Quantifying Kinematic Substructure in the Milky Way's Stellar Halo
  We present and analyze the positions, distances, and radial velocities for
over 4000 blue horizontal-branch (BHB) stars in the Milky Way's halo, drawn
from SDSS DR8. We search for position-velocity substructure in these data, a
signature of the hierarchical assembly of the stellar halo. Using a cumulative
"close pair distribution" (CPD) as a statistic in the 4-dimensional space of
sky position, distance, and velocity, we quantify the presence of
position-velocity substructure at high statistical significance among the BHB
stars: pairs of BHB stars that are close in position on the sky tend to have
more similar distances and radial velocities compared to a random sampling of
these overall distributions. We make analogous mock-observations of 11
numerical halo formation simulations, in which the stellar halo is entirely
composed of disrupted satellite debris, and find a level of substructure
comparable to that seen in the actually observed BHB star sample. This result
quantitatively confirms the hierarchical build-up of the stellar halo through a
signature in phase (position-velocity) space. In detail, the structure present
in the BHB stars is somewhat less prominent than that seen in most simulated
halos, quite possibly because BHB stars represent an older sub-population. BHB
stars located beyond 20 kpc from the Galactic center exhibit stronger
substructure than at $\rm r_{gc} < 20$ kpc.
