Statistically Optimal Modeling of Flat Eclipses and Exoplanet Transitions. The "Wall-Supported Polynomial" (WSP) Algoritms

TL;DR

The paper introduces the Wall-Supported Polynomial (WSP) algorithms for accurately modeling irregularly spaced photometric data of variable stars and exoplanet transits, improving eclipse characteristic determination.

Contribution

It presents new WSP functions and compares their effectiveness to existing methods, especially for total and transit eclipses, demonstrating superior accuracy in practical applications.

Findings

WSL method achieves 12 times better accuracy for a binary star.

WSP and WSAP are recommended for exoplanet transit modeling.

The methods extend polynomial fits with 'walls' for better approximation.

Abstract

The methods for determination of the characteristics of the extrema are discussed with an application to irregularly spaced data, which are characteristic for photometrical observations of variable stars. We introduce new special functions, which were named as the "Wall-Supported Polynomial" (WSP) of different orders. It is a parabola (WSP), constant line (WSL) or an "asymptotic" parabola (WSAP) with "walls" corresponding to more inclined descending and ascending branches of the light curve. As the interval is split generally into 3 parts, the approximations may be classified as a "non-polynomial spline". These approximations extend a parabolic/linear fit by adding the "walls" with a shape, which asymptotically corresponds to the brightness variations near phases of the inner contact. The fits are compared to that proposed by Andronov (2010, 2012) and Mikulasek (2015) and modified for the case of data near the bottom of eclipses instead of wider intervals of the light curve. The WSL method is preferred for total eclipses showing a brightness standstill. The WSP and WSAP may be generally recommended in a case of transit eclipses, especially by exoplanets. Other two methods, as well as the symmetrical polynomials of statistically optimal order, may be recommended in a general case of non-total eclipses. The method was illustrated by application to observations of a newly discovered eclipsing binary GSC 3692-00624 = 2MASS J01560160+5744488, for which the WSL method provides 12 times better accuracy.