Testing Lens Models of PLCK G165.7+67.0 Using Lensed SN H0pe

TL;DR

The paper uses SN H0pe, a multiply-imaged SN Ia in the PLCK G165.7+67.0 cluster, to test seven lens-model approaches via time-delay cosmography and magnification constraints. By de-magnifying observed light curves with model-predicted magnifications and aligning epochs by measured delays, the intrinsic SN Ia light curves are fitted with BayeSN and SALT3-NIR to yield distance moduli. Across all models and SN-SED treatments, the lens-model magnifications consistently overpredict the true magnification, with a typical offset of $\Delta \mu > 1$ mag when compared to ΛCDM expectations from Pantheon+ and DES5Y, signaling a systematic bias that can propagate into $H_0$ inferences. The results underscore the value of lensed SNe as robust tests of lens-model accuracy, the need for multiple, testable models, and the importance of incorporating magnification constraints in modeling—crucial steps as future surveys (LSST, Roman, Euclid) will discover many more glSNe. The study also identifies potential links between magnification biases and the local lens potential slope, suggesting the true cluster potential may be steeper than current models imply.

Abstract

Supernova H0pe is a multiply-imaged Type Ia supernova (SN Ia) and the second lensed SN to yield a measurement of the Hubble constant by the time-delay cosmography method, finding $H_0 = 75.4^{+8.1}_{-5.5} \text{km s}^{-1} \text{Mpc}^{-1}$. We investigate the seven lens modeling approaches used to derive $H_0$, assessing their agreement with $Λ\text{CDM}$ constraints from SN Ia surveys through a purely observational comparison. While photometrically derived magnifications yield distance moduli in line with $Λ\text{CDM}$ expectations, our comparison reveals that lens model predictions, even the most precise ones, consistently overestimate the magnification, with a offset of $ Δμ> 1$ mag. This known bias, already appreciated by modeling teams, is independently confirmed through our analysis and highlights the value of lensed SNe as a tool to test model accuracy. If unaccounted for, such magnification biases can propagate into uncertainties in derived cosmological parameters, including $H_0$, and affect the interpretation of future precision measurements. These findings highlight a critical challenge for precision cosmology using strongly lensed transients. With next-generation surveys such as LSST, Roman, and Euclid poised to discover many more gravitationally lensed supernovae, the development and validation of robust, accurate lens models will be essential for using these rare events to probe cosmology.

Figures (7)

• Figure 1: Mosaic of the central region of the PLCK G165.7+67.0 cluster field, covering a width of 1 arcminute, showing the full depth obtained in all 5 epochs for all 6 NIRCam filters F090W, F150W, F200W, F277W, F356W, and F444W (see Section \ref{['sec:obs']} for further details). The insets show a close up of each of the images of SN H0pe based on the JWST Epoch 1 data. Each of the insets has a partial crosshair that shows the location of the SN.
• Figure 2: A schematic showing the method used in this analysis. Each step has an associated section (S.), table (T.) or figure (F.) in this paper, that provides more details about the work.
• Figure 3: Light curves for SN H$0$pe photometry, de-magnified using absolute magnifications as stated in Pascale_SNH0pe_2025 as predicted by the lens modeling approach of chen_2020, are shown fitted with both SED models. The top panel shows BayeSN fit, with the residuals shown in the second panel. The third panel shows the fit using SALT3-NIR with the corresponding residuals in bottom panel. Light curves are color-coded by filter, with vertical offsets (indicated in the legend) applied for clarity. The shaded regions represent the $2 \sigma$ uncertainty intervals for each light curve. Photometric data are overplotted with error bars, also color-coded by filter. Each SN image is represented by a different marker: circles for Image 2a, squares for 2b, and triangles for 2c.
• Figure 4: Distance modulus ($\mu$) measurements for each of the lens models described in Section \ref{['sec:lens_models']} along with the photometric and spectroscopic measurements of magnification from Pierel_PhotometricTimedelay_2024a and Pascale_SNH0pe_2025. The purple regions show the normalized distribution of distance moduli found using SALT3-NIR while the pink depicts the same found using BayeSN. The expected distance modulus for Flat$\Lambda$CDM (Dotted Orange) and Flat$w_aw_0$CDM (Dot-Dashed yellow) as described in DES_5Y at $z=1.783$ are shown as well. Expected distance modulus at $z=1.783$ for Flat$\Lambda$CDM parameters given in Pantheon_2022 is shown in solid green. Each of the cosmological models has a $5\sigma$ uncertainty region shown in the respective colors as well.
• Figure 5: The weighted distance modulus for SALT3-NIR (purple) vs BayeSN (pink). The error bars for the two points show the $5~\sigma$ spread for the distribution. The distance modulus - redshift relation for three cosmological constraints are plotted as well. The DES5Y Flat$\Lambda$CDM is depicted in a orange dotted line. The DES5Y Flat$w_0w_a$CDM is shown in dotted-dashed yellow. The green solid line is the Pantheon+ Flat$\Lambda$CDM cosmology. Each cosmological model is accompanied by $5\sigma$ error regions in the respective colored shaded regions.