Probing the Origins I : Generalised Additive Model inference of birth radii for Milky Way stars in the solar vicinity

Context. As stars traverse the Galaxy, interactions with structures such as the bar and spiral arms can alter their orbits, leading either to ‘churning’, where changes in angular momentum shift their guiding radii, or ‘blurring’, where angular momentum is preserved. Churning is what is commonly known as radial migration. Aims. Here, we probe the orbital characteristics of a diverse set of stars in the thin disc observed by the Gaia-ESO survey. We aim to discern whether their orbits are predominantly influenced by churning or if they keep their orbital birth radii (i.e. were blurred or remained undisturbed). Methods. We employed a generalised additive model (GAM) to address the limitations inherent in radial metallicity gradients predicted by chemical evolution models, thereby facilitating estimation of the birth radii for the thin disc stars in our sample based on their age and chemical composition. We then juxtaposed the birth radius predictions derived from the GAM with the calculated guiding radii, among other dynamic parameters. This comparison was performed within distinct groups of our dataset, categorised through hierarchical clustering (HC) based on 21 chemical abundances spanning 18 species. Results. Our results indicate that groups of stars with different chemical abundances exhibit distinct orbital behaviours. Metal-rich stars, formed in the inner regions of the Milky Way, seem to be predominantly churned outward. Their metal-poor counterparts, formed in the outer thin disc, exhibit the opposite behaviour. Also, the proportion of blurred/undisturbed stars generally increases with decreasing metallicity when compared to their churned counterparts. Approximately three-fourths of the sample has been affected by (inward or outward) churning, while the remaining part of the sample (∼1/4) has either been influenced by blurring or remained undisturbed. These percentages vary considerably across different metallicity-stratified groups. Additionally, we identified a large age gap between churned and blurred/undisturbed sub-samples within each HC-based group: the outward-churned stars were systematically the oldest, inward-churned stars the youngest, and blurred/undisturbed stars at intermediate ages. Yet, given that our sample mostly comprises old stars, we suspect that those classified as blurred/undisturbed may have primarily undergone blurring due to their extended interactions with Galactic structures, considering that their median ages are ∼6.61 Gyr. We also detected significant differences in angular momenta in the z component for stars that have either churned inward or outward when compared to their blurred/undisturbed counterparts. The action components also provide interesting insights into the orbital history of our different metallicity- and motion-stratified groups. Additionally, we observed the potential effects of the pericentric passage of the Sagittarius dwarf galaxy in our most metal-poor subset of stars formed in the outer disc. Finally, we estimate that the Sun’s most probable birth radius is 7.08 ± 0.24 kpc, with a 3σ range spanning from 6.46 to 7.81 kpc, which is in agreement with previous studies.