We use multi-epoch spectroscopy of about 4000 white dwarfs in the Sloan Digital Sky Survey to constrain the properties of the Galactic population of binary white dwarf systems and calculate their merger rate. With a Monte Carlo code, we model the distribution of DRVmax, the maximum radial velocity shift between exposures of the same star, as a function of the binary fraction within 0.05 AU, fbin, and the power-law index in the separation distribution at the end of the common envelope phase, alpha. Although there is some degeneracy between fbin and alpha, the the fifteen high DRVmax systems that we find constrain the combination of these parameters, which determines a white dwarf merger rate per unit stellar mass of 1.4(+3.4,-1.0)e-13 /yr/Msun (1-sigma limits). This is remarkably similar to the measured rate of Type Ia supernovae per unit stellar mass in Milky-Way-like Sbc galaxies. The rate of super-Chandrasekhar mergers is only 1.0(+1.6,-0.6)e-14 /yr/Msun. We conclude that there are not enough close binary white dwarf systems to reproduce the observed Type Ia SN rate in the classic double degenerate super-Chandrasekhar scenario. On the other hand, if sub-Chandrasekhar mergers can lead to Type Ia SNe, as recently suggested by some studies, they could make a major contribution to the overall Type Ia SN rate. Although unlikely, we cannot rule out contamination of our sample by M-dwarf binaries or non-Gaussian errors. These issues will be clarified in the near future by completing the follow-up of all 15 high DRVmax systems.
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