2 The equation of transfer in comoving frame in a dusty atmosphere

The equation of line transfer in the comoving frame with absorption and emission due to dust and gas (see Peraiah & Wehrse 1978; Peraiah 1984; Wehrse & Kalkofen 1985) is given by,

$$\mu \frac {\partial I(x, \mu, r)}{\partial r} + \frac {(1 - \mu^2)} {r} \frac {\partial I (x, \mu, r)} {\partial \mu} = K (x, r) S_{\rm L} (r)$$

$$K_{\rm c} (r) S_{\rm c} (r)- \bigg [K (x, r) + K_{\rm c} (r)] I (x, \mu, r)$$

$$[(1 - \mu^2) \frac {V(r)} {r} + \mu^2 \frac {{\rm d}V(r)} {{\rm d}r}\bigg] \frac {\partial I (x, \mu, r)} {\partial x}$$

$$K_{\rm dust}{S_{\rm dust}(r, \mu, x)-I(r, \mu, x)},$$ (1)

and

$$-\mu \frac {\partial I (x, -\mu, r)} {\partial r} - \frac {(1 - \mu^2)} {r} \frac {\partial I (x, -\mu, r)} {\partial \mu} = K(x, r) S_{\rm L} (r)$$

$$+K_{\rm c} (r) S_{\rm c} (r)-\bigg[K(x, r) + K_{\rm c}(r)\bigg] I(x, -\mu, r)$$

$$+ \bigg[(1 - \mu^2) \frac {V(r)} {r} + \mu^2 \frac {{\rm d}V(r)} {{\rm d}r} \bigg] \frac {\partial I (x, -\mu, r)} {\partial x}$$

$$+K_{\rm dust}{S_{\rm dust}(r, \mu, x)-I(r, \mu, x)},$$ (2)

where all the symbols have their respective usual meanings (See Paper I). Further, $K_{\rm dust}(r)$ is the absorption coefficient of the dust and the dust source function $S_{\rm dust}(r, \pm\mu, x)$ is given by,

$$% S_{\rm dust}(r, \pm\mu, x) (1-\omega)B_{\rm dust}$$

$$\frac {\omega}{2} \int^{+\infty}_{-\infty}P(\mu, \mu^\prime, r)I(r, \mu^\prime, x){\rm d}\mu^\prime$$ (3)

where $B_{\rm dust}$ is the Planck function for the dust emission, $\omega$the albedo of the dust and P the isotropic and coherent scattering phase function. The quantity $B_{\rm dust}$ is normally neglected because the re-emission will be far away from the line centre and therefore may not contribute to the line radiation. Although we need not consider the term containing $B_{\rm dust}$, we have included it for the sake of completeness.

We have adopted the "CELL" method described by Peraiah (1984) to solve the Eqs. (1)and (2); This is done by suitable discretization in frequency, angle as well as radius. The details of the method was given in Peraiah et al. (1987).