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White dwarfs (WDs) are powerful tools to study the evolutionary history ofstars and binaries in the Galaxy. But do we understand their multiplicity froma theoretical point of view? This can be tested by a comparison with the sampleof WDs within 20 pc, which is minimally affected by selection biases. From theliterature, we compile the available information of the local WD sample with aparticular emphasis on their multiplicity, and compare this to synthetic modelsof WD formation in single stars and binaries. As part of our populationsynthesis approach, we also study the effect of different assumptionsconcerning the star formation history, binary evolution, and the initialdistributions of binary parameters. We find that the observed space densitiesof single and binary WDs are well reproduced by the models. The space densitiesof the most common WD systems (single WDs and unresolved WD-MS binaries) areconsistent within a factor two with the observed value. We find a discrepancyonly for the space density of resolved double WDs. We exclude thatobservational selection effects, fast stellar winds, or dynamical interactionswith other objects in the Milky Way explain this discrepancy. We find thateither the initial mass ratio distribution in the Solar neighbourhood is biasedtowards low mass-ratios, or more than ten resolved DWDs have been missedobservationally in the 20 pc sample. Furthermore, we show that the low binaryfraction of WD systems (~25%) compared to Solartype MS-MS binaries (~50%) isconsistent with theory, and is mainly caused by mergers in binary systems, andto a lesser degree by WDs hiding in the glare of their companion stars. Lastly,Gaia will dramatically increase the size of the volume-limited WD sample,detecting the coolest and oldest WDs out to 50 pc. We provide a detailedestimate of the number of single and binary WDs in the Gaia sample.

The binarity of the local white dwarf population