Abstract.We study the prospect of explaining the outbursts of Soft X-ray Transients (SXTs) by the thermalviscous instability in a thin disc. This instability is linked to hydrogen ionization and is significantly changed when irradiation of the disc by X-rays from the inner regions is included. We present the first numerically reliable, physically consistent calculations of the outburst cycles which include the effects of accretion disc irradiation. The decay from outburst is governed by irradiation, as pointed out by King & Ritter (1998), leading to slow exponential decays. At the end of the outburst, the disc is severely depleted, which lengthens the time needed to rebuild mass to the critical density for an outburst. Despite this, the long recurrence times and quiescent X-ray luminosities of SXTs still require the inner disc to be replaced by another type of flow in quiescence, presumably a hot advection dominated accretion flow (ADAF). We include the effects of such truncation and show that the resulting lightcurves are conclusively similar to those of SXTs like A0620-00. We conclude that the two-α disc instability model provides an adequate description of the outbursts of SXTs when both truncation and irradiation are included. The values for the viscosities in outburst and in quiescence are comparable to those used in CVs. We discuss the model in the context of present observations.

A B S T R A C TWe calculate self-consistent models of X-ray-irradiated accretion discs in close binary systems. We show that a point X-ray source powered by accretion and located in the disc plane cannot modify the disc structure, mainly because of the self-screening by the disc of its outer regions. As observations show that the emission of the outer disc regions in low-mass X-ray binaries is dominated by the reprocessed X-ray flux, accretion discs in these systems must be either warped or irradiated by a source above the disc plane, or both. We analyse the thermal-viscous stability of irradiated accretion discs and derive the stability criteria of such systems. We find that, contrary to the usual assumptions, the critical accretion rate below which a disc is unstable is rather uncertain because the correct formula describing irradiation is not well known.

We have developed 1D time-dependent numerical models of accretion discs, using an adaptive grid technique and an implicit numerical scheme, in which the disc size is allowed to vary with time. The code fully resolves the cooling and heating fronts propagating in the disc. We show that models in which the radius of the outer edge of the disc is fixed produce incorrect results, from which probably incorrect conclusions about the viscosity law have been inferred. In particular we show that outside-in outbursts are possible when a standard bimodal behaviour of the Shakura-Sunyaev viscosity parameter α is used. We also discuss to what extent insufficient grid resolutions have limited the predictive power of previous models. We find that the global properties (magnitudes, etc. ...) of transient discs can be addressed by codes using a high, but reasonable, number of fixed grid points. However, the study of the detailed physical properties of the transition fronts generally requires resolutions which are out of reach of fixed grid codes. It appears that most time-dependent models of accretion discs published in the literature have been limited by resolution effects, improper outer boundary conditions, or both.