Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems

Abstract

General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding particles and their self-consistent dressing by collective gravitational interactions. The associated Fokker-Planck equation is shown to be fully consistent with the corresponding inhomogeneous Balescu-Lenard equation and, in the weak self-gravitating limit, to the inhomogeneous Landau equation. Hence it provides an alternative derivation to both and demonstrates their equivalence. The corresponding stochastic Langevin equations are presented: they can be a practical alternative to numerically solving the inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism allows for a self-consistent description of the secular evolution of different populations covering a spectrum of masses, with a proper accounting of the induced secular mass segregation, which should be of interest to various astrophysical contexts, from galactic centers to protostellar discs.

27 pages, 1 figure

References in corpus (19)

• On Landau damping
• Resonant Relaxation in Stellar Systems
• Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations
• Spiral Instabilities in N-body Simulations I: Emergence from Noise
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Dynamical phase transitions in long-range Hamiltonian systems and Tsallis distributions with a time-dependent index
• Secular diffusion in discrete self-gravitating tepid discs II: accounting for swing amplification via the matrix method
• Noise-driven evolution in stellar systems: Theory
• Kinetic theory with angle-action variables
• Hamiltonian and Brownian systems with long-range interactions: IV. General kinetic equations from the quasilinear theory
• Dynamical flows through Dark Matter Haloes: Inner perturbative dynamics, secular evolution, and applications
• Kinetic theory of nonequilibrium stochastic long-range systems: Phase transition and bistability
• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs
• The secular evolution of discrete quasi-Keplerian systems. I. Kinetic theory of stellar clusters near black holes
• Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit
• Stellar Dynamics around a Massive Black Hole III: Resonant Relaxation of Axisymmetric Discs
• Numerical tests of dynamical friction in gravitational inhomogeneous systems

Cited by in corpus (10)

• Landau equation for self-gravitating classical and quantum particles: Application to dark matter
• A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy
• Box/peanut-shaped bulges in action space
• Relaxation in self-gravitating systems
• A simple, heuristic derivation of the Balescu-Lenard kinetic equation for stellar systems
• Origin of reduced dynamical friction by dark matter halos with net prograde rotation
• The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole
• A disturbance in the force. How force fluctuations hinder dynamical friction and induce core stalling
• Resonant Dynamical Friction in Nuclear Star Clusters: Rapid Alignment of an Intermediate-mass Black Hole with a Stellar Disk
• The status of isochrony in the formation and evolution of self-gravitating systems