We review the recent knowledge base pertaining to causes for mass accretion variations (high/low states) in highly magnetic cataclysmic variables (i.e. polars). We then examine what theory has to say about the properties of the secondary stars (the mass donors) with respect to those CVs with very short orbital periods. Finally, we use recent observations of EF Eri in an extended low state to provide direct observational evidence which shows that this CV, as well as a few others, likely contain very low mass, sub-stellar secondary stars.

The fully convective secondary stars in short-period CVs are rapidly rotating and thus should have a characteristic global magnetic field produced by an α2-Dynamo. This field is expected to be dipole-like, with an axis lying in the orbital plane, and to rotate slowly through the mass of the star on magnetic diffusion timescales of years to decades. When one of the poles of this field is near the inner Lagrange point, the reduction in the sound speed, scale-height and possibly the density in the giant “starspot” will modulate the mass-transfer to the primary. Given the extremely high Coriolis numbers (low Rosby numbers) of CV secondaries, this is a generic mechanism which is capable of explaining the extended high- and low-states in the mean light curves of shorter period MCVs and perhaps the lightcurves of non-magnetic CVs (where a disk may make it difficult to see this effect). The diffusion timescale and hence the period of rotation of the field within the secondary is of order the synchronization timescale, so shorter period polar’s are unlikely to be in rotational equilibrium.

This is a short summary of the main problems presented and discussed at the Cape Town conference.