Multi-stream radial structure of cold dark matter haloes from particle trajectories: deep inside splashback radius

By tracking trajectories of dark matter (DM) particles accreting onto halos in cosmological $N$-body simulations, we investigate the radial phase-space distribution of cold dark matter (CDM) halos, paying a special attention to their inner regions deep inside the halo boundary called the splashback radius, where the particles undergo multi-stream flows. Extending and improving previous work by Sugiura et al., we classify DM particles inside haloes by the number of apocenter passages, $p$, and succeed to count it up to $p=40$ for each halo over a wide mass range. Quantifying in particular the radial density profile for particles having the same value of $p$, we find that it generally exhibits a double-power law feature, whose indices of inner and outer slopes are well-described by $-1$ and $-8$, respectively. The characteristic density and scale of their double-power law profiles are given as a simple fitting function of $p$, with a weak halo mass dependence. Interestingly, summing up these double-power law functions beyond $p=40$ gives a converged result, which closely matches the total density profile of simulated haloes. The double-power law nature is shown to be persistent and generic not only in mass-selected haloes but also in haloes selected in different criteria. Our results are compared with a class of self-similar solutions that describes the stationary and spherical accretion of DM, and found that even introducing a non-zero angular momentum fails to reproduce the radial multi-stream structure. The analysis with particle trajectories tracing back to higher redshifts suggests that the double-power law nature have been established during an early accretion phase and remain stable.