The formation of supermassive black holes from Population III.1 seeds. II. Evolution to the local universe

Abstract: We present predictions for cosmic evolution of populations of supermassive black holes (SMBHs) forming from Population III.1 seeds, i.e., early, metal-free dark matter minihalos forming far from other sources, parameterized by isolation distance, $d_{\rm{iso}}$. Extending previous work that explored this scenario to $z=10$, we follow evolution of a $(60:{\rm{Mpc}})^3$ volume to $z=0$. We focus on evolution of SMBH comoving number densities, halo occupation fractions, angular clustering and 3D clustering, exploring a range of $d_{\rm{iso}}$ constrained by observed local number densities of SMBHs. We also compute synthetic projected observational fields, in particular a case comparable to the Hubble Ultra Deep Field. We compare Pop III.1 seeding to a simple halo mass threshold model, commonly adopted in cosmological simulations of galaxy formation. Major predictions of the Pop III.1 model include that all SMBHs form by $z\sim25$, after which their comoving number densities are near-constant, with low merger rates. Occupation fractions evolve to concentrate SMBHs in the most massive halos by $z=0$, but with rare cases in halos down to $\sim10^8:M_\odot$. The $d_{\rm{iso}}$ scale at epoch of formation, e.g., $100:$kpc-proper at $z\sim30$, i.e., $\sim3:$Mpc-comoving, is imprinted in the SMBH two-point angular correlation function, remaining discernible as a low-amplitude feature to $z\sim1$. The SMBH 3D two-point correlation function at $z=0$ also shows lower amplitude compared to equivalently massive halos. We discuss prospects for testing these predictions with observational surveys of SMBH populations.