Five old open clusters: NGC 2682, NGC 2243, Berkeley 39, NGC 188 and NGC 6791

The color-magnitude diagrams (CMD) of five old open clusters, namely NGC 2682, NGC 2243, Berkeley 39, NGC 188, and NGC 6791 are examined in detail with the aid of the synthetic color-magnitude diagram technique described by Carraro et al. (1993), and the color excess E(B-V), distance modulus (m - M), and age of each cluster are derived. The goal is to provide an homogeneous ranking of the cluster ages. The analysis is made using two types of stellar models in which, different prescriptions are adopted for the extension of the convective cores, i.e. either the classical or the overshoot scheme. The stellar models in use are from Alongi et al. (1993), Bressan et al. (1993), and Fagotto et al. (1993a,b). The evolutionary tracks go from the main sequence up to the start of the thermally pulsing regime of the asymptotic giant branch (TP-AGB) phase. The purpose is to discriminate between the two evolutionary scenarios. It turns out that all the clusters have turn-off masses either slightly greater or equal to the value of 1.1 M., at which we expect the transition from convective to radiative core H-burning to occur. As far as the mixing mechanism is concerned, the results are not very conclusive. For the youngest clusters of our sample, namely NGC 2682 and NGC 2243, models with convective overshoot seem to provide a slightly better fit of the observed CMD and luminosity function. For the oldest cluster of our sample, namely NGC 6791 with age of 8 10(9) yr, there is no appreciable difference passing from one scheme to another. Finally, for the remaining clusters, namely Berkeley 39 and NGC 188, the situation is ambiguous. This trend is not surprising, because we expect the convective core and hence associated overshoot to vanish at decreasing turn-off mass and hence increasing age. As expected the ages derived from overshoot models are slightly older than those obtained from standard models. The five clusters on consideration can be ranked as function of the age as follows (the first Value refers to classical models, the second one to models with overshoot): NGC 2682 (4.3 10(9) yr and 4.8 10(9) yr), NGC 2243 (3.5 10(9) yr and 3.9 10(9) yr), Berkeley 39, (6.0 10(9) yr and 6.5 10(9) yr), and NGC 188 (7.0 10(9) yr and 7.5 10(9) yr). No age difference is found in the case of NGC 6791 for which both types of stellar models yield 8.0 10(9) yr