The Insidious Boosting of Thermally Pulsing Asymptotic Giant Branch Stars in Intermediate-age Magellanic Cloud Clusters

In the recent controversy about the role of thermally pulsing asymptotic giant branch (TP-AGB) stars in evolutionary population synthesis (EPS) models of galaxies, one particular aspect is puzzling: TP-AGB models aimed at reproducing the lifetimes and integrated fluxes of the TP-AGB phase in Magellanic Cloud (MC) clusters, when incorporated into EPS models, are found to overestimate, to various extents, the TP-AGB contribution in resolved star counts and integrated spectra of galaxies. In this paper, we call attention to a particular evolutionary aspect, linked to the physics of stellar interiors, that in all probability is the main cause of this conundrum. As soon as stellar populations intercept the ages at which red giant branch stars first appear, a sudden and abrupt change in the lifetime of the core He-burning phase causes a temporary "boost" in the production rate of subsequent evolutionary phases, including the TP-AGB. For a timespan of about 0.1 Gyr, triple TP-AGB branches develop at slightly different initial masses, causing their frequency and contribution to the integrated luminosity of the stellar population to increase by a factor of ~2. The boost occurs for turn-off masses of ~1.75 M _⊙, just in the proximity of the expected peak in the TP-AGB lifetimes (for MC metallicities), and for ages of ~1.6 Gyr. Coincidently, this relatively narrow age interval happens to contain the few very massive MC clusters that host most of the TP-AGB stars used to constrain stellar evolution and EPS models. This concomitance makes the AGB-boosting particularly insidious in the context of present EPS models. As we discuss in this paper, the identification of this evolutionary effect brings about three main consequences. First, we claim that present estimates of the TP-AGB contribution to the integrated light of galaxies derived from MC clusters are biased toward too large values. Second, the relative TP-AGB contribution of single-burst populations falling in this critical age range cannot be accurately derived by approximations such as the fuel consumption theorem, which ignore, by construction, the above evolutionary effect. Third, a careful revision of AGB star populations in intermediate-age MC clusters is urgently demanded, promisingly with the aid of detailed sets of stellar isochrones.