Are overcontact binaries undergoing thermal relaxation oscillation with variable angular momentum loss?
Orbital period variations of five W-type overcontact binaries, GW Cep, VY Cet, V700 Cyg, EM Lac and AW Vir, are presented based on the analysis of all available times of light minimum. It is discovered that the period of GW Cep is decreasing at a rate of dP/dt=-6.62 ×10-8 d yr-1. For VY Cet and V700 Cyg, a cyclic oscillation is found superimposed on a secular period increase, which can be explained either by the light-time effect of an assumed third body or by magnetic activity cycles. For the other two, EM Lac and AW Vir, the periods show a secular increase. GW Cep is a low mass ratio system with q= 0.37, while the others are high mass ratio systems (q= 0.67, 0.65, 0.63 and 0.76, respectively). The period changes of the five sample stars are in good agreement with Qian's conclusion that low mass ratio overcontact binaries usually show a decreasing period, while the periods of high mass ratio systems are increasing.Based on the period variations of 59 overcontact binaries, a statistical investigation of period change is given. It is confirmed that the period change of a W UMa-type binary star is correlated with the mass ratio (q) and with the mass of the primary component (M1). Meanwhile, some statistical relations (M1-P, Js-M1, Js-M2 and Js-P) for overcontact binaries are presented using the absolute parameters of 78 systems. From these relations, the following results may be drawn: (i) free mass transfer in both directions exists between the components, which is assumed by thermal relaxation oscillation (TRO) theory; (ii) angular momentum loss (AML) can make a W UMa-type star maintain shallow overcontact and not evolve from overcontact to semidetached configurations as proposed by Rahunen; (iii) the evolution of the W UMa-type systems may be oscillation around a critical mass ratio, while the critical mass ratio varies with the mass of the primary component. These results can be plausibly explained by the combination of the TRO and the variable AML via a change of depth of the overcontact, which is consistent with the X-ray and IUE observations.