Spin, Accretion and the Cosmological Growth of Supermassive Black Holes

If supermassive black holes (SMBHs) are the energy sources that power quasars and active galactic nuclei, then QSO SDSS 1148+5251, the quasar with the highest redshift (z_QSO=6.43), hosts a supermassive black hole formed within 0.9 Gyr after the Big Bang. This requirement places constraints on the cosmological formation of SMBHs, believed to grow from smaller initial seeds by a combination of accretion and mergers. We focus on gas accretion onto seeds produced by the collapse of Pop III stars at high redshift. We incorporate the results of recent relativistic, MHD simulations of disk accretion onto Kerr black holes to track the coupled evolution of the masses and spins of the holes. We allow for an additional amplification of ~10^4 in the mass of a typical seed due to mergers, consistent with recent Monte Carlo simulations of hierarchical mergers of cold, dark matter halos containing black hole seeds. We find that the growth of Pop III black hole seeds to ~10^9 M_sun by z_QSO = 6.43 favors MHD accretion disks over standard thin disks. MHD disks tend to drive the holes to a submaximal equilibrium spin rate a/M ~ 0.95 and radiation efficiency epsilon_M ~ 0.2, while standard thin disks drive them to maximal spin (a/M = 1) and efficiency (epsilon_M = 0.42). This small difference in efficiency results in a huge difference in mass amplification by accretion at the Eddington limit. The MHD equilibrium efficiency is consistent with the observed ratio of the QSO plus AGN luminosity density to the local SMBH mass density. Our prototype analysis is designed to stimulate the incorporation of results from relativistic stellar collapse and MHD accretion simulations in future Monte Carlo simulations of hierarchical structure formation to better determine the cosmological role of SMBHs and their mass and spin distributions.