Statistical analysis of eclipsing binaries with monotonic orbital-period variations: A-type W UMa contact systems

TL;DR

This work statistically dissects monotonic orbital-period variations in A-type W UMa contact binaries to isolate genuine correlations between binary parameters and the rates of mass transfer, mass loss, and angular-momentum loss. Using a literature-derived sample of An and Ap systems with well-determined parameters, the study applies partial least-squares regression to a 16-parameter space, followed by partial regression analyses to identify key predictors and then derives power-law relations with ordinary least-squares fits. It finds that negative period variations are mainly governed by MTML, with MTML rates strongly dependent on the primary radius and ML relative to MTML scaling with the mass ratio, suggesting substantial L2 mass loss and extra AML. Positive period variations are linked to MTLM driven by radiation pressure, with the MTLM rate correlating with the luminosity and mass ratios, while the ML rate correlates primarily with the secondary temperature, consistent with wind-driven mass loss. The results reveal distinct evolutionary and structural differences between An and Ap systems and support L2-outflow as a major AML channel, providing observational constraints for theoretical models of W UMa evolution.

Abstract

On the basis of monotonic orbital-period variations, this study aims to identify genuine relationships between binary parameters and the rates of mass transfer (MT), mass loss (ML), and angular momentum loss (AML). Sample binaries with monotonic period variations are collected from the literature, together with well-determined binary parameters. Assuming the monotonic variations are responsible for any one of the MT, ML, and AML, their rates are calculated with the rates of change of period. After selecting crucial parameters using partial least-squares analysis, a parameter that exhibits the closest correlation with any one of the derived rates is further selected using partial regression plots. Moreover, power-law relationships are found for the discovered correlations. The properties of the sample binaries are also investigated by examining associations between binary parameters. In the systems with negative period variations, it is found that the rate of MT from more- to less-massive stars is a function of the primary radius; the AML rate is a function of the fill-out factor. In addition, the relationships between the mass ratio and stellar masses indicate that the ML rate relative to the MT rate decreases with increasing mass ratio below ~0.46. Meanwhile, in the systems with positive variations, it is found that the rate of MT from less- to more-massive stars is a function of the luminosity ratio and/or mass ratio; the ML rate is a function of the secondary temperature. The discussion also addresses possible processes occurring in the sample binaries.

Figures (14)

• Figure 1: RMSEP value as a function of the number of PLS components ($N$) for MTML (a), extra AML (b), MTLM (c), and ML (d).
• Figure 2: Plots of VIP scores (top), and histograms of weights (blue solid bars) and loadings (red shaded bars) for MTML (a), extra AML (b), MTLM (c), and ML (d). Black filled circles and green filled triangles represent the VIP scores for the first (C1) and the first to third (C3) components, respectively. The Nth histogram from the top displays the weights and loadings for the Nth component of the PLS model.
• Figure 3: Partial regression plots (the right panel of each figure) of the primary radius vs. MTML rate, controlling for the orbital period (a), mass ratio (b), and luminosity ratio (c). In each figure, the scatter plots of control variable vs. primary radius (bottom left) and vs. MTML rate (top left) are also shown. All residuals in the partial regression plots are based on the OLS bisector. The solid and dashed lines in the partial regression plots are the OLS bisector and OLS($Y|X$) lines of which slopes are $c_\mathrm{1, bs}$ and $c_\mathrm{1, yx}$, respectively. The values of $r_\mathrm{s}$ represent Spearman's rank correlation coefficients. Their corresponding $p$-values are shown in parentheses, which are computed with the null hypothesis that there is no linear (for $r_\mathrm{p}$) or monotonic (for $r_\mathrm{s}$) relationships between two variables.
• Figure 4: Partial regression plots of the fill-out factor vs. extra AML, controlling for the secondary radius (a), secondary mass (b), and angular momentum (c), together with scatter plots, as in Figure \ref{['Fig_PRP_An_ME']}. The residuals are based on the OLS bisector.
• Figure 5: Top row: Partial regression plots of the luminosity ratio vs. MTLM rate, controlling for the mass ratio (a), primary temperature (b), secondary temperature (c), and primary luminosity (d), as in Figure \ref{['Fig_PRP_An_ME']}. Bottom row: Partial regression plots of the mass ratio vs. MTLM rate, controlling for the primary temperature (e), secondary temperature (f), primary luminosity (g), and luminosity ratio (h). The residuals for panels (a,b,h) and (c-g) are based on the OLS bisector and OLS($Y|X$), respectively.