Relaxation in a Fuzzy Dark Matter Halo

Dark matter may be composed of light bosons, m(b) similar to 10(-22) eV, with a de. Broglie wavelength lambda similar to 1 kpc in typical galactic potentials. Such fuzzy dark matter (fuzzy dark matter (FDM)) behaves like cold dark matter (CDM) on much larger scales than the de. Broglie wavelength, but may resolve some of the challenges faced by CDM in explaining the properties of galaxies on small scales (less than or similar to 10 kpc). Because of its wave nature, FDM exhibits stochastic density fluctuations on the scale of the de. Broglie wavelength that never damp. The gravitational field from these fluctuations scatters stars and black holes, causing their orbits to diffuse through phase space. We show that this relaxation process can be analyzed quantitatively with the same tools used to analyze classical two-body relaxation in an N-body system, and can be described by treating the FDM fluctuations as quasiparticles, with effective mass similar to 10(7) M-circle dot (1 kpc/r)(2) (10(-22) eV/m(b))(3) in a galaxy with a constant circular speed of 200 km s(-1). This novel relaxation mechanism may stall the inspiral of supermassive black holes or globular clusters due to dynamical friction at radii of a few hundred parsecs and can heat and expand the central regions of galaxies. These processes can be used to constrain the mass of the light bosons that might comprise FDM.