Weak Lensing of Galaxy Clusters in Modified Newtonian Dynamics

We study weak gravitational lensing of galaxy clusters in terms of the MOND(MOdified Newtonian Dynamics) theory. We calculate shears and convergences ofbackground galaxies for three clusters (A1689, CL0024+1654, CL1358+6245) andthe mean profile of 42 SDSS (Sloan Digital Sky Survey) clusters and comparethem with observational data. The mass profile is modeled as a sum of X-raygas, galaxies and dark halo. For the shear as a function of the angular radius,MOND predicts a shallower slope than the data irrespective of the criticalacceleration parameter $g_0$. The dark halo is necessary to explain the datafor any $g_0$ and for three interpolation functions. If the dark halo iscomposed of massive neutrinos, its mass should be heavier than 2 eV. Howeverthe constraint still depends on the dark halo model and there are systematicuncertainties, and hence the more careful study is necessary to put a stringentconstraint.Comment: 12 pages, 7 figures, references added, minor changes, accepted for publication in Ap