Gravitational Collapse in One Dimension

TL;DR

This paper uses high-precision simulations to study one-dimensional gravitational collapse, revealing a universal density profile with a specific power-law slope and demonstrating how initial conditions influence the final state.

Contribution

It introduces detailed 1D simulations of gravitational collapse, showing the emergence of a universal density profile and the effects of initial conditions on the final equilibrium state.

Findings

Final density profile has a power-law slope of approximately 0.47.

Warming initial conditions leads to a core rather than a power-law profile.

Cold power-law initial conditions with steeper slopes retain their initial profile in the final state.

Abstract

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos 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 behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 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 {\gamma}_i > {\gamma}_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior 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.