Tomography of stellar halos: what does anisotropy in a stellar halo tell us?

The stellar halo of the Milky Way is known to have a highly lumpy structure due to the presence of tidal debris and streams accreted from the satellite galaxies. The abundance and distribution of these substructures can provide a wealth of information on the assembly history of the Milky Way. We use some information-theoretic measures to study the anisotropy in a set of Milky Way-sized stellar halos from the Bullock & Johnston suite of simulations that uses a hybrid approach coupling semi-analytic and N-body techniques. Our analysis shows that the whole-sky anisotropy in each stellar halo increases with the distance from its centre and eventually plateaus out beyond a certain radius. All the stellar halos have a very smooth structure within a radius of $\sim 50$ kpc and a highly anisotropic structure in the outskirts. At a given radius, the anisotropies at a fixed polar or azimuthal angle have two distinct components: (i) an approximately isotropic component and (ii) a component with large density fluctuations on small spatial scales. We remove the contributions of the substructures and any non-spherical shape of the halo by randomizing the polar and azimuthal coordinates of the stellar particles while keeping their radial distances fixed. We observe that the fluctuating part of the anisotropy is completely eliminated, and the approximately uniform component of the anisotropy is significantly reduced after the sphericalization. A comparison between the original halos and their sphericalized versions reveals that the approximately uniform part of the anisotropy originates from the discreteness noise and the non-spherical shape of the halo whereas the substructures contribute to the fluctuating part. We show that such distinction between the anisotropies has the potential to constrain the shape of the stellar halo and its substructures.