Dynamo Laws and Magnetic Braking in Binary Stars

It is known that a magnetically channelled wind from the secondary star in a close binary, together with tidal coupling, leads to a continuous loss of orbital angular momentum. The consequent shrinkage of the secondary's Roche lobe drives mass transfer, via overflow through the L_1 region. Expressions are derived here for the mass transfer rate, using fast rotator braking theory, for a variety of dynamo laws relating the star's surface field B_0 to its angular velocity Omega_s. For scaling from a mean solar field of Bsolar=1G, a nearer quadratic than linear dependence of B_0 on Omega_s leads to mass transfer rates in best agreement with observations, allowing for field saturation. The secondary is then driven out of thermal equilibrium as it approaches a mass of 0.3Msolar, as required in current explanations of the period gap.