Bulge-driven fueling of seed black holes

We examine radiation-regulated accretion onto intermediate-mass and massive black holes (BHs) embedded in a bulge component. Using spherically symmetric one-dimensional radiation-hydrodynamics simulations, we track the growth of BHs accreting from a cold, neutral gas reservoir with temperature $T_{\infty }={10}^4$ K. We find that the accretion rate of BHs embedded in bulges is proportional to $r_{B,eff}/r_B$, where r_B,eff is the increased effective Bondi radius that includes the gravitational potential of the bulge, and r_B is the Bondi radius of the BH. The radiative feedback from the BH suppresses the cold accretion rate to ∼1% of the Bondi rate when a bulge is not considered. However, we find that the BH fueling rate increases rapidly when the bulge mass M_bulge is greater than the critical value of ∼10⁶ M_☉ and is proportional to $r_{B,eff}/r_B\simeq M_{bulge}/M_{BH}$, where $M_{BH}$ is the BH mass. Since the critical bulge mass is independent of the central BH mass, the growth rate of BHs with masses $M_{BH}={10}^2$, 10⁴, and 10⁶ M_☉ exhibits distinct dependencies on the bulge-to-BH mass ratio. Our results imply that light seed BHs (≲10² M_☉), which might be the remnants of the Pop III stars, cannot grow through accretion coevally with the early assembly of the bulge of the host galaxies until the bulge reaches the critical mass. However, massive BH seeds (≳10⁵ M_☉), which may form via direct collapse, are more likely to be embedded in a supercritical bulge, and thus can grow efficiently coupling to the host galaxies and driving the early evolution of the M_BH–σ relationship.