The pairwise velocity difference of over 2000 BHB stars in the Milky Way halo

Models of hierarchical galaxy formation predict that the extended stellar halos of galaxies like our Milky Way show a great deal of sub-structure, arising from disrupted satellites. Spatial sub-structure is directly observed, and has been quantified, in the Milky Way's stellar halo. Phase-space conservation implies that there should be sub-structure in position-velocity space. Here, we aim to quantify such position-velocity sub-structure, using a state-of-the art data set having over 2000 blue horizontal branch (BHB) stars with photometry and spectroscopy from SDSS. For stars in dynamically cold streams (“young" streams), we expect that pairs of objects that are physically close also have similar velocities. Therefore, we apply the well-established “pairwise velocity difference" (PVD) statistic (Δr), where we expect to drop for small separations Δr. We calculate the PVD for the SDSS BHB sample and find (Δr) approx const., i.e. no such signal. By making mock-observations of the simulations by Bullock & Johnston and applying the same statistic, we show that for individual, dynamically young streams, or assemblages of such streams, drops for small distance separations Δr, as qualitatively expected. However, for a realistic complete set of halo streams, the pair-wise velocity difference shows no signal, as the simulated halos are dominated by “dynamically old" phase-mixed streams. Our findings imply that the sparse sampling and the sample sizes in SDSS DR6 are still insufficient to use the position-velocity sub-structure for a stringent quantitative data-model comparison. Therefore, alternate statistics must be explored and much more densely sampled surveys, dedicated to the structure of the Milky Way, such as LAMOST, are needed.