SIMBAD references

We report results of the first global three-dimensional (3D) magnetohydrodynamic (MHD) simulations of the waves excited in an accretion disc by a rotating star with a dipole magnetic field misaligned from the star's rotation axis (which is aligned with the disc axis). The main results are the following. (1) If the magnetosphere of the star corotates approximately with the inner disc, then we observe a strong one-armed bending wave (a warp). This warp corotates with the star and has a maximum amplitude between corotation radius and the radius of the vertical resonance. The disc's centre of mass can deviate from the equatorial plane up to the distance of zw ~ 0.1r. However, the effective height of the warp can be larger, hw ~ 0.3r, due to the finite thickness of the disc. Stars with a range of misalignment angles excite warps. However, the amplitude of the warps is larger for misalignment angles between 15° and 60^○_. The location and amplitude of the warp do not depend on viscosity, at least for relatively small values of the standard alpha-parameter, up to 0.08. (2) If the magnetosphere rotates slower than the inner disc, then a bending wave is excited at the disc-magnetosphere boundary, but does not form a large-scale warp. Instead, persistent, high-frequency oscillations become strong at the inner region of the disc. These are (a) trapped density waves which form inside the radius where the disc angular velocity has a maximum, and (b) inner bending waves which appear in the case of accretion through magnetic Rayleigh-Taylor instability. These two types of waves are connected with the inner disc and their frequencies will vary with accretion rate. Bending oscillations at lower frequencies are also excited including global oscillations of the disc. In cases where the simulation region is small, slowly precessing warp forms with the maximum amplitude at the vertical resonance. The present simulations are applicable to young stars, cataclysmic variables and accreting millisecond pulsars. A large-amplitude warp of an accretion disc can periodically obscure the light from the star. Different types of waves can be responsible for both the high- and low-frequency quasi-periodic oscillations observed in different types of stars. Inner disc waves can also leave an imprint on frequencies observed in moving hot spots on the surface of the star.