A massive thick disc around a massive black hole and its runaway instability

We investigate the runaway instability of configurations consisting of a massive dense but non-self-gravitating thick disc/torus surrounding a massive black hole (MBH). We limit our model parameters to values that result in a self-consistent thick disc around an MBH. We identify, analytically, the index of the angular momentum distribution that will form a thick disc as an initial equilibrium state, and obtain the mass ratio of the disc to the central black hole for which the disc is dominated by the radiation pressure. In our theoretical framework we find that a self-consistent thick disc with constant angular momentum leads to a runaway instability on a dynamical time-scale. However, even a slight increase of the specific angular momentum outwards has a strong stabilizing effect on the accretion process. Finally, we discuss our results and present possible applications to high-energy emission.