Gravitational Lensing Predictions from Wave Simulations of Fuzzy Dark Matter

Abstract

In the cold dark matter paradigm, ultra-light particles are emerging as strong contenders to conventional massive particles. A unique prediction of dark matter comprising such ultra-light particles, known as fuzzy dark matter (FDM), is the presence of strong density modulations throughout galactic halos due to wave interference, which -- when approximated by a Gaussian random field (GRF) -- have been proposed to account for the inability to reproduce the observed positions (when measured at sufficient precisions) and flux ratios of multiply-lensed images of quasars. Here, we predict for the first time the properties of gravitationally lensed images generated from 3-D density fields obtained by wave simulations that directly evolve the Schr\"odinger--Poisson equations. Using a novel framework to project these evolved density fields along various axes of the 3-D halo, we obtain the distribution of perturbations to the positions of lensed images. As an exacting test, we find that particles of mass $10^{-22}$ eV can reproduce the positions of the quadruply-lensed radio jets in system HS 0810+2554 to a level better than that of either the GRF approximation or, to a greater extent, an NFW best-fit solution, both of which rely on accurately capturing the global 3-D density field of dark matter halos. Our work highlights the importance of wave simulations for making accurate FDM lensing predictions and the potential for high-resolution observations of lensed systems to serve as a direct probe of the nature of dark matter.