  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.
