AM Her Stars: The Attainment of Synchronism
Even if a synchronous state exists, with a stable balance of torques, certain conditions must be met if such a state is to be attained. The synchronous state is a magnetic orientation corresponding to a minimum in a potential energy well. As corotation is approached from an over-synchronous state, the primary must be able to lose its remaining synodic rotational energy plus the energy gained via the accretion torque over a synodic period to prevent over-shooting of the synchronous state. Synodic energy is removed via dissipation of the magnetic field induced in the secondary star, and synchronism can only be attained if the stellar magnetic diffusivity is below a critical value η0. For values of η > η0, over-shooting of the synchronous state will keep occurring since the primary cannot lose sufficient rotational energy to become trapped in the energy well. A slightly asynchronous state then results, with a variation of the angular velocity due to the periodic imbalance of the torques. A stronger surface magnetic field on the primary favours the attainment of synchronism by raising the value of η0. These restrictions do not occur for an under-synchronous primary.