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Phase-space structure of cold dark matter halos inside splashback: multi-stream flows and self-similar solution

Using the motion of accreting particles onto halos in cosmological $N$-body simulations, we study the radial phase-space structures of cold dark matter (CDM) halos. In CDM cosmology, formation of virialized halos generically produces radial caustics, followed by multi-stream flows of accreted dark matter inside the halos. 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 multi-stream structure of CDM halos inside the splashback radius. To analyze this, we use and extend the SPARTA algorithm developed by Diemer. By tracking the particle trajectories accreting onto the halos, we count their number of apocenter passages, which is then used to reveal the multi-stream flows of the dark matter particles. The resultant multi-stream structure in radial phase space is compared with the prediction of the self-similar solution by Fillmore & Goldreich for each halo. We find that $\sim30\%$ of the simulated halos satisfy our criteria to be regarded as being well fitted to the self-similar solution. The fitting parameters in the self-similar solution characterizes physical properties of the halos, 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.