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We analyze radial velocity observations of the 12 extremely low-mass <0.25Msol white dwarfs (WDs) in the MMT Hypervelocity Star Survey. Eleven of the 12WDs are binaries with orbital periods shorter than 14 hours; the onenon-variable WD is possibly a pole-on system among our non-kinematicallyselected targets. Our sample is unique: it is complete in a well-defined rangeof apparent magnitude and color. The orbital mass functions imply that theunseen companions are most likely other WDs, although neutron star companionscannot be excluded. Six of the 11 systems with orbital solutions will mergewithin a Hubble time due to the loss of angular momentum through gravitationalwave radiation. The quickest merger is J0923+3028, a g=15.7 ELM WD binary witha 1.08 hr orbital period and a <130 Myr merger time. The chance of a supernovaIa event among our ELM WDs is only 1%-7%, however. Three binary systems(J0755+4906, J1233+1602, and J2119-0018) have extreme mass ratios and will mostlikely form stable mass-transfer AM CVn systems. Two of these objects, SDSSJ1233+1602 and J2119-0018, are the lowest surface gravity WDs ever found; bothshow Ca II absorption likely from accretion of circumbinary material. Wepredict that at least one of our WDs is an eclipsing detached double WD system,important for constraining helium core WD models.

The ELM Survey. I. A Complete Sample of Extremely Low Mass White Dwarfs