Tidal resonance locks in inspiraling white dwarf binaries

We calculate the tidal response of helium and carbon/oxygen ( C/O) white dwarf ( WD) binaries inspiraling due to gravitational wave emission. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We show that analogous locks between the spin and orbital frequencies can occur not only with global standing modes, but even when damping is so efficient that the resonant tidal response becomes a travelling wave. We derive simple analytic formulas for the tidal quality factor Qt and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We find that Qt similar to 107 \for orbital periods less than or similar to 1-2 h in C/O WDs, and Qt similar to 109 for Porb less than or similar to 3-10 h in helium WDs. Typically tidal heating occurs sufficiently close to the surface that the energy should be observable as surface emission. Moreover, near an orbital period of similar to 10 min, the tidal heating rate reaches similar to 10-2 L circle dot, rivalling the luminosities of our fiducial WD models. Recent observations of the 13-minute double-WD binary J0651 are roughly consistent with our theoretical predictions. Tides naturally tend to generate differential rotation; however, we show that the fossil magnetic field strength of a typical WD can maintain solid-body rotation down to at least Porb similar to 10 min even in the presence of a tidal torque concentrated near the WD surface.