Universal multi-stream radial structures of cold dark matter halos

Virialized halos of cold dark matter generically exhibit multi-stream structures of accreted dark matter within an outermost radial caustic known as the splashback radius. By tracking the particle trajectories that accrete onto the halos in cosmological $N$-body simulations, we count their number of apocenter passages ($p$), and use them to characterize the multi-stream structure of dark matter particles. We find that the radial density profile for each stream, classified by the number of apocenter passages, exhibits universal features, and can be described by a double power-law function comprising inner shallow and outer steep slopes of indices of $-1$ and $-8$, respectively. Surprisingly, these properties hold over a wide range of halo masses. The double-power law feature is persistent when dividing the sample by concentration or accretion rate. The dependence of the characteristic scale and amplitude of the profile on $p$ cannot be replicated by known self-similar solutions, requiring consideration of complexities such as the distribution of angular momentum or mergers.