Improving Precision in Kinematic Weak Lensing with MIRoRS: Model-Independent Restoration of Reflection Symmetries

We present a novel, model-independent technique for fitting the cross-component of weak lensing shear, $\gamma_\times$, along a line of sight by combining kinematic and photometric measurements of a single lensed galaxy. Rather than relying on parametric models, we fit for the shear parameter that best transforms the velocity field to restore its underlying symmetries, while also incorporating photometric data for the change in position angle due to shear. We first validate our technique with idealized mock data, exploring the method's response to variations in shear, position angle, inclination, and noise. On this idealized mock data, our combined kinematic and photometric model demonstrates superior performance compared to traditional parametric or kinematic-only approaches. Subsequently, we apply our method to a dataset of 358 halos from the Illustris TNG simulations, achieving a notable reduction in the uncertainty of $\gamma_\times$ to 0.039, marking a substantial improvement over previous analysis of the dataset with a parametric model. Finally, we introduce an outlier rejection method based on Moran's I-test for spatial autocorrelation. Identifying and filtering out halos with spatially correlated residuals reduces the overall uncertainty to 0.028. Our results underscore the efficacy of combining kinematic and photometric data for weak lensing studies, providing a more precise and targeted measurement of shear along an individual line of sight.