The binary fraction, separation distribution and merger rate of white dwarfs from SPY

From a sample of spectra of 439 white dwarfs (WDs) from the ESO-VLT Supernova-Ia Progenitor Survey (SPY), we measure the maximal changes in radial velocity (Delta RVmax) between epochs (generally two epochs, separated by up to 470 d), and model the observed Delta RVmax statistics via Monte Carlo simulations, to constrain the population characteristics of double WDs (DWDs). The DWD fraction among WDs is f(bin) = 0.10 +/- 0.02 (1 sigma, random) +0.02 (systematic), in the separation range <= 4 au within which the data are sensitive to binarity. Assuming the distribution of binary separation, a, is a power law, dN/da alpha a(alpha), at the end of the last common-envelope phase and the start of solely gravitational-wave-driven binary evolution, the constraint by the data is alpha = -1.3 +/- 0.2 (1 sigma) +/- 0.2 (systematic). If these parameters extend to small separations, the implied Galactic WD merger rate per unit stellar mass is R-merge = (1-80) x 10(-13) yr(-1)M(circle dot)(-1) (2 sigma), with a likelihood-weighted mean of R-merge = (7 +/- 2) x 10(-13) yr(-1)M(circle dot)(-1) (1 sigma). The Milky Way's specific Type Ia supernova (SN Ia) rate is likely R-Ia approximate to 1.1 x 10(-1)3 yr(-1)M(circle dot)(-1) and therefore, in terms of rates, a possibly small fraction of all merging DWDs (e.g. those with massive-enough primaryWDs) could suffice to produce most or all SNe Ia.