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

TL;DR

This work tackles the challenge of precisely locating lensing critical curves in cluster environments, where global mass models are uncertain, by exploiting the kinematics of lensed galaxies. The authors develop a method that combines a rotating-disk model on the source plane with a flexible local deflection field, then map the intrinsic velocity field to the image plane while accounting for PSF smearing. Validation with mock Dragon Arc analogs and application to archival VLT/MUSE data show a 1σ critical-curve uncertainty of approximately 0.23″, with JWST/NIRSpec IFU data expected to improve this by roughly a factor of 2–3, enabling potential detection of small-scale dark-matter substructure through subtle wiggles in the critical curve. The approach is general to caustic-crossing giant arcs and can be integrated into global lens modeling, providing a model-independent constraint on lens mapping and a new pathway to study intracluster microlensing and sub-galactic dark matter structures.

Abstract

Proximity of lensing critical curves features highly magnified portions of lensed galaxies. Accurate knowledge of the location and shape of the critical curve will be useful for understanding the nature of highly magnified stellar sources near critical curves and for revealing sub-galactic dark matter structures within the lens. In galaxy-cluster lenses, however, prediction of critical curves can be uncertain due to 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 Abell 370 cluster lensing field using archival VLT/MUSE IFU mapping of the H$β$ line, we constrain the critical curve to an uncertainty band with a half-width of 0.23" ($1σ$). This result reveals 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 H$α$ line at SNR $\simeq$ 10 (20), uncertainty could improve to 0.12" (0.08"). 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 sub-galactic dark matter substructure. Our approach is generally applicable to caustic-crossing giant arcs and can be incorporated into global lens modeling.

Figures (13)

• Figure 1: JWST NIRCam F090W image of Dragon Arc in the lensing field of galaxy cluster Abell 370. Bright foreground galaxies and stars are masked in yellow. Critical curves for the source redshift $z_s = 0.725$Richard2010Abell370 are overlaid following the prediction of four lens models: Williams v4.1 William_v4.1_model, Zitrin-Gauss v1.0 Zitrin2009lensingltmZitrin2013lensingmodel based on the Light-Traces-Mass method, BUFFALO v1.0 Bufflomodel and the lastest hybrid WSLAP+ lens model 2025DiegoModel constrained by JWST data. The orange rectangle highlights one highly magnified intersection between the critical curve and the giant arc, where two images of the lensed galaxy with opposite parity join together. While surface brightness patterns hint at roughly where critical curves cross the arc, the precise locations are uncertain. Yellow filled circles mark a few dozen microlensed red supergiant stars discovered by Fudamoto2025A370DragonLensedStars, which are anticipated to primarily show in the vicinity of the critical curve Dai2018Abell370.
• Figure 2: Line-of-sight velocity profile on the Dragon Arc derived from the H$\beta$ line using MUSE IFU data. Red and blue regions trace H ii regions redshifted and blueshifted with respect to the reference velocity, respectively. Some pixels near the arc edge showing anomalous velocity values are likely contaminated by foreground galaxies. The red solid line shows the critical curve at $z_s=0.725$ from the BUFFALO lens model Bufflomodel. One region of critical curve intersection, as enclosed by the orange rectangle in Figure \ref{['fig:Nircam']}, is where many microlensed individual highly magnified stars are detected through JWST imaging Fudamoto2025A370DragonLensedStars.
• Figure 3: VLT/MUSE IFU data reveals variation of the line-of-sight velocity across the Dragon Arc. Surface brightness varies across the arc as one scans through the $\mathrm{H}\beta$ line from $4863~\AA$ to $4858.5~\AA$ (rest frame). The red solid line shows the critical curve in the BUFFALO lens model Bufflomodel. The behavior of the spatial surface brightness profile reveals roughly symmetric velocity patterns on both sides of critical curves, as expected from lens mapping near a fold caustic.
• Figure 4: Example of Gaussian line profile fitting of the H$\beta$ line with continuum subtraction applied to one particular pixel. The blue curve shows the original MUSE spectrum, and the dashed green line is a linear fit to the local continuum. The smooth red curve is the Gaussian fit to the continuum-subtracted spectrum (cyan), whose centroid (purple dot) is used to calculate the line-of-sight velocity.
• Figure 5: Fitting a 3rd-order polynomial deflection field to the BUFFALO lens model Bufflomodel in a $2.5"\times1.3"$ vicinity of the critical curve. The magnitude of the deflection angle, $\alpha =\sqrt{\alpha_1^{2}+\alpha_2^{2}}$, is color-coded. The upper panel shows the original BUFFALO deflection field and the model critical curve (blue), while the middle panel shows the best-fit polynomial deflection field and the corresponding critical curve (red). The bottom panel shows that the fitting residuals have a root-mean-square (RMS) of $\sim 0.001"$.