Vertical Structure of the Outer Accretion Disk in Persistent Low-Mass X-Ray Binaries

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. Penetrating deep into the disk, the field of scattered X-ray photons with energy $E\gtrsim 10$,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $R\gtrsim {10}^{10}$,cm from the neutron star. At a distance $R\sim {10}^{11}$,cm, where the total surface density in the disk reaches ${\mathrm{\Sigma }}_0\sim 20$,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 $T_{atm}\sim (2÷3)\times {10}^6$,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 $\gtrsim 10$,% accuracy in the range of X-ray photon energies $E<20$,keV.