SIMBAD references

We present a new study of the Rayleigh-Taylor unstable regime of accretion on to rotating magnetized stars in a set of high grid resolution three-dimensional magnetohydrodynamic 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 ω_s=Ω_*/Ω_K(r_m), where Ω_* is the angular velocity of the star and Ω_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 ω_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_* ≲ 7, do the unstable tongues produce chaotic hotspots on the stellar surface and irregular light curves. At even smaller values of the fastness parameter, ω_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_* ≲ 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Θ=5°, and a small viscosity parameter α=0.02. Test simulations at higher α values show that many more cases become unstable, and the light curves become even more irregular. Test simulations at larger tilts of the dipole Θ show that instability is present, however, accretion in two funnel streams dominates if Θ ≳ 15°. 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 cataclysmic variables.