Estimating Teff, radius, and luminosity of M-dwarfs using high-resolution optical and NIR spectral features

We estimate effective temperature (T_eff), stellar radius, and luminosity for a sample of 271 M-dwarf stars (M0V-M7V) observed as a part of CARMENES (Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs) radial-velocity planet survey. For the first time, using the simultaneously observed high-resolution ($R\sim 90\, 000$) spectra in the optical (0.52-0.96 $\mu$m) and near-infrared (0.96-1.71 $\mu$m) bands, we derive empirical calibration relationships to estimate the fundamental parameters of these low-mass stars. We select a sample of nearby and bright M-dwarfs as our calibrators for which the physical parameters are acquired from high-precision interferometric measurements. To identify the most suitable indicators of T_eff, radius, and luminosity (log L/L_⊙), we inspect a range of spectral features and assess them for reliable correlations. We perform multivariate linear regression and find that the combination of pseudo-equivalent widths and equivalent width ratios of the Ca II at 0.854 $\mu$m and Ca II at 0.866 $\mu$m lines in the optical and the Mg I line at 1.57 $\mu$m in the near-infrared give the best fitting linear functional relations for the stellar parameters with root mean square errors of 99K, 0.06 R_⊙, and 0.22 dex, respectively. We also explore and compare our results with literature values obtained using other different methods for the same sample of M dwarfs.