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

Aims. By adopting the recently empirically derived dependence of alpha-elements on [alpha/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 alpha-elements, investigating the offset in effective temperature Delta T between these models and observations, using univariate analyses for both metallicity [Fe/H] and [alpha/Fe]. To account for potential confounding factors, we then employed a multivariate generalised additive model to study the dependence of Delta T on [Fe/H], [alpha/Fe], log g, and stellar mass. Results. The initial analysis revealed a negligible trend of Delta T with [Fe/H], in contrast with previous works in the literature, which adopt a uniform relation between the various alpha-elements and [alpha/Fe]. A slight Delta T difference of 25 K was detected between stars with high and low alpha-enhancement. Our multivariate analysis reveals a dependence of Delta T on both [Fe/H] and [alpha/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-alpha 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.