Self-gravity and quasi-stellar object discs

The outer parts of standard steady-state accretion discs around quasi-stellar objects (QSOs) are prone to self-gravity, and they might be expected to fragment into stars rather than feed the central black hole. Possible solutions to this well-known problem are examined with an emphasis on general dynamic constraints. Irradiation by the QSO is insufficient for stability even if the outer disc is strongly warped. Marginal local gravitational instability enhances viscous transport but extends the stable regions only modestly. Compton cooling in the observed QSO radiation field rules out hot thick discs unless the local accretion rate is vastly super-Eddington. The formation of stars or stellar-mass black holes, and the release of energy in these objects by fusion or accretion, may help to stabilize the remaining gas in an otherwise standard disc. But at fixed mass accretion rate, the energy inputs required for stability increase with radius; beyond a parsec, they approach the total QSO luminosity and are probably unsustainable by stars. Magnetic torques from a wind or corona, and gravitational torques from bars or global spirals, may increase the accretion speed and reduce the density of the disc. But dynamical arguments suggest that the accretion speed is at most sonic, so that instability still sets in beyond about a parsec. Alternatively, the QSO could be fed by stellar collisions in a very dense stellar cluster, but the velocity dispersion would have to be much higher than observed in nearby galactic nuclei containing quiescent black holes. In view of these difficulties, we suggest that QSO discs do not extend beyond a thousand Schwarzschild radii or so. Then they must be frequently replenished with gas of small specific angular momentum.