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 center of mass can deviate from the equatorial plane up to the distance of z _ { w } \approx 0.1 r .
However , the effective height of the warp can be larger , h _ { w } \approx 0.3 r 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 degrees .
The location and amplitude of the warp does 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 ( QPOs ) 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 .