Two important constraints on the inner radii of accretion disks

The Stefan-Boltzmann law yields a very strong constraint on the geometry of inner accretion disks in black-hole X-ray binaries. It follows from considering the irradiating flux and the effective temperature of the inner parts of the disk, which implies that a strong quasi-thermal component with the average energy higher than that of a blackbody at the effective temperature has to be present whenever relativistic Fe K fluorescence and reflection features are observed. The apparent absence of such quasi-thermal component with the color temperature of $\sim$1 keV in high-luminosity hard states is not compatible with a strongly irradiated disk extending close to the innermost stable circular orbit. Instead, the disk should be either truncated at a relatively large radius or irradiated by a corona at a large height, which would reduce the effective temperature and bring it to an agreement with the data. We also study constraints on disk/corona models following from comparing the disk densities fitted in literature using variable-density reflection codes with those calculated by us from the ionization parameter, the luminosity and the disk inner radius. We find that the fitted densities are much higher/lower in the hard/soft state of binaries, implying significant problems with the used assumptions and methods.