The Photometric Amplitude and Mass Ratio Distributions of Contact Binary Stars

The distribution of the light variation amplitudes A ( a ), in addition to determining the number of undiscovered contact binary systems falling below photometric detection thresholds and thus lost to statistics, can serve as a tool in determination of the mass ratio distribution Q ( q ), which is very important for understanding of the evolution of contact binaries. Calculations of the expected A ( a ) show that it tends to converge to a mass ratio dependent constant value for a → 0. Strong dependence of A ( a ) on Q ( q ) can be used to determine the latter distribution, but the technique is limited by the presence of unresolved visual companions and by blending in crowded areas of the sky. The bright-star sample to 7.5 mag is too small for an application of the technique, while the Baade's window sample from the OGLE project may suffer stronger blending; thus the present results are preliminary and illustrative only. Estimates based on the Baade's window data from the OGLE project, for amplitudes a > 0.3 mag, where the statistics appear to be complete allowing determination of Q ( q ) over 0.12 ≤ q ≤ 1, suggest a steep increase of Q ( q ) with q → 0. The mass ratio distribution can be approximated by a power law, either Q a ( q ) ∝ (1 - q ) a 1 with a 1 = 6 ± 2 or Q b ( q ) ∝ q b 1 with b 1 = -2 ± 0.5, with a slight preference for the former form. While both forms would predict very large numbers of small mass ratio systems, these predictions must be modified by the theoretically expected cutoff caused by a tidal instability at q min ≃ 0.07–0.1. A maximum in Q ( q ), due to the interplay of a steep power-law increase in Q ( q ) for q → 0 and of the cutoff at q min , is expected to be mapped into a local maximum in A ( a ) around a ≃ 0.2–0.25 mag. When better statistics of the amplitudes are available, the location of this maximum will shed light on the currently poorly known value of q min . The correction factor linking the apparent, inclination-uncorrected frequency of W UMa–type systems to the true spatial frequency remains poorly constrained at about 1.5 to 2 times.