SPH simulations of Shakura-Sunyaev instability at intermediate accretion rates

We show that a standard Shakura–Sunyaev accretion disc around a black hole with an accretion rate M ̇ lower than the critical Eddington limit does show the instability in the radiation pressure dominated zone. We obtain this result performing time-dependent simulations of accretion discs for a set of values of α and M ̇ . In particular we always find the occurrence of the collapse of the disc: the instability develops always towards a collapsed gas pressure dominated disc and not towards the expansion. This result is valid for all the initial configurations we tested. We find significant convective heat flux that increases the instability development time, but is not strong enough to inhibit the disc collapse. A physical explanation of the lack of the expansion phase is proposed considering the role of the radial heat advection. Our finding is relevant since it excludes the formation of the hot Comptonizing corona – often suggested to be present – around the central object by the mechanism of the Shakura–Sunyaev instability. We also show that, in the ranges of α and M ̇ values we simulated, accretion discs are crossed by significant amplitude acoustic waves.