Quantum fluctuations masquerade as halos: Bounds on ultra-light dark matter from quadruply-imaged quasars

Abstract: Ultra-light dark matter (ULDM) refers to a class of theories, including ultra-light axions, in which particles with mass $m_{\psi} < 10^{-20}\, \rm{eV}$ comprise a significant fraction of the dark matter. A galactic scale de Broglie wavelength distinguishes these theories from cold dark matter (CDM), suppressing the overall abundance of structure on sub-galactic scales, and producing wave-like interference phenomena in the density profiles of halos. With the aim of constraining the particle mass, we analyze the flux ratios in a sample of eleven quadruple-image strong gravitational lenses. We account for the suppression of the halo mass function and concentration-mass relation predicted by ULDM theories, and the wave-like fluctuations in the host halo density profile, calibrating the model for the wave interference against numerical simulations of galactic-scale halos. We show that the granular structure of halo density profiles, in particular, the amplitude of the fluctuations, significantly impacts image flux ratios, and therefore inferences on the particle mass derived from these data. We infer relative likelihoods of CDM to ULDM of 8:1, 7:1, 6:1, and 4:1 for particle masses $\log_{10}(m_\psi/\rm{eV})\in[-22.5,-22.25], [-22.25,-22.0],[-22.0,-21.75], [-21.75,-21.5]$, respectively. Repeating the analysis and omitting fluctuations associated with the wave interference effects, we obtain relative likelihoods of CDM to ULDM with a particle mass in the same ranges of 98:1, 48:1, 26:1 and 18:1, highlighting the significant perturbation to image flux ratios associated with the fluctuations. Nevertheless, our results disfavor the lightest particle masses with $m_{\psi} < 10^{-21.5}\,\rm{eV}$, adding to mounting pressure on ultra-light axions as a viable dark matter candidate.