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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&#39;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 &#34;close pair distribution&#34; (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.