Identifying dark matter haloes by the caustic boundary

The dark matter density is formally infinite at the location of caustic surfaces, where dark matter sheet folds in phase space. The caustics are boundaries between the regions with different number of streams n(str)(x) in Eulerian space. Alternatively they can be defined as boundaries between the regions with different number of flip-flops n(ff)(q) in Lagrangian space. The number of flip-flops equals the amount of turns inside out experienced by a fluid element of a collision-less medium. Physically both definitions are equivalent but discreteness of numerical models may result in some distinctions. After n(str)(x) or n(ff)(q) field is numerically evaluated the identification of caustics becomes a purely geometrical procedure which is independent on any numerical parameters. Both approaches are used in identifying a compact closed caustic surface around potential halos in an idealized N-body simulation. The set of all caustics should be the same in both cases, but comparing n(str)(x) and n(ff)(q) is not straightforward because there is no simple relation between the number of streams and number of flip-flops. The halo boundary in this simulation is found to be neither spherical nor ellipsoidal nor oval but remarkably asymmetrical. However, a convex hull is a good approximation to the halo boundaries. The analysis of the kinetic and potential energies of individual particles and the halo as a whole concludes that it is gravitationally bound. In addition, the examination of the two-dimensional phase space confirms the above conclusion. The recent finding that common shells in a sample of halos obtained from the suite of large simulations are non-ellipsoidal ovals is quite encouraging for carrying out a more detailed analysis of this approach on higher resolution simulations.

Automated summary

The study examines the density distribution of dark matter at caustic surfaces and the corresponding geometrical features, as well as the methods and challenges in identifying caustics in numerical simulations. The halo boundary is found to be asymmetrical, but a convex hull is a good approximation. Analyses of kinetic and potential energies, as well as examination of the two-dimensional phase space, confirm that the halo is gravitationally bound. The discovery of non-ellipsoidal oval shapes in a sample of halos from large simulations shows promise for further detailed analysis on higher resolution simulations.