Locking of the rotation of disk-accreting magnetized stars

We investigate the rotational equilibrium state of disk-accreting magnetized stars using axisymmetric magneto-hydrodynamic (MHD) simulations. In this "locked" state, the spin-up torque balances the spin-down torque so that the net average torque on the star is zero. We investigated two types of initial conditions: (I) a relatively weak stellar magnetic field and a high coronal density and (II) a stronger stellar field and a lower coronal density. We observed that for both initial conditions the rotation of the star is locked to the rotation of the disk. In the second case, the radial field lines carry significant angular momentum out of the star. However, this did not appreciably change the condition for locking of the rotation of the star. We find that in the equilibrium state the corotation radius r_co is related to the magnetospheric radius r_A as r_co/r_A ≈ 1.2-1.3 for case I and r_co/r_A ≈ 1.4-1.5 for case II. We estimated periods of rotation in the equilibrium state for classical T Tauri stars, dwarf novae, and X-ray millisecond pulsars.