Relaxation in self-gravitating systems

Abstract

The long timescale evolution of a self-gravitating system is generically driven by two-body encounters. In many cases, the motion of the particles is primarily governed by the mean field potential. When this potential is integrable, particles move on nearly fixed orbits, which can be described in terms of angle-action variables. The mean field potential drives fast orbital motions (angles) whose associated orbits (actions) are adiabatically conserved on short dynamical timescales. The long-term stochastic evolution of the actions is driven by the potential fluctuations around the mean field and in particular by "resonant two-body encounters", for which the angular frequencies of two particles are in resonance. We show that the stochastic gravitational fluctuations acting on the particles can generically be described by a correlated Gaussian noise. Using this approach, the so-called $\eta$-formalism, we derive a diffusion equation for the actions in the test particle limit. We show that in the appropriate limits, this diffusion equation is equivalent to the inhomogeneous Balescu-Lenard and Landau equations. This approach provides a new view of the resonant diffusion processes associated with long-term orbital distortions. Finally, by investigating the example of the Hamiltonian Mean Field Model, we show how the present method generically allows for alternative calculations of the long-term diffusion coefficients in inhomogeneous systems.

28 pages, 3 figures, submitted to MNRAS

References in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• A numerical study of vector resonant relaxation
• Scalar Resonant Relaxation of Stars Around a Massive Black Hole
• The statistical mechanics of relativistic orbits around a massive black hole
• Revisiting relaxation in globular clusters
• Unstable Disk Galaxies. I. Modal Properties
• Isotropic-Nematic Phase Transitions in Gravitational Systems II: Higher Order Multipoles
• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems
• Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs
• Relativistic Stellar Dynamics Around a Massive Black Hole in Steady State

Cited by in corpus (21)

• Relaxation in a Fuzzy Dark Matter Halo
• A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy
• Box/peanut-shaped bulges in action space
• Vector Resonant Relaxation of Stars around a Massive Black Hole
• Dynamical Friction, Buoyancy and Core-Stalling -- I. A Non-perturbative Orbit-based Analysis
• The Thermodynamics of Rotating Black-Hole Star Clusters
• Resonant and non-resonant relaxation of globular clusters
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Violent relaxation in the Hamiltonian Mean Field model: I. Cold collapse and effective dissipation
• A simple, heuristic derivation of the Balescu-Lenard kinetic equation for stellar systems
• Long-term relaxation of $1D$ self-gravitating systems
• Orbital scattering by random interactions with extended substructures
• Black Hole Discs and Spheres in Galactic Nuclei -- Exploring the Landscape of Vector Resonant Relaxation Equilibria
• Linear response theory and damped modes of stellar clusters
• Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^2$ without collective effects
• Statistical Mechanics of Collisionless Orbits. V. The approach to equilibrium for idealized self-gravitating systems
• Gravitational Brownian motion as inhomogeneous diffusion: black hole populations in globular clusters
• On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives
• The NewHorizon Simulation -- To Bar Or Not To Bar
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect
• Resonant Dynamical Friction in Nuclear Star Clusters: Rapid Alignment of an Intermediate-mass Black Hole with a Stellar Disk