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

In the potential theory, isochrony was introduced by Michel Hénon in1959to characterize astrophysical observations of some globular clusters. Today, Michel Hénon's isochrone potential is mainly used for his integrable property in numerical simulations, but is generally not really known. In a recent paper (Simon-Petit, Perez & Duval2018), we have presented new fundamental and theoretical results about isochrony that have particular importance in self-gravitating dynamics and that are detailed in this paper. In particular, new characterization of the isochrone state has been proposed, which is investigated in order to analyse 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.