Setting the Clock of Stellar Models

The study of old open clusters such as IC 4651 has brought into evidence that the age assigned to these clusters heavily depends on the type of stellar models in use, that is, standard models or models with a certain amount of convective overshoot from the core. While standard models lead to age estimates that reasonably agree among the various sources provided that the same physical assumptions (chemical composition, opacity, nuclear reaction rates, etc.) are adopted, models with convective overshoot give ages that are largely discrepant even if the same input physics is used (the efficiency of core overshoot in particular). This topic has been addressed by Nordstrom & Andersen analyzing the color-magnitude diagram of IC 4651 by Anthony-Twarog et al. They pointed out that the age given by Mazzei & Pigatto based on the overshoot models by Bertelli et al. is about a factor of 3 lower than the value estimated by Maeder and by Maeder & Meynet. Current stellar models indicate that the age of this cluster lies in the range 1.3 x 10(9) to 4 x 10(9) yr, and that the turnoff mass falls in the range 1.5-1.7 M., depending on the adopted color excess, distance modulus, and type of models (classical versus overshoot). In this paper first we show that a fundamental inconsistency affects the models with core overshoot and corresponding isochrones calculated by Maeder & Meynet, and second we re-derive the color excess, distance modulus, and age of IC 4651 with the aid of new models for both the classical and the overshoot mixing scheme. Specifically, we find that the core H-burning lifetime of the stars in this mass range published by Maeder & Meynet exceeds the maximum nuclear lifetime allowed by the structure of their own models. The maximumm lifetime is simply given by the ratio of the energy liberated by the available fuel to the minimum luminosity of the stars in this phase. This inconsistency does not occur during the central H-burning phase of stars of higher mass, whereas it is likely present during the core He-burning phase of stars of any mass. The reason of this is not understood. The study of the color-magnitude diagram of IC 4651 with the aid of the new model calculations for both standard and overshoot models by Fagotto and Alongi et al., respectively, leads to the following results. With the standard models, we get a color excess E(B-V) = 0.16, a distance modulus (m - M)0 = 9.6, and an age of 1.4 x 10(9) yr. With the overshoot models, we obtain a color excess E(B-V) = 0.14, a distance modulus (m - M)0 = 9.5, and an age of 2.0 x 10(9) yr. Reliable ages of star clusters are of the greatest importance to trace back the history of star formation in the Galactic disk.