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 magnitude is too small for an application of the technique while the 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(q)~(1-q)^a1 with a1=6+/-2 or Q(q)~q^b1, with b1=-2+/-0.5, with a slight preference for the former form. Both forms must be modified by the theoretically expected cut-off caused by a tidal instability at about q_min 0.07-0.1. An expected maximum in Q(q), is expected to be mapped into a local maximum in A(a) around 0.2-0.25 mag.Comment: AASTeX5, 12 figures, 5 tables, accepted by AJ, Aug.200

The Frequency of Binary Stars in the Core of 47 Tucanae

Differential time series photometry has been derived for 46422 main-sequence stars in the core of 47 Tucanae. The observations consisted of near-continuous 160-s exposures alternating between the F555W and F814W filters for 8.3 days in 1999 July with WFPC2 on the Hubble Space Telescope. Using Fourier and other search methods, eleven detached eclipsing binaries and fifteen W UMa stars have been discovered, plus an additional ten contact or near-contact non-eclipsing systems. After correction for non-uniform area coverage of the survey, the observed frequencies of detached eclipsing binaries and W UMa's within 90 arcseconds of the cluster center are 0.022% and 0.031% respectively. The observed detached eclipsing binary frequency, the assumptions of a flat binary distribution with log period and that the eclipsing binaries with periods longer than about 4 days have essentially their primordial periods, imply an overall binary frequency of 13 +/- 6 %. The observed W UMa frequency and the additional assumptions that W UMa's have been brought to contact according to tidal circularization and angular momentum loss theory and that the contact binary lifetime is 10^{9} years, imply an overall binary frequency of 14 +/- 4 %. An additional 71 variables with periods from 0.4 - 10 days have been found which are likely to be BY Draconis stars in binary systems. The radial distribution of these stars is the same as that of the eclipsing binaries and W UMa stars and is more centrally concentrated than average stars, but less so than the blue straggler stars. A distinct subset of six of these stars fall in an unexpected domain of the CMD, comprising what we propose to call red stragglers.Comment: Accepted for publication in the Astrophysical Journal, 65 pages including 26 figure