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
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