Full 3D MHD calculations of accretion flow structure in magnetic cataclysmic variables with strong, complex magnetic fields

We have performed three-dimensional magnetohydrodynamical calculations of stream accretion in cataclysmic variable stars for which the white dwarf primary possesses a strong, complex magnetic field. These calculations were motivated by observations of polars: cataclysmic variables containing white dwarfs with magnetic fields sufficiently strong to prevent the formation of an accretion disk. In this case, an accretion stream flows from the L1 point and impacts directly onto one or more spots on the surface of the white dwarf. Observations indicate that the white dwarfs in some binaries possess complex (non-dipolar) magnetic fields. We performed simulations of ten polars, with the only variable being the azimuthal angle of the secondary with respect to the white dwarf. These calculations are also applicable to asynchronous polars, where the spin period of the white dwarf differs by a few percent from the orbital period. Our results are equivalent to calculating the structure of one asynchronous polar at ten different spin-orbit beat phases. Our models have an aligned dipolar plus quadrupolar magnetic field centered on the whitedwarf primary. We find that, with a sufficiently strong quadrupolar component, an accretion spot arises near the magnetic equator for slightly less than half our simulations, while a polar accretion zone is active for most of the remaining simulations. For two configurations, accretion at a dominant polar region and in an equatorial zone occurs simultaneously. Most polar studies assume that the magnetic field is dipolar, especially for single-pole accretors. We demonstrate that, with the orbital parameters and magnetic-field strengths typical of polars, the accretion flow patterns can vary widely in the case of a complex magnetic field. This may make it difficult formany polars to determine observationally whether the field is pure dipolar or is more complex, but there shoulid be indications for some systems. In particular, a complex magnetic field should be suspected if there is an accretion zone near the white dwarf's equator (assumed to be in the orbital plane) or if there are two or more accretion regions that cannot be fitted by dipolar magnetic field. Magnetic-field constraints are expected to be substantially stronger for asynchronous polars, with clearer signs of complex field geometry due to changes in the accretion flow structure as a function of azimuthal angle. These indications become clearer in asynchronous polars because each azimuthal angle corresponds to a different spin-orbit beat phase.