Mass ratio estimates for overcontact binaries using the derivatives of light curves. II. Systems with deep eclipses

TL;DR

The paper tackles estimating photometric mass ratios $q$ for overcontact binaries with deep eclipses that were not addressed in the previous work. It extends a non-iterative method based on light-curve derivatives by introducing two $W$ values for SPp and SPf types and calibrating regression relations to map $W$ to $q$ using synthetic LCs from PHOEBE $2.4$ and real Kepler/TESS data. The approach yields uncertainties of approximately $\sigma \approx 0.035$ for SPp and $\sigma \approx 0.128$ for SPf, with about 69% of SPp and 83% of SPf real data estimates consistent with spectroscopic masses within those uncertainties. This work broadens spectroscopy-free mass-ratio estimation to a wider class of overcontact LC morphologies, enabling efficient analysis of large surveys while highlighting the need for further validation with larger samples.

Abstract

This is the second paper that proposes a simple method for estimating mass ratios using the derivatives of light curves for overcontact binaries. In the first paper (Kouzuma 2023, ApJ, 958, 84) , we presented a method to estimate the mass ratios for systems exhibiting a double-peak feature in the second derivatives of their light curves around eclipses. This second paper focuses on overcontact systems that are not addressed in the first paper, that is, systems lacking a double peak in the second derivative. A sample of synthetic light curves for overcontact binaries consists of 89670, covering a parameter space typical of overcontact systems. 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. We found that time intervals between two local extrema in the derivatives are associated with the mass ratio in systems that exhibit a high degree of eclipse obscuration. Using regression analysis for the identified associations, we derived empirical formulae to estimate the mass ratio and its associated uncertainty. The application of our proposed method to real overcontact binary data demonstrated its effectiveness in providing reliable estimates for both values.

Figures (4)

• Figure 1: Light curves and their first through fourth derivatives (from top to bottom) for representative sample binaries of the SPp and SPf types. Each derivative is normalized to unity. Key times used for estimating mass ratios and their associated uncertainties are labeled. Alt text: Two panels illustrate example light curves and their derivatives for the SPp and SPf types. The x-axes show the time from an eclipse, ranging from 0 to 1 day.
• Figure 2: Relationships between $W$ (equations \ref{['Eq_Wvalue-SPp']} or \ref{['Eq_Wvalue-SPf']}) and the mass ratio $q$. The solid lines represent the regression lines, accompanied by pairs of parallel dashed lines that indicate, for reference, mass ratios 0.1 higher and lower than the regression lines. The color gradient represents the orbital inclination angle, ranging from $60\tcdegree$ (orange) to $90\tcdegree$ (red). Alt text: Two scatter plots for the synthesized SPp-type (left) and SPf-type (right) LCs. The x-axes show $W$ values, ln-scaled, ranging from 1.8 to 2.8 for the SPp systems and from 2.0 to 2.4 for the SPf systems. The y-axes show the mass ratio, ranging from 0 to 0.7 for the SPp systems and from 0.5 to 1.0 for SPf systems.
• Figure 3: Comparison between our estimated ($q_\text{est}$) and the literature's spectroscopic ($q_\text{sp}$) mass ratios. Filled circles and squares represent SPp and SPf systems, respectively. The red solid and dashed lines show $q_\text{est} = q_\text{sp}$ and $q_\text{est} = q_\text{sp} \pm 0.1$, respectively. Alt text: Scatter plot of our estimated and literature's spectroscopic mass ratios. The x- and y-axes show the spectroscopic and estimated mass ratios, respectively. Both axes range from 0 to 1.
• Figure 4: Comparison between our estimated ($q_\text{est}$) and the literature's photometric ($q_\text{ph}$) mass ratios. Symbols are the same as in figure \ref{['fig:qsp-qest']}. Alt text: Scatter plot of our estimated and literature's photometric mass ratios. The x- and y-axes show the photometric and estimated mass ratios, respectively. Both axes range from 0 to 1.