Superfluid dark matter in tension with weak gravitational lensing data

We investigate superfluid dark matter (SFDM), a model that promises to reproduce the successes of both particle dark matter on cosmological scales and those of Modified Newtonian Dynamics (MOND) on galactic scales. But SFDM reproduces MOND only up to a certain distance from the galactic center and only for kinematic observables. Most importantly, it does not affect trajectories of light. We test whether or not this is in conflict with a recent analysis of weak gravitational lensing which has probed accelerations around galaxies at unprecedentedly large radii. This analysis found the data to be close to the prediction of MOND, suggesting they might be difficult to fit with SFDM. To investigate this matter, we solved the equations of motion of the model and compared the result to observational data. Our results show that the SFDM model is incompatible with the weak-lensing observations, at least in its current form.