Gravitational collapse in one dimension

Abstract

We simulate the evolution of one-dimensional gravitating collisionless systems from nonequilibrium initial conditions, similar to the conditions that lead to the formation of darkmatter haloes in three dimensions. As in the case of 3D halo formation, we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behaviour in density, ρ(x) ∝ |x|-γcrit, γ crit ~ 0.47, slightly but significantly shallower than the value γ = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent γi > γcrit, do not evolve towards the attractor but reach a final state that retains the original power-law behaviour in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.