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 $\varphi (r)=(MG{a}_0{)}^{1/2}\ln (r)$. Relativistic MOND theories predict that the lensing effects of $M$ are dictated by $\varphi (r)$ 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 $M$: $\sigma =(MG{a}_0/4{)}^{1/4}$. 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 $r^{\prime }$-band $M/L_{r^{\prime }}\sim (1–3)(M/L{)}_{\odot }$, and for “red” lenses (“elliptical” galaxies) with $M/L_{r^{\prime }}\sim (3–6)(M/L{)}_{\odot }$, both consistent with baryons only. In contradistinction, Newtonian analysis requires, typically, $M/L_{r^{\prime }}\sim 130(M/L{)}_{\odot }$, bespeaking a mass discrepancy of a factor $\sim 40$. 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 $a_0$.

Figure 1

The MOND predictions of the GGL, $\sigma -L_{r^{\prime }}$ relations, Eq. (6), for baryonic mass-to-light ratios ${{\rm Y}}_{r^{\prime }}^B=1$, 1.5, 3, 6 (lines marked with ${{\rm Y}}_{r^{\prime }}^B$). The measurements are reproduced from Fig. 28 of Ref. 14: “blue” lenses (blue squares), “red” lenses (red triangles, thick error caps where error bars overlap). The predicted lines for ${{\rm Y}}_{r^{\prime }}^B$ of 1.5 and 6 are practically the same as the best-fit relations found in Ref. 14 for the “blue” and “red” lenses, respectively.