The evolution of black hole mass and spin in active galactic nuclei

Observations show that the central black hole in galaxies has a mass M of only similar to 10(-3) of the stellar bulge mass. Thus, whatever process grows the black hole also promotes star formation with far higher efficiency. We interpret this in terms of the generic tendency of active galactic nucleus (AGN) accretion discs to become self-gravitating outside some small radius R-sg similar to 0.01-0.1 pc from the black hole. We argue that mergers consist of sequences of such episodes, each limited by self-gravity to a mass Delta M-episode similar to 10(-3) M, with angular momentum characteristic of the small part of the accretion flow which formed it. In this picture, a major merger with Delta M-merger similar to M gives rise to a long series of low-mass accretion disc episodes, all chaotically oriented with respect to one another. Thus, the angular momentum vector oscillates randomly during the accretion process, on mass-scales similar to 10(3) times smaller than the total mass accreted in a major merger event. We show that for essentially all AGN parameters, the disc produced by any accretion episode of this type has lower angular momentum than the hole, allowing stable co- and counter-alignment of the discs through the Lense-Thirring effect. A sequence of randomly oriented accretion episodes as envisaged above then produces accretion discs stably co- or counter-aligned with the black hole spin with almost equal frequency. Accretion from these discs very rapidly adjusts the hole's spin parameter to average values (a) over bar similar to 0.1-0.3 (the precise range depending slightly on the disc vertical viscosity coefficient alpha(2)) from any initial conditions, but with significant fluctuations (Delta a similar to +/- 0.2) about these. We conclude that (i) supermassive black holes (SMBH) should on average spin moderately, with the mean value (a) over bar decreasing slowly as the mass increases; (ii) SMBH coalescences leave little long-term effect on (a) over bar; (iii) SMBH coalescence products in general have modest recoil velocities, so that there is little likelihood of their being ejected from the host galaxy; (iv) black holes can grow even from stellar masses to similar to 5 x 10(9) M-circle dot at high redshift z similar to 6; and (v) jets produced in successive accretion episodes can have similar directions, but after several episodes the jet direction deviates significantly. Rare examples of massive holes with larger spin parameters could result from prograde coalescences with SMBHs of similar mass, and are most likely to be found in giant ellipticals. We compare these results with observation.