Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

TL;DR

This paper develops a novel post-collapse Lagrangian perturbation theory to analytically study the dynamics of initially cold, self-gravitating systems in one dimension, providing insights into their collapse behavior and density profiles.

Contribution

It introduces a new iterative approach to model the post-collapse evolution of cold systems, bridging analytical predictions with numerical simulations.

Findings

The theory explains the near power-law density profiles observed in simulations.

Numerical simulations confirm the analytical predictions of the system's evolution.

Speculative suggestion of a small flat core forming at late times.

Abstract

We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long term behavior of the system, i.e. after many crossing times, it explains the close to power-law behavior of the projected density observed in numerical simulations. Pushing the model at late time suggests that the system could build at some point a very small flat core, but this is very speculative. This analysis shows that understanding the dynamics of initially cold systems requires a fine grained approach for a correct description of their very central part. The analyses performed here can certainly be extended to spherical symmetry.