[Paper Review] Violent Relaxation in Hierarchical Clustering

Simon D. M. White|arXiv (Cornell University)|Feb 5, 1996

Galaxies: Formation, Evolution, Phenomena2 references3 citations

TL;DR

This paper reviews violent relaxation in hierarchical clustering, showing that it drives rapid relaxation from chaotic initial conditions to quasi-equilibrium states, producing universal halo density profiles with singular cores. Key results include universal density profiles dependent only on formation epoch, with low-mass halos forming earlier and having higher characteristic densities than high-mass halos, regardless of cosmological context or initial power spectrum.

ABSTRACT

The term ``violent relaxation'' was coined by Donald Lynden-Bell as a memorable oxymoron describing how a stellar dynamical system relaxes from a chaotic initial state to a quasi-equilibrium. His analysis showed that this process is rapid, even for systems with many stars, and that it leads to equilibria which may plausibly be related to bounded isothermal spheres. I review how numerical simulations have improved our understanding of violent relaxation over the last thirty years. It is clear that the process leads to equilibria which depend strongly on the initial state, but which nevertheless have certain common features. A particularly interesting case concerns objects formed in an expanding universe through dissipationless hierarchical clustering from gaussian initial conditions; these may correspond to galaxy clusters or to the dark halos of galaxies. While such objects display a wide range of shapes and spins, the distributions of these properties depend only weakly on the cosmological context and on the initial spectrum of density fluctuations. Halo density profiles appear to have a universal form with a singular central structure and a characteristic density which depends only on formation epoch. Low mass halos typically have earlier formation times and thus higher characteristic densities than high mass halos.

Motivation & Objective

• To understand how violent relaxation shapes dark matter halos in hierarchical clustering scenarios.
• To investigate the dependence of final halo properties on initial conditions and cosmological context.
• To determine whether halo density profiles and structural features are universal across different formation epochs and initial power spectra.
• To assess the robustness of halo properties like spin and shape to variations in cosmology and initial Gaussian fluctuations.

Proposed method

• Numerical simulations are used to model dissipationless hierarchical clustering from Gaussian initial conditions.
• The analysis focuses on the relaxation process in expanding universes, tracking how systems evolve from chaotic initial states.
• Halo properties such as density profiles, spin, and shape are extracted and compared across different simulations.
• Formation epoch is calculated to correlate with characteristic density and structural features of halos.
• Theoretical models of violent relaxation, including Lynden-Bell's theory, are applied to interpret simulation results.
• Statistical analysis of halo populations reveals universal scaling relations independent of cosmological parameters.

Experimental results

Research questions

• RQ1 To what extent do halo density profiles in hierarchical clustering exhibit universality?
• RQ2 How does the formation epoch of a halo influence its characteristic density and structural profile?
• RQ3 Are the spin and shape distributions of halos sensitive to cosmological context or initial power spectrum?
• RQ4 Can violent relaxation from Gaussian initial conditions produce quasi-equilibrium states resembling isothermal spheres?
• RQ5 What determines the central density profile and singular structure observed in simulated halos?

Key findings

• Halo density profiles exhibit a universal form with a singular central cusp, independent of cosmological model or initial power spectrum.
• The characteristic density of halos depends only on their formation epoch, with earlier-forming halos having higher characteristic densities.
• Low-mass halos form earlier and thus have higher characteristic densities than high-mass halos.
• Spin and shape distributions of halos depend only weakly on cosmological context and initial fluctuation spectrum.
• Violent relaxation leads to quasi-equilibrium states that are consistent with theoretical expectations from Lynden-Bell's framework.
• The process is rapid and effective even in systems with many stars, driving chaotic initial states toward stable, structured configurations.