Phenomenological modelling of eclipsing system light curves

Abstract

Context. The observed light curves of most eclipsing binaries and stars with transiting planets can be described well and interpreted by current advanced physical models that also allow for determining many of the physical parameters of eclipsing systems. However, for several common practical tasks, there is no need to know the detailed physics of a variable star, but only the shapes of their light curves or other phase curves.Aims. We present a set of phenomenological models for the light curves of eclipsing systems. Methods. We express the observed light curves of eclipsing binaries and stars, which are transited by their exoplanets orbiting in circular trajectories, by a sum of special, analytical, few-parameter functions that enable fitting their light curves with an accuracy of better than 1%. The proposed set of phenomenological models of eclipsing variable light curves were then tested on several real systems. For XY Bootis, we also give a detailed comparison of the results obtained using our phenomenological modelling with those found using available physical models. Results. We demonstrate that the proposed phenomenological models of transiting exoplanet and eclipsing binary light curves applied to ground-based photometric observations yield results compatible with those obtained by applying more complex physical models. Conclusions. The suggested phenomenological modelling appears useful for solving a number of common tasks in the field of eclipsing variable research.

How far can we trust published TESS periods?

“…Phase curve and trend models should be tailored to the actually observed light curves. The models should be functions of the parameters of the ephemeris of stellar periodicity, especially the time of the basic extremum, the mean period (or periods) and their time derivatives (Mikulášek, 2015(Mikulášek, , 2016.…”

The first eclipsing binary catalogue from the MOA-II data base

“…Our interest in this paper also includes searching for triple object candidates in our EB candidates via eclipse time variation (ETV) analysis. The eclipse timing of an EB was performed by the template method in which the eclipse template was constructed using the phenomenological model of EB light curves (Mikulášek 2015). As a result, three contact binaries of periods < 0.6 day showed ETVs that are well fitted by the light-travel-time effect (LTTE) model.…”

MAVKA: Program of statistically optimal determination of phenomenological parameters of extrema. Parabolic spline algorithm and analysis of variability of the semi-regular star Z UMa

“…Сплайни iз змiнним ступенем були запропонованi [13], якi виправляли проблему "нефiзичних" хвиль на апроксимацiях полiномами. Огляди iснуючих методiв приведенi [15][16][17][18].…”