Enhanced activity of massive black holes by stellar capture assisted by a self-gravitating accretion disc

Aims. We study the probability of close encounters between stars from a nuclear cluster and a massive black hole (104 M⊙ . M• . 108 M⊙). The gravitational field of the system is dominated by the black hole in its sphere of influence. It is further modified by the cluster mean field (a spherical term) and a gaseous disc/torus (an axially symmetric term) causing a secular evolution of stellar orbits via Kozai oscillations. Intermittent phases of large eccentricity increase the chance that stars become damaged inside the tidal radius of the central hole. Such events can produce debris and lead to recurring episodes of enhanced accretion activity. Methods. We introduce an effective loss cone and associate it with tidal disruptions during the high-eccentricity phases of the Kozai cycle. By numerical integration of the trajectories forming the boundary of the loss cone we determine its shape and volume. We also include the effect of relativistic advance of pericentre. Results. The potential of the disc has the efffect of enlarging the loss cone and, therefore, the predicted number of tidally disrupted stars should grow by factor of ≃ 102. On the other hand, the effect of the cluster mean potential together with the relativistic pericentre advance act against the eccentricity oscillations. In the end we expect the tidal disruption events to be approximately ten times more frequent in comparison with the model in which the three effects – the cluster mean field, the relativistic pericentre advance, and the Kozai mechanism – are all ignored. The competition of different influences suppresses the predicted star disruption rate as the black hole mass increases. Hence, the process under consideration is more important for intermediate-mass black holes, M• ≃ 104 M⊙.