4 Parameters for computations

The equations of line transfer given in the Eqs. (1) and (2) are solved following the procedure described in Peraiah et al. (1987). The optical depths along these segments $P \tau$ $P \tau^\prime$ are calculated using the Eq. (1) of Paper I. We set $\sigma$ as the electron scattering coefficient equal to (Thomson cross section) to $6.6525 \ 10^{-25}$ cm ². The lengths of the segments change between 0 and 2r where r is the radius of the component.

Figure 2: A comparison of the source function S and $S_{\rm s}$ are shown with respect to the shell numbers in a scattering medium for a static medium and for a expanding medium when the dust optical depth $\tau _{\rm d}=2$ and $\frac {r_1}{R}=\frac {1}{2}$ and $\frac {1}{5}$

We have set an electron density of 10¹⁴ cm^-3. The maximum optical depth is 97.5 while optical depth of the segment along the x-axis OO$^\prime$ is 66.525 where the radius of the star is taken to be 10¹² cm and the thickness of the atmosphere as 10¹² cm. The parameters that are used in the calculations are listed below.

$\frac {B}{A }$ = ratio of the outer to the inner radii of the atmosphere of the primary component and whose reflection effect is being studied (=2);

n = number of shells into which the atmosphere of the component is divided;

$\frac {r_1} {R}$ = ratio of the radius of the component to that of the line joining the centre of gravity of the two components $r_{1}=2 \ 10^{12}$ cm;

V_A = initial velocity of expansion in units of mtu at n = 1 (see Eqs. (12) and (13));

V_B = final velocity in units of mtu at n = 100 (see Eq. (14));

S = total source function (see Eq. (8));

$S_{\rm s}$ = source function due to self radiation;

I = ratio of incident radiation to that of self radiation of the star (see Eq. (11));

$\epsilon$ = probability per scatter that a photon is thermalised by collisional de-excitation;

$\beta$ = ratio of absorption coefficient in continuum to that in the line;

T = total optical depth;

Q = $\frac {x}{x_{\rm max}}$ (see Eq. (15));

$\frac {F_Q}{F_{\rm c}}$ = ratio of the line flux at the normalized frequency Q to that in the continuum or at $x_{\rm max}$ (see Eqs. (16) and (17)),

(R; N.R) = with reflection; with no reflection;

$\frac {H_{\rm e}}{H_{\rm a}}$ = height of the emission to the depth of absorption in the line;

T₁ = temperature in the atmosphere;

$\tau_{\rm d}$ = optical depth due to dust scattering (isotropic).

Our objective is to compute the effects of the presence of dust on the formation of the spectral lines. The number of parameters is large and this results in a large amount of output consequently we choose few sample parameters to show the effects of dust on the formation of lines. We have chosen trapezoidal points for frequency integration. We employed nine frequency points (I=9) with one frequency point at the centre of the line and two angles (m=2) in each half space which gives a matrix size of $(18 \times 18)$. With this size of frequency angle mesh, we obtain a step size which gives solution to the machine accuracy. The condition of flux conservation in a conservatively scattering medium $(\epsilon=0, \beta=0, \omega=1)$, is maintained.

Figure 3: Comparison of line profiles for different dust optical depths when $\frac {r_1}{R}=\frac {1}{2}$ and $\frac {1}{5}$ and for VB=50