  The gravitational redshift induced by stellar surface gravity is notoriously
difficult to measure for non-degenerate stars, since its amplitude is small in
comparison with the typical Doppler shift induced by stellar radial velocity.
In this study, we make use of the large observational data set of the Gaia
mission to achieve a significant reduction of noise caused by these random
stellar motions. By measuring the differences in velocities between the
components of pairs of co-moving stars and wide binaries, we are able to
statistically measure the combined effects of gravitational redshift and
convective blueshifting of spectral lines, and nullify the effect of the
peculiar motions of the stars. For the subset of stars considered in this
study, we find a positive correlation between the observed differences in Gaia
radial velocities and the differences in surface gravity and convective
blueshift inferred from effective temperature and luminosity measurements. The
results rule out a null signal at the $5\sigma$ level for our full data-set.
Additionally, we study the sub-dominant effects of binary motion, and possible
systematic errors in radial velocity measurements within Gaia. Results from the
technique presented in this study are expected to improve significantly with
data from the next Gaia data release. Such improvements could be used to
constrain the mass-luminosity relation and stellar models which predict the
magnitude of convective blueshift.
