Magnetic coupling in AM Herculis binaries

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Abstract
The magnetic field induced in the secondary by an asynchronous magnetized primary in an AM Herculis-type binary system is calculated. The resulting dissipation in the secondary leads to a spin down of the primary star towards synchronism with the orbit. It is found that as long as mass transfer is occurring exact synchronism cannot be achieved. At best the primary approaches a stable equilibrium state in which it rotates slowly relative to the orbit. This qualitative picture is independent of the magnetic diffusivity. If in the distant past mass transfer did not occur for a period comparable to, or greater than the synchronization time of the primary, then the star may have become synchronized. Pre-existing magnetic fields in the secondary might then be able to hold the primary in corotation with the orbit when mass transfer begins, but these fields are of an indeterminate nature.

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