Theoretical Models for the Gravitational Lensing of a Quasar by Dwarf Galaxy

We present theoretical models of a dwarf galaxy that has been hypothesized to be a gravitational lens for the quasi-stellar object (QSO, or quasar) J091949.16+342304.0. This lens system is notable for containing multiple quasar images as well as a faint, but detectable, Einstein ring. The observed images require a gravitational lens with a conservative mass estimate of span class="math-tex">\(\approx 2.5 x 10^{11}M_\bigodot\)/span>, but there is no corresponding detection of a high-mass galaxy, which would normally be expected for such a massive lens. We calculate the dwarf galaxy mass to be span class="math-tex">\(4.2 x 10^9M_\bigodot\)/span>, for a baryonic mass ratio of 1.68%. We begin our report by discussing the underlying principles of gravitational lensing, then apply them to different lens models. We initially consider the lens as a point mass, then as a spherical singular isothermal sphere (SIS), then progress to spherical and elliptical softened SIS models. We also explain the analytical and numerical methods that we developed to compute these models. Using an elliptical softened singular isothermal sphere model, we find a best fit to the data by using a lens with an eccentricity e= 0.22 and an isotropic velocity dispersion of sigma;v = 375 km/s. We also investigate the implications of this model, in particular the lens#39; mass distribution and rotational velocity curves, as well as potential explanations for the occurrence of this unique system./p