Star formation and evolution in accretion disks around massive black holes

We develop a model for the outer gravitationally unstable regions of accretion disks around massive black holes, for primeval or solar abundances. First we study star formation and evolution in a purely gaseous marginally unstable disk, and we show that unstable fragments should collapse rapidly and give rise to protostars which accrete at a high rate, acquire a mass of a few tens of Mo, and explode as supernovae, producing strong enriched outflows. Second we assume that the whole mass transport is ensured by the supernovae which induce a transfer of angular momentum. For a star formation rate proportional to the growth rate of gravitational instability, we find solutions for the gas and stellar densities where the gas is close to gravitational instability, between 0.1 and 10 pc M(BH) =10**6 Mo, and between 1 and 100 pc for M(BH)=10**8 Mo or larger, whatever the abundances, but for relatively low accretion rates. For larger accretion rates the number of stars becomes so large that they inhibit further star formation, and/or the rate of SN is so high that they distroy the homogeneity and the marginal stability of the disk. We postpone the study of this case. Besides the fact that the mechanism solves the problem of mass transport in a region of where global instabilities do not work, there are several consequences of this model: it can explain the high velocity metal enriched outflows implied by Broad Absorption Lines in quasars, it can account for a pregalactic enrichment, if black holes formed early, finally it can trigger starbursts in the central regions of galaxies. A check of the model would be to detect a supernova exploding within a few parsecs from the center of an AGN, an observation which can be performed in the near future.