Gravitational microlensing by the stellar population of lensing galaxies provides an important opportunity to spatially resolve the accretion disk structure in strongly lensed quasars. Some of the objects (like Einsteins cross) are reasonably consist
ent with the predictions of the standard accretion disk model. In other cases, the size of the emitting region is larger than predicted by the standard thin disk theory and practically independent on wavelength. This may be interpreted as an observational manifestation of an optically-thick scattering envelope possibly related to super-Eddington accretion with outflows.
We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. P
enetrating deep into the disk, the field of scattered X-ray photons with energy $Egtrsim10$,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $Rgtrsim10^{10}$,cm from the neutron star. At a distance $Rsim10^{11}$,cm, where the total surface density in the disk reaches $Sigma_0sim20$,g,cm$^{-2}$, X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature $T_{atm}sim(2div3)times10^6$,K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a $gtrsim10$,% accuracy in the range of X-ray photon energies $E<20$,keV.
