New atmospheric parameters and spectral interpolator for the MILES cool stars

Context: The full spectrum fitting of stellar spectra against a library of empirical spectra is a well-established approach to measure the atmospheric parameters of FGK stars with a high internal consistency. Extending it towards cooler stars still remains a challenge. Aims: We address this question by improving the interpolator of the MILES (Medium-resolution INT Library of Empirical Spectra) library in the low effective temperature regime (Tefff < 4800 K), and we refine the determination of the parameters of the cool MILES stars. Methods: We use the ULySS package to determine the atmospheric parameters (Teff, logg and [Fe/H]), and measure the biases of the results with respect to our updated compilation of parameters calibrated against theoretical spectra. After correcting some systematic effects, we compute a new interpolator that we finally use to redetermine the atmospheric parameters homogeneously and assess the biases. Results: Based on an updated literature compilation, we determine Teff in a more accurate and unbiased manner compared to those determined with the original interpolator. The validity range is extended downwards to about Teff = 2900 K compared to 3500 K previously. The mean residual biases on Teff, logg, and [Fe/H], with respect to the literature compilation for the coolest stars (Teff <= 3800 K) computed using the new interpolator, are -15 K, -0.02 dex, and 0.02 dex respectively. The corresponding estimations of the external precision are 63 K, 0.23 dex, and 0.15 dex respectively. For the stars with Teff in the range 3800 - 4200 K, the determinations of Teff and [Fe/H] have been slightly improved. At higher temperatures, the new interpolator is comparable to the original one. The new version of the interpolator is publicly available.