Intermediate-mass black holes from Population III remnants in the first galactic nuclei

We report the formation of intermediate-mass black holes (IMBHs) in suites of numerical $N$-body simulations of Population III remnant black holes (BHs) embedded in gas-rich protogalaxies at redshifts $z\gtrsim10$. We model the effects of gas drag on the BHs' orbits, and allow BHs to grow via gas accretion, including a mode of hyper-Eddington accretion in which photon trapping and rapid gas inflow suppress any negative radiative feedback. Most initial BH configurations lead to the formation of one (but never more than one) IMBH in the center of the protogalaxy, reaching a mass of $10^{3-5}\mathrm{M}_{\odot}$ through hyper-Eddington growth. Our results suggest a viable pathway to forming the earliest massive BHs in the centers of early galaxies. We also find that the nuclear IMBH typically captures a stellar-mass BH companion, making these systems observable in gravitational waves as extreme mass-ratio inspirals (EMRIs) with \textit{eLISA}.