The separation distribution and merger rate of double white dwarfs: improved constraints

We obtain new and precise information on the double white dwarf (DWD) population and on its gravitational-wave-driven merger rate, by combining the constraints on the DWD population from two previous radial-velocity-variation studies: One based on a sample of white dwarfs (WDs) from the Sloan Digital Sky Survey (SDSS, which with its low spectral resolution probes systems at separations a<0.05 au), and one based on the ESO-VLT Supernova-Ia Progenitor surveY (SPY, which, with high spectral resolution, is sensitive to a<4 au). From a joint likelihood analysis, the DWD fraction among WDs is fbin=0.095+/-0.020 (1-sigma, random) +0.010 (systematic) in the separation range ~<4 au. The index of a power-law distribution of initial WD separations (at the start of solely gravitational-wave-driven binary evolution), N(a)da ~ a^alpha da, is alpha=-1.30+/-0.15 (1-sigma) +0.05 (systematic). The Galactic WD merger rate per WD is R_merge=(9.7+/-1.1)e-12 /yr. Integrated over the Galaxy lifetime, this implies that 8.5-11 per cent of all WDs ever formed have merged with another WD. If most DWD mergers end as more-massive WDs, then some 10 per cent of WDs are DWD-merger products, consistent with the observed fraction of WDs in a "high-mass bump" in the WD mass function. The DWD merger rate is 4.5-7 times the Milky Way's specific Type-Ia supernova (SN Ia) rate. If most SN Ia explosions stem from the mergers of some DWDs (say, those with massive-enough binary components) then ~15 per cent of all WD mergers must lead to a SN Ia.