A new stellar library in the region of the CO index at 2.3 μm -: New index definition and empirical fitting functions

Context. The analysis of unresolved stellar populations demands evolutionary synthesis models with realistic physical ingredients and extended wavelength coverage. Aims. We quantitatively describe the first CO bandhead at 2.3 mu m to allow stellar population models to provide improved predictions in this wavelength range. Methods. We observed a new stellar library with a better coverage of the stellar atmospheric parameter space than in earlier works. We performed a detailed analysis of the robustness of previous CO index definitions with spectral resolution, wavelength calibration, signal-to-noise ratio, and flux calibration. Results. We define a new line-strength index for the first CO bandhead at 2.3 mu m, DCO, better suited for stellar population studies than previous index definitions. We derive empirical fitting functions for the CO feature as a function of the stellar parameters (T-eff, log g and [Fe/H]), showing a detailed quantitative metallicity dependence.