Solutions of the Polarized Transfer Equation

Abstract

We will here make the common assumption that atomic coherences in the absorption and stimulated emission terms may be neglected, and that the continuous spectrum may be treated in LTE. According to Eqs. (4.50), (5.95), and (6.104), the radiative transfer equation for the Stokes vector I _v can then be written as

$$\frac{{dI_v }} {{d\tau _c }} = \left( {\eta + E} \right)I_v - S_v ,$$

(11.1)

where τ _c represents the continuum optical depth. Note that Eq. (6.104) was given in terms of the line optical depth. The choice of depth scale influences the form of the source function, which in the case of Eq. (11.1) can be expressed as

$$S_v = S_{L\eta } 1 + S_c 1 + j_{coh} /\kappa _c .$$

(11.2)