The effect of metallicity on the minimum mass ratio of W Ursae Majoris-type systems

Abstract

According to the prevenient theoretical study, the minimum mass ratio for tidal stability of W Ursae Majoris (W UMa) systems is q(min) =(M(2)/M (1))similar to 0.071-0.078. However, the mass ratios of some observed W UMa binaries are smaller than the theoretical minimum mass ratio. Using Eggleton's stellar evolution code, we study the effects of metallicity and evolution on the minimum mass ratio of W UMa systems (M(1)=1.2M(circle dot)). We assume that k(1)(2) = k(2)(2) for the component's dimensionless gyration radii and that the contact degree is about 70 per cent. We find that the dynamical stability of W UMa binaries depends on the metallicity of W UMa systems. For the W UMa systems at age = 0 Gyr, the distribution of the minimum mass ratio has a fairly wide range, from 0.083 to 0.064, with the metallicity range from Z=0.0001 to 0.03. W UMa systems with Z=0.01 have the smallest value of the minimum mass ratio, which is about 0.064. The existence of low-q systems can be explained partly by the dependence of the dimensionless gyration radius on the metallicity. In addition, the dependence of the minimum mass ratio on the evolution, as suggested by previously work, is confirmed.