are likely lower than 100%.


Consequently EWs sampled from the aforementioned fits might still be lower than the intrinsic values. To account for this, for each simulation we use the redshift = 6 snapshot to de-absorb the sampled EWs at higher redshifts. Dropping the assumption of transmission at a redshift of about 6 being 1 means that models with varying EoR endings but sharing the same transmission at higher redshifts will predict different LAE detectabilities, thus breaking degeneracy in reionization modeling. For each galaxy, we perform 500 random realizations with each drawing (i) an intrinsic velocity offset from the log-normal distribution; (ii) an EW based on the exponential distribution; and (iii) a line of sight in the IGM to obtain skews of the local density (Delta) and neutral fraction (x_HI), which also allows us to measure size of the ionized region (R_HII). We then compute the damping-wing optical depth outside the HII region using an integral over distance (l) [miraldaescide1998apj...501...15m]. Finally, the Lyα damping-wing transmission (T) is calculated and the observed EW is simply EW_obs(z) = EW * T(z) / T(z=6).


Our results are summarized in Fig. 3, which shows the probability that a galaxy with a UV magnitude of about -19.5, -18.5, or -17.5 is located in an ionized region larger than R_HII (left panels) or has an observed Lyα emission greater than EW_obs (right panels). In the top panels, we compare the models M18, Fiducial and LargeScatter, which share the same UV ionizing fraction but differ in their Lyα modelling. As reionization morphology does not change between these models, they share the same bubble size distribution as shown in the upper left panel. We observe that fainter galaxies generally reside in smaller ionized regions but can sometimes be found in larger HII bubbles (up to about 8cMpc) when clustered around brighter neighbours. This is illustrated in the zoom-in insets of Fig. 1 and also studied by [qin2022mnras.510.3858q] in more detail. On the other hand, the Lyα detectability predictions differ among M18, Fiducial and LargeScatter. For galaxies with UV luminosities similar to JADES-GS-z13-1-LA (about -18.5 mag), our Fiducial model predicts a median Lyα transmission of around 13%.


When further restricting the modelled galaxies to those with the observed EWs of at least about 40 Angstroms -- matching that of the detected LAE -- we find a detectability rate of up to 10%. The detectability of LAEs with a given EW decreases at lower luminosities (i.e. UV magnitude between -18 and -17), as most reside in smaller ionized regions and suffer from a reduced median transmission of only 4% due to damping-wing absorption. On the other hand, despite having a higher median transmission of 24%, galaxies brighter than a UV magnitude of about -19 mag still show the same maximum detectability of 10% because their sampled EWs in Fiducial are preferentially lower (see the bottom panel of Fig. 2). Comparing Fiducial and LargeScatter, we see that increasing the variance when sampling the velocity offset results in a minor decrease in detectability. This small difference illustrates that our results are not qualitatively dependent on the assumed scatter. Our revised fit increases the probability of detection relative to the fit of M18 [mason2018apj...856....2m].


However, should the v_alpha distribution indeed follow M18, there is still approximately a 5% chance of detecting LAEs brighter than an EW of about 30 Angstroms at these high redshifts. We further probe the impact of reionization morphology on Lyα detectability in the bottom panels of Fig. 3. The three example models shown in Fig. 1 -- Fiducial, Democratic and Oligarchic -- are highlighted. Our findings indicate that, at this early universe, reionization driven by high(low)-mass galaxies leads to smaller(larger) ionized regions around faint galaxies (UV magnitude greater than about -19). However, as bright galaxies tend to reside in overdense regions, boosting the ionizing fraction of galaxies either smaller or larger than a virial mass of 10^10 solar masses can advance their local ionization. As a result, uncertainties in ionized bubble size and observed Lyα equivalent width distributions become significantly larger when reionization is driven by galaxies with varying characteristic masses.


Assuming all morphologies share an equal likelihood when compared to existing reionization constraints, we illustrate the range of possible detectabilities using the shaded region in the lower-right panel of Fig. 3, encapsulating the distributions across all 73 models with varying f_esc, for a UV magnitude between -19 and -18. While most reionization morphologies reduce the likelihood of detecting JADES-GS-z13-1-LA (as low as 3%), models with characteristics similar to Democratic and having low-mass galaxies to drive reionization, can increase the detection probability to around 12%. Probability that a galaxy in three UV magnitude bins is located in an ionized region larger than R_HII (left panels) or has an observed Lyα emission greater than EW_obs (right panels). The top panels compare different Lyα sampling models (M18, Fiducial and LargeScatter) while the bottom panels assess the impact of reionization morphology (Fiducial, Democratic and Oligarchic). In the lower-right panel, the shaded region encapsulate the EW_obs distribution across all 73 models used in this work for UV magnitude between -19 and -18.


Tabulated in the upper left panel are the median Lyα transmissions, T_bar, for all redshift=13 galaxies in the Fiducial model within each of the UV magnitude bins. Correspondingly, the range of T_bar for all 73 varying-f_esc models is listed in the lower left panel. In this study, we explored the detectability of Lyα emission from galaxies during the onset of reionization. By integrating galaxy formation models with detailed IGM reionization simulations, we constructed high-redshift galaxy catalogues that are statistically representative of the real Universe. These catalogues enable us to empirically model Lyα profiles for galaxies at a redshift of 13, considering key intrinsic properties like velocity offset and equivalent width (EW). Our results indicate that while Lyα emission is attenuated by neutral hydrogen in the IGM, specific conditions such as large ionized regions around clustered galaxies and highly redshifted intrinsic emission can enable the detection of LAEs, even at these early cosmic epochs.


For a galaxy as bright as JADES-GS-z13-1-LA [Witstok2024arXiv240816608W], with a UV magnitude of approximately -18.5, we estimate a Lyα transmission of about 13%. Additionally, under fiducial conditions there is a roughly 10% probability of detecting its Lyα emission with an EW of about 40 Angstroms, matching that of JADES-GS-z13-1-LA. Reionization morphology plays a crucial role in shaping Lyα visibility. Our analysis shows that when reionization is driven by low-mass galaxies (e.g., the Democratic model), the probability of detecting JADES-GS-z13-1-LA-like LAEs can increase to as high as 12%. In contrast, reionization driven by massive galaxies tends to shrink ionized regions around fainter galaxies, further limiting their detectability. We find that fainter galaxies, which generally reside in smaller ionized regions, experience stronger damping-wing absorption and lower Lyα transmission. Conversely, brighter galaxies, despite having larger ionized regions and higher transmission, remain constrained by their lower intrinsic EWs, limiting their overall detectability.


Our modeling indicates that around 1 in 10 galaxies is expected to be observed in Lyα, even at these very high redshifts. At the time of writing there are about 15 Lyman-break candidates with a redshift between 12 and 14 and a UV magnitude between -19 and -18 (see Fig. 2 of [Carniani2024arXiv240518485C] and references therein). Of these candididates, JADES-GS-z13-1-LA [Witstok2024arXiv240816608W] is the only galaxy observed as a LAE, with another two spectroscopically confirmed galaxies showing no sign of Lyα [Curtis-Lake2023NatAs...7..622C]. This work highlights the complexities in detecting Lyα emission from the early Universe and underscores the importance of considering both galaxy properties and reionization morphology when interpreting these high-redshift observations. As the sample of LAEs identified by JWST continues to grow, this study offers valuable insights into the conditions required for early Lyα emission detection and their implications for the onset of cosmic reionization. The data underlying this article will be shared on reasonable request to the corresponding author.


Simulating Population (Pop.) III star formation in mini-halos in a large cosmological simulation is an extremely challenging task but it is crucial to estimate its impact on the 21cm power spectrum. In this work, we develop a framework within the semi-analytical code MERAXES to estimate the radiative backgrounds from Pop. III stars needed for the computation of the 21cm signal. We computed the 21cm global signal and power spectrum for different Pop. III models varying star formation efficiency, initial mass function (IMF) and specific X-ray luminosity per unit of star formation (Lx/SFR). In all the models considered, we find Pop. III stars have little to no impact on the reionization history but significantly affect the thermal state of the intergalactic medium (IGM) due to the strong injection of X-ray photons from their remnants that heat the neutral IGM at redshift of 15 or greater. This is reflected not only on the 21cm sky-averaged global signal during the Cosmic Dawn but also on the 21cm power spectrum at redshift of 10 or less where models with strong Pop. III X-ray emission have larger power than models with no or mild Pop. III X-ray emission. We estimate observational uncertainties on the power spectrum using 21CMSENSE and find that models where Pop. III stars have a stronger X-ray emission than Pop. II are distinguishable from models with no or mild Pop. III X-ray emission with 1000 hours observations of the upcoming SKA1-low.


When and where did Population III (Pop. III) stars form? What role did they play in the Cosmic Dawn and Epoch of Reionization (EoR)? And what is the best way to detect them? These questions remain open as no definitive observation of a mini-halo or Pop. III star has been reported. Up to the present day, we are relying on several cosmological simulations that investigate gas cooling and star formation in metal-free mini-halos (mass of around 10^5 to 10^7 solar masses). To gain insight, small size and high-resolution hydrodynamical simulations have been performed [e.g. Greif2011, Hirano2018, Chon2021, Chon2022, Toyouchi2023, Sadanari2024] that suggest that metal-free (or poor) mini-halos favour the formation of Pop. III stars with a more top-heavy Initial Mass Function (IMF) and with lower star formation efficiencies than observed today. It is also thought that Pop. III star formation might occur down to the end of the EoR at redshift less than approximately 6 in pristine metal free pockets of gas [e.g. Venditti2023]. The variety and complexity of the processes involved in Pop. III star formation and the resolution required to keep track of the evolution of the gas particles, limits the size of these hydrodynamical simulations to ~ 100 kpc. In order to mitigate this problem, semi-analytical models that account for Pop. III star formation have been developed [e.g. Visbal2020,Hegde2023,Boyuan2024]. These models allow a statistical study of Pop. III star formation in mini-halos out to scales of ~ 10 Mpc.


While these volumes start to investigate the chemical enrichment of the intergalactic medium (IGM) and the Pop. III/II transition, they are still too small to study the EoR as volumes of at least ~ 200 Mpc are required ([Iliev2014, Kaur2020, Balu2023]). Observations and models are converging on a scenario where the Universe was completely ionized by redshift of ~ 5.3 [e.g. Fan2006, Ouchi2010, McGreer2015, Qin2021, Bosman2022,Qin2024] with reionization likely driven by low-mass halos [e.g. Kuhlen2012, Qin2021b, Saxena2024, Mutch2024]. However, the impact of Pop. III stars and mini-halos on the EoR is unclear. Pop. III stars are likely to be the dominant contribution to the total star formation rate density (SFRD) at redshift greater than 15-20 and, if their IMF is more top-heavy than the present day one, Pop. III could significantly contribute to the heating and the ionization of the IGM which determines the evolution and shape of the 21cm signal [e.g. Qin2020, Jones2022, Sartorio2023]. The 21cm signal represents our most promising tool to put constraints on the thermal state of the IGM during the Cosmic Dawn and EoR. Even though no confirmed detection has been reported so far, the first upper limits on the 21cm power spectrum obtained with HERA phase I strongly disfavour cold reionization scenarios ([Hera2023]). While individual bubbles will be too small to be detected, it is possible to directly detect the EoR at z of approximately 10 by stacking redshifted 21-cm spectra centered on known galaxies [Geil2017]. In the last few years, the impact of Pop.


III stars on the 21cm signal has been studied using both analytical and semi-analytical models [e.g. Cohen2017, Chatterjee2020, Mebane2020]. However these models either did not compute reionization (e.g. [magg2022, Hegde2023, Hector2024]), focusing only on the absorption trough of the 21cm signal occurring at redshift of around 13-20, or used a very simple analytical approach to compute reionization (e.g.[Ventura2023]). On the other hand, [Cohen2017], [Qin2021] and [munoz2022] used a simple analytical model for modeling Pop. III star formation but computed the reionization self-consistently. In this work, we overcome these challenges using a realistic Pop. III star formation and mini-halo model ([Ventura2024]) developed within the semi-analytical model MERAXES designed to self-consistently couple galaxy formation and reionization. While in [Ventura2024] we ran this model on a small (L = 10 h-1 cMpc) and high-resolution box, here we extend it to a significantly larger volume simulation (L = 210 h-1 cMpc) enabling the study of cosmic reionization. Since at such large volumes we cannot directly resolve mini-halos, we implemented scaling relations between the SFRD and the dark matter density field calibrated on the results from the small and high-resolution box discussed in [Ventura2024]. With this new model we are able to accurately follow the evolution of the radiative backgrounds relevant to the EoR and 21cm signal (X-rays, Lyman-alpha, ionizing UV, Lyman-Werner) and to disentangle the contribution of Pop.


III star formation to the 21cm global signal and power spectrum. Pop. III stars are expected to have a stronger impact at redshift of 15 or greater where they dominate star formation and ionization. Differently from previous works who explored the differences in the 21cm signal at Cosmic Dawn due to various Pop. III models, here we focus our attention on the residual signature of Pop. III on the 21cm power spectrum at redshift of 10 or less where the sensitivity of SKA is expected to be significantly better and a detection is more plausible. To achieve this, it is crucial to model both Pop. III star formation and reionization in a self-consistent framework. This study allows us to assess under which conditions an early heating of the IGM from Pop. III stars leaves a detectable imprint on the 21cm power spectrum at redshift of 10 or less. This paper is structured as follows. In Section 2 we give a brief overview of Pop. III star formation in MERAXES. In Section 3 we present the scaling relation between the SFRD in mini-halos and the density field calibrated from the small and high-resolution box which is implemented in the large (210 h-1 cMpc)^3 box. In Section 4 we discuss the impact of different Pop. III star formation models on the 21cm power spectrum and in Section 5 we make forecasts on the observability of these power spectra with SKA. Finally, we summarize our main results and conclusions in Section 6.


Our simulations use the best-fit parameters from the [Planck16]: h = 0.6751, Omega_m = 0.3121, Omega_b = 0.0490, Omega_Lambda = 0.6879, sigma_8 = 0.8150, and n_s = 0.9653. MERAXES is a semi-analytical model (SAM) designed to study the interplay between galaxy formation and reionization ([Mutch2016, Qin2017, Qiu2019, Ventura2024]). MERAXES includes a number of free parameters that are calibrated against observations (see Tables 1 and 2). Values in Table 1 are calibrated against observed luminosity functions and stellar mass functions at redshift of around 5-8 while those in Table 2 are calibrated against constraints on the neutral hydrogen fraction, ionizing emissivity and the Thomson scattering optical depth tau_e from [Planck2020]. The most recent version of MERAXES ([Ventura2024], V24) includes Pop. III star formation and mini-halo physics. As shown in V24, the Pop. III parameters with the largest impact are the star formation efficiency alpha for Pop III and the shape of the IMF. The latter has a large impact on galaxy evolution as it determines the strength of the feedback and the emission properties of the Pop. III stellar population. In the following sections we quickly summarize the main features of MERAXES relevant for this work. Main free parameters for galaxy formation. Main free parameters for reionization. MERAXES post-processes the output of an N-body dark matter only simulation, reading the spatial and physical information of dark matter halos and computing the baryonic physics of galaxy formation.


In particular processes included are: (i) gas infall onto dark matter halos, (ii) radiative cooling of the infalling gas, (iii) star formation and (iv) supernova and AGN feedback. In V24 the cooling prescriptions were updated to account for H2 cooling (the main cooling channel in mini-halos) and a more detailed metal enrichment model to keep track of the metallicity of each gas reservoir in a halo (which is crucial to distinguish between Pop. III and Pop. II star formation episodes). We also account for the effects of both baryon-dark matter streaming velocity and H2 photo-dissociation by the Lyman-Werner background which increases the minimum mass of a mini-halo capable of hosting stars [e.g. Schauer2021]. Our model accounts for spatial variations only for the LW background, while for the relative velocity we assume a mean value throughout the entire box. For this work, we updated MERAXES by adding the effect of H2 self-shielding which counteracts the H2 photo-dissociation, increasing the Pop. III SFRD by up to one order of magnitude at redshift of around 10 (see e.g. [Feathers2024]). We discuss the details of the implementation and impact of H2 self-shielding in MERAXES in the Appendix A. We refer the reader to [Mutch2016] for a more detailed explanation of the main architecture of MERAXES, [Qiu2019] for the supernova model and V24 for the mini-halo model. The main free parameters that regulate the galaxy formation in MERAXES are summarized in Table 1.


The Pop. II related ones are taken from [Balu2023] where MERAXES was run on a cosmological volume of L = 210 h-1 cMpc resolving all atomic cooling halos and calibrated in order to match the observed UV luminosity functions at redshift of around 4-7 (the agreement holds up to redshift of around 13 as shown in [Qin2023]) and the stellar mass functions at redshift of around 5-8. Given the lack of observations of Pop. III stars, the Pop. III parameters are largely unconstrained. The fiducial values adopted in this work are taken from V24 and their values are suggested from hydrodynamical simulations [e.g. Chon2021]. Together with galaxy formation, MERAXES self-consistently computes the reionization and thermal evolution of the IGM using a modified version of the semi-numerical code 21cmFAST ([Mesinger2011]). In this work, we compute the backgrounds relevant for the computation of the 21cm signal: the UV ionizing, X-rays, Lyman-alpha and Lyman-Werner (LW). The first is crucial to study the evolution of the reionization, while the X-ray and the Lyman-alpha backgrounds determine the thermal state of the IGM. In particular the X-ray background is likely to be the dominant contribution to the heating of the IGM once the first galaxies form and the lyman-alpha background is responsible for the coupling between the kinetic and the spin temperature of the neutral hydrogen.


The LW background does not directly affect the IGM temperature, but determines whether or not mini-halos have enough molecular hydrogen to cool the gas and form Pop. III stars. Hereafter, we briefly summarize the key quantities that determine the evolution of these backgrounds. For a more detailed explanation on the implementations of these backgrounds, we refer the reader to [Balu2023] for the UV, Lyman-alpha and X-ray and to V24 for the LW. The ionizing background is mostly dependent on the SFRD, the average number of ionizing photons per stellar baryon N-gamma and the escape fraction of the UV photons f_esc. The second quantity is mostly determined by the IMF: for Pop. II stars we adopt a Kroupa IMF which leads to N-gamma of approximately 6000. Since the Pop. III IMF is a free parameter in our model, N-gamma for Pop III is computed from the IMF adopted using the Pop. III stellar spectra from ([Raiter2010]; N-gamma for Pop III of approximately 20000 - 70000). f_esc is tuned to reproduce the EoR histories in agreement with observations. As per [Balu2023], we adopt a redshift-dependent escape fraction defined as followed: The escape fraction is given by an equation where the escape fraction equals a baseline value multiplied by a factor related to redshift. X-ray emission is mostly associated with high mass X-ray binaries (HMXB) and its contribution is proportional to the SFRD.


In this work we use the widely adopted approximation for the comoving X-ray specific emissivity (erg s-1 Mpc-3) is proportional to Lx / SFR x SFRD. Finally, we need to account for the fact that only photons with an energy below 2 keV (soft X-rays) are able to heat the IGM. As a result the main free parameter that regulates X-ray emissivity is the soft X-ray luminosity per unit star formation L_X<2keV / SFR. For Pop. II stars, this quantity is estimated from theoretical studies of emission spectra of HMXBs in low metallicity environments [e.g. Fragos2013, Madau2017, Das2017, Qin2020,Kaur2022]. For Pop. III stars there are no observational constraints as this quantity depends on the unknown Pop. III IMF. Recently, [Sartorio2023] estimated the Lx / SFR for Pop. III stars and found that for more top-heavy IMFs this quantity can be up to two orders of magnitude higher than the Pop. II value. We highlight that in this work we separately compute the backgrounds from Pop. III and Pop. II stars due to the different spectra, properties and star formation rate density of the two distinct populations. Using the radiative backgrounds computed from the galaxy population in MERAXES, we can estimate the 21cm signal. We encourage the reader to see [FurlanettoRev], [Morales2010], [PritchardRev] and [LiuRev] for reviews on the topic. Hereafter we only summarize the key equations used in this work (see also [Balu2023]).


We start with the 21cm brightness temperature field (delta T_b) which measures the deviation of the spin temperature of the neutral hydrogen (Ts) from the cosmic background T-gamma (i.e. the CMB). This is given by the 21cm brightness temperature equation, which measures the deviation of the spin temperature of the neutral hydrogen from the cosmic background temperature. It depends on the neutral hydrogen fraction, density contrast, Hubble parameter, and the ratio of the spin temperature to the cosmic microwave background temperature. where tau at frequency nu0 is the optical depth at the 21cm transition frequency nu0, xH is the neutral hydrogen fraction, 1 + delta_nl is the density contrast in the dark matter field, H(z) is the Hubble parameter at the redshift z, and dv_r /dr is the radial derivative of the line-of-sight component of the peculiar velocity. Once the cosmological model ([Planck16]) and the velocity and density field (from the N-body simulation) are fixed, delta T_b is determined by the ionization and the spin temperature fields. The latter quantifies the population ratio of the two HI hyperfine energy levels and is sensitive to the thermal state (i.e. the kinetic temperature TK) of the gas as follows: The spin temperature is determined by a formula involving the cosmic microwave background temperature, kinetic temperature, and the Lyman-alpha and collisional coupling coefficients. where T-alpha is the colour temperature which we take equal to TK while x-alpha and x_c are the Lyman-alpha and collisional coupling coefficients, respectively.


These coefficients quantify the strength of the processes (resonant scattering of Lyman-alpha photons, [Wouthuysen1952], and collisions with free electrons) that drive the spin temperature towards the kinetic temperature (when x-alpha + x_c >> 1, Ts is approximately TK otherwise Ts is approximately T-gamma). TK is sensitive to the adiabatic cooling and to all the processes able to heat up (or cool) the IGM with the most dominant coming from the X-ray emission. Hence in this work we will consider only the X-ray heating neglecting the other source of heating such as primordial magnetic fields ([Minoda2019,Bera2020,Cruz2024a]), Lyman-alpha ([Ciardi2010,Reis2021,Mittal2021]), shocks ([Furlanetto2004,Gnedin2004,Ma2021]), cosmic rays ([Bera2023]), early accreting black holes ([Mebane2020, Ventura2023]) and decaying or annihilating dark matter ([Liu2018, Sun2023, Hou2024, Facchinetti2024]). Ultimately, the evolution of Ts during the Cosmic Dawn and the EoR is mostly determined by the Lyman-alpha (for the coupling between Ts and TK) and X-ray flux. Using Eq. 1 we can estimate both the all-sky averaged global signal and its fluctuations (i.e. the power spectrum). In this work we will often use the reduced power spectrum, unless otherwise stated. In this section, we present a novel approach that enables us to efficiently estimate the SFRD from mini-halos in a large box (that does not directly resolve these objects) using results from a small, high-resolution box.


In Table 3 we summarize the key parameters for both the small (L10) and large (L210) box. Our starting point is the small (L = 10 h-1 cMpc) high-resolution (halo mass resolution of M of approximately 4.7x 10^5 solar masses) simulation used in V24. When building a scaling relation between SFR and other physical quantity, the first obvious choice is the dark matter density field delta. For instance [Munoz2023] showed, as a first-order approximation, SFR scales as e to the power of delta_R where delta_R is the density field smoothed over a certain radius R and this relationship works quite well for delta of approximately 0 and large R (greater than or equal to 3Mpc). To link our SFR in mini-halos with the density field, we first compute density, delta(x, z), and SFR grids for both Pop. III, SFR for Pop III (x, z), and Pop. II, SFR for Pop II (x, z), in the L10 box using the same grid resolution used in [Balu2023] to compute reionization (L_pixel of approximately 0.3 cMpc) and accounting for the SFR within mini-halos. We highlight that our L_pixel is quite small compared to the smoothing radius R adopted by [Munoz2023], hence we expect a significant scatter in the above relation. We also split the contribution between Pop. III and Pop.


II stars (a chemically enriched mini-halo will form Pop. II stars). In the left panel of Fig. 1 we show our Pop. III SFR distribution as a function of the overdensity delta and with the grey line we highlight the SFR is proportional to e to the power of delta_R relation as in [Munoz2023]. Despite the significant scatter for the reasons outlined above (sigma of approximately 0.65), the analytical approximation agrees with our results. The results shown hereafter are obtained from our fiducial simulation in V24. We start by investigating the distribution function of log10(SFR) at a fixed overdensity delta and redshift log10(SFR(delta, z))) finding that it follows a Gaussian distribution (or lognormal in the linear space). We show results for log10(SFR for Pop III) and selected values of delta in the smaller panels in Fig. 1. Hence, we can write: A formula describing the distribution of star formation rates given overdensity and redshift, which follows a Gaussian form. where the normalization A, the mean log10(mean SFR) and the standard deviation sigma all depend on the overdensity and redshift. The normalization is defined as the ratio between the number of SF pixels and the total number of pixels. We found the best fit parameters for each delta (grouped in bins of width = 0.1) and snapshot of the simulation.


We tested whether the log10(SFR) distribution function is indeed Gaussian by conducting a K-S test. P-values are calculated for each cell with SFR > 0 and taking a predefined significance level of 0.05 below which the null hypothesis will be rejected. Results are shown in Fig. 2 for both SFR for Pop III and SFR for Pop II. P-values always exceed the significance level for both Pop. III (left panel) and Pop. II (right panel) SFR suggesting that the Gaussian distribution reproduces the distribution of star formation rates given overdensity and redshift both in the Pop. III and Pop. II cases. As expected, we see that there are far more Pop. III star forming pixels than Pop. II ones as mini-halos are more likely to form Pop. III stars. The next step is to study how the mean, standard deviation and normalization evolve with delta and z. In Fig. 3 we show the redshift evolution of these parameters for delta = 0.5 (black), 1.0 (grey), 1.5 (purple), 2.0 (red), 2.5 (green) and 3.0 (blue). mean SFR for Pop III exhibits an almost constant trend in redshift and a correlation with delta (higher delta results in higher mean SFR for Pop III). This demonstrates that mean SFR for Pop III is mostly determined by the number of Pop.


III star forming halos in a pixel, which is higher for more overdense regions. Since Pop. III star formation episodes in mini-halos are often the first episode of star formation experienced by a galaxy, it is not impacted by supernova feedback so the Pop. III SFR is almost constant at all redshift. This also explains why sigma is constant for all z and delta (sigma for Pop III of approximately 0.65). The parameter that is more sensitive to both delta and z is the normalization. For very overdense regions (delta greater than or equal to 2) it is almost one, meaning that almost all the overdense pixels host Pop. III SF mini-halos. For lower delta there is also an evolution in z as, with cosmic time, lower density regions will host a larger number of mini-halos above the minimum mass for star formation. We repeated the same analysis for Pop. II star forming pixels (see Fig. 4). In this case the evolution is more scattered as Pop. II star formation episodes are not the first star forming episodes within a galaxy and so will be affected by both mechanical and chemical feedback from the previous history of the galaxy. This is also demonstrated by the larger standard deviation (sigma for Pop II of approximately 0.8). The average value of mean SFR for Pop II is ~ 1 order of magnitude higher than for Pop. III.


This reflects the higher Pop. II star formation efficiency. Finally, A for Pop II is always smaller than A for Pop III showing that it is less likely for a mini-halo to form Pop. II stars. We test this parametrization on the small box by estimating the mini-halo contribution to the Pop. III and Pop. II SFRD from the matter density field. To do this, we read the density grid at each z and for each pixel assign a a value of Pop. III SFR drawn randomly from the distribution of star formation rate using delta of the pixel. We repeat the same procedure for SFR for Pop II adding the constraint that in order to have SFR for Pop II > 0 that pixel needs to already have experienced a Pop. III star formation episode. This latter condition ensures a more realistic enrichment model (a pixel cannot have Pop. II star formation if it has not previously hosted Pop. III star formation). We ran twenty different realizations and for each realization estimated the SFRD for Pop III and SFRD for Pop II and compared with results of the simulations. Results are shown in Fig. 5. In the upper panels we show the Pop. III (left) and Pop. II (right) SFRD from MERAXES output (black line) and from each realization using the method outlined above (cyan shaded lines).


In the lower panels we show the ratio between the average of the 20 realizations and the true SFRD from MERAXES. All the realizations are in reasonable agreement with the data and the ratio is always lower than ~ 10% for both populations. This demonstrates the validity of the method outlined above. The main advantage of this method is that it allows estimation of the SFRD from mini-halos in a simulation where these are not directly resolved. Parametrizing SFRD with a Gaussian distribution enables us to account for stochastic star formation (different pixels with same delta can have different SFR), without losing the correlation with the matter density field (mean SFR, sigma and A all depend on delta). This method can be applied as long as the density field from both the low and the high resolution simulation share the same properties (mean, standard deviation) and it can be calibrated for any choice of parameters. We can now apply the methodology outlined in the previous section to the L210 box that can only resolve the atomic cooling halos by reading the density field and applying the distribution of star formation rate calibrated on different models. In Fig. 6 the mini-halo contribution to the Pop. III SFRD shows a good agreement between the two different simulations.


We highlight that our scaling relations do not explicitly depend on the Lyman-Werner background (except for the regions that are strongly irradiated by LW flux for which the distribution of star formation rate = 0). This implicitly assumes that both the L10 and L210 box have similar LW backgrounds. We verify this assumption by computing the average LW background and LW maps in both simulations (See Fig. 7 ). In the bottom right panel we show the redshift evolution of the LW background (in units of 10 to the power of -21 erg per second per square centimeter per Hertz per steradian) in the L10 (black line) and in the L210 box (red line). The two lines share similar trends showing that both simulations have a similar average LW background. The left and top right panels show the 2D projections of the LW field in the large and small box. These maps illustrate that the LW background is roughly uniform (as expected given that the mean free path of LW photons is ~ 100 Mpc). These plots demonstrate that the LW fields in the small and large box are indeed comparable showing that the estimation of the star formation in mini-halos with the scaling relations accounts for the radiative feedback. Differently from what has been done by [Hazlett2024] who calibrated a semi-analytical model to the Reinassance simulation in order to account for Pop.


III star formation by adding the previous star formation history to each atomic cooling galaxy resolved in the simulation, the methodology described in this section allows us to estimate only the total SFRD occurring in mini-halos within a certain pixel of the simulation. In this work we focus on three models of Pop. III star formation by varying three main parameters: the star formation efficiency, the IMF and the specific Pop. III X-ray luminosity per unit star formation while all the other free parameters (e.g. the escape fraction) are fixed at the fiducial value (see Tables 1 and 2). We chose to focus only on these three parameters since these have the strongest impact on both the evolution of the Pop. III SFRD and the amount of UV and X-ray photons emitted. The values chosen for the specific Pop. III X-ray luminosity per unit star formation are similar to those found in [Sartorio2023] for the different IMFs explored in their work. Hereafter, we analyze three different Pop. III models designed to have the minimum, intermediate and maximum impact from Pop. III star formation in mini-halos, each model is summarized in Table 4. The IMFs considered in this model are a Salpeter between 1 and 500 solar masses and a log-Normal IMF centered at 60 solar masses (see V24 for more details).


We highlight that in our extreme Pop. III model we enhance star formation efficiency, Lx/SFR and the top-heaviness of the IMF at the same time. Each of these parameters has a different impact on the evolution of the 21cm signal (see Appendix B for a more detailed discussion of how each Pop. III parameter changes the evolution of the 21cm global signal and power spectrum). We can now estimate how different Pop. III star formation models in MERAXES affect the 21cm signal. We started by verifying that, after introducing the additional Pop. III contribution to the fiducial Pop. II only model ([Balu2023]) we still obtain reionization histories consistent with the observational constraints on the Thomson scattering optical depth tau_e (Fig. 6) and neutral hydrogen fraction (Fig. 7). The reionization histories from the models with Pop. III stars are only slightly modified and this negligible contribution comes from the secondary ionizations from X-rays. This is expected given that at z less than or equal to 15 the Pop. III SFRD is at least one order of magnitude lower than Pop. II and their main contribution is expected from the X-ray emission rather than the UV. We compute the sky-averaged 21cm global signal (see Fig. 8) without (black line) and with (grey, cyan and red line for weak, moderate and extreme Pop. III respectively) Pop.


III star formation. As expected, introducing a Pop. III population with the same X-ray properties as Pop. II ones (i.e. weak Pop. III), simply shifts the absorption through to earlier epochs in virtue of the stronger coupling at higher-z (see also [Ventura2023,Hegde2023]). However, if Pop. III stars have a stronger X-ray emission (i.e. moderate and extreme models) as suggested by [Sartorio2023], the absorption signal is quickly suppressed turning into an emission signal as early as redshift of around 18 for the extreme Pop. III model and at z of approximately 13 for the moderate Pop. III one. We note that a similar result has been found by a contemporaneous work by [Jones2025] who found an analogous variation in the timing (Delta-z of approximately 3) and depth (Delta-delta-T_b of approximately 50 mK) of the absorption trough when considering a stronger X-ray contribution from Pop. III stars (in their model the Lx/SFR is self-consistently modeled from the IMF so that the difference between their Int-0 and Sal model is of 2 orders of magnitudes.) As shown in Fig. 10 earlier coupling and heating from Pop. III impacts the 21cm power spectrum both at the large and small scales. The models considered here produce 21cm signals that are different not only during the coupling and heating epoch (redshift of around 10 - 20), but also at lower redshift when the reionization is in progress.


The impact is stronger at smaller scales where models with a stronger heating exhibit a larger power spectrum at redshift of around 7 - 10. This is of crucial importance as current and upcoming facilities are improving their observations at z less than or equal to 10 (see more discussion in Section 5). We compare our results with the ones in [munoz2022] who studied how different Pop. III parameters impact the 21cm signal using 21cmFAST. In the left panel of Fig. 10 the yellow and brown dashed lines are obtained by changing the specific Pop. III X-ray luminosity by a factor of 9. The global trends are similar with our models with stronger Pop. III X-ray emission (dashed yellow line and red/cyan lines) showing an earlier and weaker first peak compared to low X-ray models (dashed brown and grey lines). In their model, different Pop. III X-ray properties strongly impact the position and amplitude also of the second peak. In our models instead, the position of the second peak is only slightly anticipated in the strong X-ray models. This difference is likely due to the fact that our second peak occurs at much lower redshift (z of approximately 10) when most of the emission comes from Pop. II stars. Finally, differently from [munoz2022] at z of approximately 10 simulations with a stronger Pop.


III X-ray heating have a significantly larger power spectrum compared to weak X-ray models (a similar result has been found also by [Jones2025]). This analysis shows that Pop. III star formation not only impacts the 21cm global signal during the cosmic dawn as previously assessed [e.g. Qin2020, Jones2022, Ventura2023, Hegde2023, Hector2024] but also that an early (redshift of 15 or greater) heating of the IGM provided by this population leaves a strong signature on the power spectrum during the EoR (z less than or equal to 10). The impact on the power spectrum is stronger for models that have a large Pop. III X-ray emissivity (i.e. moderate and extreme Pop. III models) while models with a milder X-ray emission (i.e. weak Pop. III) have a stronger effect on the global signal. Ultimately, this tells us that the power spectrum during the EoR can be used to disentangle different heating models and potentially constrain the properties of Pop. III stars. We highlight that here we considered only the X-ray emission from stellar remnants. While there might be other sources that significantly heat the IGM at redshift of 15 or greater (see discussion at end of Section 2.3), the other effects are likely to be either subdominant, still related to Pop. III stars (e.g. cosmic rays) or dominant only at the dark-ages (e.g. dark matter annihilation).


Finally, we note that in this work we did not include the effect of the X-ray feedback on Pop. III star formation. As noted by [Ricotti2016,Park2021], X-rays have both a positive and negative effect on Pop. III star formation as they heat the gas and increase the electron fraction. The heating makes gas accretion more difficult (hence delaying star formation) and free electrons promote the formation of H2 making the molecular cooling more efficient. In presence of a strong X-ray background this latter effect is dominant at 10 < z < 20 (see e.g. Fig. 9 in [Hegde2023]). Hence, including the X-ray feedback would likely increase the Pop. III SFRD making the impact of Pop. III stars even stronger than what predicted here especially for the moderate and extreme models. In the previous section we showed that an early heating of the IGM significantly affects the 21cm power spectrum during the EoR. Now we want to investigate how our models compare with the currently available upper limits and whether their differences will be observable with SKA. In this section we consider the power spectrum at z less than or equal to 10 as the current and upcoming interferometers are significantly less sensitive at higher redshift.


To better appreciate this, in Fig. 11 we show the power spectrum noise (mK squared) with SKA as a function of redshift at k of approximately 0.2 and 0.9 cMpc-1 assuming a 1000 hours (solid lines) and 180 hours (dashed lines) observations with SKA. At higher redshift the noise steadily increases and already at redshift of 10 or greater the noise is of the order of 10s to 100s mK squared with 1000 hours observation. Firstly, we compare our predictions with current upper limits from a number of facilities including MWA, LOFAR, GMRT, PAPER and HERA (we focus at z = 7 - 10 where most of the measurements have been taken). In Fig. 12 we show the 21cm power spectrum at z = 10, 9, 8 and 7 for all the four models together with the available upper limits (see label). All our models are below these upper limits. However, the moderate and extreme Pop. III models are closer to the current HERA constraints at z = 8 suggesting that soon these models can be either detected or ruled out. In our model the main effect of different Pop. III models is to change the timing and amplitude of the peaks in the 21cm power spectrum rather than introducing a specific feature.