Detailed AGB evolutionary models and near infrared colours of intermediate-age stellar populations: Tests on star clusters

We investigate the influence of asymptotic giant branch (AGB) stars on integrated colours of star clusters of ages between ∼100 Myr and a few gigayears, and composition typical for the Magellanic Clouds. We use state-of-the-art stellar evolution models that cover the full thermal pulse phase, and take the influence of dusty envelopes on the emerging spectra into account. We present an alternative approach to the usual isochrone method, and compute integrated fluxes and colours using a Monte Carlo technique that enables us to take into account statistical fluctuations due to the typical small number of cluster stars. We demonstrate how the statistical variations in the number of AGB stars and the temperature and luminosity variations during thermal pulses fundamentally limit the accuracy of the comparison (and calibration, for population synthesis models that require a calibration of the AGB contribution to the total luminosity) with star cluster integrated photometries. When compared to observed integrated colours of individual and stacked clusters in the Magellanic Clouds, our predictions match most of the observations well, when statistical fluctuations are taken into account, although there are discrepancies in narrow age ranges with some (but not all) sets of observations.