2000A&A...361..952H

The optical brightness of magnetic cataclysmic variables without accretion discs is a direct measure of the near-instantaneous mass-transfer rates from the late-type secondary stars to the magnetic white dwarfs in these semi-detached binary systems. We derive the mass-transfer history of the magnetic cataclysmic variable AM Herculis from its long-term visual light curve and from bolometric corrections obtained from a number of X-ray observations covering various accretion states. On average, less than 25% of the maximum observed mass-transfer rate occurs. Assuming that the mass-transfer rate is modulated by stellar starspots on the secondary stars, we convert the derived mass-transfer rates into spot filling factors at the L₁-point. A statistical model for the coverage fraction and size distribution of random spots near the L₁-point in AM Her suggests that the spot filling factor is roughly 0.5 for a fitted power-law distribution of starspot radii, i.e. about half the surface of the star near the L₁-point is covered with spots. This density can only be explained if the spottedness of the L₁-point is unusual - for instance if spot groups are forced to wander towards the L₁-point - or if a large-scale magnetic spot group produced by an α²-dynamo slowly drifts in and out of the L₁-region. The former solution predicts that the occurrence of long-term high- and low-states is random and the latter that the long-term light curves of polars are quasi-periodic; the light curve of AMHer may suggest periods of order a decade. Finally, we discuss the relevance of this result to the mass-transfer variations of other cataclysmic variables.