Fourier Analysis of the Light Curves of Eclipsing Variables, XV

A new general expression for the theoretical momentsA_2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA_2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA_2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA_2m of the light curves. The theoretical functionsf₀,f₂,f₄,f₆,g₂ andg₄ which are the functions ofa andc₀, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf₂,f₄ andf₆ have also been derived (Section 3) in terms of Kopal'sI-integrals. The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.