On the ultimate fate of AM Her stars

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We suggest, that the magnetic field of the white dwarf in AM Her systems loses coupling to the secondary star when the latter becomes non-magnetic at the transition from a late main sequence star to a cool degenerate brown dwarf. This leads to spin-up of the primary white dwarf. After synchronous rotation is lost the systems do not appear as AM Her stars anymore. We discuss the further evolution of such systems.
accepted for publication in A&A letters

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