Let us now investigate the influence of limb darkening on the
line photometry. In the simple Milne-Eddington approximation of
a plane-parallel atmosphere the observed specific intensity for
direction cosine 
is given by
The source-function can be taken constant within the line-profile
and approximately linear in a mean (e.g. Rosseland) optical depth
,
If the opacity both in the continuum (
) and in
the line (
, where 
is
normalized line profile) can be taken approximately proportional
to the mean opacity (
) through the optical depths
where the line is formed, then
and
The limb-darkening is thus generally steeper in continuum than
in a line. During an eclipse, the ratio z of visible and total
(i.e. visible plus eclipsed) light is different at different
(i.e. 
). Consequently, the contribution of the
eclipsed component to the total specific intensity is
where
are moments of 
, which are algebraically independent.
Unlike the case of a homogeneous stellar disk investigated
in the previous section, where both the continuum and line
intensities were proportional to a single factor z, the
contribution of the eclipsed component to the total intensity
in continuum (i.e. at 
)
is now affected by both 
and 
, while its
contribution to the line intensity
by 
only. The generalization of Eqs. (9 (click here)), (10 (click here))
for observed changes of line intensities thus reads
Figure 2: Preliminary results of relative line photometry of V436 Per.
Magnitude differences between the primary and secondary component
(calculated according to Eq. (14) for H
line (
) and He I 6678 (+)) are plotted in dependence on the
orbital phase (from periastron). The secondary minimum
occurs close to phase 0.42 and the primary minimum at phase
0.98
The eclipse of an edge of the stellar disk, where 
, can have negligible effect on 
and the line
intensity, but observable effect on 
and the continuum
intensity. This can lead to enhancement of relative line
intensity even of the eclipsed component at this stage of
eclipse. This effect is also marginally observable in the
example
of V436 Per shown in Fig. 2 (click here)
(see Harmanec et al. 1997 for details on this system).
Moreover, there seems to be a systematically higher effect in
the stronger H
line than in the He I line. The reason for
this may lie beyond the Milne-Eddington approximation and the
assumption (18 (click here)).
Unlike the case simplified in the previous section by the assumption
of homogeneous stellar disk, all free parameters (
,
for each exposure and 
, 
) can not be
directly calculated now. Instead of this, radii and orbital
parameters which should match the geometry of eclipse to the
orbital phase are to be fitted to the observed data together
with appropriate models of stellar atmospheres. In such an
application the relative line photometry can yield an additional
test on model atmospheres.
Acknowledgements
The author is indebted to D. Holmgren, J. Kubát and R.E. Wilson for useful discussions and comments. The suggestions of an anonymous referee are also highly appreciated. This study was supported by the grant 205/96/0162 of the Grant Agency of the Czech Republic, project K1-003-601 and grant 303401 of the Grant Agency of Academy of Sciences.