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(Abridged) Low-mass stars have been recognised as promising targets in thesearch for rocky, small planets with the potential of supporting life. Dopplersearch programmes using high-resolution spectrographs like HARPS or HARPS-N areproviding huge quantities of optical spectra of M dwarfs. We aim to calibrateempirical relationships to determine stellar parameters for early M dwarfs(spectral types M0-M4.5) using the same spectra that are used for the radialvelocity determinations. Our methodology consists in the use of ratios ofpseudo equivalent widths of spectral features as a temperature diagnostic.Stars with effective temperatures obtained from interferometric estimates oftheir radii are used as calibrators. Empirical calibrations for the spectraltype are also provided. Combinations of features and ratios of features areused to derive calibrations for the stellar metallicity. Our methods are thenapplied to a large sample of M dwarfs that are being observed in the frameworkof the HARPS search for extrasolar planets.The derived temperatures andmetallicities are used together with photometric estimates of mass, radius, andsurface gravity to calibrate empirical relationships for these parameters. Atotal of 112 temperature sensitive ratios have been calibrated over the range3100-3950 K, providing Teff values with typical uncertainties of the order of70 K. Eighty-two ratios of pseudo equivalent widths of features were calibratedto derive spectral types. Regarding stellar metallicity, 696 combinations ofpseudo equivalent widths of individual features and temperature-sensitiveratios have been calibrated, over the metallicity range from -0.54 to +0.24dex, with estimated uncertainties in the range of 0.07-0.10 dex. We provide ourown empirical calibrations for stellar mass, radius, and surface gravity.

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