Evolution of action-space coherence in a Milky Way-like simulation

TL;DR

This work investigates whether stellar birth clusters leave enduring imprints in action space within a realistic, time-dependent Milky Way–like disc by using a high-resolution MHD simulation. It develops a rigorous method to quantify action-space coherence for coeval star pairs, showing that close pairs preserve correlated actions for up to ~0.5 Gyr, with vertical actions decohering on sub-kpc scales and radial/azimuthal actions on kpc scales. A probabilistic inference framework then maps present-day action distributions of observed moving groups to their birth sizes, applied to 438 Gaia-based streams, revealing a dichotomy between compact, cluster-origin streams and resonant or dynamically induced structures. The results provide a concrete calibration for co-natal tagging and a scalable approach to leveraging Gaia DR4 data, with caveats regarding membership completeness and model assumptions that can be mitigated with future refinements and more detailed Galactic perturbation modeling.

Abstract

Efforts to dynamically trace stars back to the now-dissolved clusters in which they formed rely implicitly on the assumption that stellar orbital actions are conserved. While this holds in a static, axisymmetric potential, it is unknown how strongly the time-varying, non-axisymmetric structure of a real galactic disk drives action drift that inhibits cluster reconstruction. We answer this question using a high-resolution magnetohydrodynamic simulation of a Milky Way-like spiral disc galaxy. We show that, while stars experience significant action evolution over $\lesssim 100$ Myr, they do so in a correlated fashion whereby stars born in close proximity maintain very similar actions for up to 0.5 Gyr. The degree of coherence shows no significant dependence on galactocentric radius, but varies between action components: vertical actions decohere for stars born more than a few hundred parsecs apart (likely due to giant molecular clouds), while radial and azimuthal actions remain correlated on kiloparsec scales (likely influenced by spiral arms). We use our measurements of the rate of action decoherence to develop a probabilistic framework that lets us infer the initial sizes of the star cluster progenitors of present-day stellar streams from their measured action distributions, which we apply to 438 known moving groups. Our results suggest that most of these streams likely originated from compact clusters, but that a significant minority are instead likely to be resonant or dynamically induced structures. This method of classifying streams complements existing methods, optimises the use of expensive spectroscopic abundance measurements, and will be enhanced by the more precise kinematic data that will soon become available from \textit{Gaia} DR4.

Figures (14)

• Figure 1: The distribution of 5th nearest neighbour distances $d_5$ for coeval stars at different ages (shown in the legend). We show the 30 pc limit that we use to separate cluster stars from dispersed stars as the red dashed vertical line.
• Figure 2: Median of absolute change in action difference (row-wise in order: $\delta_{\text{abs}}\Delta J_R, \delta_{\text{abs}}\Delta J_z$ and $\delta_{\text{abs}}\Delta J_{\phi}$) versus time for coeval pairs of stars binned by stellar separation at birth; birth distance bins are indicated by colour, as shown in the legend. For comparison, the blue dashed line shows the change in the action of single stars relative to their own initial actions as a function of age gap; this result is taken from from arunima2025. As expected, for stars both at large separations (lighter-coloured solid lines) the actions change in essentially uncorrelated ways, so the changes in action between pairs of stars are similar to the changes for individual stars (blue dashed line), but stars born close together (darker solid lines) change their actions in correlated ways, and so the relative change in action for pairs of stars is much smaller than the change in actions for single stars.
• Figure 3: Same as \ref{['fig:abs_change']}, but now showing changes in relative action $\delta_\mathrm{rel}\Delta J_{R,z,\phi}$ rather than absolute action $\delta_\mathrm{abs}\Delta J_{R,z,\phi}$.
• Figure 4: Median of relative change in action difference (row-wise in order: $\delta_{\text{rel}}\Delta J_R, \delta_{\text{rel}}\Delta J_z$ and $\delta_{\text{rel}}\Delta J_{\phi}$ in order) for coeval pairs of stars in time with their birth distances in the 0.5 -- 2 pc bin. The darker blues represent higher radii. The red curve shows the median of the relative change in action differences for the entire dataset of pairs of coeval stars born within 0.5 -- 2 pc of each other.
• Figure 5: Relative action differences calculated for some of the observed moving groups (markers) placed on the theoretical grid of action-space evolution (coloured lines indicating different birth distance bins as shown in the legend). Rows from top to bottom show $\delta_\mathrm{rel}\Delta J_{R,z,\phi}$, respectively. Each point represents the median of the distribution $\{\delta\Delta J_\text{obs}\}$ and age of a moving group, with error bars showing the 16th and 84th percentiles. The lines are identical to those shown in \ref{['fig:rel_change']}, though we show only a subset here to minimise clutter.