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Kinematic weak lensing describes the distortion of a galaxy's projectedvelocity field due to lensing shear, an effect recently reported for the firsttime by Gurri et al. based on a sample of 18 galaxies at $z \sim 0.1$. In thispaper, we develop a new formalism that combines the shape information fromimaging surveys with the kinematic information from resolved spectroscopy tobetter constrain the lensing distortion of source galaxies and to potentiallyaddress systematic errors that affect conventional weak-lensing analyses. Usinga Bayesian forward model applied to mock galaxy observations, we modeldistortions in the source galaxy's velocity field simultaneously with theapparent shear-induced offset between the kinematic and photometric major axes.We show that this combination dramatically reduces the statistical uncertaintyon the inferred shear, yielding statistical error gains of a factor of 2--6compared to kinematics alone. While we have not accounted for errors fromintrinsic kinematic irregularities, our approach opens kinematic lensingstudies to higher redshifts where resolved spectroscopy is more challenging.For example, we show that ground-based integral-field spectroscopy ofbackground galaxies at $z \sim 0.7$ can deliver gravitational shearmeasurements with S/N $\sim 1$ per source galaxy at 1 arcminute separationsfrom a galaxy cluster at $z \sim 0.3$. This suggests that even modest samplesobserved with existing instruments could deliver improved galaxy cluster massmeasurements and well-sampled probes of their halo mass profiles to largeradii.

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