Stellar parameters of early-M dwarfs from ratios of spectral features at optical wavelengths

Low-mass stars have been recognised as promising targets in
the search for rocky, small planets with the potential of supporting
life. Doppler search programmes using high-resolution spectrographs like
HARPS or HARPS-N are providing huge quantities of optical spectra of M
dwarfs. We aim to calibrate empirical relationships to determine stellar
parameters for early M dwarfs (spectral types M0-M4.5) using the same
spectra that are used for the radial velocity determinations. Our
methodology consists in the use of ratios of pseudo equivalent widths of
spectral features as a temperature diagnostic. Stars with effective
temperatures obtained from interferometric estimates of their radii are
used as calibrators. Empirical calibrations for the spectral type are
also provided. Combinations of features and ratios of features are used
to derive calibrations for the stellar metallicity. Our methods are then
applied to a large sample of M dwarfs that are being observed in the
framework of the HARPS search for extrasolar planets.The derived
temperatures and metallicities are used together with photometric
estimates of mass, radius, and surface gravity to calibrate empirical
relationships for these parameters. A total of 112 temperature sensitive
ratios have been calibrated over the range 3100-3950 K, providing Teff
values with typical uncertainties of the order of 70 K. Eighty-two
ratios of pseudo equivalent widths of features were calibrated to derive
spectral types. Regarding stellar metallicity, 696 combinations of
pseudo equivalent widths of individual features and
temperature-sensitive ratios have been calibrated, over the metallicity
range from -0.54 to +0.24 dex, with estimated uncertainties in the range
of 0.07-0.10 dex. We provide our own empirical calibrations for stellar
mass, radius, and surface gravity.