The photometric amplitude and mass ratio distributions of contact binary stars

The distribution of the light variation amplitudes A(a), in addition to det ermining the number of undiscovered contact binary systems falling below ph otometric detection thresholds and thus lost to statistics, can serve as a tool in determination of the mass ratio distribution Q(q), which is very im portant for understanding of the evolution of contact binaries. Calculation s of the expected A(a) show that it tends to converge to a mass ratio depen dent constant value for a-->0. Strong dependence of A(a) on Q(q) can be use d 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 applicati on 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 com plete allowing determination of Q(q) over 0.12 less than or equal to q less than or equal to 1, suggest a steep increase of Q(q) with q --> 0. The mas s ratio distribution can be approximated by a power law, either Qa(q) propo rtional to (1-q)(a1) with a(1) = 6 +/- 2 or Q(b)(q) proportional to q(b1) w ith 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, th ese predictions must be modified by the theoretically expected cutoff cause d by a tidal instability at q(min) similar or equal to 0.07-01. A maximum i n 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 maxi mum in A(a) around a a similar or equal to 0.2-0.25 mag. When better statis tics of the amplitudes are available, the location of this maximum will she d light on the currently poorly known value of q(min). The correction facto r linking the apparent, inclination-uncorrected frequency of W UMa-type sys tems to the true spatial frequency remains poorly constrained at about 1.5 to 2 times.