Dynamical Friction in a Fuzzy Dark Matter Universe

Abstract: We present an in-depth exploration of the phenomenon of dynamical friction in a universe where the dark matter is composed entirely of so-called Fuzzy Dark Matter (FDM), ultralight bosons of mass $m\sim\mathcal{O}(10^{-22})\,$eV. We review the classical treatment of dynamical friction before presenting analytic results in the case of FDM for point masses, extended mass distributions, and FDM backgrounds with finite velocity dispersion. We then test these results against a large suite of fully non-linear simulations that allow us to assess the regime of applicability of the analytic results. We apply these results to a variety of astrophysical problems of interest, including infalling satellites in a galactic dark matter background, and determine that \emph{(1)}~for FDM masses $m\gtrsim 10^{-21}\, {\rm eV}\, c^{-2}$, the timing problem of the Fornax dwarf spheroidal's globular clusters is no longer solved and \emph{(2)}~the effects of FDM on the process of dynamical friction for satellites of total mass $M$ and relative velocity $v_{\rm rel}$ should require detailed numerical simulations for $\left(M/10^9~M_{\odot}\right) \left(m/10^{-22}~{\rm eV}\right)\left(100~{\rm km}~{\rm s}^{-1}/v_{\rm rel}\right) \sim 1$, parameters which would lie outside the validated range of applicability of any currently developed analytic theory, due to transient wave structures in the time-dependent regime.