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 ha los of galaxies using weak gravitational lensing. Extending the standard ga laxy-galaxy lensing method, we show that the shape parameters of the mass d istribution 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 galax ies as well as an estimate of the degree of alignment between the stellar c omponent and dark matter. We choose the specific case of an elliptical, iso thermal profile and estimate the feasibility and significance of the detect ion of this signal. The prospects for applying this technique are excellent with large ongoing surveys like the Sloan Digital Sky Survey. The expected signal is smaller but comparable in significance to that of the mass in st andard galaxy-galaxy lensing analyses. Since shapes of halos depend on the degree of dissipation and the transfer of angular momentum during galaxy as sembly, constraints obtained from the analysis will provide important input to models of galaxy formation.