Asteroseismic data can be used to determine surface gravities with precisions of < 0.05 dex by using the global seismic quantities Deltanu and nu_max along with Teff and [Fe/H]. Surface gravity is also one of the four stellar properties to be derived by automatic analyses for 1 billion stars from Gaia data (workpackage GSP_Phot). We explore seismic data from MS F, G, K stars (solar-like stars) observed by Kepler as a potential calibration source for methods that Gaia will use for object characterisation (log g). We calculate log g for bright nearby stars for which radii and masses are known, and using their global seismic quantities in a grid-based method, we determine an asteroseismic log g to within 0.01 dex of the direct calculation, thus validating the accuracy of our method. We find that errors in Teff and mainly [Fe/H] can cause systematic errors of 0.02 dex. We then apply our method to a list of 40 stars to deliver precise values of surface gravity, i.e. sigma < 0.02 dex, and we find agreement with recent literature values. Finally, we explore the precision we expect in a sample of 400+ Kepler stars which have their global seismic quantities measured. We find a mean uncertainty (precision) on the order of <0.02 dex in log g over the full explored range 3.8 < log g < 4.6, with the mean value varying only with stellar magnitude (0.01 - 0.02 dex). We study sources of systematic errors in log g and find possible biases on the order of 0.04 dex, independent of log g and magnitude, which accounts for errors in the Teff and [Fe/H] measurements, as well as from using a different grid-based method. We conclude that Kepler stars provide a wealth of reliable information that can help to calibrate methods that Gaia will use, in particular, for source characterisation with GSP_Phot where excellent precision (small uncertainties) and accuracy in log g is obtained from seismic data.
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