Boundary between Stable and Unstable Regimes of Accretion. Ordered and Chaotic Unstable Regimes

We present a study of the Rayleigh-Taylor unstable regime of accretion onto rotating magnetized stars in a set of high grid resolution three-dimensional (3D) magnetohydrodynamic (MHD) simulations performed in low-viscosity discs. We find that the boundary between the stable and unstable regimes is determined almost entirely by the fastness parameter omega_s=Omega_star/Omega_K(r_m), where Omega_star is the angular velocity of the star and Omega_K(r_m) is the angular velocity of the Keplerian disc at the disc-magnetosphere boundary r=r_m. We found that accretion is unstable if omega_s < 0.6. Accretion through instabilities is present in stars with different magnetospheric sizes. However, only in stars with relatively small magnetospheres, r_m/R_star < 7, do the unstable tongues produce chaotic hot spots on the stellar surface and irregular light-curves. At even smaller values of the fastness parameter, omega_s < 0.45, multiple irregular tongues merge, forming one or two ordered unstable tongues that rotate with the angular frequency of the inner disc. This transition occurs in stars with even smaller magnetospheres, r_m/R_star < 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Theta=5 degrees, and a small viscosity parameter alpha=0.02. Test simulations at higher alpha values show that many more cases become unstable, and the light-curves become even more irregular. Test simulations at larger tilts of the dipole Theta show that instability is present, however, accretion in two funnel streams dominates if Theta > 15 degrees. The results of these simulations can be applied to accreting magnetized stars with relatively small magnetospheres: Classical T Tauri stars, accreting millisecond X-ray pulsars, and cataclysmics variables.

MHD Simulations of Magnetospheric Accretion, Ejection and Plasma-field Interaction

We review recent axisymmetric and three-dimensional (3D) magnetohydrodynamic (MHD) numerical simulations of magnetospheric accretion, plasma-field interaction and outflows from the disk-magnetosphere boundary.

Oscillations of the Boundary Layer and High-frequency QPOs

We observed persistent high-frequency oscillations of the boundary layer near an accreting, weakly-magnetized star in global 3D MHD simulations. The tilted dipole magnetic field is not strong enough to open a gap between the star and the disk. Instead, it forms a highly-wrapped azimuthal field near the surface of the star which slows down rotation of the disk matter, while a small tilt of the field excites oscillations of the boundary layer with a frequency below the Keplerian frequency. This mechanism may be responsible for the high-frequency oscillations in accreting neutron stars, white dwarfs and classical T Tauri stars.

Boundary Between Stable and Unstable Regimes of Accretion

We investigated the boundary between stable and unstable regimes of accretion and its dependence on different parameters. Simulations were performed using a cubed sphere code with high grid resolution (244 grid points in the azimuthal direction), which is twice as high as that used in our earlier studies. We chose a very low viscosity value, with alpha-parameter alpha=0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius r_m (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius r_cor (where the Keplerian velocity in the disk is equal to the angular velocity of the star). For a small misalignment angle of the dipole field, Theta=5 degrees, accretion is unstable if r_cor/r_m>1.35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, Theta=20 degrees, instability occurs at slightly larger values, r_cor/r_m>1.41.