Dynamical evolution of active detached binaries on the log Jo-log M diagram and contact binary formation

Orbital angular momentum (OAM, J(o)), systemic mass (M) and orbital period (P) distributions of chromospherically active binaries (CAB) and W Ursae Majoris (W UMa) systems were investigated. The diagrams of logJ(o)-IogP, logM-logP and logJ(o)-IogM were fortned from 119 CAB and 102 W UMa stars. The log J(o)-Iog M diagram is found to be most meaningful in demonstrating dynamical evolution of binary star orbits. A slightly curved borderline (contact border) separating the detached and the contact systems was discovered on the log J(o)-Iog M diagram. Since the orbital size (a) and period (P) of binaries are determined by their current J(o), M and mass ratio, q, the rates of OAM loss (d log J(o)/dt) and mass loss (d log M/dt) are primary parameters to determine the direction and the speed of the dynamical evolution. A detached system becomes a contact system if its own dynamical evolution enables it to pass the contact border on the log J(o)-log M diagram. The evolution of q for a mass-losing detached system is unknown unless the mass-loss rate for each component is known. Assuming q is constant in the first approximation and using the mean decreasing rates of J(o) and M from the kinematical ages of CAB stars, it has been predicted that 11, 23 and 39 per cent of current CAB stars would transform to W UMa systems if their nuclear evolution permits them to live 2, 4 and 6 Gyr, respectively.