The modelling of intermediate-age stellar populations. II. Average spectra for upper AGB stars, and their use

The upper Asymptotic Giant Branch (AGB) is populated with oxygen rich and carbon rich Long Period Variables (LPVs). These stars are essential contributors to the near-IR light of intermediate age stellar populations. Individual observed spectra of LPVs are so diverse that they cannot be used directly in the synthesis of galaxy spectra. In this paper, the library of individual spectra of Lançon & Wood (\cite{LM00_fluct}) is used to construct averages that can be incorporated conveniently in population synthesis work. The connection between such spectra and stellar evolution tracks is discussed. In order to select a sorting criterion and to define averaging bins for the LPV spectra, correlations between their spectrophotometric properties are reexamined. While optical properties and broad baseline colours such as (I-K) are well correlated, a large dispersion is observed when these indices are plotted against near-IR ones. This is partly due to the intrinsic width of the upper AGB, which is illustrated by locating each of the multiple observations of individual LPVs on the HR diagram. It is argued that broad baseline colour-temperatures are the most sensible sorting criteria. The properties of the resulting sequence of average spectra indeed vary regularly. We further address: (i) the bolometric corrections and temperature scales needed to associate a spectrum with a given point on a theoretical stellar evolution track (or isochrone), (ii) the simplifying assumptions that will be implicitely made when using the average spectra, (iii) potential biases in the sample of Lançon & Wood and their effects, (iv) the small contribution of LPVs to the interstellar hydrogen emission lines in galaxies. It is emphasized that an a posteriori calibration of the effective temperature scale remains necessary, until consistent models for the evolution, the pulsation and the spectral appearance of LPVs become available. We suggest a recipe for the use of the average spectra at various metallicities.