Fourier Analysis of the Light Curves of Eclipsing Variables, XXIII
Abstract
The method of evaluating the photometric perturbations B _{2m } of eclipsing variables in the frequency domain, developed by Kopal (1959, 1975e, 1978) for an interpretation of mutual eclipses in systems whose components are distorted by axial rotation and mutual tidal action. The aim of the present paper has been to establish explicit expressions for the photometric perturbation B _{2m } in such systems, regardless of the kind of eclipses and nonintegral values ofm. Recently, Kopal (1978) introduced two different kinds of integrals with respect to associated αfunctions andIintegrals which have been expressed in terms of certain general types of series that can be easily programmed for automatic computation within seconds of real time on highspeed computers. Following a brief introduction (Section 1) in which the need of this new approach will be expounded, in Section 3 we shall deduce the integral <MediaObject> <ImageObject FileRef="10509_2004_Article_BF01023929_TeX2GIFE1.gif" Format="GIF" Color="BlackWhite" Type="Linedraw" Rendition="HTML"/> </MediaObject> int_0^{θ ' } {tfrac{{α _n^' }}{δ }} d(sin^{2m} θ ) in terms of a certain general type of series and also βfunction, which should enable us to evaluate explicit expressions forf {_{*}/^{(h)}},f {_{1}/^{(h)}},f {_{2}/^{(h)}} as well as B _{2m }.
 Publication:

Astrophysics and Space Science
 Pub Date:
 December 1978
 DOI:
 10.1007/BF01023929
 Bibcode:
 1978Ap&SS..59..431A
 Keywords:

 Astronomical Photometry;
 Eclipsing Binary Stars;
 Fourier Analysis;
 Light Curve;
 Stellar Luminosity;
 Variable Stars;
 Computer Techniques;
 Frequency Distribution;
 Integral Equations;
 Limb Darkening;
 Perturbation Theory;
 Series (Mathematics);
 Astrophysics