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.
