Modelling of intermediate age stellar populations III. Effects of dust-shells around AGB stars

In this paper we present single stellar population models of intermediate age stellar populations where dust-enshrouded Asymptotic Giant Branch (AGB) stars are introduced. The formation of carbon stars is also accounted for, and is taken to be a function of both initial stellar mass and metallicity. The effects of the dusty envelopes around AGB stars on the optical near-infrared spectral energy distribution were introduced using semi-empirical models where the mass-loss and the photospheric chemistry determine the spectral properties of a star along the AGB sequence. The spectral dichotomy between oxygen-rich stars and carbon stars is taken into account in the modelling. We have investigated the AGB sequence morphology in the near-infrared colour-magnitude diagram as a function of time and metallicity. We show that this diagram is characterized by three morphological features, occupied by optically bright oxygen-rich stars, optically bright carbon stars, and dust-enshrouded oxygen rich and carbon stars respectively. Our models are able to reproduce the distribution of the three AGB subtype stellar populations in colour-colour diagrams. Effects of dusty envelopes on the luminosity function are also investigated. We have extended our investigations to the integrated spectro-photometric properties of stellar populations. We find that the contribution of AGB stars to the near-infrared integrated light decreases, making optical near-infrared colours of intermediate age populations bluer than what is expected from pure photospheric emission models.