The origin of the magnetic field distribution in accreting white dwarfs

Recent work (King, Frank & Ritter) on the secular evolution of magnetic cataclysmic variables (CVs) has shown that the magnetic moments μ of the white dwarfs in these accreting binary systems must lie in a narrow range,$${10}^{33}\lesssim\mu\lesssim {10}^{34}\,\text{G}\,\text{cm}^{3}$$, in order to explain the observed distribution of orbital periods in the synchronous (AM Her) and non-synchronous (intermediate polar) systems. All other CVs must have considerably weaker fields:$$\mu\lesssim {10}^{30}\,\text{G}\,\text{cm}^{3}$$. Here I show that this distribution of field strengths arises naturally because of the tendency for rapid rotation to submerge the magnetic fields in stars, making their surface field strengths considerably weaker than those in the interior.