DARK HALO MERGERS AND THE FORMATION OF A UNIVERSAL PROFILE

We argue that a universal density profile for dark matter haloes arise s 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(-al pha), with cr determined by the way in which the characteristic densit y of haloes scales with their mass. if small haloes are dense, then al pha is large. The mass-density relation can be related to the power sp ectrum of initial fluctuations, P(k), through 'formation time' argumen ts. Early structure formation leads to steep cusps. For P(k) similar t o k(n) we find alpha similar or equal to 3(3 + n)/(5 + n). The univers al profile is generated by tidal stripping of small haloes as they mer ge with larger objects.