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Hierarchical Formation of Dark Matter Halos and the Free Streaming Scale

The smallest dark matter halos are formed first in the early universe. According to recent studies, the central density cusp is much steeper in these halos than in larger halos and scales as $ρ\propto r^{-(1.5-1.3)}$. We present results of very large cosmological $N$-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. We confirmed early studies that the inner density cusps are steeper in halos at the free streaming scale. The cusp slope gradually becomes shallower as the halo mass increases. The slope of halos 50 times more massive than the smallest halo is approximately $-1.3$. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the free streaming scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be $60-70$, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Microhalos could still exist in the present universe with the same steep density profiles.