A large sample of calibration stars for Gaia: log g from Kepler and CoRoT fields

Asteroseismic data can be used to determine stellar surface gravities with precisions of <0.05 dex by using the global seismic quantities <Delta nu > and nu(max) along with standard atmospheric data such as T-eff and metallicity. Surface gravity is also one of the four stellar properties to be derived by automatic analyses for one billion stars from Gaia data (work-package GSP_PHOT). In this paper, we explore seismic data from main-sequence F, G, K stars (solar-like stars) observed by the Kepler spacecraft as a potential calibration source for the methods that Gaia will use for object characterization (log g). We calculate log g for some bright nearby stars for which radii and masses are known (e. g. from interferometry or binaries), 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 also find that errors in adopted atmospheric parameters (mainly [Fe/H]) can, however, cause systematic errors of the order of 0.02 dex. We then apply our method to a list of 40 stars to deliver precise values of surface gravity, i.e. uncertainties of the order of 0.02 dex, and we find agreement with recent literature values. Finally, we explore the typical precision that we expect in a sample of more than 400 Kepler stars which have their global seismic quantities measured. We find a mean uncertainty (precision) of the order of better than 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 of the order of 0.04 dex, independent of log g and magnitude, which accounts for errors in the T-eff 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 characterization with GSP_PHOT, where excellent precision (small uncertainties) and accuracy in log g is obtained from seismic data.