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 cosmological N-body simulations, in combination with the GALFORM semi-analytic galaxy formation model. The stellar haloes in the these simulations, which form from disrupted satellites accreted between redshifts 1 and 7, show considerable scatter in the nature of their substructure. We find that our statistic can distinguish between these different realizations of plausible models for the global structure of the Milky Way stellar halo. We apply our statistic to a catalogue of blue horizontal branch stars identified in the Sloan Digital Sky Survey. In our Λ cold dark matter simulations, we find examples of haloes with spatial and kinematic substructure consistent with the available Milky Way data in the outer halo. For the inner halo, the models predict stronger clustering than observed, suggesting the existence of a smooth component, not currently included in our simulations.