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Relaxation in a Fuzzy Dark Matter Halo. II. Self-consistent kinetic equations
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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.
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Bracketing the soliton-halo relation of ultralight dark matter
Numerical simulations and analytic equivalences show that the soliton-halo relation for ultralight dark matter is bracketed by the 1/2 relation as a lower bound and the 1/3 relation as an upper bound.
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