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 haloes in cosmological $N$-body simulations, we investigate the radial phase-space distribution of cold dark matter (CDM) haloes, paying attention to their inner regions deep inside the halo boundary called the splashback radius, where the particles undergo multi-stream flows. Improving the analysis by Sugiura et al., we classify DM particles by the number of apocenter passages, $p$, and count it up to $p=40$ for each halo over a wide mass range. Quantifying 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. Its characteristic scale and density are given as a simple fitting function of $p$, with a weak halo mass dependence. Interestingly, summing up these double-power law profiles beyond $p=40$ reproduces well the total density profile of simulated haloes. The double-power law nature is persistent and generic not only in mass-selected haloes but also in haloes selected in different criteria. Our results are compared with self-similar solutions that describe the stationary and spherical accretion of DM. We find that even when introducing a non-zero angular momentum, none of them explain the radial multi-stream structure. The analysis with particle trajectories tracing back to higher redshifts suggests that the double-power law nature has been established during an early accretion phase and remains stable.