ApJ, in press Preprint typeset using L ATEX style emulateapj v. 04/03/99 THE DISTRIBUTION AND COSMIC EVOLUTION OF MASSIVE BLACK HOLE SPINS

We study the expected distribution of massive black hole (MBH) spins and its evolution with cosmic time in the context of hierarchical galaxy formation theories. Our model uses Monte Carlo realizations of the merger hierarchy in a ΛCDM cosmology, coupled with semianalytical recipes, to follow the merger history of dark matter halos, the dynamics of the MBHs they host, and their growth via gas accretion and binary coalescences. The coalescence of comparable-mass holes increases the spin of MBHs, while the capture of smaller companions in randomly oriented orbits acts to spin holes down. We find that, given the distribution of MBH binary mass ratios in hierarchical models, binary coalescences alone do not lead to a systematic spin-up or spin-down of MBHs with time: the spin distribution retains memory of its initial conditions. By contrast, because of the alignment of a MBH with the angular momentum of the outer accretion disk, gas accretion tends to spin holes up even if the direction of the spin axis varies in time. In our models, accretion dominates over black hole captures and efficiently spins holes up. The spin distribution is heavily skewed toward fast-rotating Kerr holes, is already in place at early epochs, and does not change much below redshift 5. If accretion is via a thin disk, about 70% of all MBHs are maximally rotating and have radiative efficiencies approaching 30% (assuming a "standard" spin-efficiency conversion). Even in the conservative case in which accretion is via a geometrically thick disk, about 80% of all MBHs have spin parameters a/mBH > 0.8 and accretion efficiencies >12%. Rapidly spinning holes with high radiative efficiencies may satisfy constraints based on comparing the local MBH mass density with the mass density inferred from luminous quasars (Soltan's argument). Since most holes rotate rapidly at all epochs, our results suggest that spin is not a necessary and sufficient condition for producing a radio-loud quasar.