Most double degenerate low-mass white dwarf binaries merge

We estimate the merger rate of double degenerate binaries containing extremely low mass (ELM; $<0.3$ M _⊙) white dwarfs (WDs) in the Galaxy. Such WDs are detectable for timescales of 0.1–1 Gyr in the ELM Survey; the binaries they reside in have gravitational wave merger times of 0.001–100 Gyr. To explain the observed distribution requires that most ELM WD binary progenitors detach from the common envelope phase with <1 hr orbital periods. We calculate the local space density of ELM WD binaries and estimate a merger rate of 3 × 10⁻³ yr⁻¹ over the entire disk of the Milky Way; the merger rate in the halo is 10 times smaller. The ELM WD binary merger rate exceeds by a factor of 40 the formation rate of stable mass transfer AM CVn binaries, marginally exceeds the rate of underluminous supernovae, and is identical to the formation rate of R CrB stars. On this basis, we conclude that ELM WD binaries can be the progenitors of all observed AM CVn and possibly underluminous supernovae; however, the majority of He+CO WD binaries go through unstable mass transfer and merge, e.g., into single massive ∼1 M _⊙ WDs.