A Two-Point Correlation Function For Galactic Halo Stars

We describe a correlation function statistic that quantifies the amount of spatial and kinematic substructure in the stellar halo. We test this statistic using model stellar halo realizations constructed from the Aquarius suite of six high-resolution N-body simulations in combination with the Galform semi-analytic galaxy formation model. These simulations show considerable scatter in the properties of stellar haloes. We find that our statistic can distinguish between these plausible alternatives for the global structure of the Milky Way stellar halo. We compare with observational data and show that pencil beam surveys of ~100 tracer stars (such as the Spaghetti Survey) are not sufficient to constrain the degree of structure in the Milky Way halo with this statistic. Larger area surveys with >1000 tracer stars (such as BHB stars in the Sloan Digital Sky Survey) provide much tighter constraints on comparisons between models and data. In our simulations, we find examples of haloes with spatial and kinematic substructure consistent with the available Milky Way data.