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 .