Reduced magnetic braking in synchronously rotating magnetic cataclysmic variables

A model for magnetic braking via a stellar wind for synchronously rotating magnetic binaries is presented. It is found that the magnetic field lines of the secondary form closed loops or connect to the field lines of the white dwarf primary, leading to a reduction of the magnetic flux in open field lines responsible for magnetic braking. We show in particular that, for parameters typical for AM Herculis-type binary systems, magnetic braking is drastically reduced in comparison to values that are usually adopted based on wind theories for single stars. The cut-off in magnetic braking is sharp, occurring at a polar field strength of about |$7 \times 10^7\, {\rm G}$| for an AM Herculis-type binary system with a white dwarf mass of |$0.7\, {\rm M}_{\odot}$| and an orbital period of 5 h.