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Description
We present the final sample of 98 detached double white dwarf (WD) binaries found in the Extremely Low Mass (ELM) Survey, a spectroscopic survey targeting <0.3M_{sun}_ He-core WDs completed in the Sloan Digital Sky Survey footprint. Over the course of the survey we observed ancillary low-mass WD candidates like GD 278, which we show is a P=0.19d double WD binary, as well as candidates that turn out to be field blue straggler/subdwarf A-type stars with luminosities too high to be WDs given their Gaia parallaxes. Here, we define a clean sample of ELM WDs that is complete within our target selection and magnitude range 15<g_0_<20mag. The measurements are consistent with 100% of ELM WDs being 0.0089<P<1.5d double WD binaries, 35% of which belong to the Galactic halo. We infer that these are mostly He+CO WD binaries given the measurement constraints. The merger rate of the observed He+CO WD binaries exceeds the formation rate of stable mass-transfer AM CVn binaries by a factor of 25, and so the majority of He+CO WD binaries must experience unstable mass transfer and merge. The systems with the shortest periods, such as J0651+2844, are signature LISA verification binaries that can be studied with gravitational waves and light.
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