  For stars with unresolved companions, motions of the centre of light and that
of mass decouple, causing a single-source astrometric model to perform poorly.
We show that such stars can be easily detected with the reduced chi2 statistic,
or RUWE, provided as part of Gaia DR2. We convert RUWE into the amplitude of
the image centroid wobble, which, if scaled by the source distance, is
proportional to the physical separation between companions (for periods up to
several years). We test this idea on a sample of known spectroscopic binaries
and demonstrate that the amplitude of the centroid perturbation scales with the
binary period and the mass ratio as expected. We apply this technique to the
Gaia DR2 data and show how the binary fraction evolves across the
Hertzsprung--Russell diagram. The observed incidence of unresolved companions
is high for massive young stars and drops steadily with stellar mass, reaching
its lowest levels for white dwarfs. We highlight the elevated binary fraction
for the nearby Blue Stragglers and Blue Horizontal Branch stars. We also
illustrate how unresolved hierarchical triples inflate the relative velocity
signal in wide binaries. Finally, we point out a hint of evidence for the
existence of additional companions to the hosts of extrasolar hot jupiters.
