On the properties of inner cool disks in the hard state of black hole X-ray transient systems

We investigate the formation of cool disks in the innermost regions of black hole X-ray transient systems in the low/hard state. Taking into account the combined cooling associated with the Compton and conductive energy transport processes in a corona, we describe the radial structure of a disk 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 in the corona. The model is applied to the observations of the low/hard state of the black hole source GX 339-4 at luminosities of ∼0.01L_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 0.001L_Edd.