The formation of supermassive black holes from Population III.1 seeds. I. Cosmic formation histories and clustering properties

We calculate cosmic distributions in space and time of the formation sites of the first, 'Pop III.1' stars, exploring a model in which these are the progenitors of all supermassive black holes (SMBHs), seen in the centres of most large galaxies. Pop III.1 stars are defined to form from primordial composition gas in dark matter minihaloes with similar to 10(6) M-circle dot that are isolated from neighbouring astrophysical sources by a given isolation distance, d(iso). We assume Pop III.1 sources are seeds of SMBHs, based on protostellar support by dark matter annihilation heating that allows them to accrete a large fraction of their minihalo gas, i.e. similar to 10(5) M-circle dot. Exploring d(iso) from 10 to 100 kpc (proper distances), we predict the redshift evolution of Pop III.1 source and SMBH remnant number densities. The local, z = 0 density of SMBH sconstrains d(iso) less than or similar to 100 kpc (i.e. 3 Mpc comoving distance at z similar or equal to 30). In our simulated (similar to 60 Mpc)(3) comoving volume, Pop III.1 stars start forming just after z = 40. Their formation is largely complete by z similar or equal to 25-20 for d(iso) = 100-50 kpc. We follow source evolution to z = 10, by which point most SMBHs reside in haloes with greater than or similar to 10(8) M-circle dot. Over this period, there is relatively limited merging of SMBHs for these values of d(iso). We also predict SMBH clustering properties at z = 10: feedback suppression of neighbouring sources leads to relatively flat angular correlation functions.