# Predicting Steady States of One-dimensional Collisionless Gravitating Systems

## TL;DR

This paper introduces a novel Hermite-Legendre analysis technique to determine steady states in one-dimensional collisionless gravitating systems, aiding understanding of their relaxation and implications for dark matter structures.

## Contribution

It presents a new method for identifying steady states and analyzing their stability, emphasizing the role of initial conditions in system evolution.

## Key findings

- Physically motivated parameter ranges for steady states identified.
- Any initial condition in the linear regime can be decomposed into unique modes.
- Steady states can be described by combinations of time-independent modes.

## Abstract

Building on the development of a Hermite-Legendre analysis of one-dimensional gravitating collisionless systems, we present a technique for determining the steady states of such systems. This provides an important component for understanding the physics involved in the relaxation of these kinds of systems. As the dark matter structures in the universe should have traits in common with these systems, insight into this relaxation can provide clues to larger astrophysical questions. For large perturbation strengths, we determine physically motivated parameter ranges for the simplest families of steady states as well as their stability. We also demonstrate that any set of initial conditions in the linear regime can be resolved into unique time-independent and time-dependent modes. Combinations of time-independent modes then describe the steady state of any system linearly perturbed from equilibrium. These results highlight the importance of initial conditions over relaxation mechanisms in the evolution of these systems.