Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent kinetic equations

TL;DR

This paper derives and solves kinetic equations for fuzzy dark matter halos, revealing how density fluctuations induce relaxation similar to classical systems, and analyzes wave behavior in such halos.

Contribution

It introduces the FDM analog of the Fokker-Planck kinetic equation and provides solutions for velocity evolution and wave dispersion in FDM halos.

Findings

Derived the FDM kinetic equation analogous to Fokker-Planck.

Solved for velocity distribution evolution in FDM halos.

Determined dielectric function and wave dispersion relations.

Abstract

Fuzzy dark matter (FDM) is composed of ultra-light bosons having a de Broglie wavelength that is comparable to the size of the stellar component of galaxies at typical galactic velocities. FDM behaves like cold dark matter on large scales. However, on the scale of the de Broglie wavelength, an FDM halo exhibits density fluctuations that lead to relaxation, a process similar to the two-body relaxation that occurs in classical gravitational N-body systems and is described by the Fokker-Planck equation. We derive the FDM analog of that kinetic equation, and solve it to find the evolution of the velocity distribution in a spatially homogeneous FDM halo. We also determine the dielectric function and the dispersion relation for linear waves in an FDM halo.