Three-dimensional Simulations of Accretion to Stars with Complex   Magnetic Fields
  Disk accretion to rotating stars with complex magnetic fields is investigated using full three-dimensional magnetohydrodynamic (MHD) simulations. The studied magnetic configurations include superpositions of misaligned dipole and quadrupole fields and off-centre dipoles. The simulations show that when the quadrupole component is comparable to the dipole component, the magnetic field has a complex structure with three major magnetic poles on the surface of the star and three sets of loops of field lines connecting them. A significant amount of matter flows to the quadrupole "belt", forming a ring-like hot spot on the star. If the maximum strength of the magnetic field on the star is fixed, then we observe that the mass accretion rate, the torque on the star, and the area covered by hot spots are several times smaller in the quadrupole-dominant cases than in the pure dipole cases. The influence of the quadrupole component on the shape of the hot spots becomes noticeable when the ratio of the quadrupole and dipole field strengths $B_q/B_d\gtrsim0.5$, and becomes dominant when $B_q/B_d\gtrsim1$. In the case of an off-centre dipole field, most of the matter flows through a one-armed accretion stream, forming a large hot spot on the surface, with a second much smaller secondary spot. The light curves may have simple, sinusoidal shapes, thus mimicking stars with pure dipole fields. Or, they may be complex and unusual. In some cases the light curves may be indicators of a complex field, in particular if the inclination angle is known independently. We also note that in the case of complex fields, magnetospheric gaps are often not empty, and this may be important for the survival of close-in exosolar planets. 
M. Long, M.M. Romanova, and R.V.E. Lovelace