Using Action Space Clustering to Constrain the Accretion History of Milky Way like Galaxies

In the currently favored cosmological paradigm galaxies form hierarchically through the accretion of numerous satellite galaxies. Since the satellites are much less massive than the host halo, they occupy a small fraction of the volume in action space defined by the potential of the host halo. Since actions are conserved when the potential of the host halo changes adiabatically, stars from an accreted satellite are expected to remain clustered in action space as the host halo evolves. In this paper, we identify accreted satellites in three Milky Way like disk galaxies from the cosmological baryonic FIRE-2 simulations by tracking satellite galaxies through simulation snapshots. We then try to recover these satellites by applying the cluster analysis algorithm Enlink to the orbital actions of accreted star particles in the present-day snapshot. We define several metrics to quantify the success of the clustering algorithm and use these metrics to identify well-recovered and poorly-recovered satellites. We plot these satellites in the infall time-progenitor mass (or stellar mass) space, and determine the boundaries between the well-recovered and poorly-recovered satellites in these two spaces with classification tree method. The groups found by Enlink are more likely to correspond to a real satellite if they have high significance, a quantity assigned by Enlink. Since cosmological simulations predict that most stellar halos have a population of insitu stars, we test the ability of Enlink to recover satellites when the sample is contaminated by 10-50% of insitu star particles, and show that most of the satellites well-recovered by Enlink in the absence of insitu stars, stay well-recovered even with 50% contamination. We thus expect that, in the future, cluster analysis in action space will be useful in upcoming data sets (e.g. Gaia) for identifying accreted satellites in the Milky Way.