Tidal Heating in Detached Double White Dwarf Binaries

Short-period ( P < 1 hr orbits) detached double white dwarf binary (DWDB) components identified with transient surveys (e.g., SDSS, Zwicky Transient Facility, hereafter ZTF) have hot surface temperatures (>10,000 K) and observed radii a factor of 2 larger than completely degenerate white dwarfs. We formulate tidal heating in helium composition, extremely low-mass white dwarf components of detached DWDBs, which reach mass transfer within a Hubble time. We combine a mass–radius relation that varies with surface temperature and the equilibrium tidal friction model of Hut 1981, where the additional orbital energy loss from tidal friction is accounted for by increases in the primary surface temperature, and hence increasing radius. Applying this heating model to the current sample of binaries with ZTF, we predict temperature increases from the present day of up to ∼40% before the onset of mass transfer. We find that helium white dwarfs are generically hot and large at the onset of mass transfer, even for the oldest DWDBs whose components can cool to be degenerate by the present day. In the population of Galactic DWDBs, we find that the onset of mass transfer should occur at orbital periods as long as 1000 s (17 minutes), or binary gravitational-wave frequency of 2 mHz. This is over 3 times longer than periods expected for degenerate white dwarfs (5 minutes). Since mass transferring DWDBs are progenitors for a variety of transients and stellar populations, e.g., RCrB stars, AM CVn binaries, so-called Type .Ia supernova, the finite temperature of donor white dwarfs should be taken into account.