S-curves of X-ray heated accretion discs and the black hole soft X-ray transients

It has recently been suggested that the thermal stability of accretion discs in the high Ṁ regime may be influenced by X-rays that irradiate the disc. We investigate this problem by calculating the vertical structure of externally X-ray irradiated accretion discs using a two-stream bi-grey approximation for radiative transfer. The effects of X-ray heating depend on the hardness of the incident X-ray spectrum, and on the magnitude of the X-ray flux relative to the viscously generated flux. For heating by soft X-rays, a temperature inversion occurs in the upper atmosphere of the disc when X-ray heating dominates. For heating by hard X-rays, no significant X-ray inversion occurs. In general, the S-curves become increasingly distorted as the irradiation flux increases. The location of the upper critical point of the S-curve, and the corresponding critical mass transfer rate Ṁ_crit above which the disc is thermally stable, is significantly reduced if the heating is predominantly by soft X-rays. Our results are used to discuss the stability of accretion discs in black hole (BH) soft X-ray transients (SXTs). In particular, we show that the BH-SXTs lie below the X-ray irradiated instability lines, and that the BH-SXT GRO1655-40 is in the regime where the disc instability is first triggered close to the outer edge of the disc.