Landau equation for self-gravitating classical and quantum particles: Application to dark matter

Abstract

We develop the kinetic theory of classical and quantum particles (fermions and bosons) in gravitational interaction. The kinetic theory of quantum particles may have applications in the context of dark matter. For simplicity, we consider an infinite and spatially homogeneous system (or make a local approximation) and neglect collective effects. This leads to the quantum Landau equation derived heuristically in [Chavanis, Physica A 332, 89 (2004)]. We establish its main properties: conservation laws, $H$-theorem, equilibrium state, relaxation time, quantum diffusion and friction coefficients, quantum Rosenbluth potentials, self-consistent evolution, (thermal) bath approximation, quantum Fokker-Planck equation, quantum King model... For bosonic particles, the Landau equation can describe the process of Bose-Einstein condensation. We discuss the relation of our study with the works of [Levkov et al., Phys. Rev. Lett. 121, 151301 (2018); Bar-Or et al., Astrophys. J. 871, 28 (2019)] on fuzzy dark matter halos and the formation of Bose stars and solitons.

References in corpus (50)

• The Structure of Cold Dark Matter Halos
• Observational evidence for self-interacting cold dark matter
• Axion Cosmology
• Cold and Fuzzy Dark Matter
• Ultralight scalars as cosmological dark matter
• The Structure of Dark Matter Haloes in Dwarf Galaxies
• Cosmic Structure as the Quantum Interference of a Coherent Dark Wave
• Non Linear Kinetics underlying Generalized Statistics
• Understanding the Core-Halo Relation of Quantum Wave Dark Matter, $\psi$DM, from 3D Simulations
• Formation of Solitonic Stars Through Gravitational Cooling
• Galaxy Formation with BECDM: I. Turbulence and relaxation of idealised haloes
• Simulations of solitonic core mergers in ultra-light axion dark matter cosmologies
• Gravitational Bose-Einstein condensation in the kinetic regime
• Self-Interacting Dark Matter Halos and the Gravothermal Catastrophe
• Formation and structure of ultralight bosonic dark matter halos
• Strong Constraints on Fuzzy Dark Matter from Ultrafaint Dwarf Galaxy Eridanus II
• Evolution of the Schrödinger--Newton system for a self--gravitating scalar field
• A Review on the Scalar Field/ Bose-Einstein Condensate Dark Matter Model
• Gravitational cooling of self-gravitating Bose-Condensates
• Galactic Rotation Curves vs. Ultra-Light Dark Matter: Implications of the Soliton -- Host Halo Relation
• Relativistic axions from collapsing Bose stars
• First star-forming structures in fuzzy cosmic filaments
• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• Thermodynamics of self-gravitating systems
• Relaxation in a Fuzzy Dark Matter Halo
• Formation and mass growth of axion stars in axion miniclusters
• On the Schrodinger-Poisson--Vlasov-Poisson correspondence
• Collapse of a self-gravitating Bose-Einstein condensate with attractive self-interaction
• Galaxy Formation with BECDM -- II. Cosmic Filaments and First Galaxies
• AxioNyx: Simulating Mixed Fuzzy and Cold Dark Matter
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Generalized thermodynamics and kinetic equations: Boltzmann, Landau, Kramers and Smoluchowski
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Models of dark matter halos based on statistical mechanics: II. The fermionic King model
• Baryon-driven growth of solitonic cores in fuzzy dark matter halos
• A predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere
• Models of dark matter halos based on statistical mechanics: I. The classical King model
• BEC dark matter, Zeldovich approximation and generalized Burgers equation
• Relaxation times for Bose-Einstein condensation in axion miniclusters
• Logotropic distributions
• The effect of fluctuating fuzzy axion haloes on stellar dynamics: a stochastic model
• Dynamics of the Bose-Einstein condensation: analogy with the collapse dynamics of a classical self-gravitating Brownian gas
• Hamiltonian and Brownian systems with long-range interactions: IV. General kinetic equations from the quasilinear theory
• Statistical mechanics of self-gravitating systems in general relativity: I. The quantum Fermi gas
• Finding new signature effects on galactic dynamics to constrain Bose-Einstein-condensed cold dark matter
• Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method
• Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems
• Generalized Euler, Smoluchowski and Schrödinger equations admitting self-similar solutions with a Tsallis invariant profile
• Quantum tunneling rate of dilute axion stars close to the maximum mass
• Escape of stars from gravitational clusters in the Chandrasekhar model

Cited by in corpus (19)

• Boson Stars and Oscillatons: A Review
• On the Random Motion of Nuclear Objects in a Fuzzy Dark Matter Halo
• Dynamical Friction in fuzzy dark matter: circular orbits
• Kinetic relaxation and Bose-star formation in multicomponent dark matter- I
• On the Dynamical Heating of Dwarf Galaxies in a Fuzzy Dark Matter Halo
• Assessing the Fornax globular cluster timing problem in different models of dark matter
• Structure, Kinematics, and Observability of the Large Magellanic Cloud's Dynamical Friction Wake in Cold vs. Fuzzy Dark Matter
• Adiabatically compressed wave dark matter halo and intermediate-mass ratio inspirals
• Kinetic relaxation and nucleation of Bose stars in self-interacting wave dark matter
• Kinetic theory of collisionless relaxation for systems with long-range interactions
• Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere
• Can ultralight dark matter explain the age-velocity dispersion relation of the Milky Way disc: A revised and improved treatment
• A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
• Galactic Rotation Curves of LSB Galaxies using core-halo FDM configurations
• A new logotropic model based on a complex scalar field with a logarithmic potential
• Bracketing the soliton-halo relation of ultralight dark matter
• Fuzzy dark matter simulations
• Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation
• Self-similar kinetics for gravitational Bose-Einstein condensation