Multivariate statistical analysis of contact binaries with a low mass ratio: Definition, dynamical stability, and parameter relations

This study explores multiple aspects of W Ursae Majoris (W UMa) contact binary systems with low mass ratios. We provide empirical insights into their definition, structure, rotational stability, and parameter relations. We first examined the range of mass ratios that characterize these systems, and based on an analysis of 818 contact binaries, we established an empirical threshold of q ≈ 0.27 to identify systems with a low mass ratio. To investigate the 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 spin / J orb ). While k 1 remains nearly constant, k 2 and J spin / J orb decrease slightly with increasing mass ratio. This emphasizes the role of the secondary star’s internal structure. Moreover, we compiled a dedicated sample of 115 contact binaries with a low mass ratio and estimated their absolute parameters using Gaia DR3 parallaxes. From this dataset, we derived empirical parameter relations for systems with a low mass ratio that 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.

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