On the thermal stability of transonic accretion discs

Abstract

Non-linear time-dependent calculations have been carried out in order to study the evolution of the thermal instability for vertically integrated, non-self-gravitating models of optically thick, transonic, slim accretion discs around black holes. In these calculations we investigated only the original version of the slim-disc model with low viscosity (α = 0.001) and for a stellar-mass (10 M⊙) black hole. This original version of the model does not yet include several important non-local effects (viscous forces in the radial equation of motion, diffusion-type formulation for the viscosity in the angular momentum equation, viscous dissipation rate associated with the stress in the azimuthal direction, and radiative losses in the radial direction in the energy balance equation). It is clear, therefore, that this treatment is greatly simplified, but our strategy is to consider this as a standard reference against which to compare results from forthcoming studies in which the additional effects will be added one by one, thus giving a systematic way of understanding the contribution from each of them. We consider an already-formed disc, and study its stability against small axisymmetric perturbations. Those models that were stable according to local analysis remain stable and stationary to a good approximation, as also do models for which local analysis predicts an unstable region with radial dimension smaller than the shortest wavelength of the unstable modes. In terms of luminosity, all models with luminosity less than or equal to 0.08LE are stable. For models with higher luminosity than this but which are still sub-Eddington, a shock-like structure forms near to the sonic point, probably leading to subsequent disruption of the disc. The model with Eddington luminosity evolves in a violent way, with the shock-like structure being formed already within the first second of evolution. From an examination of phase-space trajectories, our preliminary conclusion is that the stabilizing effect of advection is not strong enough in these models to allow for limit-cycle behaviour to occur. However, in order to make a definitive statement on this, it would be necessary to implement special numerical techniques for treatment of the shock-like structure, which becomes very extreme, and this lies beyond the scope of the present paper.