8.2 Weak lensing by galaxies

A gravitational lens not only produces multiple images close to caustics, but also weakly distorted images (arclets) of other background sources. The weak and noisy signals from several individual arclets (not necessarily detected by eye, but rather numerically exploited with the help of image analysis) can be averaged by statistical techniques to get the shear components γ1 and γ2 in Eq. 114View Equation from the mean ellipticity of the images. One can then get the convergence κ from the azimuthal average of the tangential component of the shear. This is what is known as weak lensing. In the case of galaxy-galaxy weak lensing, since the gravitational distortions induced by an individual lens are too small to be detected, one has to resort to the study of the ensemble averaged signal around a large number of lenses. This has been investigated in the context of MOND for a sample of relatively-isolated galaxy-lenses, stacked by luminosity ranges [456]. The derived MOND masses were obtained by fitting a point mass model to the lensing data within a distance of 200 kpc from the lens. While the MOND masses are perfectly compatible with the baryonic masses in all galaxies less luminous than 11 10 L āŠ™, it was found that the required MOND mass-to-light ratios tended to be slightly too high (M āˆ•L ā‰ƒ 10) for the most massive and luminous galaxies (L > 1011LāŠ™). However, this whole result is dictated by only one data point, which “pulls up” the result and make all the data points lie below the “best fit”, and the curve is “pulled up” strongly by only the first point. Thus, the mass-to-light ratios could easily be scaled down by a factor of two, making these galaxies in perfect agreement with MOND. But it is also worth noting that due to the very large distances probed, the presence of some weakly-clustering residual mass (hot dark matter, or some sort of “dark field” in the relativistic MOND theories) could start playing a role at these distances. While ordinary neutrinos are still too weakly clustering, a slightly more massive fermion such as a 10 eV-scale sterile neutrino could cluster on these scales, and, of course, the presence of baryonic dark matter in the form of dense molecular gas clouds could also be present around these very massive objects (see Section 6.6.4).

Also related to weak lensing, it is important to recall that the “phantom dark matter” of MOND (Eq. 33View Equation) can sometimes become negative in cones perpendicular to the direction of the external gravitational field in which a system is embedded: with accurate enough weak-lensing data, detecting these pockets of negative phantom densities around a sample of non-isolated galaxies could, in principle, be a smoking gun for MOND [490], but such an effect would be extremely sensitive to the detailed distribution of the baryonic matter, and finding a sample of galaxies with similar gravitational environments would also be extremely difficult.

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