Relaxation in a Fuzzy Dark Matter Halo

Abstract

Dark matter may be composed of light bosons, , with a de Broglie wavelength 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 ( ). 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 in a galaxy with a constant circular speed of . 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.