Tidal disruption rate of stars by spinning supermassive black holes

A supermassive black hole can disrupt a star when its tidal field exceeds the star's self-gravity, and can directly capture stars that cross its event horizon. For black holes with mass M > 10^7 solar masses, tidal disruption of main-sequence stars occurs close enough to the event horizon that a Newtonian treatment of the tidal field is no longer valid. The fraction of stars that are directly captured is also no longer negligible. We calculate generically oriented stellar orbits in the Kerr metric, and evaluate the relativistic tidal tensor at pericenter for those stars not directly captured by the black hole. We combine this relativistic analysis with previous calculations of how these orbits are populated to determine tidal-disruption rates for spinning black holes. We find, consistent with previous results, that black-hole spin increases the upper limit on the mass of a black hole capable of tidally disrupting solar-like stars to ~7 x 10^8 solar masses. More quantitatively, we find that direct stellar capture reduces tidal-disruption rates by a factor 2/3 (1/10) at M = 10^7 (10^8) solar masses. The strong dependence of tidal-disruption rates on black-hole spin for M > 10^8 solar masses implies that future surveys like LSST that discover thousands of tidal disruption events can constrain supermassive black-hole spin demographics.