On the stability of thick accretion disks around black holes

Discerning the likelihood of the so-called runaway instability of thick accretion disks orbiting black holes is an important issue for most models of cosmic gamma-ray bursts. To this aim we investigate this phenomenon by means of time-dependent, hydrodynamical simulations of black hole plus torus systems in general relativity. The evolution of the central black hole is assumed to be that of a sequence of Kerr black holes of increasing mass and spin, whose growth rate is controlled by the transfer of mass and angular momentum from the material of the disk spiralling in through the event horizon of the black hole. The self-gravity of the disk is neglected. We find that when the black hole mass and spin are allowed to increase, constant angular momentum disks undergo a runaway instability on a dynamical timescale (a few orbital periods). However, our simulations show that a slight increase of the specific angular momentum of the disk outwards has a dramatic stabilizing effect. Our results, obtained in the framework of general relativity, are in broad agreement with earlier studies based both on stationary models and on time-dependent simulations with Newtonian and pseudo-Newtonian gravitational potentials.