The In Situ Growth of Stellar-mass "Light" Seed Black Holes in Nuclear Star Clusters

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 $\rho_{\rm BH}\sim 10^4$--$10^6\,M_\odot\,{\rm pc}^{-3}$). 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.