Internal Radiative Feedback Triggers Global Collapse and Direct-Collapse Black Hole Formation in Metal-free Atomic-Cooling Haloes

abstract · abstract

The formation of heavy seed black holes from the collapse of supermassive stars (SMSs) is a promising pathway to the supermassive black holes (SMBHs). In the conventional direct-collapse scenario, however, SMS formation requires an extremely strong external far-ultraviolet (FUV) field to suppress H$_2$ cooling and fragmentation. Here, we use cosmological radiation-hydrodynamic simulations to show that SMSs can form in metal-free atomic-cooling haloes even under subcritical FUV backgrounds with $J_{21}=1$-$10^2$. We follow the evolution for $\sim1$-$2~{\rm Myr}$ after the onset of star formation, including FUV and ionizing radiation from stars formed within the halo. Star formation proceeds through a characteristic two-stage evolution. H$_2$ cooling initially induces fragmentation and the formation of ordinary Pop III stars. Internal FUV radiation from these stars then photodissociates H$_2$ and suppresses further fragmentation, while the surrounding warm gas reservoir contracts under self-gravity and undergoes global collapse through atomic cooling. This collapse drives inflow rates of $\sim0.1$-$1~{\rm M_\odot~yr^{-1}}$ and produces rapidly accreting protostars that reach $\sim2$-$6\times10^4~{\rm M_\odot}$ by the simulations end. Since rapid accretion is still ongoing, these objects are expected to grow to $\sim10^5~{\rm M_\odot}$ SMSs and then form direct-collapse black holes (DCBHs). The global collapse is accompanied by clustered star formation, producing a compact, top-heavy stellar system around the SMSs. The estimated DCBH abundance, $n_{\rm DCBH}\sim10^{-3}$-$10^{-2}~{\rm cMpc^{-3}}$, is high enough to provide a plausible progenitor population for Little Red Dots and present-day SMBHs. Our results demonstrate that internal stellar feedback can trigger, rather than prevent, SMS formation, substantially relaxing the external FUV requirement for heavy-seed formation.

S5: 5 CONCLUSION / block 1 · html

The global collapse is not monolithic but is accompanied by clustered star formation. Numerous stars with m ⋆ ≲ 10 3 ​ M ⊙ m_{\star}\lesssim 10^{3}~{\rm M_{\odot}} form, but ∼ 90 % \sim 90\% of the stellar mass accreted during this phase is concentrated in a small number of rapidly accreting protostars with m ⋆ ≳ 10 4 ​ M ⊙ m_{\star}\gtrsim 10^{4}~{\rm M_{\odot}} . The resulting stellar system can therefore be characterized as a strongly top-heavy system containing a few central SMSs surrounded by a compact young stellar component.

S4.SS1: 4.1 Subsequent growth and fate of the most massive stars / block 1 · html

In the optimistic case, we assume that the gas reservoir survives supernova feedback and continues to supply gas to the most massive stars until the upper mass limit given by equation ( 12 ) is reached. The resulting final stellar masses are summarized in Table 2 .

S1: 1 INTRODUCTION / block 1 · html

We find that star formation proceeds through a characteristic two-stage evolution. Once self-shielding allows H 2 cooling to become effective, the gas fragments and Pop III stars form in the resulting dense cores. Internal FUV radiation from these stars subsequently photodissociates H 2 and suppresses further fragmentation, while the surrounding atomic-cooling gas reservoir continues to contract under self-gravity and eventually undergoes global collapse. This global collapse produces rapidly accreting SMSs in the central region, surrounded by a compact, strongly top-heavy Pop III stellar system. This mechanism substantially relaxes the external FUV intensity required for SMS and heavy BH seed formation, suggesting that heavy seeds may form in a wider range of environments than previously considered.

S4.SS3.SSS2: 4.3.2 Recombination-line emission / block 1 · html

Table 3: Summary of the comparison between the compact stellar components in our simulations and observed compact metal-poor systems. For our simulations, the first row shows the current snapshots, while the second gives an optimistic extrapolation assuming continued star formation for a few Myr. For the observed systems, M ⋆ , comp M_{\star,{\rm comp}} is the stellar mass required to reproduce the indicated observable using the simple models adopted in this work, rather than the stellar mass inferred in the original observational studies.

S4.SS4: 4.4 Comparison with Previous Studies / block 1 · html

Our main result is that SMS formation can occur under moderate external FUV irradiation even after H 2 cooling has already triggered fragmentation and Pop III star formation. Radiative feedback from these stars subsequently suppress H 2 cooling in the surrounding atomic-cooling gas, leading to its global collapse on a timescale of ∼ 1 \sim 1 – 2 ​ Myr 2~{\rm Myr} . Previous studies provide useful comparisons for different stages and aspects of this evolution.

S5: 5 CONCLUSION / block 1 · html

In this study, we used cosmological radiation-hydrodynamic simulations to follow the evolution of an atomic-cooling halo for ∼ 1 \sim 1 – 2 ​ Myr 2~{\rm Myr} after the onset of star formation. We focused on how internal radiative feedback from stars formed during the initial star-formation phase affects the subsequent gas dynamics, clustered star formation, and supermassive star (SMS) formation under subcritical external FUV backgrounds of J 21 = 1 J_{21}=1 – 10 2 10^{2} .

S5: 5 CONCLUSION / block 1 · html

Our main results are summarized as follows.

S5: 5 CONCLUSION / block 1 · html

In all runs, star formation in the atomic-cooling halo proceeds through a characteristic two-stage evolution. The gas first undergoes an initial collapse driven by H 2 cooling, similar to ordinary Pop III star formation. Internal radiative feedback from the stars formed during this phase then suppresses H 2 cooling and small-scale fragmentation, while the surrounding atomic-cooling gas reservoir contracts under self-gravity and undergoes global collapse.

S5: 5 CONCLUSION / block 1 · html

The global collapse involves a gravitationally bound gas reservoir extending over ∼ 10 \sim 10 – 100 ​ pc 100~{\rm pc} . It leads to the formation of protostars with high accretion rates of ∼ 0.1 \sim 0.1 – 1 ​ M ⊙ ​ yr − 1 1~{\rm M_{\odot}~yr^{-1}} , with the most massive objects reaching ∼ 10 4 ​ M ⊙ \sim 10^{4}~{\rm M_{\odot}} by the end of the simulations. Their accretion rates remain well above the critical value ≃ 0.04 ​ M ⊙ ​ yr − 1 \simeq 0.04~{\rm M_{\odot}~yr^{-1}} required to maintain the inflated supergiant-protostar state. Since accretion is still ongoing, these objects are expected to grow further toward ∼ 10 5 ​ M ⊙ \sim 10^{5}~{\rm M_{\odot}} and become SMSs.

S2.SS2: 2.2 Stars and black holes / block 1 · html

Stars with masses in the type II (11 - 20 M ⊙ ) supernovae (SNe) or the hypernova (20 - 40 M ⊙ ) mass bands will experience an explosion and undergo some degree of mass loss. The explosion energy and resulting black hole remnant mass are calculated from the stellar mass as taken from Nomoto et al. (2006) , and the explosion is modelled with an isotropic injection of thermal energy into the surrounding 10 pc. The particle is then converted into a black hole particle.

S5: 5 Conclusions / block 1 · html

Here we have presented a new cosmological simulation using the SEEDZ framework, with enhanced resolution compared to the original suite. The simulation was performed with the hydrodynamics code Arepo2 and probes scales of ∼ \sim 0.5 physical pc. On top of the base code, the SEEDZ framework includes subgrid models for PopIII star formation, supernovae explosions, metal enrichment, PopII star formation, black hole formation, and heavy seed black hole formation. Heavy seeds form in regions where the mass inflow into 10 pc regions surrounding a gravitationally unstable sub-pc sized cell exceeds 1 M ⊙ yr -1 . By splitting our catalogue of early galaxies into two groups – those that form heavy seeds and those that do not – we investigate the conditions necessary for high inflow environments to occur and by extension the conditions necessary for SMS and/or dense stellar cluster formation. We make the following conclusions:

S4: IV Summary and Conclusion / block 1 · html

Successful Matching of Observed Spectra: By applying physically motivated broadening mechanisms, including a powerful stellar wind ( v ∞ ≈ 1500 ​ km ​ s − 1 v_{\infty}\approx 1500\,\mathrm{km\,s^{-1}} ) and large-scale macroturbulence ( σ v ≈ 1250 − 1500 ​ km ​ s − 1 \sigma_{v}\approx 1250-1500\,\mathrm{km\,s^{-1}} ), our model quantitatively reproduces the broad line profiles observed in both LRD targets, matching the measured FWHM of MoM-BH*-1 to within 4%.

S4: IV Summary and Conclusion / block 1 · html

We have presented a first-principles investigation into whether Population III supermassive stars (SMSs) can serve as the central engines for the enigmatic class of objects known as Little Red Dots (LRDs). By developing a novel pipeline that combines a GENEC stellar evolution model with a detailed radiative transfer and spectral synthesis code, we have demonstrated that a single, non-rotating 10 6 ​ M ⊙ 10^{6}M_{\odot} SMS can successfully reproduce the key observational features of two prominent LRDs: MoM-BH*-1 at z = 7.76 z=7.76 and The Cliff at z = 3.55 z=3.55 .

S2.SS3: II.3 Envelope binding energy and collapse energetics / block 1 · html

As this is a key intermediary result of our manuscript, with important implications on the plausibility that collapsed SMDSs lead to late stage quasi-star like configurations, we validate it analytically in Appendix A , where we derive useful closed form approximations for the binding energy of a radiation dominated shell using a modified form of the virial theorem for a truncated envelope.

S3.SS2: III.2 Envelope inflation energetics / block 1 · html

Thus the desired inflation requires an energy input comparable to, but slightly below, the original envelope binding energy. Motivated by this result, in what follows we will assume Δ ​ E infl ∼ | E bind | \Delta E_{\rm infl}\sim|E_{\rm bind}| .

S7: VII Summary and Conclusions / block 1 · html

The observed redshift distribution of LRDs, from the distribution of gas-rich major galaxy mergers.

S7: VII Summary and Conclusions / block 1 · html

Constraints on the size of LRD galactic hosts.

abstract · abstract

Direct collapse of pristine gas in early galaxies is a promissing pathway for forming supermassive black holes (BHs) powering active galactic nuclei (AGNs) at the epoch of reionization (EoR). This seeding mechanism requires suppression of molecular hydrogen (H$_2$) cooling during primordial star formation via intense far-ultraviolet radiation from nearby starburst galaxies clustered in overdense regions. However, non-detection of 21 cm signals from the EoR reported by the Hydrogen Epoch of Reionization Array (HERA) experiment suggests that such galaxies may also emit X-rays more efficiently than in the local universe, promoting H$_2$ production and thereby potentially quenching massive BH seed formation. In this study, we examine the thermal and chemical evolution of collapsing gas in dark matter halos using a semi-analytic model incorporating observationally calibrated X-ray intensities. We find that strong X-ray irradiation, as suggested by HERA, significantly suppresses direct collapse and leads most halos to experience H$_2$ cooling. Nevertheless, massive BH seeds with $M_\mathrm{BH} \gtrsim 10^4~M_\odot$ still form by $z\simeq 15$, particularly in regions with baryonic streaming motion, and their abundance reaches $\sim 10^{-4}~\mathrm{Mpc}^{-3}$ sufficient to explain the SMBHs identified by JWST spectroscopy at $3<z<6$. While the formation of highly overmassive BHs with masses comparable to their host galaxies is prohibited by X-ray ionization, our model predicts that BH-to-stellar mass ratios of $\simeq 0.01-0.1$ were already established at seeding.

S1: 1 Direct Collapse Black Hole Model / block 1 · html

The inner regions are characterized by high densities reaching > 10 7 − 8 ​ cm − 3 >10^{7-8}\,\rm cm^{-3} in the inner core, and high temperatures due to compressional heating, caused by accretion onto the DCBH [ 25 ] . As a result of the process leading to the DCBH formation, the density distribution of the halo gas (with mass M g ≈ 10 7 ​ M ⊙ M_{g}\approx 10^{7}\,{\rm M_{\odot}} ) has contracted from the virial radius of the parent halo ( ≈ 1 \approx 1 kpc) to a few parsecs [ 27 ] . At 75 75 Myr after seeding (i.e., the RHD snapshot used in this study), the total cumulative gas column density has increased to N H ≈ 3 × 10 25 ​ cm − 2 N_{\rm H}\approx 3\times 10^{25}\rm cm^{-2} ; thus, the system is heavily Compton-thick.

S2: 2 Synthetic LRD Spectra / block 1 · html

The key spectral features can be understood as follows. The input DCBH accretion disk spectrum, extending to energies ∼ > 300 \lower 2.15277pt\hbox{$\;\mathrel{\mathop{\kern 0.0pt\sim}\limits^{>}}\;$}300\ keV, is filtered by the Compton-thick accretion flow before escaping. As a result, photons in the energy range 13.6 ​ eV < E < 1 ​ keV 13.6\ {\rm eV}<E<1\ {\rm keV} suffer complete photoelectric absorption; more energetic X-rays can instead (partially) escape. Hence, these objects contribute negligibly to cosmic reionization. The absorbed energy is re-emitted as “nebular emission” with contributions from free-free, free-bound, and two-photon processes. Ly α \alpha emission is not included, as at these large column densities, Ly α \alpha photons are resonantly trapped in the surrounding gas ( 36 ) . Hence, n = 2 → n = 1 n=2\to n=1 transitions will eventually produce two-photon emission.

A1.SS8: A.8 Velocity scales and shell estimates / block 1 · html

Finally, we translate the episode-integrated results into a small set of observer-facing quantities. Alongside the escape speed, we define two characteristic pulsation speed scales,

A1.SS10: A.10 Metallicity dependence of the shell and ejecta diagnostics / block 1 · html

The shell quantities strengthen the same conclusion. Across the entire grid, the shell identified in Table A2 remains compact and optically thick, with τ es \tau_{\rm es} between ∼ 7.4 × 10 2 \sim 7.4\times 10^{2} and 1.3 × 10 4 1.3\times 10^{4} . Thus, the production of a dense inner shell is not restricted to one metallicity. What changes with Z Z is the balance between total ejecta mass, shell compactness, and terminal stellar state. In this sense, the Z = 10 − 2 ​ Z ⊙ Z=10^{-2}\,Z_{\odot} model is not special because it maximizes the ejected mass. It is special because it provides the clearest LRD analogue, combining the coolest enriched terminal state with a compact optically thick shell.

S3.SS1: 3.1 Model Selection / block 1 · html

We also use the simulation results from Nagele & Umeda 2024 . We here take the explosion energy and ejecta mass from their models with 0.1 0.1 – 1 ​ M ⊙ ​ yr − 1 1\,M_{\odot}\mathrm{yr^{-1}} . For their pulsating and exploding models, we take the values as in their Table 1. For the collapsing models, we assume that the relation between the SMS core mass, ejecta from the core and explosion energy found in Fujibayashi et al. 2025 holds: we take as the ejecta mass 1 % 1\% of the core mass ( M eje , c ∼ 0.01 ​ M core M_{\mathrm{eje,c}}\sim 0.01M_{\mathrm{core}} ) and add to that the mass outside of the core. For the explosion energy, we use that E kin , eje ∼ 0.5 ​ M eje , c ​ ( 0.2 ​ c ) 2 ∼ 0.5 × 0.01 ​ M core × ( 0.2 ​ c ) 2 E_{\mathrm{kin,eje}}\sim 0.5M_{\mathrm{eje,c}}(0.2c)^{2}\sim 0.5\times 0.01M_{\mathrm{core}}\times(0.2c)^{2} ( Fujibayashi et al., 2025 ) . We collect the model parameters that we use in our work in Tab. 2 .

S5: 5 Conclusions / block 1 · html

We also found that all sources show small variability. The timescale in which the source varies brightness by similar amounts to LRDs ( 20 % 20\% ) is 0.5 0.5 – 9 9\, yrs in the source frame. Thus, light curve variations of SMS explosions would remain undetected for ∼ 0.5 \sim 0.5 – 9 ​ ( 1 + z ) 9\,(1+z)\, yrs in the observer frame. This is longer than the current operational time of JWST for sources at z > 7 z>7 . We therefore presume that some suspected persistent sources could be slowly varying SMS transients instead.