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Astron. Astrophys. 361, 952-958 (2000)

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1. Introduction

Cataclysmic variables (CV) of the AM Her or "polar" sub-class consist of late-type secondary stars in semi-detached orbits around highly magnetic white dwarfs. The secondary loses mass via the L1-point at a rate which is set by the scale height and density of the secondary's atmosphere within the L1-region. The lost matter falls in the potential well of the primary until it is captured by and accreted along the white dwarf 's magnetic field. Strong fields can prevent the formation of an accretion disc, so - without a disc acting as a buffer for the transferred mass - the mass-transfer rate from the secondary nearly equals the instantaneous mass-accretion rate onto the white dwarf, i.e. [FORMULA] (the free-fall time is [FORMULA] a day).

None of the known polars show signs of nearly constant mass-transfer rates. The optical long-term light curve of the best-observed polar, AM Herculis itself, is shown in Fig. 1. Typical of many polars, there are long periods of up to hundreds of days during which the mass-accretion (and hence mass-transfer) rates are stably either very high or very low, and other times during which the system varies erratically on timescales down to a day. There are no obvious correlations between the appearance or properties of the extreme states and the orbital or magnetic properties of the system (e.g. masses, mass-ratios, orbital periods, magnetic moments).

[FIGURE] Fig. 1. Visual light curve of AM Her from June 1977 to May 1998, obtained from the archives of the AAVSO.

Extended "low-states" are seen in a large fraction of all CV's: they occur in all well-observed polars, a sizeable fraction of novalike variables, and in some SU UMa subtype dwarf novae and intermediate polars. The durations of such states range from days to years and occur at irregular intervals. AM Her occasionally drops into low-states within a few days, so that the transition from a higher state to a low-state marks a significant and dramatic change in the accretion behaviour (see Warner 1999 and Hessman 2000 for recent reviews of the phenomenology of low-states). In novalikes, it appears that the extended low-states are created by the combination of very low mass-transfer rates and the heating of the inner discs in systems with hot white dwarfs (Leach et al. 1999).

Livio & Pringle (1994) discuss several models for the origin of mass-transfer (as opposed to mass-accretion) variations and conclude that starspots at the L1-point are the most likely explanation. Given that CV secondaries are rapidly rotating late-type stars with a partially or fully convective inner structure, [FORMULA] or [FORMULA] dynamos should result in intensive spottedness. In order to maintain pressure equilibrium with the surrounding photosphere, the spots have to have a lower thermal pressure, i.e. a lower temperature and/or density. The density in the spot at the level of the surrounding photosphere and, hence, the mass-transfer rate through such a spot may be lower by several orders of magnitude.

In the next section, we take archival X-ray data and the visual observations of many dedicated amateur astronomers and construct the recent mass-transfer history of AM Her. In the following section, the statistical properties of this history are derived, permitting us to construct a statistical model of the spottedness. Finally, we discuss what physical consequences the simulated spot distribution has for the observed properties of AM Her and other cataclysmic variables.

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© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000