The effect of coronal radiation on a residual inner disk in the low/hard spectral state of black hole X-ray binary systems

Thermal conduction between a cool accretion disk and a hot inner corona can result in either evaporation of the disk or condensation of the hot corona. At low mass accretion rates, evaporation dominates and can completely remove the inner disk. At higher mass accretion rates, condensation becomes more efficient in the very inner regions, so that part of the mass accretes via a weak (initially formed) inner disk which is separated from the outer disk by a fully evaporated region at mid radii. At still higher mass accretion rates, condensation dominates everywhere, so there is a continuous cool disk extending to the innermost stable circular orbit. We extend these calculations by including the effect of irradiation by the hot corona on the disk structure. The flux which is not reflected is reprocessed in the disk, adding to the intrinsic thermal emission from gravitational energy release. This increases the seed photons for Compton cooling of the hot corona, enhancing condensation of the hot flow and re-inforcing the residual inner disk rather than evaporating it. Our calculations confirm that a residual inner disk can co-exist with a hard, coronally dominated, spectrum over a range of $0.006<\dot m<0.016$ (for $\alpha=0.2$). This provides an explanation for the weak thermal component seen recently in the low/hard state of black hole X-ray binary systems.