We present the results of a statistical investigation of the period-color and period-bolometric magnitude relations using a carefully selected sample of 120 contact systems with known physical parameters.Keywords Eclipsing binaries . W UMa stars . Physical parameters
Aims of the programThe primary aim of this program is the discussion of certain relations between the most important parameters of contact binary systems. Our approach is novel in that the absolute parameters (masses, radii and luminosities) of the systems have been derived for a homogeneous sample obtained by observation according to the following criteria: 1) The star has a mass ratio q sp determined spectroscopically. 2) The complete light curve for a given system is obtained at one observatory using the same telescope and the same instrument (a CCD camera or a multichannel photoelectric photometer) with an accuracy of at least ±0.01 mag.3) The light curves are obtained in the shortest possible time to avoid any possible changes in the light curve due to, for example, spot activity. In total, 41 systems were observed with the results from light curve modelling available in the series of papers: . In all cases, the light curve modelling was performed using the Wilson-Devinney code (Wilson, 1979(Wilson, , 1993 supplemented by a Monte Carlo search method. The effective temperature was derived from the spectral type, while the mass ratio q was deduced from spectroscopic measurements. The separation a and fill-out factor f were obtained as a result, allowing calculation of the effective surface S(q, f )a 2 of the binary (see Mochnacki, 1984). The above quantities, together with the temperature difference between the components, was used to compute the bolometric absolute magnitude M bol of the system. The mean color index (B −V ), bolometric correction BC and absolute visible magnitude M V were derived assuming that the radiative properties of the common envelope can be described using formulae adequate for main sequence stars (e.g. Popper, 1980). The sample of 41 contact systems obtained in this way was augmented using data from the literature. Only parameters derived from models with spectroscopically-determined mass ratios were taken into account.
Relations between some parametersW UMa stars are interesting objects as distance tracers. Extensive work concerning the M V (log P, B −V ) calibration has been done in the series of papers by Rucinski and co-workers e.g. Rucinski (2000) or Rucinski and Duerbeck Springer