Two-Dimensional Galaxy-Galaxy Lensing: A Direct Measure of the Flattening and Alignment of Light and Mass in Galaxies

We propose a new technique to directly measure the shapes of dark matter halos of galaxies using weak gravitational lensing. Extending the standard galaxy-galaxy lensing method, we show that the shape parameters of the mass distribution of foreground galaxies can be measured from the two-dimensional shear field derived from background galaxies. This enables the comparison of the ellipticity of the mass distribution with that of the light in galaxies, as well as an estimate of the degree of alignment between the stellar component and dark matter. We choose the specific case of an elliptical, isothermal profile and estimate the feasibility and significance of the detection of this signal. The prospects for applying this technique are excellent with large on-going surveys like the Sloan Digital Sky Survey. The expected signal is smaller, but comparable in significance to that of the mass in standard galaxy-galaxy lensing analyses. Since shapes of halos depend on the degree of dissipation and the transfer of angular momentum during galaxy assembly, constraints obtained from our analysis will provide an important input to models of galaxy formation.