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

TL;DR

The paper tackles estimating the fill-out factor $f$ for overcontact binaries by exploiting derivatives of light curves (LCs). It develops a derivative-based, non-iterative method focused on SPf-type LCs, deriving an empirical relation $f = 0.385\,W_f - 1.359$ with $W_f = \frac{P}{t_{33}-t'_{33}}$ that links $f$ to the time interval between local extrema in the third derivative, calibrated from $74{,}431$ synthetic LCs produced with PHOEBE 2.4. When applied to 688 real binaries from Latkovic 2021 with TESS/Kepler data, the method yields $f_{est}$ with uncertainties and shows good agreement with literature values for about 57% of cases within those uncertainties, confirming practical utility and highlighting dispersion mainly from mass ratio and observational factors. The approach is computationally efficient (no iterations) and scalable for population studies, with potential enhancements from incorporating ML and joint estimation of other binary parameters.

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.

Figures (3)

• Figure S1: Light curves and their first through fourth derivatives (from top to bottom) for a representative SPf-type LC. The green points in the LC represent the average values of the synthesized LC in 100 bins, and the blue curve simply connects these points. The derivatives were calculated using the LC averaged in 100 bins. Each derivative is normalized to unity. The key times used for estimating the fill-out factor and its associated uncertainty are labeled.
• Figure S2: Relationship between $W_f$ (Equation \ref{['eq:Wvalue-SPf']}) and the fill-out factor $f$. The solid line represents the regression line. The dashed lines show linear regression fits of the RMSEs, as expressed by Equation (\ref{['eq:sigmaWf']}), for each fill-out factor. The color gradient represents the mass ratio, ranging from 0 (orange) to 1 (red).
• Figure S3: Comparison between the fill-out factors estimated by the proposed method ($f_\text{est}$) and those reported in the literature ($f_\text{lit}$). The filled and open circles represent the fill-out factors of the spectroscopic and photometric sample LCs, respectively. The solid and dashed lines show $f_\text{est}=f_\text{lit}$ and $f_\text{est}=f_\text{lit} \pm 0.093$, respectively.