The in-situ growth of stellar-mass "light" seed black holes in nuclear star clusters

Abstract

Remnant black holes (BHs) of massive stars (``light seeds'') are a potential origin for supermassive black holes (SMBHs). We use magnetohydrodynamic simulations to study the formation and growth of light seeds in star-forming giant molecular clouds (GMCs) with masses $10^5$--$10^9\,M_\odot$, which evolve for $\sim 10$--$30\,\rm Myr$ and form compact star clusters, akin to high-redshift nuclear star clusters. In particular, the simulations resolve very massive stars (VMSs, 100--$300\,M_\odot$), including their radiative and mechanical feedback, and model feedback-regulated accretion onto remnant BHs. We find that, even in compact GMCs capable of forming deep potential wells, the gas reservoir is expelled by sustained stellar feedback and rapidly dispersed after supernova explosions. Remnant BH populations emerge $\sim 3\,\rm Myr$ after the starburst and concentrate at the cluster center (where $ρ_{\rm BH}\sim 10^4$--$10^6\,M_\odot\,{\rm pc}^{-3}$). With our fiducial sub-grid BH accretion/feedback model, in-situ BH accretion is inefficient for forming heavy seeds: some direct-collapse BHs briefly accrete at $\sim$\,(1--10)$\times$ the Eddington rate, but they reach only $\sim 400$--$500\,M_\odot$. A top-heavy initial mass function or natal kicks do not change this conclusion. Runaway accretion is only possible if the sub-grid BH model allows a high fraction of Bondi inflow to reach the BH, in which case a few seeds can grow to $\sim 10^6\,M_\odot$. We also discuss multiple-generation star formation that may be intrinsically correlated with remnant BH accretion.

Figures (6)

• Figure 1: Treatment of stellar evolution and feedback in this work ShiDaiMurray_2025arXiv251015823S, which splits resolved VMSs (with $m_{\rm ZAMS}>m_{\rm cut}$, here $m_{\rm cut}=100\,M_\odot$) from FIRE SSPs following the IMF. The VMS sub-grid model tracks four phases: (a) hydrogen-burning, (b) Wolf-Rayet, (c) supernova, (d) remnant BH formation and feedback-regulated accretion. Meanwhile, FIRE SSPs evolve with an IMF correction to avoid double-counting of stellar feedback.
• Figure 2: Star formation rate (SFR; dashed) and BH formation rate (BHFR; solid) throughout the evolution of each simulation. Here, BHFR is defined as the rate that VMSs turn into remnant BHs at the end of their life.
• Figure 3: Density profiles of the final star cluster and "BH cluster." Each density profile is calculated by setting the center $\mathbf{x}_{\rm center}$ from the minimum of the potential field, as a function of $r_{\rm cl} \equiv |\mathbf{x} - \mathbf{x}_{\rm center}|$. Note that some curves are noisy since no regular-shaped globular clusters form in these simulations.
• Figure 4: Mass spectrum of remnant BHs at the end of the simulation for different simulations. In different panels, we vary the metallicity from $Z_\odot$ (Z1) to $0.01\,Z_\odot$ (Z0.01).
• Figure 5: Mass accretion history of selected remnant BHs. Here we present two simulation runs, M1e7_R50_Z0.01 (top) and M1e9_R500_Z0.01 (bottom). Left.--Remnant BH mass at formation versus the accreted mass, where 5 BHs with the most accretion are emphasized with colored circles. Middle.--The mass evolution of the selected stars and their remnants (matching the colors to the left panels). Right.--The accretion rate of selected BHs, compared with the Eddington accretion rate of a $300\,M_\odot$ BH (black dotted).