THE STRUCTURE AND DYNAMICAL EVOLUTION OF DARK-MATTER HALOES

We use N-body simulations to investigate the structure and dynamical e volution of dark matter haloes in clusters of galaxies. Our sample con sists of nine massive haloes from an Einstein-De Sitter universe with scale-free power spectrum and spectral index n = - 1. Haloes are resol ved by 20 000 particles each, on average, and have a dynamical resolut ion of 20-25 kpc, as shown by extensive tests. Large-scale tidal field s are included up to a scale L = 150 Mpc using background particles. W e find that the halo formation process can be characterized by the alt ernation of two dynamical configurations: a merging phase and a relaxa tion phase, defined by their signature on the evolution of the total m ass and root mean square (rms) velocity. Haloes spend on average one-t hird of their evolution in the merging phase and two-thirds in the rel axation phase. Using this definition, we study the density profiles an d show how they change during the halo dynamical history. In particula r, we find that the average density profiles of our haloes are fitted by the Navarro, Frenk & White analytical model with an rms residual of 17 per cent between the virial radius R-v and 0.01R(v). The Hernquist analytical density profile fits the same haloes with an rms residual of 26 per cent. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey: compared wit h their results our haloes are more centrally concentrated, and the re lation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical ev olution within haloes and to fluctuations in the halo population. We a nalyse the dynamical equilibrium of our haloes using the Jeans equatio n, and find that on average they are approximately in equilibrium with in their virial radius. Finally, we find that the projected mass profi les of our simulated haloes are in very good agreement with the profil es of three rich galaxy clusters derived from strong and weak gravitat ional lensing observations.