The relation between stellar mass and weak lensing signal around galaxies: Implications for MOND

We study the amplitude of the weak gravitational lensing signal as a function of stellar mass around a sample of relatively isolated galaxies. This selection of lenses simplifies the interpretation of the observations, which consist of data from the Red- sequence Cluster Survey and the Sloan Digital Sky Survey. We find that the amplitude of the lensing signal as a function of stellar mass is well described by a power law with a best fit slope \alpha= 0.74 \pm 0.08. This result is inconsistent with Modified Newtonian Dynamics, which predicts \alpha = 0.5 (we find \alpha > 0.5 with 99.7% confidence). As a related test, we determine the MOND mass-to-light ratio as a function of luminosity. Our results require dark matter for the most luminous galaxies (L >=10^11 L_sun). We rule out an extended halo of gas or active neutrinos as a way of reconciling our findings with MOND. Although we focus on a single alternative gravity model, we note that our results provide an important test for any alternative theory of gravity.