ANGULAR-MOMENTUM OF A SUPERMASSIVE BLACK-HOLE IN A DENSE STAR CLUSTER

We consider the evolution of the angular momentum of a supermassive (M(h) is similar to 10(7)-10(9) M.) black hole in the centre of a dense star cluster of mass M(c) > M(h). Our treatment of this problem is based on general relativity. We take into account the spin-up of the black hole due to disc accretion of the gas component, and the spin-down due to direct capture of stars from the cluster, and find the equilibrium value of the Kerr angular momentum parameter. We calculate the rate of gas supply to the disc due both to tidal disruption of stars by the black hole, and to liberation of gas through non-elastic star-star collisions far from the black hole. We calculate numerically the cross-section of tidal disruption, compare it with the capture cross-section and average both these cross-sections over the cluster. In the range of black hole masses under consideration and in the case of a dense star cluster (R is similar to 1 pc), the interaction of the black hole with the stars occurs in the regime of the depleted loss cone. In the limit of a supermassive black hole (M(h) > 10(8) M.), when tidal disruptions are suppressed, we calculate the equilibrium angular momentum analytically. It is shown that the black holes surrounded by the most luminous accretion discs should rotate with an angular momentum parameter close to the extremum.