An astrometric search method for individually resolvable gravitational
  wave sources with Gaia
  Gravitational waves (GWs) cause the apparent position of distant stars to
oscillate with a characteristic pattern on the sky. Astrometric measurements
(e.g. those made by Gaia) therefore provide a new way to search for GWs. The
main difficulty facing such a search is the large size of the data set; Gaia
observes more than one billion stars. In this letter the problem of searching
for GWs from individually resolvable supermassive black hole binaries using
astrometry is addressed for the first time; it is demonstrated how the data set
can be compressed by a factor of more than $10^6$, with a loss of sensitivity
of less than $1\%$. This technique is successfully used to recover artificially
injected GWs from mock Gaia data. Repeated injections are used to calculate the
sensitivity of Gaia as a function of frequency, and Gaia's directional
sensitivity variation, or antenna pattern. Throughout the letter the
complementarity of Gaia and pulsar timing searches for GWs is highlighted.
