The Assembly of the Virgo Cluster, Traced by its Galaxy Halos
  Kinematic studies have produced accurate measurements of the total dark
matter mass and mean dark matter density within the optical extent of galaxies,
for large samples of objects. Here we consider theoretical predictions for the
latter quantity, $\bar{\rho}_{dm}$, measured within the isophotal radius
$R_{23.5}$, for isolated halos with universal density profiles. Through a
combination of empirical scaling relations, we show that $\bar{\rho}_{dm}$ is
expected to depend weakly on halo mass and strongly on redshift. When galaxy
halos fall into larger groups or clusters they become tidally stripped,
reducing their total dark matter mass, but this process is expected to preserve
central density until an object is close to disruption. We confirm this with
collisonless simulations of cluster formation, finding that subhalos have
values of $\bar{\rho}_{dm}$ close to the analytic predictions. This suggests
that $\bar{\rho}_{dm}$ may be a useful indicator of infall redshift onto the
cluster. We test this hypothesis with data from the SHIVir survey, which covers
a reasonable fraction of the Virgo cluster. We find that galaxies with high
$\bar{\rho}_{dm}$ do indeed trace the densest regions of the cluster, with a
few notable exceptions. Samples selected by environment have higher densities
at a significance of 3.5-4$\sigma$, while samples selected by density are more
clustered at 3-3.5$\sigma$ significance. We conclude that halo density can be a
powerful tracer of the assembly history of clusters and their member galaxies.
