Is there evidence for field restructuring or decay in accreting magnetic white dwarfs?

The evolution of the magnetic field of an accreting magnetic white dwarf with an initially dipolar field at the surface has been studied for non-spherical accretion under simplifying assumptions. Accretion on to the polar regions tends to advect the field toward the stellar equator which is then buried. This tendency is countered by Ohmic diffusion and magnetohydrodynamic instabilities. It is argued that if matter is accreted at a rate of and the total mass accreted exceeds a critical value ΔM_crit ∼ 0.1-0.2 M_⊙, the field may be expected to be restructured, and the polar field to be reduced reaching a minimum value of ∼10³ G (the 'bottom field') independently of the initial field strength. Below this critical accretion rate, the field diffuses faster than it can be advected, and accretion has little effect on field strength and structure. In polars, where the magnetic field strength (∼10⁷-10⁸ G) is strong enough to lock the magnetic white dwarf into synchronous rotation with the orbit and a disc does not form, magnetic braking is severely curtailed as the stellar wind from the secondary becomes trapped in the combined magnetosphere of the two stars. The mass transfer rate in such systems is typically ≲10¹⁶ g s^-1, and field restructuring is not expected. In systems with fields not strong enough to achieve synchronism and where accretion occurs via a truncated disc (the intermediate polars), normal magnetic braking may be expected. The mass transfer rates are then typically ≳10¹⁶ g s^-1 above the 2-3 h cataclysmic variable period gap, and thus a significant reduction of the polar field strength could occur if such a system accumulates the required critical mass M_crit. However, due to mass loss during nova eruptions, only a small fraction of such systems (those that first come into contact at long orbital periods) may accumulate sufficient mass to reach the bottom field configuration. We argue that the observed properties of the magnetic cataclysmic variables can generally be explained by a model where the field is at most only partially restructured due to accretion. If there are systems that have reached the bottom field, they may be found among the dwarf novae, and be expected to exhibit quasi-periodic oscillations.