Asteroseismic ages for 17,000 stars in Kepler, K2 and TESS

The availability of asteroseismic constraints for tens of thousands of red giant (RG) stars has opened the door to robust age estimates, enabling time-resolved studies of different populations of stars in the Milky Way. This study leverages data from Kepler, K2, and TESS, in conjunction with astrometric data from Gaia DR3 and spectroscopic constraints from APOGEE DR17 and GALAH DR3, to infer parameters for over 17,000 RGs. We use the code PARAM to homogeneously infer stellar properties considering in detail the sensitivity of our results to different choices of observational constraints. We focus on age estimation, identifying potentially unreliable age determinations, and highlight stars with unreliable $\Delta\nu$ measurements based on comparisons using Gaia luminosities. These are particularly relevant in K2 data due to the short duration of the observations of each campaign, and therefore important to characterise for Galactic archaeology studies where the spatial range of K2 is a benefit. Thanks to the combination of data from different missions we explore trends in age, mass, and orbital parameters such as $R_\mathrm{g}$ and $Z_\mathrm{max}$, and examine time-resolved [$\alpha$/M]-[Fe/H] planes across different Galactic regions. Additionally, we compare age distributions in low- and high-$\alpha$ populations and chemically selected ex situ stars. The study also extends known mass-[C/N] ratio relationships to lower masses. The catalogues resulting from this work will be instrumental in addressing key questions in Galactic archaeology and stellar evolution, and to improve training sets for machine-learning-based age estimations.