| Summary: | 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 α=0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius rm (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius rcor (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, Θ = 5°, accretion is unstable if rcor/rm> 1.35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, Θ = 20°, instability occurs at slightly larger values, rcor/rm> 1.41
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