The stability of accretion tori – III. The effect of self-gravity

We investigate the influence of self-gravity on the Papaloizou–Pringle (PP) instability in shearing accretion tori. We analyse two models: (i) a fully three-dimensional slender incompressible torus with constant angular momentum, and (ii) a two-dimensionally incompressible slender annulus with arbitrary (linear) angular momentum profile. We find that in both cases self-gravity inhibits the PP instability. This can be understood in terms of the coupled edge-wave interpretation given earlier. With increasing strength of self-gravity, the following sequence of events is seen in both models. Initially, the parameter range over which the principal branch of the PP instability occurs shrinks until the instability disappears altogether for all angular momentum profiles of interest. Then, a new overstable mode appears, whose physics we do not understand. Finally, a third unstable mode appears. We identify this with the well-known Jeans instability, caused by the tendency of the fluid to form clumps. The second and third unstable modes survive for arbitrarily strong self-gravity.