Accretion to Stars with Non-dipole Magnetic Fields
  Disc accretion to a rotating star with a non-dipole magnetic field is investigated for the first time in full three-dimensional (3D) magnetohydrodynamic (MHD) simulations. We investigated the cases of (1) pure dipole, (2) pure quadrupole, and (3) dipole plus quadrupole fields. Simulations have shown that in each case the structure of the funnel streams and associated hot spots on the surface of the star have specific features connected with the magnetic field configuration. In the case (1), matter accretes in two funnel streams which form two arch-like spots near the magnetic poles. In the case (3), most of the matter flows through the quadrupole "belt" forming a ring-shaped hot region on the magnetic equator. In the case (2), magnetic flux in the northern magnetic hemisphere is larger than that in the southern, and the quadrupole belt and the ring are displaced to the south. The stronger the quadrupole, the closer the ring is to the magnetic equator. At sufficiently large misalignment angle $\Theta$, matter also flows to the south pole, forming a hot spot near the pole. The light curves have a variety of different features which makes it difficult to derive the magnetic field configuration from the light curves. There are specific features which are different in cases of dipole and quadrupole dominated magnetic field: (1) Angular momentum flow between the star and disc is more efficient in the case of the dipole field; (2) Hot spots are hotter and brighter in case of the dipole field because the matter accelerates over a longer distance compared with the flow in a quadrupole case. 
M. Long, M.M. Romanova, R.V.E. Lovelace