Rapid Growth of Seed Black Holes during Early Bulge Formation

We study the early growth of massive seed black holes (BHs) via accretion in protogalactic nuclei where the stellar bulge component is assembled, performing axisymmetric two-dimensional radiation hydrodynamical simulations. We find that when a seed BH with M _• ~ 10⁵ M _⊙ is embedded in dense metal-poor gas (Z = 0.01 Z _⊙) with a density of ≳ 100 cm^-3 and bulge stars with a total mass of M _⋆ ≳ 100 M _•, a massive gaseous disk feeds the BH efficiently at rates of ≳ 0.3-1 M _⊙ yr^-1, and the BH mass increases nearly tenfold within ~2 Myr. This rapid accretion phase lasts until a good fraction of the gas bounded within the bulge accretes onto the BH, although the feeding rate is regulated owing to strong outflows driven by ionizing radiation emitted from the accreting BH. The transient growing mode can be triggered for seed BHs formed in massive dark-matter halos with masses of ≳ 10⁹ M _⊙ at z ~ 15-20 (the virial temperature is T _vir ≃ 10⁵ K). The host halos are heavier and rarer than those of typical first galaxies, but are more likely to end up in quasar hosts by z ≃ 6. This mechanism naturally yields a mass ratio of M _•/M _⋆ > 0.01 higher than the value seen in the local universe. The existence of such overmassive BHs provides us with a unique opportunity to detect highly accreting seed BHs at z ~ 15 with AB magnitude of m _AB ~ 26-29 mag at 2 μm (rest frame 10 eV) by the upcoming observations by the James Webb Space Telescope and Nancy Grace Roman Space Telescope.