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