Modelling chemical clocks

Context. Chemical clocks based on [s-process element/α element] ratios are widely used to estimate the ages of Galactic stellar populations. However, the [s/α] versus age relations are not universal, varying with metallicity, location in the Galactic disc, and specific s-process elements. Moreover, current Galactic chemical evolution models struggle to reproduce the observed [s/α] increase at young ages, particularly for Ba. Aims. Our aim is to provide chemical evolution models for different regions of the Milky Way (MW) disc in order to identify the conditions required to reproduce the observed [s/H], [s/Fe], and [s/α] versus age relations. Methods. We adopted a detailed multi-zone chemical evolution model for the MW including state-of-the-art nucleosynthesis prescriptions for neutron-capture elements. The s-process elements were synthesised in asymptotic giant branch (AGB) stars and rotating massive stars, while r-process elements originate from neutron star mergers and magneto-rotational supernovae. Starting from a baseline model that successfully reproduces a wide range of neutron-capture element abundance patterns, we explored variations in gas infall/star formation history scenarios, AGB yield dependencies on progenitor stars, and rotational velocity distributions for massive stars. We compared the results of our model with the open clusters dataset from the sixth data release of the Gaia-ESO survey. Results. A three-infall scenario for disc formation aligns better with the observed trends. The models capture the rise of [s/α] with age in the outer regions but fail towards the inner regions, with larger discrepancies for second s-process peak elements. Specifically, Ba production in the last 3 Gyr of chemical evolution would need to increase by slightly more than half to match the observations. The s-process contribution from low-mass (∼1.1 M⊙) AGB stars helps reconcile predictions with data but it requires a too-strong increase that is not predicted by current nucleosynthesis calculations, even with a potential i-process contribution. Variations in the metallicity dependence of AGB yields either worsen the agreement or show inconsistent effects across elements, while distributions of massive star rotational velocities with lower velocity at high metallicities fail to improve results due to balanced effects on different elements. Conclusions. The predictions of our model confirm, as expected, that there is no single relationship [s/α] versus age and that it varies along the MW disc. However, the current prescriptions for neutron-capture element yields are not able to fully capture the complexity of evolution, particularly in the inner disc.