  The third data release of Gaia was the first to include orbital solutions
assuming non-single stars. Here, we apply the astrometric triage technique of
Shahaf et al. to identify binary star systems with companions that are not
single main-sequence stars. Gaia's synthetic photometry of these binaries is
used to distinguish between systems likely to have white-dwarf companions and
those that may be hierarchical triples. The study uncovered a population of
nearly 3200 binaries, characterised by orbital separations on the order of an
astronomical unit, in which the faint astrometric companion is probably a white
dwarf. This sample increases the number of orbitally solved binary systems of
this type by about two orders of magnitude. Remarkably, over 110 of these
systems exhibit significant ultraviolet excess flux, confirming this
classification and, in some cases, indicating their relatively young cooling
ages. We show that the sample is not currently represented in synthetic binary
populations, and is not easily reproduced by available binary population
synthesis codes. Therefore, it challenges current binary evolution models,
offering a unique opportunity to gain insights into the processes governing
white-dwarf formation, binary evolution, and mass transfer.
