Hydrostatic Equilibrium Constraints on the Fuzzy Dark Matter Mass from Dwarf Spheroidals: Method, Systematics, and Robustness

Abstract: We present the analysis of a non-parametric estimator of the fuzzy (wave) dark matter (FDM) boson mass based on local hydrostatic equilibrium: the classical gravitational acceleration must be balanced by the gradient of the quantum potential of the Schrödinger-Poisson-Madelung system. We apply this condition, without assuming a soliton or any other parametric profile, to the non-parametric density and enclosed mass posteriors from pyGravSphere of the nine Milky Way dwarf spheroidal (dSph) galaxies. For each posterior realization we solve, in a least squares sense over a fixed radial window, for the boson mass that best balances the two terms, which yields a posterior distribution of mass for each galaxy. The per galaxy medians span $m\sim(0.8$-$4.6)\times10<sup>{-20}\,\mathrm{eV}$, with Draco and Ursa Minor the lightest and Carina and Sextans the heaviest. A weighted mass estimate gives $m=(1.3\pm3.5)\times10<sup>{-20}$ eV, dominated by Draco and Ursa Minor. We characterize the systematics in detail.