Using Light Curve Derivatives to Estimate the Fill-out Factor of Overcontact Binaries

TL;DR

This paper introduces a new method to estimate the fill-out factor of overcontact binary stars using derivatives of their light curves, validated through extensive simulations and real data application.

Contribution

The study presents an empirical formula based on light curve derivatives to accurately estimate the fill-out factor, advancing binary star analysis techniques.

Findings

Strong correlation between third derivative extrema and fill-out factor in high mass ratio systems

Empirical formula provides reliable fill-out factor estimates from light curve data

Method validated with synthesized and real binary star light curves

Abstract

We propose a simple method for estimating the fill-out factor of overcontact binary systems using the derivatives of light curves. We synthesized 74,431 sample light curves, covering the typical parameter space of overcontact binaries. On the basis of a recent study that proposed a new classification scheme using light curve derivatives up to the fourth order, the sample light curves were classified. Among the classified types, for systems exhibiting high mass ratios and high inclinations (i.e., SPf type), we found that the fill-out factor has a strong correlation with the time interval between two local extrema in the third derivatives of their light curves. An empirical formula to estimate the fill-out factor was derived using regression analysis for the identified correlation. Application to real overcontact binary data demonstrated that the proposed method is practical for obtaining reliable estimates of the fill-out factor and its associated uncertainties.