DC Circuit Powered by Orbital Motion: Magnetic Interactions in Compact Object Binaries and Exoplanetary Systems

The unipolar induction DC circuit model, originally developed by Goldreich & Lynden-Bell for the Jupiter-Io system, has been applied to different types of binary systems in recent years. We show that there exists an upper limit to the magnetic interaction torque and energy dissipation rate in such model. This arises because when the resistance of the circuit is too small, the large current flow severely twists the magnetic flux tube connecting the two binary components, leading to breakdown of the circuit. Applying this limit, we find that in coalescing neutron star binaries, magnetic interactions produce negligible correction to the phase evolution of the gravitational waveform, even for magnetar-like field strengths. However, energy dissipation in the binary magnetosphere may still give rise to electromagnetic radiation prior to the final merger. For ultra-compact white dwarf binaries, we find that DC circuit does not provide adequate energy dissipation to explain the observed X-ray luminosities of several sources. For exoplanetary systems containing close-in Jupiters or super-Earths, magnetic torque and dissipation are negligible, except possibly during the early T Tauri phase, when the stellar magnetic field is stronger than 10^3G.