Dark halo mergers and the formation of a universal profile

We argue that a universal density profile for dark matter haloes 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 central cusp profile. At small radii, the density should vary as r(-alpha), with cr determined by the way in which the characteristic density of haloes scales with their mass. if small haloes 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) similar to k(n) we find alpha similar or equal to 3(3 + n)/(5 + n). The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.