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 br where 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 form at the magnetospheric radius r m where the magnetic pressure is equal to the total, kinetic plus thermal, pressure of the matter.Funnel flows (FF), 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 funnel flow 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 magneto-centrifugally 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.

An investigation is made of disk accretion of matter onto a rotating star with an aligned dipole magnetic field. A new aspect of this work is that when the angular velocity of the star and disk differ substantially we argue that the B field linking the star and disk rapidly inflates to give regions of open field lines extending from the polar caps of the star and from the disk. The open field line region of the disk leads to the possibility of magnetically driven outflows. An analysis is made of the outflows and their back affect on the disk structure assuming an "α" turbulent viscosity model for the disk and a magnetic diffusivity comparable to this viscosity. The outflows are found to extend over a range of radial distances inward to a distance close to r to , which is the distance of the maximum of the angular rotation rate of the disk. We find that r to depends on the star's magnetic moment, the accretion rate, and the disk's magnetic diffusivity. The outflow regime is accompanied in general by a spin-up of the rotation rate of the star. When r to exceeds the star's corotation radius r cr = (GM/ω 2 * ) 1 3 , we argue that outflow solutions do not occur, but instead that "magnetic braking" of the star by the disk due to field-line twisting occurs in the vicinity of r cr . The magnetic braking solutions can give spin-up or spin-down (or no spin change) of the star depending mainly on the star's magnetic moment and the mass accretion rate. For a system with r to comparable to r cr , bimodal behavior is possible where extraneous perturbations (for example, intermittency of α, B field flux introduced from the companion star, or variations in the mass accretion rate) cause the system to flip between spin-up (with outflows, r to < r cr ) and spin-down (or spin-up) (with no outflows, r to > r cr ).

We investigate the rotational equilibrium state of a disk accreting magnetized stars using axisymmetric magnetohydrodynamic (MHD) simulations. In this "locked" state, the spin-up torque balances the spindown torque so that the net average torque on the star is zero. We investigated two types of initial conditions, one with a relatively weak stellar magnetic field and a high coronal density, and the other with 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 (1) and r co /r A ≈ 1.4 − 1.5 for case (2). We estimated periods of rotation in the equilibrium state for classical T Tauri stars, dwarf novae and X-ray millisecond pulsars. ABSTRACTWe investigate the rotational equilibrium state of a disk accreting magnetized stars using axisymmetric magnetohydrodynamic (MHD) simulations. In this "locked" state, the spin-up torque balances the spindown torque so that the net average torque on the star is zero. We investigated two types of initial conditions, one with a relatively weak stellar magnetic field and a high coronal density, and the other with 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 (1) and r co /r A ≈ 1.4 − 1.5 for case (2). We estimated periods of rotation in the equilibrium state for classical T Tauri stars, dwarf novae and X-ray millisecond pulsars.

We present results of axisymmetric magnetohydrodynamic simulations of the interaction of a rapidly rotating, magnetized star with an accretion disk. The disk is considered to have a finite viscosity and magnetic diffusivity. The main parameters of the system are the star's angular velocity and magnetic moment, and the disk's viscosity and diffusivity. We focus on the "propeller" regime where the inner radius of the disk is larger than the corotation radius. Two types of magnetohydrodynamic flows have been found as a result of simulations: "weak" and "strong" propellers. The strong propellers are characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star. The weak propellers have only weak outflows. We investigated the time-averaged characteristics of the interaction between the main elements of the system, the star, the disk, the wind from the disk, and the jet. Rates of exchange of mass and angular momentum between the elements of the system are derived as a function of the main parameters. The propeller mechanism may be responsible for the fast spinningdown of the classical T Tauri stars in the initial stages of their evolution, and for the spinning-down of accreting millisecond pulsars.

We report on the first global three-dimensional (3D) MHD simulations of disk accretion onto a rotating magnetized star through the Rayleigh-Taylor instability. The star has a dipole field misaligned relative to the rotation axis by a small angle V. Simulations show that, depending on the accretion rate, a star may be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates deep into the magnetosphere through several elongated "tongues" which deposit matter at random places on the surface of the star, leading to stochastic light curves. In the stable regime, matter accretes in ordered funnel streams and the light curves are almost periodic. A star may switch between these two regimes depending on the accretion rate and may thus show alternate episodes of ordered pulsations and stochastic light curves. In the intermediate regime, both stochastic and ordered pulsations are observed. For , the instability is suppressed and stable accretion V 1 30Њ through funnel streams dominates.