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We study tidal interactions in white dwarf binaries in the limiting case ofquasi-static tides. The formalism is valid for arbitrary orbital eccentricitiesand therefore applicable to white dwarf binaries in the Galactic disk as wellas globular clusters. In the quasi-static limit, the total perturbation of thegravitational potential shows a phase shift with respect to the position of thecompanion, the magnitude of which is determined primarily by the efficiency ofenergy dissipation through convective damping. We determine rates of secularevolution of the orbital elements and white dwarf rotational angular velocityfor a 0.3 solar mass helium white dwarf in binaries with orbital frequencies inthe LISA gravitational wave frequency band and companion masses ranging from0.3 to 10^5 solar masses. The resulting tidal evolution time scales for theorbital semi-major axis are longer than a Hubble time, so that convectivedamping of quasi-static tides need not be considered in the construction ofgravitational wave templates of white dwarf binaries in the LISA band. Spin-upof the white dwarf, on the other hand, can occur on time scales of less than10Myr, provided that the white dwarf is initially rotating with a frequencymuch smaller than the orbital frequency. For semi-detached white dwarf binariesspin-up can occur on time scales of less than 1Myr. Nevertheless, the timescales remain longer than the orbital inspiral time scales due to gravitationalradiation, so that the degree of asynchronism in these binaries increases. As aconsequence, tidal forcing eventually occurs at forcing frequencies beyond thequasi-static tide approximation. For the shortest period binaries, energydissipation is therefore expected to take place through dynamic tides andresonantly excited g-modes.

Energy Dissipation through Quasi-Static Tides in White Dwarf Binaries