The Distribution and Cosmic Evolution of Massive Black Hole Spins

We study the expected distribution of massive black hole (MBH) spins and itsevolution with cosmic time in the context of hierarchical galaxy formationtheories. Our model uses Monte Carlo realizations of the merger hierarchy in aLCDM cosmology, coupled to semi-analytical recipes, to follow the mergerhistory of dark matter halos, the dynamics of the MBHs they host, and theirgrowth via gas accretion and binary coalescences. The coalescence of comparablemass holes increases the spin of MBHs, while the capture of smaller companionsin randomly-oriented orbits acts to spin holes down. We find that, given thedistribution of MBH binary mass ratios in hierarchical models, binarycoalescences alone do not lead to a systematic spin-up or spin-down of MBHswith time: the spin distribution retains memory of its initial conditions. Bycontrast, because of the Bardeen-Petterson effect, gas accretion via a thindisk tends to spin holes up even if the direction of the spin axis changesrandomly in time. In our models, accretion dominates over black hole capturesand efficiently spins holes up. The spin distribution is heavily skewed towardsfast-rotating Kerr holes, is already in place at early epochs, and does notchange much below redshift 5. If accretion is via a thin disk, about 70% of allMBHs are maximally rotating and have radiative efficiencies approaching 30%(assuming a "standard'' spin-efficiency conversion). Even in the conservativecase where accretion is via a geometrically thick disk, about 80% of all MBHshave spin parameters a/m > 0.8 and accretion efficiencies > 12%. Rapidlyspinning holes with high radiative efficiencies may satisfy constraints basedon comparing the local MBH mass density with the mass density inferred fromluminous quasars (Soltan's argument).Comment: 15 pages, 9 figures, accepted for publication in the Astrophysical Journa