Early-type galaxies at z~1.3. II. Masses and ages of early-type galaxies in different environments and their dependence on stellar population model assumptions

We have derived masses and ages for 79 early-type galaxies (ETGs) in different environments at z~1.3 in the Lynx supercluster and in the GOODS/CDF-S field using multiwavelength (0.6-4.5 $\mu$m; KPNO, Palomar, Keck, HST, Spitzer) datasets. At this redshift the contribution of the TP-AGB phase is important for ETGs, and the mass and age estimates depend on the choice of the stellar population model used in the spectral energy distribution fits. We describe in detail the differences among model predictions for a large range of galaxy ages, showing the dependence of these differences on age. Current models still yield large uncertainties. While recent models from Maraston and Charlot & Bruzual offer better modeling of the TP-AGB phase with respect to less recent Bruzual & Charlot models, their predictions do not often match. The modeling of this TP-AGB phase has a significant impact on the derived parameters for galaxies observed at high-redshift. Some of our results do not depend on the choice of the model: for all models, the most massive galaxies are the oldest ones, independent of the environment. When using Maraston and Charlot & Bruzual models, the mass distribution is similar in the clusters and in the groups, whereas in our field sample there is a deficit of massive (M $\gtrsim$ 10^11 Msun) ETGs. According to those last models, ETGs belonging to the cluster environment host on average older stars with respect to group and field populations. This difference is less significant than the age difference in galaxies of different masses.