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

Double WD parameter space
1σ and 2σ likelihood contours in the plane of fbin, the fraction of WDs in binaries with separations less than 4 au, and α, the power-law index of the initial double WD separation distribution, for the SDSS WD sample in blue, for the SPY sample in green, and joint likelihood contours from combining the two sets of results in red. Straight lines are loci of constant double WD merger rate, as marked in units of mergers per year per WD (Maoz, Hallakoun, & Badenes 2018).

From a sample of spectra of 439 WDs from the ESO-VLT Supernova-Ia Progenitor Survey (SPY), we measured the maximal changes in radial velocity (ΔRVmax) between epochs, and model the observed ΔRVmax statistics via Monte Carlo simulations, to constrain the population characteristics of double WDs. We then combined these constraints with those obtained by Badenes and Maoz 2012 for a sample of ~4000 WDs from the Sloan Digital Sky Survey (SDSS). We found that about 10% of WDs are double WDs with separations up to 4 AU, and that the Galactic WD merger rate per WD is about 10-11 per year. Integrated over the Galaxy lifetime, this implies that 8.5–11% of all WDs ever formed have merged with another WD. If most double WD mergers end as more-massive WDs, then some 10% of WDs are double WD-merger products, consistent with the observed fraction of WDs in a ‘high-mass bump’ in the WD mass function. The double WD merger rate is 4.5–7 times the Milky Way’s specific SN Ia rate. If most SN Ia explosions stem from the mergers of some double WDs (say, those with massive-enough binary components) then ∼15% of all WD mergers must lead to a SN Ia.

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