The power of co-ordinate transformations in dynamical interpretations of Galactic structure

TL;DR

This paper explores how coordinate transformations to actions and angles affect the interpretation of galactic structures in Gaia data, emphasizing the importance of correct frame choice for understanding stellar dynamics.

Contribution

It demonstrates that features in the Milky Way's structure, previously attributed to spiral arms, are actually known kinematic groups, highlighting the significance of coordinate choices in galactic analysis.

Findings

Features in Gaia data are kinematic moving groups, not spiral structures.

Transformations to action-angle coordinates can enhance the visibility of certain velocity waves.

Simulations show transient spiral structures can reproduce observed velocity patterns.

Abstract

$Gaia$ DR2 has provided an unprecedented wealth of information about the positions and motions of stars in our Galaxy, and has highlighted the degree of disequilibria in the disc. As we collect data over a wider area of the disc it becomes increasingly appealing to start analysing stellar actions and angles, which specifically label orbit space, instead of their current phase space location. Conceptually, while $\bar{x}$ and $\bar{v}$ tell us about the potential and local interactions, grouping in action puts together stars that have similar frequencies and hence similar responses to dynamical effects occurring over several orbits. Grouping in actions and angles refines this further to isolate stars which are travelling together through space and hence have shared histories. Mixing these coordinate systems can confuse the interpretation. For example, it has been suggested that by moving stars to their guiding radius, the Milky Way spiral structure is visible as ridge-like overdensities in the $Gaia$ data \citep{Khoperskov+19b}. However, in this work, we show that these features are in fact the known kinematic moving groups, both in the $L_z-\phi$ and the $v_{\mathrm{R}}-v_{\phi}$ planes. Using simulations we show how this distinction will become even more important as we move to a global view of the Milky Way. As an example, we show that the radial velocity wave seen in the Galactic disc in $Gaia$ and APOGEE should become stronger in the action-angle frame, and that it can be reproduced by transient spiral structure.