Violent relaxation in hierarchical clustering

The term ``violent relaxation'' was coined by Donald Lynden-Bell as a memorable oxymoron describing how a stellar dynamical system relaxes from a chaotic initial state to a quasi-equilibrium. His analysis showed that this process is rapid, even for systems with many stars, and that it leads to equilibria which may plausibly be related to bounded isothermal spheres. I review how numerical simulations have improved our understanding of violent relaxation over the last thirty years. It is clear that the process leads to equilibria which depend strongly on the initial state, but which nevertheless have certain common features. A particularly interesting case concerns objects formed in an expanding universe through dissipationless hierarchical clustering from gaussian initial conditions; these may correspond to galaxy clusters or to the dark halos of galaxies. While such objects display a wide range of shapes and spins, the distributions of these properties depend only weakly on the cosmological context and on the initial spectrum of density fluctuations. Halo density profiles appear to have a universal form with a singular central structure and a characteristic density which depends only on formation epoch. Low mass halos typically have earlier formation times and thus higher characteristic densities than high mass halos