Actions are weak stellar age indicators in the Milky Way disk

The orbital properties of stars in the disk are signatures of their formation, but they are also expected to change over time due to the dynamical evolution of the Galaxy. Stellar orbits can be quantified by three dynamical actions, J_r, L_z, and J_z, which provide measures of the orbital eccentricity, guiding radius, and non-planarity, respectively. Changes in these dynamical actions over time reflect the strength and efficiency of the evolutionary processes that drive stellar redistributions. We examine how dynamical actions of stars are correlated with their age using two samples of stars with well-determined ages: 78 solar twin stars (with ages to ~5%) and 4376 stars from the APOKASC2 sample (~20%). We compute actions using spectroscopic radial velocities from previous surveys and parallax and proper motion measurements from Gaia DR2. We find weak gradients in all actions with stellar age, of (7.51 +/- 0.52, -29.0 +/- 1.83, 1.54 +/- 0.18) kpc km/s/Gyr for J_r, L_z, and J_z, respectively. There is, however, significant scatter in the action-age relation. We caution that our results will be affected by the restricted spatial extent of our sample, particularly in the case of J_z. Nevertheless, these action-age gradients and their associated variances provide strong constraints on the efficiency of the mechanisms that drive the redistribution of stellar orbits over time and demonstrate that actions are informative as to stellar age. The shallow action-age gradients combined with the large dispersion in each action at a given age, however, renders the prospect of age inference from orbits of individual stars bleak. Using the precision measurements of [Fe/H] and [$\alpha$/Fe] for our stars we investigate the abundance-action relationship and find weak correlations. Similar to our stellar age results, dynamical actions afford little discriminating power between low- and high-$\alpha$ stars.