On the radiative equilibrium of a stellar atmosphere. XV.

Abstract

In this paper the general equations of transfer for an atmosphere scattering radiation in accordance with Rayleigh's law and allowing for a partial elliptic polarization of the radiation field are formulated. It is shown that, under these conditions, we must consider, in addition to the intensities I_l and I_r in two directions at right angles to each other in the plane of the electric and the magnetic vectors, the two further quantities U=(I_l-I_r)tan 2χ and V=(I_l-I_r) tan 2β9 sec 2χ, where χ denotes the inclination of the plane of polarization to the direction to which l refers and -π/2≤β≤π/2 is an angle, the tangent of which is equal to the ratio of axes of the ellipse characterizing the state of polarization. (The sign of β depends on whether the polarization is right handed or left handed.) It is found that the equations of transfer for I_l, I_r, and U are of exactly the same forms as in cases in which only partial plane-polarization is contemplated and that the equation for V is independent of others. On Rayleigh's law, V is scattered in accordance with a phase function,3/2cosθ. The solution of the equation for V appropriate for the problem of diffuse reflection by a semi-infinite atmosphere is also given.