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.
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