Testing the MOND Paradigm of Modified Dynamics with Galaxy-Galaxy Gravitational Lensing

The MOND paradigm of modified dynamics predicts that the asymptotic gravitational potential of an isolated, bounded (baryonic) mass, M, is phi(r) = (MGa0)(1/2) ln(r). Relativistic MOND theories predict that the lensing effects of M are dictated by phi(r) as general-relativity lensing is dictated by the Newtonian potential. Thus MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have (1) a logarithmic r dependence, and (2) a normalization (parametrized standardly as 2 sigma(2)) that depends only on M: sigma = (MGa0/4)(1/4). I compare these predictions with recent results of galaxy-galaxy lensing, and find agreement on all counts. For the blue-lenses subsample (spiral galaxies) MOND reproduces the observations well with an r'-band M/L-r' similar to (1-3)(M/L)(circle dot), and for red lenses (elliptical galaxies) with M/L-r' similar to (3-6)(M/L)(circle dot), both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, M/L-r' similar to 130(M/L)(circle dot), bespeaking a mass discrepancy of a factor similar to 40. Compared with the staple, rotation-curve tests, MOND is here tested in a wider population of galaxies, through a different phenomenon, using relativistic test objects, and is probed to several-times-lower accelerations-as low as a few percent of a(0).