Tidal Interactions in Merging White Dwarf Binaries

Abstract

The recently discovered system J0651 is the tightest known detached white dwarf (WD) binary. Since it has not yet initiated Roche-lobe overflow, it provides a relatively clean environment for testing our understanding of tidal interactions. I investigate the tidal heating of each WD, parameterized in terms of its tidal Q parameter. Assuming that the heating can be radiated efficiently, the current luminosities are consistent with Q_1=7*10^{10} and Q_2=2*10^7, for the He and C/O WDs, respectively. Conversely, if the observed luminosities are merely from the cooling of the WDs, these estimated values of Q represent upper limits. A large Q_1 for the He WD means its spin velocity will be slower than that expected if it was tidally locked, which, since the binary is eclipsing, may be measurable via the Rossiter-McLaughlin effect. After one year, gravitational wave emission shifts the time of eclipses by 5.5 s, but tidal interactions cause the orbit to shrink more rapidly, changing the time by up to an additional 0.3 s after a year. Future eclipse timing measurements may therefore infer the degree of tidal locking.