Modelling intermediate age and old stellar populations in the Infrared

In this paper we have investigated the spectrophotometric properties of the Asymptotic Giant Branch (AGB) stars and their contribution to the integrated infrared emission in simple stellar populations (SSP). Adopting analytical relations describing the evolution of these stars in the HR diagram and empirical relations for the mass-loss rate and the wind terminal velocity, we were able to model the effects of the dusty envelope around these stars, with a minimal number of parameters. After deriving simple scaling relations which allow us to account for the metallicity of the star, we computed isochrones at different age and initial metal content. We compare our models with existing infrared colors of M giants and Mira stars and with IRAS PSC data. The former data are fairly well reproduced by our models, though a possible inadequacy of the adopted atmospheric models is indicated. Though being characterized by different metallicity, the isochrones follow a single path in the IRAS two color diagram, fixed by the composition and optical properties of the dust mixture. The bulk of the data in the latter diagram is delimited by the curves corresponding to a mixture of silicate grains and one of carbonaceous grains. We also discuss the effects of detached shells of matter but we do not take into account this phenomenon in the present computations. Contrary to previous models, in the new isochrones the mass-loss rate, which establishes the duration of the AGB phase, also determines the spectral properties of the stars. The contribution of these stars to the integrated light of the population is thus obtained in a consistent way. We find that the emission in the mid infrared is about one order of magnitude larger when dust is taken into account in an intermediate age population, irrespective of the particular mixture adopted. The dependence of the integrated colors on the metallicity and age is discussed, with particular emphasis on the problem of age-metallicity degeneracy. We show that, contrary to the case of optical or near infrared colors, the adoption of a suitable pass-band in the mid infrared allows a fair separation of the two effects. We suggest intermediate redshift elliptical galaxies as possible targets of this method of solving the age-metallicity dilemma. The new SSP models constitute a first step in a more extended study aimed at modelling the spectral properties of the galaxies from the ultraviolet to the far infrared.