Rotational evolution of magnetic T Tauri stars with accretion discs

We have investigated the exchange of angular momentum between a solar-mass protostar and a protostellar accretion disc during Hayashi track evolution. As the stellar magnetic field threads the disc, the field lines are drawn out by the shear at the disc-magnetosphere boundary. The resulting magnetic stresses disrupt the inner parts of the disc completely. They also serve to transfer angular momentum from the star to the disc beyond the co-rotation radius, whereas angular momentum is transferred from the inner edge of the disc to the star inside the co-rotation radius. Our purpose is to investigate whether an equilibrium between these torques can be attained on a contracting star during the few million years of the T Tauri phase. We have computed a set of models of the rotational evolution of a solar-mass star throughout Hayashi-track contraction. They incorporate the changes in the star's moment of inertia and magnetic field strength, and an exponential decrease in the accretion rate. We find that for a stellar magnetic field of dipole form, with a polar strength of a few hundred gauss, and an accretion rate of a few times 10(-8) M., y-1, the star's rotation rate is quickly forced into a state where it evolves in quasi-static equilibrium for the remainder of the Hayashi phase. The resulting rotation rates are an order of magnitude lower than the values expected for direct accretion on to the stellar surface, and are consistent with observed values.