Signatures of simulated spiral arms on radial actions

Spiral arms play a key role in the evolution of disc galaxies, defining their morphology, star formation, chemistry, and dynamics. Among their various implications, it has been observed in the Milky Way disc that the distribution of Gaia Data Release 3 (DR3) radial actions exhibits structures that might be related to the spiral arms. Our goal is to investigate the relationship between regions of low radial action identified in simulated discs and the location of the spiral arms, such as that suggested for the Galaxy in previous studies For a sample of 23 simulated spiral galaxies, we modelled the axisymmetric component of their gravitational potential to compute the radial action of their stellar particles using the Stäckel fudge. The spatial distribution of the radial action was then compared to the location of the spiral arms, identified as overdensities in the stellar surface density using a kernel density estimator. Our analysis reveals a strong correlation between the radial action distribution and the spiral arms in 18 of 23 simulated galaxies. However, notable discrepancies are observed in the remaining five, since they are profoundly out-of-equilibrium systems, such as galaxies influenced by external interactions or spiral arms still in the process of winding up. Additionally, spiral arms are consistently traced across young, intermediate, and old stellar populations (≥3 Gyr) in most simulations, suggesting that they are supported by stars spanning a broad age range. We have confirmed that, in general, there is a tendency for spatial correlation between spiral arms and stellar populations featuring low values of the radial action as discussed in the literature using Gaia DR3 data . However, discrepancies between features in the radial action distribution and the spiral structure can be interpreted as signatures of recent disturbances, a scenario applicable to the Milky Way. Furthermore, populations at least as old as $3$ Gyr trace the spiral arms with no significant misalignment across age bins, suggesting a possible theoretical interpretation of the observations obtained with Gaia data. A linear relation between the maximum value of the radial action of the spiral arms and the vertical scale-length is found, which is also satisfied by the Milky Way.