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.