Kinematic Mapping of Giant Arcs: A New Method to Locate Lensing Critical Curves

The vicinity of lensing critical curves features highly magnified portions of lensed galaxies. Accurate knowledge of the location and shape of the critical curve is useful for understanding the nature of highly magnified sources near critical curves and for revealing dark matter substructures in the lens. In galaxy-cluster lenses, however, the prediction of critical curves can be uncertain, due to the complexity in global mass modeling. We explore and validate a kinematics-based method for locating the critical curve. This method leverages the continuous line-of-sight velocity profile of the lensed galaxy mapped through integral field spectroscopy of emission lines, and combines an agnostic local lens model and a disk rotation model. Applying our method to a highly magnified region of the Dragon Arc in the A370 cluster lensing field using archival Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer (MUSE) integral field unit (IFU) mapping of the Hβ line, we constrain the critical curve to an uncertainty band with a half-width of 0 $\stackrel{\text{″}}{.}$ 23 (1σ). This result reveals the locations of recently detected extremely magnified stars biased toward the negative-parity side of the critical curve, as predicted for intracluster microlensing. With future JWST/NIRSpec IFU mapping of the Hα line at signal-to-noise ratio (SNR) ≃ 10 (20), the uncertainty could improve to 0 $\stackrel{\text{″}}{.}$ 12 (0 $\stackrel{\text{″}}{.}$ 08). A measurement of this type with sufficiently small uncertainty may reveal small-scale wiggles in the shape of the critical curve, which can arise from the lensing perturbation of subgalactic dark matter substructure. Our approach is generally applicable to caustic-crossing giant arcs and can be incorporated into global lens modeling.