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 −α , with α determined by the way in which the characteristic density of haloes scales with their mass. If small haloes are dense, then α 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 ) ∼  k n we find α ≃ 3(3 +  n )/(5 +  n ). The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.