Shells of dust around AGB stars: Effects on the integrated spectrum of Single Stellar Populations

In this paper we present models for Single Stellar Populations (SSPs) of intermediate and old ages where dust enshrouded Asymptotic Giant Branch (AGB) stars are introduced. As long known AGB stars are surrounded by dust-rich shells of matter caused by their own stellar wind, which absorb the radiation coming from the central object and re-emit it in the far infrared (IR). To this aim, particular care is devoted to follow the evolution of the AGB stars throughout the quiet and thermally pulsing regimes, to evaluate the effect of self contamination in the outermost layers by the third dredge-up mechanism, to follow the transition from oxygen-rich to carbon-rich objects (as appropriate to their initial mass and chemical composition), and finally to estimate the efficiency of mass-loss by stellar winds, all aspects that concur to the formation and properties of the dusty shells around. In addition to this, accurate physical models of the dusty shells are presented in which the re-processing of radiation from the central stars is calculated by solving the radiative transfer equations in presence of dust particles of different chemical composition. The resulting spectral energy distribution (SED) is examined to show how important features, like the 10(mu)m Si-O stretching mode feature and the 11(mu)m SiC feature, evolve with time. The SEDs are then convolved with the IRAS filters to obtain the flux in various pass-bands, i.e. 12, 25 and 60 (mu)m, for individual AGB stars of different mass, chemical composition, and age. The comparison is made by means of SSPs along which AGB stars of the same age but different initial masses are located. This allows us to explore the whole range of masses and ages spanned by AGB stars. The theoretical results are compared to the observational data for selected groups of stars. The same is made for the J,H,K,L pass-bands of the Johnson system. Finally, from the integrated SEDs of the SSPs, we derive the integrated Johnson J,H,K,L magnitudes and colors to be compared to infrared data for star clusters of the Magellanic Clouds. In general good agreement with the data is possible if the effects of the circumstellar shells of dust are taken into account.