W Uma Type Contact Binary Observations And Theoretical Models

A galaxy or a star cluster consists mainly of the stars. Most of (more than 50 per cent)stars are members of binaries or multiple-star systems. W UMa systems are very common, comprising some 95 per cent of eclipsing variables in the solar neighbourhood. Allowing for selection effect, about 1 per cent of all F and G dwarfs are W UMa systems, and so understanding the origin and evolution of W UMa stars are of importance for investigations in the evolution of the star clusters and galaxies.We have collected some observational data of some W UMa type systems, and studied the period and the light curve changes. Some physical processes which take place in these systems and play an important role in the evolution of these systems are found from these investigations. We obtain their mass transfer rate to be about 10-8 M o/yr by studying period variations of W UMa type systems AB And, AM Leo, AK Her, and AP Leo. We find that the mechanism causing angular momentum loss of these systems is most likely magnetic braking.Combined with the observational properties, we have constructed a theoretical model of a contact binary with a total mass of 1.8 Mo. Our initial model is a detached binary in which the primary is very close to its Roche lobe. It evolves into a semi-detached binary after about 2.7 Myr, and its secondary fills its Roche robe after 34.5 Myr, and then evolves into a contact binary. Contact phase is characterized by energy transfer between the components through a common envelope. Thereafter, it is found that the binary exhibits cyclic behavior on thermal timescale. The model agree with the observed light curve in most parts of the cycle. We calculate a model with angular momentum loss caused by gravitational radiation, and find that the binary undergo cyclic evolution as well. However, the period of the cycle becomes shorter, and the ratio of the time spent in the semi-detached phase to the time spent in the contact phase in a cycle becomes smaller. Since the stellar rotation is taken into account, our model is located very near to the upper boundary of period-color diagram which is obtained from observations of W UMa type systems. Our model shows a great improvement on Flannery's (1976) and Robertson & Eggleton's (1977) results.