Relaxation in a Fuzzy Dark Matter Halo

Abstract

Dark matter may be composed of light bosons, m b ∼ 10 −22 eV, with a de Broglie wavelength λ ∼ 1 kpc in typical galactic potentials. Such "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 ( 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 ∼ 10 7 M ⊙ (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. * Hubble Fellow

Small-scale structure of fuzzy and axion-like dark matter

“…A similar lower bound on m is found from dynamical heating of stellar streams in the Milky Way [180]. Furthermore, [176] evaluated the competition of dynamical friction and gravitational heating on the inspiral of massive objects.…”

“…Wave interference produces density power spectra with correlations near the de Broglie wavelength and white noise characteristics on large scales. The diffusion coefficients, effective mass, and distribution functions that follow from evaluating the force fluctuations coincide with those from [176] (Eq. (83)) in the diffusion limit.…”

“…Bar-Or et al [176] provided a basis for the quasiparticle picture by explicitly deriving the diffusion coefficients for FDM relaxation and showing that they are identical to those for classical particles ([175]) if the classical particle mass and velocity distribution are replaced by…”

“…Consequently, the halo indeed behaves as if it were composed of quasiparticles that depend on the local density and velocity distribution. For example, a singular isothermal sphere with Maxwellian velocity distribution leads to the effective mass and de Broglie wavelength [176]:…”

“…with mass m t in an FDM halo lose energy (cool) by dynamical friction (backreaction of the object onto dark matter) proportional to m t and gain energy (heat up) by potential fluctuations produced by FDM proportional to m eff . If m t m eff , heating dominates and the heating timescale is approximately [176] τ heat 3σ…”