CURLING -- II. Improvement on the $H_{0}$ Inference from Pixelized Cluster Strong Lens Modeling

TL;DR

This paper evaluates how pixel-based lens modeling, which utilizes the full extended surface brightness of lensed arcs, improves $H_0$ inference from strongly lensed supernovae in galaxy clusters. Using a realistic MACS J0138.0-2155–like mock with SN Requiem at $z_s=1.95$, the authors compare traditional image-plane modeling (Lenstool) against a pixelized approach, under LSST- and CSST-MCI-like observing conditions. The pixel-based method yields $H_0=70.39^{+0.82}_{-0.60}$ km s$^{-1}$ Mpc$^{-1}$, a substantial precision gain over Lenstool’s $H_0=69.91^{+6.27}_{-5.50}$ km s$^{-1}$ Mpc$^{-1}$, indicating that lens modeling uncertainties dominate the error budget with next-generation data and that incorporating extended surface brightness is crucial. The results underscore the potential of pixelized lens modeling to unlock-percent-level constraints on cosmology from glSNe, while acknowledging idealizations and outlining paths to include microlensing, line-of-sight structures, and scalable computation.

Abstract

Strongly lensed supernovae (glSNe) provide a powerful, independent method to measure the Hubble constant, $H_{0}$, through time delays between their multiple images. The accuracy of this measurement depends critically on both the precision of time delay estimation and the robustness of lens modeling. In many current cluster-scale modeling algorithms, all multiple images used for modeling are simplified as point sources to reduce computational costs. In the first paper of the CURLING program, we demonstrated that such a point-like approximation can introduce significant uncertainties and biases in both magnification reconstruction and cosmological inference. In this study, we explore how such simplifications affect $H_0$ measurements from glSNe. We simulate a lensed supernova at $z=1.95$, lensed by a galaxy cluster at $z=0.336$, assuming time delays are measured from LSST-like light curves. The lens model is constructed using JWST-like imaging data, utilizing both Lenstool and a pixelated method developed in CURLING. Under a fiducial cosmology with $H_0=70\rm \ km \ s^{-1}\ Mpc^{-1}$, the Lenstool model yields $H_0=69.91^{+6.27}_{-5.50}\rm \ km\ s^{-1}\ Mpc^{-1}$, whereas the pixelated framework improves the precision by over an order of magnitude, $H_0=70.39^{+0.82}_{-0.60}\rm \ km \ s^{-1}\ Mpc^{-1}$. Our results indicate that in the next-generation observations (e.g., JWST), uncertainties from lens modeling dominate the error budget for $H_0$ inference, emphasizing the importance of incorporating the extended surface brightness of multiple images to fully leverage the potential of glSNe for cosmology.

Figures (5)

• Figure 1: Left: JWST NIRCam (F277W) Observation on the lensing cluster MACS J0138.0-2155. Right: Mock image of the simulated cluster used in this work. Member galaxies, multiple images as lensing constraints, and lensed supernova images are marked with white ellipses, cyan/magenta boxes, and orange crosses, respectively. The field-of-view (FoV) is $60^{\prime\prime}\times 60^{\prime\prime}$.
• Figure 2: Light curves of the three multiple images of the simulated supernova under the LSST observational configuration. Each panel corresponds to one of the SN images. The dashed lines represent the theoretical light curves computed from the intrinsic supernova model and the associated lensing magnification and arrival time. Data points with error bars show the measured fluxes, incorporating observational effects from LSST. Solid lines indicate the best-fit light curves obtained using the sntd package.
• Figure 3: Posterior distributions (1-$\sigma$ and 2-$\sigma$ confidence levels) of the lens mass parameters for the main halo. The left panel compares the results obtained using Lenstool (orange) and the pixel-based modeling approach (black). The right panel provides a zoomed-in view of the pixel-based modeling posteriors.
• Figure 4: Inferred$H_{0}$ from lens model obtained with lenstool (dashed) and pixelized method (solid curve). The fiducial value of $H_{0, \rm \ fid}$ is marked as the vertical dash-dotted line.
• Figure 5: Light curves of the three multiple images of the simulated supernova under the CSST-MCI observational configuration. The line styles are consistent with those in Figure \ref{['fig2']}.