Dark halo mergers and the formation of a universal profile

Abstract

We argue that a universal density profile for dark matter halos arises as a natural consequence of hierarchical structure formation. It is a fixed point in the process of repeated mergers. We present analytic and numerical arguments for the emergence of a particular form of the profile. At small radii, the density should vary as $r^{-\alpha}$, with $\alpha$ determined by the way the characteristic density of halos scales with their mass. If small halos are dense, then $\alpha$ is large. The mass-density relation can be related to the power spectrum of initial fluctuations, $P(k)$, through `formation time' arguments. Early structure formation leads to steep cusps. For $P(k)\sim k^n$ we find $\alpha\simeq 3(3+n)/(5+n)$. The universal profile is generated by tidal stripping of small halos as they merge with larger objects.