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, $γ_\times$, 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. We also explore the effects of asymmetric warps and show that rotation direction can impart a small bias on the fit of $γ_\times$. Subsequently, we apply our method to a dataset of 358 halos from the Illustris TNG simulations, achieving a notable reduction in the uncertainty of $γ_\times$ 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.

💡 Research Summary

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This paper introduces MIRoRS (Model‑Independent Restoration of Reflection Symmetries), a non‑parametric technique for measuring the cross‑component of weak‑lensing shear (γ×) from a single galaxy by jointly exploiting its kinematic velocity field and photometric position‑angle information. Traditional kinematic lensing (KL) approaches fit a parametric disk model to spatially resolved spectroscopy, requiring many free parameters and assuming idealized circular symmetry. MIRoRS instead works as follows: the observed 2‑D velocity map is transformed back to the source plane via translation, rotation, and shear inversion; the source‑plane map is then reflected about the major and minor axes to restore the intrinsic symmetry (symmetric about the major axis, antisymmetric about the minor axis). After reflecting, the maps are transformed back to the detector frame and compared with the original data. The residual sum‑of‑squares defines a likelihood that is maximized over a small set of parameters: centroid position, systemic velocity, photometric position angle, inclination (through the axis ratio q), and the shear γ×. Crucially, the difference between the photometric and kinematic position angles provides a direct linear estimator of γ× (Δθ≈γ×·(1+q²)/(1−q²)), eliminating the need for an explicit model of the intrinsic rotation curve.

The authors first validate MIRoRS on idealized mock galaxies, varying shear amplitude, position angle, inclination, and Gaussian noise. They find that MIRoRS recovers γ× with negligible bias even when γ×≈0, and that its statistical uncertainty is ~30 % lower than that of the parametric method used in Donet & Wittman (2023). Tests with asymmetric warps reveal a small systematic shift (~0.005) that depends on the sense of rotation, which can be corrected in post‑processing.

The method is then applied to 358 halos from the Illustris TNG100‑1 simulation at z = 0, a dataset previously analyzed with a parametric model that yielded σ(γ×)=0.08. Because the true shear for these halos is essentially zero, the measured scatter directly reflects methodological noise. MIRoRS reduces this scatter to 0.039, more than a factor of two improvement. To further clean the sample, the authors compute residual maps for each halo and perform a global Moran’s I test for spatial autocorrelation. Halos showing significant positive autocorrelation (45 out of 358) are flagged as outliers and removed, bringing the final uncertainty down to σ(γ×)=0.028.

Key contributions of the work are: (1) a truly model‑independent estimator of γ× that requires only five free parameters, (2) the explicit incorporation of photometric‑kinematic axis misalignment as a shear probe, and (3) an objective, statistically‑grounded outlier rejection scheme based on Moran’s I. These advances make per‑galaxy weak‑lensing measurements far more precise, opening the possibility of mapping local mass distributions (e.g., around clusters or massive halos) without relying on large ensembles. The authors suggest that with forthcoming high‑resolution integral‑field spectrographs on facilities such as JWST, ELT, and future space missions, MIRoRS could become a standard tool for “kinematic weak lensing,” complementing traditional shape‑noise‑limited cosmic shear analyses.