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

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 minihaloes forming far from other sources, parametrized by isolation distance, d(iso). Extending previous work that explored this scenario to z = 10, we follow evolution of a (60 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(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 similar to 25, after which their comoving number densities are near-constant, with low merger rates. Occupation fractions evolve to concentrate SMBHs in the most massive haloes by z = 0, but with rare cases of SMBHs in haloes down to similar to 10(8) M-circle dot. The d(iso) scale at epoch of formation, e.g. 100 kpc-proper at z similar to 30, i.e. similar to 3 Mpc-comoving, is imprinted in the SMBH two-point angular correlation function, remaining discernible as a low-amplitude feature to z similar to 1. The SMBH 3D two-point correlation function at z = 0 also shows lower amplitude compared to equivalently massive haloes. We discuss prospects for testing these predictions with observational surveys of SMBH populations.