2002ApJ...578..420R

Magnetohydrodynamic (MHD) simulations have been used to study disk accretion to a rotating magnetized star with an aligned dipole moment. Quiescent initial conditions were developed in order to avoid the fast initial evolution seen in earlier studies. A set of simulations was performed for different stellar magnetic moments and rotation rates. Simulations have shown that the disk structure is significantly changed inside a radius r_brwhere magnetic braking is significant. In this region the disk is strongly inhomogeneous. Radial accretion of matter slows as it approaches the area of strong magnetic field, and a dense ring and funnel flow (FF) form at the magnetospheric radius r_m, where the magnetic pressure is equal to the total, kinetic plus thermal, pressure of the matter. FFs, where the disk matter moves away from the disk plane and flows along the stellar magnetic field, are found to be stable features during many rotations of the disk. The dominant force driving matter into the FF is the pressure gradient force, while gravitational force accelerates it as it approaches the star. The magnetic force is much smaller than the other forces. The FF is found to be strongly sub-Alfvénic everywhere. The FF is subsonic close to the disk, but it becomes supersonic well above the disk. Matter reaches the star with a velocity close to that of free fall. Angular momentum is transported to the star dominantly by the magnetic field. In the disk the transport of angular momentum is mainly by the matter, but closer to the star the matter transfers its angular momentum to the magnetic field, and the magnetic field is dominant in transporting angular momentum to the surface of the star. For slowly rotating stars we observed that magnetic braking leads to the deceleration of the inner regions of the disk, and the star spins up. For a rapidly rotating star, the inner regions of the disk rotate with a super-Keplerian velocity, and the star spins down. The average torque is found to be zero when the corotation radius r_cor~1.5r_m. The evolution of the magnetic field in the corona of the disk depends on the ratio of magnetic to matter energies in the corona and in the disk. Most of the simulations were performed in the regime of a relatively dense corona where the matter energy-density was larger than the magnetic energy-density. In this case the coronal magnetic field gradually opens, but the velocity and density of outflowing matter are small. In a test case where a significant part of the corona was in the field-dominated regime, more dramatic opening of the magnetic field was observed with the formation of magnetocentrifugally driven outflows. Numerical applications of our simulation results are made to T Tauri stars. We conclude that our quasi-stationary simulations correspond to the classical T Tauri stage of evolution. Our results are also relevant to cataclysmic variables and magnetized neutron stars in X-ray binaries.