Limb Darkening due to the Incidence of a Parallel Beam of Radiation

Abstract

We have investigated how the radiation is distributed from the centre to the limb when the atmosphere receives a parallel beam of radiation from infinity. We have considered a purely reflecting surface at the bottom of the atmosphere when the outer layers are illuminated uniformly from all directions. We have considered an electron scattering atmosphere with decreasing density from inner radius towards the outer radius. The atmosphere under question is half the radius of the star itself. The density of the electrons at the bottom of the atmosphere is set to be equal to 10/sup13/ cm/sup-3/. The nature of limb darkening is very similar when Ne = 10/sup13/ cm/sup-3/ whereas when Ne = 10/sup14/ cm/sup-3/ there is considerable amount of differences between spherical and plane parallel cases. Although the extension of the atmosphere is quite small the differences in the laws of limb darkening are considerable, the differences are further accentuated when the radiation is assumed to be totality reflected from the bottom of the atmosphere, the situation can be very similar to that of a planetary atmosphere.