  Gravitational redshifts in solar-type main-sequence stars are expected to be
some 500 ms$^{-1}$ greater than those in giants. Such a signature is searched
for between groups of open-cluster stars which share the same average space
motion and thus have the same average Doppler shift. 144 main-sequence stars
and cool giants were observed in the M67 open cluster using the ESO FEROS
spectrograph, obtaining radial velocities by cross correlation with a spectral
template. M67 dwarf and giant radial-velocity distributions are well
represented by Gaussian functions, sharing the same apparent average radial
velocity within $\simeq$ 100 ms$^{-1}$. In addition, dwarfs in M67 appear to be
dynamically hotter ($\sigma$ = 0.90 kms$^{-1}$) than giants ($\sigma$ = 0.68
kms$^{-1}$). Explanations for the lack of an expected signal are sought: a
likely cause is the differential wavelength shifts produced by different
hydrodynamics in dwarf and giant atmospheres. Radial-velocity differences
measured between unblended lines in low-noise averaged spectra vary with
line-strength: stronger lines are more blushifted in dwarfs than in giants,
apparently 'compensating' for the gravitational redshift. Synthetic
high-resolution spectra are computed from 3-dimensional hydrodynamic model
atmospheres for both giants and dwarfs, and synthetic wavelength shifts
obtained. In agreement with observations, 3D models predict substantially
smaller wavelength-shift differences than expected from gravitational redshift
only. The procedures developed could be used to test 3D models for different
classes of stars, but will ultimately require high-fidelity spectra for
measurements of wavelength shifts in individual spectral lines.
