  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.
