# Dynamics to the universal structure of one-dimensional self-gravitating systems in the quasi-equilibrium state

## TL;DR

This paper explores the universal structure of one-dimensional self-gravitating systems in quasi-equilibrium, revealing conditions for universality, proposing a phenomenological model, and explaining the system's size determination.

## Contribution

It demonstrates that the null virial condition leads to universal density profiles and introduces a Langevin-based model to describe these structures.

## Key findings

- Universal density profile similar to higher-dimensional systems
- Null virial condition ensures universality
- A mechanism for system size determination

## Abstract

We investigate the quasi-equilibrium state of one-dimensional self-gravitating systems. If the null virial condition is satisfied at initial time, it is found that the number density around the center of the system at the quasi-equilibrium state has the universality similar to two- and three-dimensional self-gravitating systems reported in \cite{Tashiro16,Tashiro10}. The reason why the null virial condition is sufficient for the universality is unveiled by the envelope equation. We present a phenomenological model to describe the universal structure by using a special Langevin equation with a distinctive random noise to self-gravitating systems. Additionally, we unveil a mechanism which decides the radius of the system.