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 a , with a determined by the way in which the characteristic density of haloes scales with their mass. If small haloes are dense, then a is large. The mass-density relation can be related to the power spectrum of initial fluctuations, Pk, through 'formation time' arguments. Early structure formation leads to steep cusps. For Pk k n we find a 33 n=5 n. The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.