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 (ΔRV_max) between epochs (generally two epochs, separated by up to 470 d), and model the observed ΔRV_max 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 (1s, 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 ∝ a^α, 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 α = -1.3 ± 0.2 (1σ) ±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) × 10^-13 yr^-1M^-1 _⊙ (2σ), with a likelihood-weighted mean of R_merge = (7 ± 2) × 10^-13 yr^-1M^-1 _⊙ (1σ). The Milky Way's specific Type Ia supernova (SN Ia) rate is likely R_Ia ≈ 1.1 × 10^-13 yr^-1M^-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.