Halo Mass Function Constraints on Early Galaxy and AGN Populations in the JWST Era

abstract · abstract

The discovery by the James Webb Space Telescope (JWST) of massive galaxies and luminous active galactic nuclei (AGN) at high redshift provides an increasingly sensitive test of the connection between cosmological structure formation and the astrophysical processes that make dark matter halos observable. We develop a framework connecting the linear matter power spectrum to the mass variance, peak height, halo mass function (HMF), cumulative halo abundance, and observable galaxy and AGN populations. We use the Sheth-Tormen (ST) HMF as the baseline and compare it with an illustrative Bolshoi-Klypin-calibrated modification (KST) to quantify the sensitivity of predictions to the calibration of the HMF against cosmological N-body simulations. We apply the framework to three complementary tests: the baryonic and stellar mass reservoir available to massive galaxies, the abundance of halos capable of hosting luminous AGN, and the rest frame ultraviolet luminosity function of high redshift galaxies. Because the most massive systems occupy the rare, high peak tail of the halo distribution, modest changes in inferred host mass, baryonic conversion efficiency, black-hole occupation or duty cycle, and HMF calibration can produce large changes in predicted abundances. The ST-KST comparison shows that uncertainty in the high redshift halo population can materially affect the inferred host supply, particularly toward large z (10). Comparison with representative JWST massive galaxy, AGN, and UV luminosity function measurements demonstrates that matching the properties of an individual source is not sufficient for population consistency; the corresponding host halos must also exist in adequate numbers. Current observations provide increasingly stringent quantitative stress tests of both cosmological halo abundances and the baryonic and black hole physics at cosmic dawn.

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These results are therefore best interpreted as quantitative stress tests of the combined cosmological and baryonic model rather than as binary falsification criteria. A robust claim of inconsistency would require the discrepancy to persist across physically plausible uncertainties in stellar population modeling, stellar mass, redshift, lensing magnification, completeness, survey volume, cosmic variance, halo-mass definition, and baryonic conversion efficiency ( Boylan-Kolchin, 2023 ) . Within the controlled comparison developed here, the background cosmology and baryonic mapping are held fixed between ST and KST, so their difference isolates the sensitivity of the massive-galaxy constraint to the adopted halo-abundance calibration.

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and the efficiencies in Equation (82). The resulting halo-to-UV luminosity tracks are compared with the spectroscopically confirmed high-redshift GLASS/NIRSpec sources of Napolitano and others (2025) and with the massive-galaxy benchmarks reported by Labb’e and others (2023) (L23), whose implications for the available halo and baryonic reservoirs were examined by Boylan-Kolchin (2023) . These comparisons place the simple halo-to-light mapping in direct observational context across the JWST redshift range. Increasing halo mass produces a brighter UV source, while increasing ϵ ⋆ \epsilon_{\star} allows a lower-mass halo to reach a comparable luminosity.

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Together with the massive-galaxy and AGN abundance tests, the UV luminosity function completes the three observational applications of the common halo framework. The resulting comparison separates the cosmological abundance of potential hosts from the baryonic and black-hole processes that determine which of those hosts become observable at cosmic dawn.

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The high-redshift galaxy and AGN populations observed by JWST provide a sensitive test of the connection between cosmological structure formation and the baryonic processes that make dark-matter halos observable. The three applications considered in this work—massive galaxies, AGN host abundance, and the rest-frame UV luminosity function—probe different observables, but they share the same underlying question: does the cosmological halo population provide a sufficiently large reservoir of hosts once the mapping from halo mass to the observed population is specified?

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This distinction separates the problem into two coupled components. The cosmological component determines the abundance and mass distribution of halos. The astrophysical component determines how stellar mass, black-hole activity, and UV luminosity are assigned to those halos. At low redshift, moderate changes in either component may have relatively limited effects on predicted number densities. At cosmic dawn, however, massive systems occupy the rare, high- ν \nu tail of the halo distribution, where the abundance changes rapidly with both halo mass and redshift. Uncertainties in the observable-to-halo mapping and in the HMF calibration can therefore be strongly amplified.

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The standard Sheth–Tormen (ST) HMF provides the principal analytic baseline throughout the analysis. The Bolshoi/Klypin-corrected ST (KST) prescription provides an illustrative simulation-motivated test of the sensitivity to high-redshift HMF calibration. Since the KST factor in the adopted implementation is independent of halo mass at fixed redshift, it changes the available halo abundance without changing the common power spectrum, mass variance, peak-height calculation, or the baryonic and luminosity mappings. This separation makes it possible to identify which conclusions arise from the cosmological halo supply and which arise from the astrophysical mapping.

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The rare-halo tail amplifies the combined effect. A relatively small shift in an inferred stellar mass, Eddington ratio, or characteristic host mass may correspond to a much larger change in the predicted number of halos. Strong cosmological conclusions therefore require a joint treatment of observational errors, astrophysical scatter, and HMF calibration rather than variation of only one ingredient at a time.

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Three conclusions follow from this framework. First, the most massive high-redshift galaxies and luminous AGN probe the rare-halo regime in which small changes in host mass or redshift can produce large abundance changes. Second, the calibration of the HMF is itself an important component of the prediction; the ST–KST comparison demonstrates that uncertainty in the high-redshift halo supply can materially affect massive-galaxy, AGN, and UV luminosity-function tests. Third, the cosmological halo supply and the astrophysical observable-to-halo mapping must be treated as distinct but coupled components of the inference.

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The emerging JWST populations therefore provide quantitative stress tests of Λ \Lambda CDM structure formation and of the baryonic and black-hole physics that connect halos to observable sources. The most robust cosmological conclusions will come from discrepancies that persist after observational uncertainties, stochastic halo-to-light mappings, host-halo inference, and high-redshift HMF calibration uncertainties are treated jointly. In this sense, the earliest galaxies and AGN provide a direct observational bridge between primordial density fluctuations, nonlinear gravitational collapse, baryonic conversion, and black-hole growth.

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The last region is interesting as a possible pathway to form globular clusters, whose formation is still not well understood. Our results show that overdensities forming with initial amplitudes greater than δ c , 0 ≳ 4 × 10 − 3 \delta_{c,0}\gtrsim 4\times 10^{-3} at a wavenumber of k ∼ 200 k\sim 200 Mpc -1 can form star clusters with stellar masses of approximately Ω b Ω m ​ M halo ​ f ∗ ∼ 5000 ​ M ⊙ \frac{\Omega_{b}}{\Omega_{m}}M_{\mathrm{halo}}f_{*}\sim 5000\,M_{\odot} , which is at the low end of observed globular cluster masses [ 11 ] , although the cluster mass may be higher if f ∗ f_{*} is larger than the value of 0.04 assumed here—this uncertainty was discussed in Section III.2 . Larger clusters can also result if the overdensity forms from a lower wavenumber mode and higher initial value. This mechanism also links the formation of star clusters to dwarf galaxies, since both would be formed from relatively small dark matter halos, with efficient dynamical friction leading to the former. A link between the origins of these two classes of objects is an interesting consequence, given suggestions that the populations are not entirely separate [ 31 , 47 ] .

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In this work, we have explored the formation of stellar systems from enhanced density fluctuations. We showed that the higher density of the resulting early halos raises their virial temperature, and therefore allows halos to form stars below the usual ∼ 10 8 ​ M ⊙ \sim 10^{8}\,M_{\odot} threshold. If the effect of supernova feedback is also strong, then some of the halos that form stars will eject their stars and gas, leaving behind only a dark halo, with a density much higher than expected in Λ ​ CDM \Lambda{\rm CDM} . In addition, the dynamical friction timescales for stars in these dense halos can be short enough that stars can come to dominate the gravitational potential, even for relatively modest density fluctuations at wavenumbers above k ∼ 200 k\sim 200 Mpc -1 ; hence, the stars in such halos will appear as old star clusters as opposed to old galaxies. We also discuss various astrophysical uncertainties associated with these calculations, which alter the amplitudes of the different thresholds but not their scalings with wavenumber or halo mass.

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Across the four bins, a DESI-footprint survey reaches σ D V / r d = 0.78 , 0.40 , 0.33 , \sigma_{D_{V}/r_{d}}=0.78,\,0.40,\,0.33, and 0.28 % 0.28\% at bin centers z = 4.5 , 5.5 , 6.5 , z=4.5,\,5.5,\,6.5, and 8.0 8.0 (Fig. 4 , Table 1 ). These are percent-level measurements in a currently unconstrained part of redshift space. They are competitive with DESI’s low-redshift bins, and substantially smaller than the high-redshift quasar constraints. This follows from the combination of large volume, high bias, and sufficient number density as seen in Figure 3 .

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We then convert this halo mass track to a linear bias using the Tinker et al. [71] halo-bias relation. The resulting bias track is shown in the top panel of Fig. 3 . For the four LRD forecast bins used in this work, the inferred halo biases are b LRD = 3.4 , 4.5 , 5.8 , 8.1 b_{\rm LRD}=3.4,\ 4.5,\ 5.8,\ 8.1 at bin centers z = 4.5 , 5.5 , 6.5 , 8.0 z=4.5,\ 5.5,\ 6.5,\ 8.0 . Across all four bins the LRD bias exceeds that of every DESI tracer ( b ≈ 1.2 − 2.1 b\approx 1.2-2.1 ), rising to ∼ 4 × \sim 4\times the DESI samples at the highest redshift as seen in Table 1 . The corresponding clustering amplitudes are b ⁡ ( z ) ​ D ​ ( z ) = 0.80 , 0.89 , 0.99 , b(z)D(z)=0.80,\,0.89,\,0.99, and 1.13 1.13 , comparable to the b ⁡ ( z ) ​ D ​ ( z ) ≃ 0.6 − 1.6 b(z)D(z)\simeq 0.6-1.6 spanned by DESI tracers. The large LRD bias compensates for the suppressed matter growth at high redshift, yielding a clustering amplitude similar to that of established BAO samples.

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By z ∼ 7 z\sim 7 , growing black holes in the heavy-seed astrophysical models ( hs-edd1 and hs-edd5 ) generally accrete a fraction of the available gas mass (since this is lower than the fractional Eddington mass). This results in a convergence of the BHMFs - for example, for a black hole mass of 10 7 ​ M ⊙ 10^{7}\mathrm{M}_{\odot} , the number densities predicted by these two models are only different by a factor 2. The black holes in these models grow to masses of about 10 10 ​ M ⊙ 10^{10}\mathrm{M}_{\odot} for number densities of about 10 − 8 ​ c ​ M ​ p ​ c − 3 10^{-8}{\mathrm{c}Mpc^{-3}} . While black holes with M B ​ H ∼ < 10 7 ​ M ⊙ \mathrm{M}_{BH}\lower 2.15277pt\hbox{$\;\mathrel{\mathop{\kern 0.0pt\sim}\limits^{<}}\;$}10^{7}\mathrm{M}_{\odot} still grow slower in the ls-edd5 model, for higher masses, that BHMF lies between the heavy Eddington-limited and super-Eddington models and reaches out to 10 10 ​ M ⊙ 10^{10}\mathrm{M}_{\odot} . Again, the ls-edd1 model shows the lower limit to the growth of light black holes, only reaching maximal masses of about 10 7.5 ​ M ⊙ 10^{7.5}\mathrm{M}_{\odot} for a number density of 10 − 8 ​ c ​ M ​ p ​ c − 3 10^{-8}{\mathrm{c}Mpc^{-3}} . Interestingly, the PBH BHMF shows a clear excess - by about two orders of magnitude - of intermediate-mass black holes at M B ​ H ∼ 10 3 − 4 ​ M ⊙ \mathrm{M}_{BH}\sim 10^{3-4}\mathrm{M}_{\odot} compared to any astrophysical seeding model; at M B ​ H ∼ 10 5 − 8 ​ M ⊙ \mathrm{M}_{BH}\sim 10^{5-8}\mathrm{M}_{\odot} , it predicts results that are very similar to the heavy seeding models. We also find both the heavy seeding ( hs-edd1 and hs-edd5 ) and PBH models to be in excellent agreement with the observationally-inferred BHMF at z ∼ 7 z\sim 7 ( Fei et al., 2026 ) . Light seeding models predict a much flatter slope than the observations although the ls-edd5 model is in accord with data for black holes with M B ​ H ∼ > 10 6.5 ​ M ⊙ \mathrm{M}_{BH}\lower 2.15277pt\hbox{$\;\mathrel{\mathop{\kern 0.0pt\sim}\limits^{>}}\;$}10^{6.5}\mathrm{M}_{\odot} ; given the slower growth of light-seeded Eddington limited black holes, these observations can already be used to rule out the ls-edd1 model. We

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briefly note that given our “heavy seeds” have a range of masses between 10 3 − 5 ​ M ⊙ 10^{3-5}\mathrm{M}_{\odot} , we do not find any specific peak in the BHMF; this is in contrast to the results of Jeon et al. (2025) who find a well-defined peak at 10 5 ​ M ⊙ 10^{5}\mathrm{M}_{\odot} , possibly since all of their heavy seeds are initiated with this fixed mass.

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Table 1: Summary statistics for DESI DR1 and DR2 samples used - the redshift interval, median redshift ( z med z_{\mathrm{med}} ), effective area of the sky footprint weighted by completeness ( A eff A_{\mathrm{eff}} ), number of galaxies ( N N ), and effective volume ( V eff V_{\mathrm{eff}} ).

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The resulting Uchuu halo catalogs enable us to populate mock galaxy catalogs. We do this using a Subhalo Abundance Matching (SHAM) technique and DESI Survey data. The resulting mock lightcones effectively reproduce the observed number densities and clustering patterns of each DESI tracer. A detailed account of the lightcone construction process is provided in our paper using the One percent Survey data ( Prada et al., 2025 ) . In Section 6 , we compare the clustering predictions from the mocks with the measurements from the DESI DR1 and DR2, allowing us to study the halo occupation distribution and large-scale bias of ELGs and QSOs. We applied the aforementioned steps to the ELG and QSO tracers to create their respective full-sky lightcones. The lightcones were then cut to match the northern and southern areas of the DESI data.

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Dedicated tests have been carried out but the conclusions are controversial. In some works, the cosmological coupling is favored. For instance, Cadoni et al. [33] reached the same conclusion as Ref. [ 16 ] based on similar data. The gravitational-wave background (GWB) from SMBHs measured by pulsar timing arrays favors the strong coupling strength k ≈ 3 k\approx 3 [ 34 ] . A strong coupling strength k > 2 k>2 is preferred by comparing the GWB spectral index of SMBH mergers and the current GWB measurements [ 35 ] . While in some other works, the cosmological coupling is not supported. For example, Andrae and El-Badry [36] found that the probability of the non-cosmological coupling was 77% from Gaia observations. The high-redshift AGNs observed by JWST tend to suggest the absence of cosmological coupling [ 37 ] . The minimal formation mass of the BHs in the GWTC-3 gravitational wave observations disfavors the cosmological coupling model at 2 ​ σ 2\sigma level [ 38 ] . A non-coupling BH population is favored with stellar-mass BHs in X-ray binaries using their masses and ages [ 39 ] . The strongest constraint comes from the study with the mass function of black holes in the globular cluster NGC 3201, for which there was only a probability of 10 − 4 10^{-4} for the BHs’ cosmological coupling [ 40 ] , i.e., such a possibility is disfavored at a confidence level of 3.8 ​ σ 3.8\sigma . Anyhow, a decisive constraint at a confidence level above 5 ​ σ 5\sigma is still lacking.

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During the subsequent evolutionary phase from z ∼ 1.61 z\sim 1.61 to z ∼ 0.85 z\sim 0.85 , we therefore set the SFR values of the simulated sample as SFR = 0 ​ M ⊙ ​ yr − 1 \rm{SFR}=0\,M_{\odot}\,yr^{-1} with log-normal scatter of 0.8 dex (the conclusion is unchanged if we still take the initial non-zero star formation rate), while maintaining the black hole accretion rates at their previous levels.

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Here we present the results of the three simulations of the AGN at 1000, 100, and 10 kpc, which we refer to as Scenarios A, B, and C, respectively. Figure 1 shows the build-up of dark matter mass in the simulated halo as a function of redshift. Runaway gravitational collapse of the primordial gas occurred at z z = 24.99, 15.46, and 12.63, for Scenarios A, B, and C, respectively. Our DM halo grew to a mass of 2.23 × 10 9 2.23\times 10^{9} M ⊙ at the time of runaway gravitational collapse in Scenario C. In Scenarios B and C, Compton scattering from the quasar background was powerful enough to keep the free electrons and photons in thermal equilibrium, meaning that the gas stayed ionized, preventing it from cooling via atomic electron transitions, and keeping it at a temperature of 78,000 ​ K 78,\!000\ \text{K} , corresponding to the median photon energy of 26.95 eV of our adopted spectrum. The virial temperature ( Barkana & Loeb, 2001 ) , also plotted in Figure 1 , grew with the DM halo mass roughly until it reached the temperature of the gas for each respective scenario, at which point a runaway gravitational collapse occurred.

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We have presented three-dimensional radiation-hydrodynamics simulations of three scenarios, corresponding to DM haloes exposed to the radiation from an SMBH with a bolometric luminosity of 1.26 × 10 47 1.26\times 10^{47} erg s -1 . We ran simulations with background radiation fields of the SMBH at respective distances of 1000, 100, and 10 kpc from our DM halo (Scenarios A, B, and C, respectively), using an isotropic radiation background, calculated using an SED ( Haardt & Madau, 2012 ) that extends from 3 − 10 6 ​ eV 3-10^{6}\ \rm eV . Our main findings are the following:

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Table 1 : Summary of best fit parameters for the four SMDSs spectroscopic candidates found in Ilie et al. (2025) . ∗

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Refs. Zhang et al. (2024) ; Ilie et al. (2025) ; Mahmud et al. (2025) ; Siddiqa et al. (2025) offer further details on Dark Stars and the potential to detect them (for a brief summary see Appendix B ; for a review see Freese et al. (2016) ). As JWST continues to discover more high redshift objects, some of them lensed to high magnification, it will become possible for future spectroscopic studies with the low-resolution spectrograph on JWST’s Mid-Infrared Instrument (MIRI) and the Near Infrared Spectrograph (NIRSpec) to differentiate between SMDS and galaxy interpretations ( Ilie et al., 2023 ) . The unambiguous discovery of even a single dark star, based on smoking gun spectral signatures such as a Helium absorption features (e.g. 1640 Å, 3 3 3 We note here that accretion onto Direct Collapse Black Holes (DCBHs) is expected to produce strong nebular emission due to Helium-II at the same 1640 ​ Å 1640~\mathrm{\AA} wavelength ( Johnson et al., 2010 ) . or 2511 Å) would constitute (indirect) detection of Dark Matter. Additionally, it would usher a new era in astronomy, where Dark Matter parameters estimations are extracted from observable properties of Dark Stars.

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We have presented the one-loop EFT model for the cross spectrum of the Ly ​ α \text{Ly}\alpha forest and a generic biased tracer of matter. Our work is primarily aimed at the analytic description of the Ly ​ α \text{Ly}\alpha forest – galaxy and Ly ​ α \text{Ly}\alpha forest – quasar cross correlations. We have found an excellent agreement between our theoretical model and the Ly ​ α \text{Ly}\alpha -halo data from the Sherwood hydrodynamical simulation data on quasi-linear scales. Specifically, the 1-loop EFT model provides a percent-level accuracy in fitting these data at k max ≃ 1 ​ h ​ Mpc − 1 k_{\rm max}\simeq 1~\,h\text{Mpc}^{-1} . Our model can be readily applied to the cross-correlation data from eBOSS and DESI surveys.

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Our analysis suggests several directions for further improvements. From the simulation side, we have only analyzed the friends-of-friends halo catalogs, which underestimate the non-linear redshift-space distortions, known as the fingers-of-God [ 74 ] . Thus, it will be important to extend our study to Rockstar [ 75 ] and COMPASO [ 76 ] halo finders, which captures fingers-of-God more accurately (see e.g. [ 77 , 66 ] and references therein). In addition, it will be interesting to apply our model to simulated galaxies whose properties are close to the realistic samples.