Building up the Stellar Halo of the Galaxy

We study numerical simulations of satellite galaxy disruption in a potential resembling that of the Milky Way. Our goal is to assess whether a merger origin for the stellar halo would leave observable fossil structure in the phase-space distribution of nearby stars. We show how mixing of disrupted satellites can be quantified using a coarse-grained entropy. Although after 10 Gyr few obvious asymmetries remain in the distribution of particles in configuration space, strong correlations are still present in velocity space. We give a simple analytic description of these effects, based on a linearised treatment in action-angle variables, which shows how the kinematic and density structure of the debris stream changes with time. By applying this description we find that a single satellite of current luminosity 10^8 L_\sun disrupted 10 Gyr ago from an orbit circulating in the inner halo (mean apocentre $\sim 12$ kpc) would contribute about $\sim 30$ kinematically cold streams with internal velocity dispersions below 5 km/s to the local stellar halo. If the whole stellar halo were built by disrupted satellites, it should consist locally of 300 - 500 such streams. Clear detection of all these structures would require a sample of a few thousand stars with 3-D velocities accurate to better than 5 km/s. Even with velocity errors several times worse than this, the expected clumpiness should be quite evident. We apply our formalism to a group of stars detected near the North Galactic Pole, and derive an order of magnitude estimate for the initial properties of the progenitor system.Comment: 28 pages, 10 figures, minor changes, matches the version to appear in MNRAS, Vol. 307, p.495-517 (August 1999