Dynamical tides in compact white dwarf binaries: tidal synchronization and dissipation

In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions (such as rotation rate and temperature) of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency omega = 2(Omega - Omega(s)) (where Omega is the orbital frequency and Omega(s) is the spin frequency) for several realistic carbon-oxygen WD models, under the assumption that the outgoing propagating waves are efficiently dissipated in the outer layer of the star by non-linear effects or radiative damping. Unlike main-sequence stars with distinct radiative and convection zones, the mechanism of wave excitation in WDs is more complex due to the sharp features associated with composition changes inside the WD. In our WD models, the gravity waves are launched just below the helium-carbon boundary and propagate outwards. We find that the tidal torque on the WD and the related tidal energy transfer rate, (E) over dot(tide), depend on omega in an erratic way, with (E) over dot(tide) varying by orders of magnitude over small frequency ranges. On average, (E) over dot(tide) scales approximately as Omega(5)omega(5) for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries prior to mass transfer or merger. Above a critical orbital frequency Omega(c), corresponding to an orbital period of the order of 1h (depending on WD models), dynamical tides efficiently drive Omega(s) towards Omega, although a small, almost constant degree of synchronization (Omega - Omega(s) similar to constant) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce a significant phase error in the low-frequency gravitational waveforms, detectable by the planned Laser Interferometer Space Antenna project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.