The Photometric Amplitude and Mass Ratio Distributions of Contact Binary Stars

The distribution of the light-variation amplitudes, A(a), in addition todetermining the number of undiscovered contact binary systems falling belowphotometric detection thresholds and thus lost to statistics, can serve as atool in determination of the mass-ratio distribution, Q(q), which is veryimportant for understanding of the evolution of contact binaries. Calculationsof the expected A(a) show that it tends to converge to a mass-ratio dependentconstant value for a->0. Strong dependence of A(a) on Q(q) can be used todetermine the latter distribution, but the technique is limited by the presenceof unresolved visual companions and by blending in crowded areas of the sky.The bright-star sample to 7.5 magnitude is too small for an application of thetechnique while the the Baade's Window sample from the OGLE project may sufferstronger blending; thus the present results are preliminary and illustrativeonly. Estimates based on the Baade's Window data from the OGLE project, foramplitudes a>0.3 mag. where the statistics appear to be complete allowingdetermination of Q(q) over 0.120. The mass-ratio distribution can be approximated by a power law, eitherQ(q)~(1-q)^a1 with a1=6+/-2 or Q(q)~q^b1, with b1=-2+/-0.5, with a slightpreference for the former form. Both forms must be modified by thetheoretically expected cut-off caused by a tidal instability at about q_min0.07-0.1. An expected maximum in Q(q), is expected to be mapped into a localmaximum in A(a) around 0.2-0.25 mag.Comment: AASTeX5, 12 figures, 5 tables, accepted by AJ, Aug.200