Dynamical evolution of active detached binaries on the log J o –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 and log  J o –log  M were formed from 119 CAB and 102 W UMa stars. The log  J o –log  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 –log  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 /d t ) and mass loss (d log  M /d t ) 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.