A Novel Framework for Modeling Weakly Lensing Shear Using Kinematics and Imaging at Moderate Redshift

Kinematic weak lensing describes the distortion of a galaxy's projected velocity field due to lensing shear, an effect recently reported for the first time by Gurri et al. based on a sample of 18 galaxies at $z \sim 0.1$. In this paper, we develop a new formalism that combines the shape information from imaging surveys with the kinematic information from resolved spectroscopy to better constrain the lensing distortion of source galaxies and to potentially address systematic errors that affect conventional weak-lensing analyses. Using a Bayesian forward model applied to mock galaxy observations, we model distortions in the source galaxy's velocity field simultaneously with the apparent shear-induced offset between the kinematic and photometric major axes. We show that this combination dramatically reduces the statistical uncertainty on the inferred shear, yielding statistical error gains of a factor of 2--6 compared to kinematics alone. While we have not accounted for errors from intrinsic kinematic irregularities, our approach opens kinematic lensing studies to higher redshifts where resolved spectroscopy is more challenging. For example, we show that ground-based integral-field spectroscopy of background galaxies at $z \sim 0.7$ can deliver gravitational shear measurements with S/N $\sim 1$ per source galaxy at 1 arcminute separations from a galaxy cluster at $z \sim 0.3$. This suggests that even modest samples observed with existing instruments could deliver improved galaxy cluster mass measurements and well-sampled probes of their halo mass profiles to large radii.