The orbital period of a close binary system (P ~ a few days), formed by two solar type components, evolves under the influence of angular momentum loss (AML) by electromagnetic braking and of spin↔orbit angular momentum transfer (AMT) by tidal coupling. Because of AMT, which tends to reestablish the spin-orbit synchronization destroyed by AML, the loss of AM takes finally place at the expenses of the orbital reservoir and produces shrinking of the orbit and spinning-up of the components. The variation with time of wK and w, respectively the orbital and the rotational angular velocity, is expressed by a system of (stiff) ordinary differential equations and the results of the (numerical) integration strongly depend on the AML and AMT laws. A series of recent papers (Maceroni and Van ’t Veer 1991, 1992, Van’t Veer and Macerord 1992, hereafter MVI, MV2 and VM) presents the resulting orbital period evolution function (PEF) with a variety of choices. A typical result, in terms of orbital period, and for a binary formed by two identical G5 V components, is shown in fig. IA. The solution shown here corresponds to the braking law a) of fig. IB, to the AMT according to Zahn (1977) and to stars rotating as rigid bodies; different assumptions have been tried in MVland VM.
RW Doradus: A solar-type shallow contact binary with a new orbital period investigation