The evolution of the V - K colours of single stellar populations

Models of evolutionary population synthesis of galaxies rely on the properties of the so-called single stellar populations (SSP). In this paper, we discuss how the integrated near-infrared colours, and especially V-K, of SSPs evolve with age and metallicity. Some of the uncertainties associated with the properties of the underlying stellar models are thoroughly discussed. Our models include all the relevant stellar evolutionary phases, with particular attention being dedicated to the asymptotic giant branch (AGB), which plays a fundamental role in the evolution of the near-infrared part of the spectrum. First, we present the effects that different formulations for the mass-loss rates produce on the final remnant mass (i.e., on the initial-final mass relation), and hence on the AGE-termination luminosity and the relative contribution of these stars to the integrated Light. The results for the evolution of the V - K colour are very different depending on the choice of the mass-loss prescription; the same is true also for the B - V colour in the case of low-metallicity SSPs. Secondly, we describe the changes occurring in the integrated colours at the onset of the AGE and red giant (RGB) branches. According to the classical formalism for the AGE evolution, the onset of this evolutionary phase is marked by a colour jump to the red, the amplitude of which is shown here to be highly dependent on the metallicity and mass-loss rates adopted in the models. We then consider the effect of the overluminosity with respect to the standard core mass-luminosity relation that occurs in the most massive AGE stars. Different simplified formulations for this effect are tested in the models; they cause a smoothing of the colour evolution in the age range at which the AGE starts to develop, rather than a splitting of the colour jump into two separate events. On the other hand, we find that a temporary red phase takes place similar to 1.5 x 10(8) yr after the RGB develops. Thanks to the transient nature of this feature, the onset of the RGB is probably not able to cause marked features in the spectral evolution of galaxies. We then discuss the possible reasons for the transition of V - K colours (from similar to 1.5 to 3) that takes place in LMC clusters of SWB type IV. A revision of the ages attributed to the single clusters reveals that the transition may not be as fast as originally suggested. The comparison of the data with the models indicates that the transition results mainly from the development of the AGE. A gradual (or delayed) transition of the colours, as predicted by models which include the overluminosity of the most massive AGE stars, seems to describe the data better than the sudden colour jump predicted by classical models.