MV = MV(LOG-P, LOG TE) CALIBRATIONS FOR W-URSAE-MAJORIS SYSTEMS

We use the basic expression for luminosities of contact systems, L pro portional-to area.T(e)4, to derive calibrations of their absolute magn itudes M(V) in terms of the orbital period and color indices B-V and V - I(C). These calibrations can serve as a consistency check on members hip of W Ursae Majoris systems in stellar clusters and will permit the use of W UMa binaries as distance indicators for stellar systems cons isting of solar-type stars. The calibrating sample at this time is bas ed on three systems with trigonometric parallaxes, eleven systems in h igh galactic latitude open clusters, and three systems with main-seque nce visual companions. The ranges in period and color are quite narrow and the results must be considered as preliminary, especially for the V-I(C) calibration. One of possible applications of the calibrations, as a sieve to remove the foreground interlopers, is illustrated. The result is that the cluster and field frequencies of optically detected W UMa systems seem to be equal at about 1 per about 280 surveyed star s (uncorrected for the inclination bias of about 2 times), which is ab out 3-4 times higher in the field than estimated before.