  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 gravitational redshift 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 inferred from
effective temperature and luminosity measurements. This corresponds to the
first ever measurement of extra-Solar surface gravity induced gravitational
redshift in non-degenerate stars. Additionally, we study the sub-dominant
effects of convective blueshifting of emission lines, 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.
