Multivariate Statistical Analysis of Low Mass Ratio Contact Binaries: Definition, Dynamical Stability, and Parameter Relationships

Abstract

This study explores multiple aspects of W Ursae Majoris (W UMa) contact binary systems with low mass ratios, providing empirical insights into their definition, structure, rotational stability, and parameter relationships. We first examined the range of mass ratios that characterize these systems and, based on an analysis of 818 contact binaries, established an empirical threshold of $q\approx 0.27$ to identify low mass ratio systems. To investigate rotational stability, we conducted a Monte Carlo analysis of the squared gyration radii ($k_1^2$ and $k_2^2$) and assessed the resulting spin-to-orbital angular momentum ratio ($J_{\mathrm{spin}}/J_{\mathrm{orb}}$), finding that while $k_1$ remains nearly constant, $k_2$ and $J_{\mathrm{spin}}/J_{\mathrm{orb}}$ decrease slightly with increasing mass ratio, emphasizing the role of the secondary star's internal structure. Moreover, we compiled a dedicated sample of 115 low mass ratio contact binaries and estimated their absolute parameters using Gaia DR3 parallaxes. From this dataset, we derived empirical parameter relationships for low mass ratio systems, which provide a useful reference for future observational and theoretical studies. The resulting datasets and statistical summaries offer benchmarks for modeling, stability evaluation, and evolutionary studies of W UMa-type binaries with low mass ratios.

Accepted by the A&A journal

References in corpus (13)

• Evolutionary tracks and isochrones for low- and intermediate-mass stars: from 0.15 to 7 M_sun, and from Z=0.0004 to 0.03
• V1309 Scorpii: merger of a contact binary
• THE MINIMUM MASS RATIO OF W URSAE MAJORIS BINARIES
• Dynamical evolution of active detached binaries on log Jo - log M diagram and contact binary formation
• Statistics of 700 individually studied W UMa stars
• The dynamical stability of W Ursae Majoris-type systems
• The photometric-amplitude and mass-ratio distributions of contact binary stars
• ZZ Piscis Austrinus (ZZ PsA): A bright red nova progenitor and the instability mass ratio of contact binary stars
• Investigation of the Orbital Period and Mass Relations for W UMa-type Contact Systems
• The First Photometric and Orbital Period Investigation of an Extremely Low Mass Ratio Contact Binary with a Sudden Period Change, TYC 4002-2628-1
• Detection of the lowest mass ratio contact binary in the universe: TYC 3801-1529-1
• Mass-ratio distribution of contact binary stars
• Detailed Investigation of a W UMa Contact Binary with an Ultralow Mass Ratio and a Third-Body as a Potential Merger Candidate