# The status of isochrony in the formation and evolution of self-gravitating systems

## TL;DR

This paper investigates the role of isochrony in the formation and evolution of self-gravitating systems, proposing new theoretical characterizations and analyzing their relevance to the quasi-equilibrium states post-relaxation.

## Contribution

It introduces new fundamental results and characterizations of isochrony, challenging existing paradigms about the relaxation states of self-gravitating systems.

## Key findings

- Isochrone models better reproduce post-relaxation quasi-equilibrium states.
- The traditional lowered isothermal sphere paradigm fails to match isochrone model results.
- New theoretical characterizations of isochrony are proposed and analyzed.

## Abstract

In the potential theory, isochrony was introduced by Michel H\'enon in 1959 to characterize astrophysical observations of some globular clusters. Today, Michel Henon's isochrone potential is mainly used for his integrable property in numerical simulations, but is generally not really known. In a recent paper [29], we have presented new fundamental and theoretical results about isochrony that have particular importance in self-gravitating dynamics and which are detailed in this paper. In particular, new characterization of the isochrone state has been proposed which are investigated in order to analyze the product of the fast relaxation of a self-gravitating system. The general paradigm consists in considering that this product is a lowered isothermal sphere (King Model). By a detailed numerical study we show that this paradigm fails when the isochrone model succeeds in reproducing the quasi-equilibrium state obtained just after fast relaxation.