On the thermal stability of transonic accretion discs

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 (alpha = 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.