Phenomenological modeling of the light curves of algol-type eclipsing binary stars

摘要

We propose a special class of functions for mathematical modeling of periodic signals of a special type with a nonuniform distribution of the arguments. This method has been developed for determining the phenomenological characteristics of light curves required for listing in the "General Catalog of Variable Stars" (GCVS) and other data bases. For eclipsing binary stars with smooth light curves (types EB and EW) a trigonometric polynomial of optimal degree in a complete or symmetric form is recommended. For eclipsing binary systems with relatively narrow minima, approximating the light curves by a class of nonpolynomial spline functions is statistically optimal. A combination of a second order trigonometric polynomial (TP2, which describes "reflection", ellipsoidal and "spotting" effects) and localized contributions of the minima (parametrized with respect to depth and profile separately for the primary and secondary minima) is used. This approach is characterized by a statistical accuracy of the smoothing curve that is a factor of ~1. 5-2 times better than for a trigonometric polynomial of statistically optimal degree, and by the absence of false "waves" in the light curve associated with the Gibbs effect. Besides finding the width of the minimum, which cannot be determined using a trigonometric polynomial approximation, this method can be used to determine its depth with better accuracy, and to separate the effects of the eclipse and the part outside the eclipse. For multicolor observations, the improved accuracy of the smoothing curve for each filter makes it possible to obtain more accurate plots of the variation in the color index. The efficiency of the proposed method increases as the width of the eclipse becomes smaller. This method supplements the trigonometric polynomial approximation. The method, referred to as the NAV (New Algol Variable) method, is illustrated by applying it to the eclipsing binary systems VSX J022427. 8-104034=USNO-B1. 0 0793-0023471 and BM UMa. An alternative "double period" model is examined for VSX J022427. 8-104034.