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

The currently favored cosmological paradigm suggests that galaxies form hierarchically through the accretion of numerous satellite subhalos. Since these satellites are much less massive than the host halo, they only 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 galaxy evolves. In this paper, we identify accreted satellites in three Milky Way like disk galaxies from the cosmological hydrodynamical FIRE-2 simulations by tracking subhalos through multiple 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 snapshot at z=0. We then define several metrics to quantify the success of the clustering algorithm and use these metrics to show that the satellites that were accreted less than 7 Gyr ago and had total masses at the time of accretion 10⁹M⊙ are well recovered by Enlink. The groups found by Enlink are more likely to correspond to a real (accreted) satellite if they have high values of significance, a quantity that measures the density of the group relative to the background, that does not depend on knowledge of properties of the accreted satellites. Since cosmological simulations predict that most stellar halos have a population of in situ stars, we test the ability of Enlink to recover satellites when the sample is contaminated by between 10-50% of in situ star particles, and show that most of the satellites well-identified by Enlink in the absence of in situ stars, stay well-identified even with 50% contamination. In this study we do not use information on the chemical abundances/metallicities of stars. In the future, the inclusion of these quantities can help to determine the masses of individual satellites (through the mass-metallicity relationship) and hence action-space clustering can be used to determine the number of accreted satellites per unit mass N(M), a parameter which is a sensitive probe of the type of dark matter.