A gap in the double white dwarf separation distribution caused by the common-envelope evolution: astrometric evidence from Gaia

The trajectory of the center of light of an unresolved binary is different from that of its center of mass. Binary-induced stellar centroid wobbling can therefore be detected as an excess in the goodness-of-fit of the single-star astrometric model. We use reduced $\chi^2$ of the astrometric fit in the {\it Gaia} Early Data Release 3 to detect the likely unresolved double white dwarfs (DWDs). Using parallax-based distances we convert the excess of reduced $\chi^2$ into the amplitude of the centroid wobble $\delta a$, which is proportional to the binary separation $a$. The measured $\delta a$ distribution drops towards larger wobble amplitudes and shows a break around $\delta a \approx 0.2$ where it steepens. The integral of the distribution yields DWD fraction of $6.5 \pm 3.7$ per cent in the range $0.01 < a (\text{au}) < 2$. Using synthetic models of the Galactic DWDs we demonstrate that the break in the $\delta a$ distribution corresponds to one side of a deep gap in the DWD separation distribution at around $a\approx 1$ au. Model DWDs with separations less than several au shrink dramatically due to (al least one) common envelope phase, reshaping the original separation distribution, clearing a gap and creating a pile-up of systems with $a\approx 0.01$ au and $\delta a < 0.01$. Our models reproduce the overall shape of the observed $\delta a$ distribution and its normalisation, however the predicted drop in the numbers of DWDs beyond the break is steeper than in the data.