Applications of weak gravitational lensing: Constraining the dark matter in clusters and galaxies

Weak gravitational lensing has become a popular tool in cosmology because it can place strong constraints on the amount and distribution of dark matter in the universe. Here I investigate the use of weak lensing to constrain the dark matter in galaxies and clusters of galaxies.; Many studies of weak lensing by clusters assume a priori that the cluster gravitational potentials may be modeled as isothermal spheres. I investigate systematic trends in the mass profile and total cluster mass as derived from the shear field under this assumption, using clusters generated by high resolution N-body simulations. When the shear field is measured across the entire cluster, a very good estimate of the total cluster mass is obtained. However, the shear field measured on smaller scales underestimates both the projected mass and the three-dimensional mass.; Several recent numerical investigations suggest a universal density profile for dark matter halos which form via dissipationless collapse. I investigate the lensing properties of dark matter halos that have a Navarro, Frenk, & White (NFW) density profile, and I quantify the errors in lens masses that are determined under the assumption of an isothermal sphere, when the actual lens mass distribution is NFW. I find that the total mass is overestimated for objects on mass scales from $1011M\odot$–$1015M\odot$. The overestimate is significant for galaxy-sized halos, but quite small for rich clusters.; Finally, I examine a new application of weak lensing by galaxies to constrain the mean projected ellipticity of dark matter galaxy halos. I run detailed Monte Carlo simulations to determine the feasibility of detecting flattened halos by the anisotropic shear signal they induce about their centers. For a deep, ground-based data set with realistic noise properties, 20–30 square degrees of sky are necessary for a 4σ detection. Foreground mass concentrations induce correlations in the lens and source image shapes, which suppress the anisotropy signal. I derive, in terms of observable quantities, a correction factor to remove the effects of the lens-source correlation, and demonstrate that it recovers the true signal to within 1.5σ.