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.
