*Astron. Astrophys. 349, 151-168 (1999)*
## Appendix A
**1** - For elliptical structures where
the most frequent situations
encountered in our calculations can be classified as follows:
**(a) .** The angle
is shown in Fig. 7 and is given by
, where
, the coordinates in the
plane of the CE-star interception
are:
The uncovered fraction of stellar area projected in the plane
perpendicular to the line of sight:
, the area of fraccion covered by
the CE: and that of the CE not
intercepted by the star: , are given
by:
where is the whole area (in
units of the projected stellar area
) of the ellipsoidal CE projected on
the plane perpendicular to the line of sight and
.
**(b) .** To shorten the
writing of mathematical expressions, in what follows we use the
following notation which arises from transformation of the
representation of the ellipsoidal CE in the
system to another system directed
towards the observer:
The angle between the
*y*-axis and the lower tangent to the CE where the envelope
intercepts the star (see Fig. 7) is given by
. For the present inclination-angle
interval the fractional projected areas are:
where , the *x* coordinate
of the intersection of the stellar limb with the CE:
For the remaining fractional areas we have:
where:
for and
for
. In the above expressions we have:
**(c) .**
As in preceding cases, we have now:
where:
**2** - In all cases where ,
it is: ,
and
for all values of *i*.
© European Southern Observatory (ESO) 1999
Online publication: August 25, 1999
helpdesk.link@springer.de |