Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent Kinetic Equations

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