Prospects for detection of detached double white dwarf binaries with Gaia, LSST and LISA

Double white dwarf (DWD) binaries are expected to be very common in the Milky Way, but their intrinsic faintness challenges the detection of these systems. Currently, only a few tens of detached DWDs are know. Such systems offer the best chance of extracting the physical properties that would allow us to address a wealth of outstanding questions ranging from the nature of white dwarfs, over stellar and binary evolution to mapping the Galaxy. In this paper we explore the prospects for detections of ultra-compact (with binary separations of a few solar radii or less) detached DWDs in: 1) optical radiation with Gaia and the LSST and 2) gravitational wave radiation with LISA. We show that Gaia, LSST and LISA have the potential to detect respectively around a few hundreds, a thousand, and 25 thousand DWD systems. Moreover, Gaia and LSST data will extend by respectively a factor of two and seven the guaranteed sample of binaries detected in electromagnetic and gravitational wave radiation, opening the era of multi-messenger astronomy for these sources.