Feedback-regulated seed black hole growth in star-forming molecular clouds and galactic nuclei

Context. The detection of supermassive black holes (SMBHs) in high-redshift luminous quasars may require a phase of rapid accretion, and as a precondition, substantial gas influx toward seed black holes (BHs) from kiloparsec or parsec scales. Our previous research demonstrated the plausibility of such gas supply for BH seeds within star-forming giant molecular clouds (GMCs) with high surface density (∼10⁴ M⊙ pc⁻²), facilitating "hyper-Eddington" accretion via efficient feeding by dense clumps, which are driven by turbulence and stellar feedback. Aims. This article presents an investigation of the impacts of feedback from accreting BHs on this process, including radiation, mechanical jets, and highly relativistic cosmic rays. Methods. We ran a suite of numerical simulations to explore diverse parameter spaces of BH feedback, including the subgrid accretion model, feedback energy efficiency, mass loading factor, and initial metallicity. Results. Using radiative feedback models inferred from the slim disk, we find that hyper-Eddington accretion is still achievable, yielding BH bolometric luminosities of as high as 10⁴¹ − 10⁴⁴ erg/s, depending on the GMC properties and specific feedback model assumed. We find that the maximum possible mass growth of seed BHs (ΔM_(max)^(BH)) is regulated by the momentum-deposition rate from BH feedback, ṗfeedback/(Ṁ_(BH)c), which leads to an analytic scaling that agrees well with simulations. This scenario predicts the rapid formation of ∼10⁴ M⊙ intermediate-massive BHs (IMBHs) from stellar-mass BHs within ∼1 Myr. Furthermore, we examine the impacts of subgrid accretion models and how BH feedback may influence star formation within these cloud complexes.