The direct detection of dark matter on Earth depends crucially on its density and its velocity distribution on a milliparsec scale. Conventional N-body simulations are unable to access this scale, making the development of other approaches necessary.
In this paper, we apply the method developed in Fantin et al. 2008 to a cosmologically-based merger tree, transforming it into a useful instrument to reproduce and analyse the merger history of a Milky Way-like system. The aim of the model is to investigate the implications of any ultra-fine structure for the current and next generation of directional dark matter detectors. We find that the velocity distribution of a Milky Way-like Galaxy is almost smooth, due to the overlap of many streams of particles generated by multiple mergers. Only the merger of a 10^10 Msun analyse can generate significant features in the ultra-local velocity distribution, detectable at the resolution attainable by current experiments.
Various laboratory-based experiments are underway attempting to detect dark matter directly. The event rates and detailed signals expected in these experiments depend on the dark matter phase space distribution on sub-milliparsec scales. These scales
are many orders of magnitude smaller than those that can be resolved by conventional N-body simulations, so one cannot hope to use such tools to investigate the effect of mergers in the history of the Milky Way on the detailed phase-space structure probed by the current experiments. In this paper we present an alternative approach to investigating the results of such mergers, by studying a simplified model for a merger of a sub-halo with a larger parent halo. With an appropriate choice of parent halo potential, the evolution of material from the sub-halo can be expressed analytically in action-angle variables, so it is possible to obtain its entire orbit history very rapidly without numerical integration. Furthermore by evolving backwards in time, we can obtain arbitrarily-high spatial resolution for the current velocity distribution at a fixed point. Although this model cannot provide a detailed quantitative comparison with the Milky Way, its properties are sufficiently generic that it offers qualitative insight into the expected structure arising from a merger at a resolution that cannot be approached with full numerical simulations. Preliminary results indicate that the velocity-space distribution of dark matter particles remains characterized by discrete and well-defined peaks over an extended period of time, both for single and multi-merging systems, in contrast to the simple smooth velocity distributions sometimes assumed in predicting laboratory experiment detection rates.
