Theoretical Modeling of Weakly Lensed Polarized Radio Sources

In this paper we present the theoretical basis for the modeling of weaklygravitationally lensed extended sources that are polarized. This technique hasbeen used in the past to constrain the mass profiles of galaxies projectedagainst the jet of the quasar 3C9. Since then, work has been done to improveboth the measurement and theoretical modeling of the lensing signal, whichmanifests itself as an alignment breaking between the morphology and thepolarization, parametrized as eta-g. To this end, we present the mathematicalderivation of the theoretical value of eta-g as well as numerical simulationsof expected signals in polarized radio jets. We use the radio jet sources 3C9and 1253+104 as illustrative examples of the measurement and modeling of theeta-g signal. For 3C9, we present constraints on the parameters of the twointervening lenses and quantify their confidence intervals. One lens has nomeasured redshift and in this case, we show the dependence of mass andmass-to-light ratio on assumed redshift.Comment: 26 pages, 14 figures. Accepted for publication in the Astrophysical Journal (Oct. 2004