A boost in the precision of cluster-mass models: Exploiting the extended surface brightness of the lensed supernova Refsdal host galaxy

TL;DR

The paper addresses the limited precision of cluster-mass reconstructions in time-delay cosmography by incorporating the extended surface-brightness of the SN Refsdal host into the strong-lensing analysis of MACS J1149.5+2223. Using the Gleesey framework, it compares four weighting schemes that combine 77,000 SN host pixels with 106 point-like images, revealing a 1–2 order of magnitude reduction in the statistical uncertainties of 34 mass-model parameters and dramatically tighter predictions for time delays and magnifications. The extended-image models yield a consistent cumulative mass profile, sub-percent uncertainties on key time delays, and a delensed SN host across multiple bands, illustrating the power of pixel-level constraints for high-precision cosmology and high-redshift source studies. The results highlight the potential and needed care in treating systematic uncertainties as the precision frontier advances, with implications for future surveys (Euclid, JWST, Rubin/LSST) and extended-source lens modeling methods. Mathematically, the work demonstrates that supplementing position-only constraints with brightness information effectively breaks degeneracies and tightens parameter posteriors, enabling more reliable inferences of cosmological parameters and lensed-source properties.

Abstract

Combining deep Hubble Space Telescope (HST) images and extensive data from the Multi-Unit Spectroscopic Explorer, we present new mass models of the cluster MACS J1149.5+2223, strongly lensing the supernova (SN) Refsdal, fully exploiting the source surface-brightness distribution of the SN host for the first time. In detail, we incorporated 77,000 HST pixels, in addition to the known 106 point-like multiple images, in our modeling. We considered four different models to explore the effect of the relative weighting of the point-like multiple image positions and flux distribution of the SN host on the model optimization. When the SN host's extended image is included, we find that the statistical uncertainties of all 34 free model parameters are reduced by factors ranging from one to two orders of magnitude compared to the statistical uncertainty of the point-like only model, irrespective of the adopted different image weights. We quantified the remarkably increased level of precision with which the cluster's total mass and the predicted time delays of the SN Refsdal multiple image positions can be reconstructed. We also show the delensed image of the SN host, a spiral galaxy at zSN = 1.49, in multiple HST bands. In all those applications, we obtain a significant reduction of the statistical uncertainty, which is now below the level of even the small systematic uncertainty on the mass model that could be assessed by the different approaches. These results demonstrate that with extended image models of lensing clusters it is possible to measure the cluster's total mass distribution, the values of the cosmological parameters, and the physical properties of high-redshift sources with an unparalleled precision, making the typically not-quantified systematic uncertainties now crucial.

Figures (7)

• Figure 1: Color-composite image (F435W for blue, F606W + F814W for green, and F105W + F125W + F140W + F160W for red) of the cluster core with the SN Refsdal and its host. Shown are the cluster members (red triangles for photometrically selected members and red circles for spectroscopically confirmed members) and the multiple image systems (blue squares for SN Refsdal and the host and blue pentagons otherwise). We indicate the regions (in orange) used for the SN host reconstruction and extended image model.
• Figure 2: Surface-brightness reconstruction from model Ew (top row), showing the best reconstruction, and from the point-like model schuldt24a (bottom row), which was not optimized on the extended image. We show, from left to right, the observed image, the model-predicted image, the normalized residuals, and the reconstructed source (the SN host galaxy). We illustrate the sizes of the images and of the reconstructed sources with green bars of 5 and 1, respectively. We again note that the Ew model is optimized with an approximate point spread function (see Sect. \ref{['sec:model:ext']} for details), which slightly affects the final appearances of the reconstructed image and source.
• Figure 3: Comparison of normalized residuals (NRes) of the model Ew and the point-like model by schuldt24a, as an absolute ratio (left) and absolute difference (right). The bottom panels show the 1D histograms, and the top panels show the corresponding 2D image color-coded in the same way as the histograms.
• Figure 4: Relative errors of the 34 free parameters (left) and of the magnification factors at the model-predicted positions of the point-like multiple images (right) from the five different models (indicated by different colors and symbols). For the definition of the individual model parameters, see Sects. \ref{['sec:model:parameterization']} and schuldt24a. While the 106 multiple images are, for simplicity, not labeled, we highlight those belonging to the SN and its host (and thus excluded in models Ewo and Swo; white background), those with variable redshift (since no spectroscopic redshift is known; light gray), those belonging to the northern galaxy group (see Fig. 2 of schuldt24a; medium gray), and those from additional sources in the cluster core (dark gray). We observe a significant reduction in the statistical uncertainties of the model parameters (left) and magnifications (right) when we include the 77,000 HST pixels as direct constraints in the strong lensing model.
• Figure 5: Cumulative projected total mass profile $M(<R)$ of MACS1149 as function of the radius, $R$, measured from the brightest cluster galaxy [see][]grillo16. The plotted bands correspond to the $1\sigma$ intervals obtained from 100 random iterations of the final sampling chains. We compared our four new extended image models with the point-like model from schuldt24a and found significantly smaller statistical uncertainties for the extended image models. The positions of the multiple images are marked with small dashes on the lower $x$-axis and color-coded according to their redshifts. The bar lengths reflect the positional uncertainties (a small dash corresponds to an HST identification, while a long dash corresponds to a MUSE-only identification; see schuldt24a for details). We further show the positions of the 77,000 HST image pixels used in the extended image models with a gray histogram, where the height (in log-scale) corresponds to the number of pixels per radial bin.