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 of background galaxies for three clusters (A1689, CL 0024+1654, and CL 1358+6245) and the mean profile of 42 SDSS (Sloan Digital Sky Survey) clusters and compare them with observational data. The mass profile is modeled as a sum of X-ray gas, 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 critical acceleration parameter g(0). The dark halo is necessary to explain the data for any g(0) and for three interpolation functions. If the dark halo is composed of massive neutrinos, its mass should be heavier than 2 eV. However, the constraint still depends on the dark halo model and there are systematic uncertainties, and hence a more careful study is necessary for a more stringent constraint.