Cosmology with supernova Encore in the strong lensing cluster MACS J0138-2155: Lens model comparison and H0 measurement

Abstract

MACS J0138-2155 is the only known cluster to strongly lens two supernovae (SNe), Requiem and Encore, from the same host galaxy at z=1.949. We present seven independent mass models of the galaxy cluster built using six software packages. By conducting a blind analysis (no exchanges of results between modeling teams), we quantified uncertainties due to modeling and software. Through HST, JWST and MUSE observations, we assembled high-quality data products, including eight "gold" lensed image systems consisting of 23 images with secure spectroscopic redshifts, and one "silver" system with a likely redshift value. Restricting to the gold images, we obtain overall consistent model predictions of the positions, magnifications and time delays of SN Encore and SN Requiem images, especially for models with $χ^2 \leq 25$. We predict the appearance of the next images of SNe Encore and Requiem with a time delay of >~3000 days and of ~3700 to 4000 days, respectively, based on a fiducial cosmological model of $H_0 = 70 {\rm\ km\ s^{-1}\ Mpc^{-1}}$ and $Ω_{\rm m} = 0.3$. We obtain relations between $H_0$ and the time delays of SNe Encore and Requiem. In particular, for $H_0 = 73 {\rm\ km\ s^{-1}\ Mpc^{-1}}$, the four lowest $χ^2$ models predict SN Requiem to reappear in ~Apr-Dec 2026; for $H_0 = 67 {\rm\ km\ s^{-1}\ Mpc^{-1}}$, in ~Mar-Nov 2027. Using the newly measured time delay between the two detected images of SN Encore by Pierel et al. (2026) and our mass models, we jointly infer $H_0 = {\rm 66.9^{+11.2}_{-8.1}\ km\ s^{-1}\ Mpc^{-1}}$, where the uncertainty is dominated by that of the time delay. The long delays of the next-appearing SN Requiem and SN Encore images provide excellent opportunities to measure $H_0$ with an uncertainty of 2-3%. Our mass models form the basis for cosmological inference from this unique lens cluster with two strongly lensed SNe. (Abridged)

Figures (17)

• Figure 1: MACS J0138$-$2155 as observed through HST and JWST with the following combinations of filters for the color image: F105W+F115W+F125W (blue), F150W+F160W+F200W (green), and F277W+F356W+F444W (red). The positions of the "gold" multiple-image systems are shown with circles. SN Encore is System 1, and SN Requiem is System 2. The foreground (fg) and background (bg) galaxies are marked by cyan diamonds. The dashed squares identify some of the freely optimized cluster members in the lens model, i.e., not constrained by the scaling relations for the cluster members (gray for the Zitrin-analytic lens model, maroon for the Lenstool I, and that labeled with $\rm ID_{\rm phot}=116$ for the GLEE and Zitrin-analytic models). The three jellyfish galaxies are labeled with light-green crosses as JF-1, JF-2, and JF-3.
• Figure 2: Total average surface-mass-density profiles of MACS J0138$-$2155 as a function of projected distance from the BCG center for the different best-fit strong-lensing models. The vertical lines (at the bottom of the panel) show the observed positions of the 23 multiple images in the gold sample, where the positions of the multiple images of SN Encore and SN Requiem are highlighted in red and blue, respectively. The vertical gray lines (at the top of the panel) mark the positions of the JF-1, JF-2, and bg galaxies, which contribute significantly to the surface mass density at their locations in some models. The inset shows a zoom-in of the region delimited by the dashed rectangle, where the observed multiple images of the two SNe are located.
• Figure 3: Model predictions for SN Encore's image positions (left), magnifications (middle), and time delays (right) for a fixed cosmological model (flat $\Lambda$CDM with $H_0 = 70\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ and $\Omega_{\rm m} = 0.3 = 1-\Omega_{\rm \Lambda}$). Each row corresponds to one lensed image, as labeled in the top-left corner of each panel in the left column. The coordinate positions are relative to the BCG in arc seconds. The black circle marks the observed image positions of 1a and 1b (left panel in first and second rows, respectively) with the circular radius corresponding to the 1$\sigma$ positional uncertainty. The insets for the image positions 1a and 1b (left panels) show a zoom-in of the region near the observed image position. The time delays (in days) are relative to image 1a of SN Encore, discovered in November 2023, i.e., $\Delta t_{i,{\rm 1a}} \equiv t_{i}-t_{\rm 1a}$.
• Figure 3: Continued.
• Figure 4: Model predictions for SN Requiem's image positions (left), magnifications (middle), and time delays (right) for a fixed cosmological model (flat $\Lambda$CDM with $H_0 = 70\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$ and $\Omega_{\rm m} = 0.3 = 1-\Omega_{\rm \Lambda}$), in the same format as Fig. \ref{['fig:SN_Encore_pos_mag_td']}. The black circle marks the observed image positions of 2a, 2b, and 2c with the circular radius corresponding to the 1$\sigma$ positional uncertainty. The time delays (in days) are relative to image 2a of SN Requiem. The measurements of $\Delta t_{\rm 2b,2a}$ and $\Delta t_{\rm 2c,2a}$ from Rodney+2021 based on the color curves of the SN Ia template are shown by the vertical line, with the shaded interval marking the 1$\sigma$ uncertainty.