Semi-analytical radiative transfer in plane-parallel geometry: application to accretion disk coronae

A simplified frequency-integrated radiative transfer equation is solved to study Compton scatterings in the corona of the disk by using numerical iterating method. We find that the vertical thickness of the corona cannot be used as the typical length to measure the optical depth of the corona. A semi-analytical approach is proposed to calculate the energy dissipations in the corona of the disk. We demonstrate that our approach can reproduce the numerical solutions to an accuracy of <2 %.