The Radiative Transfer in Accretion Discs with Linear Plank Function: Role of Scattering Effect

Radiative transfer in a geometrically thin accretion disc with fnite optical depth is considered under the plane-parallel approximation. The Eddington factor that is defned as the ratio of the mean intensity to radiation stress tensor, is assumed be constant. We have focused our attention on the scattering effect and the optical depth. The emergent intensity as well as other radiative quantities are analytically obtained related to the vertical structure of disc while a linear Planck function is applied. The effect of scattering on the radiative quantities is considered for two cases: (i) isothermal and (ii) temperature gradient and both cases are assumed to be in local thermodynamical equilibrium (LTE), too. Our results show the scattering for an isothermal atmosphere is more signifcant than an atmosphere with temperature gradient. Moreover, the emergent intensity is changed by the disc optical depth. We also explore the limb-darkening effect for the both thick and thin optically discs, separately.