On the Properties of Inner Cool Disks in the Hard State of Black Hole X-Ray Transient Systems

The formation of a cool disk in the innermost regions of black hole X-ray transient systems in the low hard state is investigated. Taking into account the combined cooling associated with the Compton and conductive energy transport processes in a corona, the radial structure of a disk is described for a range of mass accretion rates. The mass flow in an optically thick inner region can be maintained by the condensation of matter from a corona with the disk temperature and luminosity varying continuously as a function of the accretion rate. Although such a disk component can be present, the contribution of the optically thick disk component to the total luminosity can be small since the mass flow due to condensation in the optically thick disk underlying the corona can be significantly less than the mass flow rate in the corona. The model is applied to the observations of the low quiescent state of the black hole source GX 339-4 at luminosities of around $0.01 L_{Edd}$ and is able to explain the temperature of the thermal component at the observed luminosities. Since conductive cooling dominates Compton cooling at low mass accretion rates, the luminosity corresponding to the critical mass accretion rate above which a weak thermal disk component can be present in the low hard state is estimated to be as low as $0.001 L_{Edd}$.