Detection of Double White Dwarf Binaries with Gaia, LSST and eLISA

According to simulations around 10(8) double degenerate white dwarf binaries are expected to be present in the Milky Way. Due to their intrinsic faintness, the detection of these systems is a challenge, and the total number of detected sources so far amounts only to a few tens. This will change in the next two decades with the advent of Gaia, the LSST and eLISA. We present an estimation of how many compact DWDs with orbital periods less than a few hours we will be able to detect 1) through electromagnetic radiation with Gaia and LSST and 2) through gravitational wave radiation with eLISA. We find that the sample of simultaneous electromagnetic and gravitational waves detections is expected to be substantial, and will provide us a powerful tool for probing the white dwarf astrophysics and the structure of the Milky Way, letting us into the era of multi-messenger astronomy for these sources.