Thermal instability and evaporation of accretion disc atmospheres

We investigate the vertical structure of the outer layers of accretion discs in which the local viscous energy dissipation rate scales with the pressure as for standard Shakura-Sunyaev discs. It has been pointed out by several authors that a thermal instability occurs in the outer layers of such discs when the gas pressure drops below a certain value. When the density becomes too low thermal equilibrium can no longer be maintained and the gas heats up, forming a hot corona or possibly a wind. To assess the importance of this effect we estimate the pressure and temperature at which this instability will occur, where the instability point lies with respect to the total vertical disc structure, and whether the instability is likely to be important for the disc as a whole. The main difference between our work and earlier estimates lies in a more detailed treatment of the heating and cooling processes and the inclusion of the effects of an external radiation field. By solving for the accretion disc vertical structure using the grey two-stream approximation instead of the usual diffusion approximation for the radiative transfer, we first show that the thermal structure of the optically thin outer layers is in first approximation independent of radiative transfer effects, and follows the thermal equilibrium curve for optically thin plasmas in the pressure-temperature plane. We then calculate the thermal structure using the detailed photoionization code MAPPINGS, which includes much more accurate heating and cooling physics than the mean opacity used in the vertical structure calculations. This approach also allows a straightforward inclusion of the effects of an external radiation field from the centre of the accretion flow. We apply our method to cataclysmic variable (CV) and stellar mass black hole discs, and show that evaporation due to the thermal instability can be important under a variety of conditions. In the case of CVs, radiative heating by photons emanating from the boundary layer can increase the evaporation rate significantly over the non-irradiated case, but for steady-state CV discs the evaporation by the mechanism considered here is still not sufficient to evaporate the entire disc. It may become important however in non-steady discs in dwarf novae if the accretion-heated white dwarf plays a role in irradiating the disc after an outburst. In the case of black hole soft X-ray transients, the evaporation can have a significant effect on the structure of the outer regions of the disc, resulting in mass loss rates comparable to the local mass accretion rate through the disc for Ṁ ≲ 10¹⁶ gs^-1 for a 10-solar-mass black hole. Accretion in such systems could therefore proceed mainly from a hot thick disc formed by evaporation from the outer regions of the thin disc. The evaporation can be quenched by Compton cooling only for mass transfer rates of Ṁ ≳ 10¹⁸ g s^-1 and low values of the viscous heating parameter α.