SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 349, 151-168 (1999)

Previous Section Next Section Title Page Table of Contents

Appendix A

1 - For elliptical structures where [FORMULA] the most frequent situations encountered in our calculations can be classified as follows:

(a) [FORMULA]. The angle [FORMULA] is shown in Fig. 7 and is given by [FORMULA], where [FORMULA], the coordinates in the [FORMULA] plane of the CE-star interception are:

[EQUATION]

The uncovered fraction of stellar area projected in the plane perpendicular to the line of sight: [FORMULA], the area of fraccion covered by the CE: [FORMULA] and that of the CE not intercepted by the star: [FORMULA], are given by:

[EQUATION]

where [FORMULA] is the whole area (in units of the projected stellar area [FORMULA]) of the ellipsoidal CE projected on the plane perpendicular to the line of sight and [FORMULA] [FORMULA].

(b) [FORMULA]. 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 [FORMULA] system to another system directed towards the observer:

[EQUATION]

The angle [FORMULA] between the y-axis and the lower tangent to the CE where the envelope intercepts the star (see Fig. 7) is given by [FORMULA]. For the present inclination-angle interval the fractional projected areas are:

[EQUATION]

where [FORMULA], the x coordinate of the intersection of the stellar limb with the CE:

[EQUATION]

For the remaining fractional areas we have:

[EQUATION]

where:

[EQUATION]

for [FORMULA] and [FORMULA] for [FORMULA]. In the above expressions we have:

[EQUATION]

(c) [FORMULA].

[EQUATION]

As in preceding cases, we have now:

[EQUATION]

where:

[EQUATION]

2 - In all cases where [FORMULA], it is: [FORMULA], [FORMULA] and [FORMULA] for all values of i.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999
helpdesk.link@springer.de