Stellar model tests and age determination for RGB stars from the APO-K2 catalogue

Aims. By adopting the recently empirically derived dependence of α -elements on α /Fe instead of the conventionally applied uniform one, we tested the agreement between stellar model predictions and observations for red giant branch (RGB) stars in the APO-K2 catalogue. We particularly focused on the biases in effective temperature scales and on the robustness of age estimations. Methods. We computed a grid of stellar models relying on the empirical scaling of α -elements, investigating the offset in effective temperature Δ T between these models and observations, using univariate analyses for both metallicity Fe/H and α /Fe. To account for potential confounding factors, we then employed a multivariate generalised additive model to study the dependence of Δ T on Fe/H, α /Fe, log g , and stellar mass. Results. The initial analysis revealed a negligible trend of Δ T with Fe/H, in contrast with previous works in the literature, which adopt a uniform relation between the various α -elements and α /Fe. A slight Δ T difference of 25 K was detected between stars with high and low α -enhancement. Our multivariate analysis reveals a dependence of Δ T on both Fe/H and α /Fe, and highlights a significant dependence on stellar mass. This suggests a discrepancy in how effective temperature scales with stellar mass in the models compared to observations. Despite differences in assumed chemical composition, our analysis, through a fortunate cancellation effect, yields ages that are largely consistent with recent studies of the same sample. Notably, our analysis identifies a 6% fraction of stars younger than 4 Ga within the high- α population. However, our analysis of the C/N ratio supports the possible origin of these stars as a result of mergers or mass transfer events.