Black hole spin evolution

We consider a subset of the physical processes that determine the spin j ≡ a/M of astrophysical black holes. These include (1) Initial conditions. Recent models suggest that the collapse of a supermassive star is likely to produce a black hole with j ∼ 0.7. (2) Major mergers. The outcome of a nearly equal mass black hole-black hole merger is not yet known, but we review the current best guesses and analytic bounds. (3) Minor mergers. We recover the result of Blandford & Hughes that accretion of small companions with isotropically distributed orbital angular momenta results in spin-down, with j ∼ M^-7/3. (4) Accretion. We present new results from fully relativistic magnetohydrodynamic (MHD) accretion simulations. These show that, at least for one sequence of flow models, spin equilibrium (dj/dt = 0) is reached for j ∼ 0.9, far less than the canonical value 0.998 of Thorne that was derived in the absence of MHD effects. This equilibrium value may be inapplicable to some accretion flows, particularly thin disks. Nevertheless, it opens the possibility that black holes that have grown primarily through accretion are not maximally rotating.