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 $M_\bullet \sim 10^5~M_\odot$ is embedded in dense metal-poor gas ($Z=0.01~Z_\odot$) with a density of $\gtrsim 100~{\rm cm}^{-3}$ and bulge stars with a total mass of $M_\star \gtrsim 100~M_\bullet$, a massive gaseous disk feeds the BH efficiently at rates of $\gtrsim 0.3-1~M_\odot~{\rm yr}^{-1}$ and the BH mass increases nearly tenfold within $\sim 2$ 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 $\gtrsim 10^9~M_\odot$ at $z\sim 15-20$ (the virial temperature is $T_{\rm vir}\simeq 10^5~{\rm K}$). The host halos are heavier and rarer than those of typical first galaxies, but are more likely to end up in quasar hosts by $z\simeq 6$. This mechanism naturally yields a mass ratio of $M_\bullet/M_\star >0.01$ higher than the value seen in the local universe and the existence of such overmassive BHs provides us a unique opportunity of detecting highly accreting seed BHs at $z\sim 15$ with AB magnitude of $m_{\rm AB} \sim26 - 29$ mag at $2~\mu{\rm m}$ (rest-frame 10 eV) by the upcoming observations by the James Webb Space Telescope and Nancy Grace Roman Space Telescope.