Up: Radiative transfer in the
The atmosphere in question is divided into n shells where n = 1
corresponds
and n = 100 corresponding to ,
and
is the optical depth at any point
and T is the total optical depth. The total optical depth is set in advance.
We assume that no radiation is incident from outside the spherical shell at
r=B and ,
while radiation of unit intensity is incident at r=A,
,
in the case of purely scattering medium.
Thus we have,
and in the case of the boundary condition of the frequency derivative,
we have:



(5) 
We have set the velocities at r=A as V_{A}, and at r=B as V_{B}which is set equal to 0 and 50 mtu. If the spherical shell
expands with constant velocity, we have;
if there are velocity gradients, then we have;



(7) 
Finally we calculate total source function S by adding the source function
(1) due to reflected radiation
and due to the self radiation
(See Paper I)

(8) 
We calculate the set of source functions at the points of intersection
of the ray parallel to the line of sight and the shell boundaries. These
source functions are used to calculate the emergent specific intensities
at infinity (or at the observer's point), by using the formula
(see Peraiah & Srinivasa Rao 1983)

(9) 
where I_{n}(r) corresponds to the specific intensity of the ray
passing through the shell bounded by r_{n} and r_{n+1} corresponding to
perpendicular
to the axis OO
(See Fig. 1 of Paper I) at different radii.
I_{0}(n) corresponds to
the incident intensity at the boundary of the shell and
is the
optical depth in the sector along the ray path. The source function
S(t) is calculated by linear interpolation between S(t_{n}) and
S(t_{n+1}). The specific intensity at the boundary of each shell is
calculated by using Eq. (9).

Figure:
The source functions S are shown with respect to the shell numbers in
a scattering medium for different dust optical depths, velocities,
with
and I=5 
The incident radiation at Q, the bottom of the atmosphere, (See Fig. 1 of Paper I) is given as

(10) 
The incident radiation from the secondary is given in terms
of
in the ratio I, where I is given by

(11) 
The velocities of expansion of the gas are expressed in terms of mean thermal
units
(mtu) given by,

(12) 
where k is the Boltzmann constant and T_{1} is the temperature and m_{i} is the
mass of the ion. The velocity at n=1 or
is V_{A} and V_{B} is the velocity at
n = 100 or
are given in terms of mtu or
as

(13) 

(14) 
where v_{A} and v_{B} are the velocities at the inner radius A, outer radius
B at radial point r respectively in units of mtu of the gas.
We assume uniform expansion of the gases for the sake of simplicity.
The proximity of the component
is measured in terms of separation parameter
,
where r_{1} is the radius of the primary and R is the
separation of
centre of gravity of the two components.
The ratio of the outer to the inner radii
of the atmosphere is
always taken to be 2. The actual thickness in the components could be much
larger than what we have considered here. As the number of parameters is
large, we restricted our calculations to this modest thickness of the atmosphere.
The line
profile fluxes
are plotted against the normalized frequency Q,
where

(15) 

(17) 
and

(18) 

(19) 

(20) 
x lies between
5 units. The equivalent widths are calculated by the relation,

(21) 
where

(22) 
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