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.

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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