1305.3516 (Mordehai Milgrom)

Testing MOND with galaxy-galaxy gravitational lensing    [PDF]

Mordehai Milgrom

MOND 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. MOND's phi(R) has the R-dependence of the Newtonian potential of an isothermal sphere of dispersion s: phi(R)=2s^2ln(R). Thus MOND predicts that the asymptotic Newtonian potential deduced from galaxy-galaxy gravitational lensing will have: 1. a logarithmic R dependence. 2. a s value that depends only on M: s=(MGa0/4)^{1/4}. Thus, in terms of the directly observed luminosity, L: s=(LGa0/4)^{1/4}(M/L)^{1/4}, with M/L values of baryons alone, i.e., with no dark matter. 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 requires an r'-band M/L (1-3) solar units, and for `red' lenses (`elliptical' galaxies) M/L(3-6) solar units, both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, M/L130 solar units, bespeaking a mass discrepancy of a factor ~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 a0.

View original: http://arxiv.org/abs/1305.3516