Disc instability models for X-ray transients: evidence for evaporation andlow alpha-viscosity?

We construct time-dependent models of accretion discs around black holes an d neutron stars. We investigate the effect that evaporation of the inner di sc regions during quiescence has upon the predictions of the disc instabili ty model (DIM) for these systems. We do not include irradiation of the disc in the models. Removing the inner, most unstable, parts of the accretion disc increases th e predicted recurrence times. However, DIMs with values of the viscosity pa rameter alpha(hot)similar to 0.1 and alpha(cold)similar to 0.02 (values typ ically used in applications of the DIM to standard dwarf nova outbursts) fa il to reproduce the long recurrence times of soft X-ray transients (unless we resort to fine-tuning the parameters), independent of the evaporation st rength. We show that models in which evaporation is included and a smaller value of alpha(cold) (similar to 0.005) used do reproduce the long recurren ce times and the accretion rates at the level of the Eddington rate observe d in outburst. The large difference between the values of alpha(hot) and al pha(cold), if confirmed once disc irradiation is included, suggests that se veral viscosity mechanisms operate in these accretion discs. For some parameter sets our models predict re-flares during the decline fro m outburst. The re-flares are a physical property of the model and result f rom the formation of a heating front in the wake of an initial cooling fron t, and subsequent multiple front reflections. The re-flares disappear in lo w-alpha models where front reflection cannot occur.