ABSTRACT
Using the motion of accreting particles on to haloes in cosmological N-body simulations, we study the radial phase-space structures of cold dark matter (CDM) haloes. In CDM cosmology, formation of virialized haloes generically produces radial caustics, followed by multistream flows of accreted dark matter inside the haloes. In particular, the radius of the outermost caustic called the splashback radius exhibits a sharp drop in the slope of the density profile. Here, we focus on the multistream structure of CDM haloes inside the splashback radius. To analyse this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting on to the haloes, we count their number of apocentre passages, which is then used to reveal the multistream flows of the dark matter particles. The resultant multistream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim \!30{{\ \rm per\ cent}}$ of the simulated haloes satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterize physical properties of the haloes, including the mass accretion rate and the size of the outermost caustic (i.e. the splashback radius). We discuss in detail the correlation of these fitting parameters and other measures directly extracted from the N-body simulation.
On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions