We note that we did not account for spatial variations in the velocity acoustic oscillations (see Section 2.1) which would introduce wiggles in the power spectrum at scales k of approximately 0.1 Mpc-1 ([Hector2024]). While this effect can be important when focusing on the 21cm power spectrum during the coupling and heating epochs, these fluctuations are quickly washed out at z less than approximately 13 (see Fig. 13 and Section 6C in [Hector2024]). We next consider the upcoming SKA. In order to estimate the observability of the four models analyzed so far, we perform a similar analysis as in [Balu2023b] that we briefly summarize hereafter. The sensitivity of a radio interferometer is mostly regulated by the thermal noise and the cosmic variance with the former dominating the noise at small scales and the latter at large scales. The thermal noise is related to the bandwidths of the instrument, beam factor (see [Parsons2014]), the integration time of the mode k and the temperature of the system (given as the sum of the sky and receiver temperature) ([Morales2005,McQuinn2006,Parsons2012]). We can hence write the total noise by summing these two components: A formula for the inverse square of the total noise on the power spectrum, calculated by summing over individual noise components. By doing so, we are effectively assuming that the errors are Gaussian distributed, which is reasonable for the relevant scales in this work ([Qin2021,Prelogovic2023]).


Finally, a 21cm detection is heavily limited by the ability of removing the foregrounds. We used the python package 21CMSENSE ([Pober2013,Pober2014]) which, given the specifics of an interferometer, a mock 21cm power spectrum and an observational campaign, computes the interferometer sensitivity to the 21cm power spectrum under different assumptions of foreground removals. We used the assumption 'moderate' foreground removals and we focused on the first phase of SKA (i.e. SKA1-low), in particular we included the stations in the 'Central Area' of the SKA1-low, resulting in 296 stations of diameter 35m distributed across a circular area with 1.7 km diameter. We assumed two different observational campaigns: one of 180 hours (six hours per night for 30 days) and another of 1080 hours (six hours per night for 180 days). Additionally, we avoid the modes that are contained within the foreground wedge ([Datta2010]) so that effectively we are limited to k_min = 0.16 Mpc-1 for our analysis and k_max = 1.4 Mpc-1 (the latter arises from a combination of the spatial scales that are probed by the SKA1-low and the shot noise from our simulation). To quantify the detectability of a Pop. III model we compute by how many sigma its power spectrum differs from the one arising from the No Pop.


III model: An equation defining the detectability of a model, calculated as the difference between its power spectrum and a baseline model's power spectrum, divided by the combined uncertainty. where the subscript i refers to the Pop. III model considered and 0 to the No Pop. III model. To detect a Pop. III model the difference between its power spectrum and the No Pop. III one needs to be at least of 1-sigma otherwise the model is not detectable. In Fig. 13 we show the evolution in redshift of this quantity at k of approximately 0.2 (upper panel) and k of approximately 0.9 Mpc-1 (lower panel) for each Pop. III model and assuming 1080 (solid lines) and 180 (dashed lines) observation hours. The weak Pop. III model (grey line) is different from the No Pop. III one by less than 1-sigma both at the small and large scales even with an observation of 1080 hours. The moderate Pop. III model is several sigma away from the No Pop. III model at 7 < z < 10 both at the small and large scales with a 1080 hours observation while with a 180 hours the model is detectable only at the large scales where the difference is between 1 and 2 sigma. The extreme Pop.


III model is the one with the largest difference from the No Pop. III model being potentially detectable at both large and small scales even with a 180 hours observations. However, Finally, we highlight the differences between each Pop. III model by showing their power spectrum noise (shaded regions) assuming 180 and 1080 hours of observations in Fig. 14 and 15. Models with stronger X-ray contribution (red and cyan lines) have a power spectrum that differs from the models with no or mild Pop. III contribution (dark and light grey regions) by more than the observational uncertainty. The 1-sigma region of its power spectrum (pink shaded region) is above the models with no or mild Pop. III contribution at z = 7 and 8 for all the k-modes, at z = 9 at k less than approximately 0.7 Mpc-1 and at z = 10 only at the largest scales considered (k less than approximately 0.4 Mpc-1). With only 180 hours observations however, it is not possible to clearly distinguish between the intermediate and extreme Pop. III model (blue an pink shaded regions). At z = 6 it is not possible to distinguish any of these models since at this redshift the power spectrum is mostly determined by the ionization state of the IGM which is identical for all the four models considered.


The sensitivity greatly improves for an observational campaign of 1000 hours (Fig. 15). In this case, models accounting for Pop. III early heating which is stronger than Pop. II are clearly distinguishable from models with no or mild Pop. III contribution. At z = 10, 9 and 8, it is even possible to distinguish between intermediate and extreme Pop. III models at all scales within k_min and k_max, indicating that SKA observations of the 21cm power spectrum during the EoR are sensitive to the IGM heating occurred at redshift of 15 or greater. At z = 7, the difference between the various models are less evident but intermediate and extreme Pop. III models still fall outside the uncertainty regions of weak Pop. III and No Pop. III. This indicates that models with a harder Pop. III X-ray emission can be disentangled from models with no or mild Pop. III X-ray emission even at z = 7. Also [Jones2025] focused on the possibility of detecting difference Pop. III models using 21cm observations. In their analysis they included both REACH (sensitive to the 21cm global signal) and SKA-Low confirming that an observation of ~ 3000 hours with SKA-Low can constrain the Pop. III IMF due to their difference in the X-ray heating.


Finally, we highlight that the impact of Pop. III stars is visible on the power spectrum as long as their X-ray contribution is boosted compared to Pop. II. The differences between the weak Pop. III and the No Pop. III scenario are so small they will not be visible even with 1000 SKA hours. This demonstrates that an upcoming 21cm power spectrum detection will shed light on the properties of the first sources establishing their contribution to the heating of the IGM. In this work we investigated how the early (redshift of 15 or greater) heating of the IGM due to Pop. III stars impacts the 21cm power spectrum during the EoR (z less than or equal to 10) which will be observable by the SKA. We developed a framework of scaling relations between Pop. III star formation rate in mini-halos and the density field within the semi-analytical model MERAXES that allows us to account for the radiative contribution of mini-halos that cannot be directly resolved in a large (L = 210 h-1 cMpc) cosmological simulation. The scaling relations are calibrated on a smaller and higher resolution simulation able to resolve all the mini-halos. We then investigated three Pop. III models each with different IMF, star formation efficiency and specific X-ray luminosity.


This formalism is both based on realistic galaxy population and it provides an accurate estimation of the Pop. III backgrounds yielding a computation of the ionization and thermal state of the IGM which is crucial to obtain a reliable estimation of the 21cm signal and power spectrum during the EoR ( z less than approximately 10). The key results can be summarized as follows: 1. The inclusion of Pop. III stars does not significantly change the EoR history as their main contribution comes from the secondary ionizations from their X-ray emission. As a result, all the models that we considered give reionization histories consistent with the latest constraints on the neutral hydrogen fraction and the Thomson scattering optical depth. 2. As previously known, the evolution of the 21cm global signal during the Cosmic Dawn is significantly impacted by Pop. III stars. In a model where Pop. III and Pop. II have the same X-ray specific luminosity (weak Pop. III) the absorption through of the 21cm global signal is slightly deeper and occurs at higher-z. If instead Pop. III stars have a larger Lx / SFR, the signal is seen in emission at higher-z (z of ~14 for the intermediate Pop. III model and z of ~18 for the extreme Pop. III model).


3. The heating from Pop. III stars significantly increases the 21cm power spectrum during the EoR both at large and small scales. This is more evident for models with an increased specific X-ray luminosity where the difference can be of more than a factor of 4 at z greater than or equal to 7. This shows that the 21cm power spectrum during the EoR is sensitive to the heating occurred at much higher redshift. 4. Focusing on a possible future detection of the 21cm power spectrum, we estimated the observational uncertainty of each model using the python package 21CMSENSE assuming an observational campaign with SKA1-low of 180 and 1080 hours respectively. We found that 180 hours are not enough to distinguish different Pop. III models but they already can confirm/exclude the presence of a stronger heating from Pop. III stars at high-z since their power spectra differs by more than 1-sigma from the No Pop. III model. However, using ~ 1000 hours of SKA, models with a stronger Pop. III contribution (stronger X-ray emission and/or higher Pop. III star formation efficiency) become clearly distinguishable at z greater than or equal to 7. This does not apply toward the end of the EoR (z less than or equal to 6) or for a model with the a lower Pop.


III X-ray emissivity (weak Pop. III). In the former case this is because at z of ~6 the power spectrum is mostly determined by the ionization state of the IGM (which is not impacted by Pop. III star formation in our models). When the Pop. III X-ray emissivity is the same as the Pop. II one, the 21cm power spectrum is only very mildly increased compared to the scenario without Pop. III stars. The power spectrum towards the end of the EoR (z less than or equal to 6) does not distinguish Pop. III models. We thank the anonymous referee for very constructive comments that help improve the quality of this paper. This research was supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D, project #CE170100013). This work was performed on the OzSTAR national facility at Swinburne University of Technology. OzSTAR is funded by Swinburne University of Technology and the National Collaborative Research Infrastructure Strategy (NCRIS). This research was also undertaken with the assistance of resources from the National Computational Infrastructure (NCI Australia), an NCRIS enabled capability supported by the Australian Government. SB acknowledges support from grant PID2022-138855NB-C32 funded by MICIU/AEI/10.13039/501100011033 and ERDF/EU, and project PPIT2024-31833, cofunded by EU--Ministerio de Hacienda y Funcion Publica--Fondos Europeos--Junta de Andalucia--Consejeria de Universidad, Investigacion e Innovacion.


YQ is supported by the ARC Discovery Early Career Researcher Award (DECRA) through fellowship #DE240101129. Finally, EMV thank A. Mesinger and J. B. Munoz for insightful discussions regarding the development of the scaling relation model and C. Power for assistance with the N-body simulation. The main data presented in this work have been analysed with the publicly available python package DRAGONS. The latest version of MERAXES is publicly available on GitHub. Further data and codes will be shared on reasonable request to the corresponding author. Many recent simulations [e.g. Nebrin2023,Hegde2023] have assessed the importance of incorporating H2 self-shielding in mini-halos as it significantly changes the minimum mass of mini-halos capable of cooling down the gas via molecular cooling. While this was not implemented in V24, for this work we now included it by updating M_crit, MC (Eq. 4 in V24) taking the fitting function found in [Kulkarni2021]: A formula defining the critical mass for molecular cooling, dependent on Lyman-Werner flux and streaming velocity. where a second formula defines the critical mass at z=20, and a third defines the redshift evolution power-law index. M_crit, MC is a function of the Lyman-Werner flux (J_LW) in 10 to the power of -21 erg per second per square centimeter and the rms streaming velocity at recombination (v_bc) in km per second.


This result is normalized to the minimum halo mass at z = 20 in absence of LW background and streaming velocity (M_z = 20)_0 and to typical values for LW background and streaming velocity (J_0 = 1, v_0 = 30). alpha_n and beta_n are free parameters calibrated to fit results of hydrodynamical simulations in [Kulkarni2021]. This fit accounts for the H2 self-shielding, so it makes the effect of the LW background on M_crit,MC less strong compared to what was previously assumed in V24 ([Visbal2015]). As shown in Fig. 14, accounting for self-shielding increases the Pop. III SFRD, especially when the Lyman-Werner background starts to build up. At z less than or equal to 15 the Pop. III SFRD when the H2 self-shield is considered (cyan dashed line) is ~ 1 order of magnitude higher than the no self-shield scenario (cyan solid). Similar results have been found by [Feathers2024]. While the 21cm power spectrum at z less than or equal to 10 is mostly sensitive to the amount of X-ray photons from Pop. III remnants, changing the star formation efficiency and the shape of the IMF impacts the 21cm signal evolution during the coupling and heating epochs.


In Fig. 15 and 16 we show the evolution of the 21cm global signal and power spectrum for the No Pop. III model (black line), Weak (grey line), Moderate (cyan line), high SFE (dashed grey line) and LogE (dashed red line) models. Compared to the Weak Pop. III model, increasing the Pop. III star formation efficiency, increases both the amount of Lyman-alpha and X-ray photons (they are both linked to SFR), hence the absorption trough shifts towards higher-z (Delta-z of ~1). Considering instead a top-heavy IMF, increases just the amount of Lyman-alpha photons hence the absorption trough becomes significantly deeper while still being at the same redshift compared to the weak Pop. III model. We note that this result is a consequence of the fact that we are considering the Lx/SFR and the shape of the IMF as two independent parameters. If, as shown in [Sartorio2023], the X-ray emissivity is linked to the shape of the IMF, the LogE model is not realistic as we would need to enhance the X-ray emissivity as well. We highlight that both the star formation efficiency and the shape of the IMF alone do not significantly affect neither the 21cm global signal nor the power spectrum at z less than or equal to 12 so a future 21cm detection with SKA-low likely will not help to constrain these parameters if they are not linked to a significantly stronger X-ray emissivity.