In this paper, we revisit the arguments for the basis of the time evolution of the flares expected to arise when a star is disrupted by a supermassive black hole. We present a simple analytic model relating the light curve to the internal density structure of the star. We thus show that the standard light curve proportional to t −5/3 only holds at late times. Close to the peak luminosity the light curve is shallower, deviating more strongly from t −5/3 for more centrally concentrated (e.g. solar type) stars. We test our model numerically by simulating the tidal disruption of several stellar models, described by simple polytropic spheres with index γ . The simulations agree with the analytical model given two considerations. First, the stars are somewhat inflated on reaching pericentre because of the effective reduction of gravity in the tidal field of the black hole. This is well described by a homologous expansion by a factor which becomes smaller as the polytropic index becomes larger. Secondly, for large polytropic indices wings appear in the tails of the energy distribution, indicating that some material is pushed further away from parabolic orbits by shocks in the tidal tails. In all our simulations, the t −5/3 light curve is achieved only at late stages. In particular, we predict that for solar-type stars, this happens only after the luminosity has dropped by at least 2 mag from the peak. We discuss our results in the light of recent observations of flares in otherwise quiescent galaxies and note the dependence of these results on further parameters, such as the star/hole mass ratio and the stellar orbit.

No abstract

Two‐dimensional (axially symmetric) numerical hydrodynamical calculations of accretion flows that cannot cool through emission of radiation are presented. The calculations begin from an equilibrium configuration consisting of a thick torus with constant specific angular momentum. Accretion is induced by the addition of a small anomalous azimuthal shear stress which is characterized by a function ν. We study the flows generated as the amplitude and form of ν are varied. A spherical polar grid which spans more than two orders of magnitude in radius is used to resolve the flow over a wide range of spatial scales. We find that convection in the inner regions produces significant outward mass motions that carry away both the energy liberated by and a large fraction of the mass participating in the accretion flow. Although the instantaneous structure of the flow is complex and dominated by convective eddies, long‐time averages of the dynamical variables show remarkable correspondence to certain steady‐state solutions. The two‐dimensional structure of the time‐averaged flow is marginally stable to the Høiland criterion, indicating that convection is efficient. Near the equatorial plane, the radial profiles of the time‐averaged variables are power laws with an index that depends on the radial scaling of the shear stress. A stress in which ν∝r1/2 recovers the widely studied self‐similar solution corresponding to an ‘α‐disc’. We find that, regardless of the adiabatic index of the gas, or the form or magnitude of the shear stress, the mass inflow rate is a strongly increasing function of radius, and is everywhere nearly exactly balanced by mass outflow. The net mass accretion rate through the disc is only a fraction of the rate at which mass is supplied to the inflow at large radii, and is given by the local, viscous accretion rate associated with the flow properties near the central object.