The relation between stellar mass and weak lensing signal around galaxies: implications for modified Newtonian dynamics

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-fitting slope alpha = 0.74 +/- 0.08. This result is inconsistent with modified Newtonian dynamics (MOND), which predicts alpha = 0.5 (we find alpha > 0.5 with 99.7 per cent 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 greater than or similar to 10(11) L-circle dot). 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.