Solving Eqs. (9 (click here)) and (10 (click here)), the factor z can be
simply expressed as
and the ratio of continua intensities
Obviously, if z<1, then and . This behavior can help to distinguish the variations caused by the "geometrical'' reasons (or their equivalent) from intrinsic variations of line intensities of a component or from the observational noise.
In the usual case of k exposures, the factors
of the darkenings of the component "1'' can be calculated independently
for each exposure from according to Eq. (11 (click here)).
The ratio of continua intensities can be then obtained by least
square fit of Eqs. (9 (click here)) and (10 (click here)) e.g. on a logarithmic
(i.e. magnitude) scale, i.e. by solving the condition
for the variation , i.e. simply by numerical minimization of function . The differences of magnitudes of both components at the time of chosen exposure can be then expressed by
If the secondary component is supposed to be constant during the primary eclipse, then the magnitude of the whole system is given by
Vice versa, the total magnitude of the system in the course of secondary eclipse can be estimated by
The applicability of the method of relative line photometry in the above given approximation is certainly limited by the implicitly included assumptions that (i) the change of intensity is the same for the line and the continuum of the eclipsed component, (ii) the intensities of both component are constant outside their eclipses and (iii) that the shape of line profile is constant. The first assumption can be violated even in the case of a pure eclipse due to the limb darkening, which is different in the continuum and in the line. This problem will be studied in the next section. The second assumption is crucial to have well defined the "normal'' state (in which are directly observed), so that the line-intensity of the non-eclipsed component can be used as a "comparison''. This assumption can be violated e.g. for ellipsoidal variables. Obviously, a more sophisticated procedure (analogous to the light-curves solution) of fitting the observed values of (related to a reasonably chosen "reference'' state of ) by a theoretical model can yield an additional information in such a case. Finally, the third assumption can be violated e.g. by Rossiter effect when different equatorial parts of a rotating star are eclipsed. This assumption is crucial for the disentangling according to Eq. (1 (click here)). However, as far as the rotational broadening (even for a partially eclipsed component) is also given by a convolution in x, it is, in principle, possible to generalize the method of the disentangling and line photometry even to this case. On the other hand, such effects can be negligible in many cases not only for a pure eclipse, but in some approximation also for elliptic, reflecting or pulsating components of binaries.