Cosmology with supernova Encore in the strong lensing cluster MACS J0138–2155

Lens model comparison and H₀ measurement

¹ Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Straße 1, 85748 Garching, Germany
² Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Straße 1, 85748 Garching, Germany
³ Instituto de Física de Cantabria (CSIC-UC), Avda. Los Castros s/n, 39005 Santander, Spain
⁴ INAF – IASF Milano, Via A. Corti 12, I-20133 Milano, Italy
⁵ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy
⁶ INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, I-40129 Bologna, Italy
⁷ Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seoul 03722, Korea
⁸ School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85716, USA
⁹ Department of Astronomy/Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, USA
¹⁰ Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
¹¹ Dipartimento di Fisica e Scienze della Terra, Universitá degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
¹² Institute of Cosmology and Gravitation, University of Portsmouth, Burnaby Rd, Portsmouth PO1 3FX, UK
¹³ Pyörrekuja 5 A, 04300 Tuusula, Finland
¹⁴ Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA
¹⁵ School of Earth and Space Exploration, Arizona State University, PO Box 876004 Tempe, AZ 85287-6004, USA
¹⁶ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
¹⁷ Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653 Be’er-Sheva, 84105, Israel
¹⁸ Department of Physics, Indian Institute of Science, Bengaluru 560012, India
¹⁹ Observatories, Carnegie Science, Pasadena, CA 91101, USA
²⁰ Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-Cho, Inage-Ku, Chiba 263-8522, Japan
²¹ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
²² Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
²³ Institute for Particle Physics and Astrophysics, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland
²⁴ University Observatory, Ludwig-Maximilians-Universität München, Scheinerstraße 1, 81679 München, Germany

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Received: 13 September 2025
Accepted: 21 January 2026

Abstract

Robust mass modeling of strong-lensing galaxy clusters is crucial for studying cosmology and galaxy evolution. We present and compare seven mass models of the galaxy cluster MACS J0138−2155, constructed using six independent modeling software programs, including parametric and free-form approaches. By conducting a blind analysis where all the mass-modeling teams constructed their models independently without exchanging results, we quantified uncertainties arising from modeling software and assumptions. MACS J0138−2155 is unique as the only cluster found to strongly lens two supernovae (SNe), Requiem and Encore, from the same host galaxy at a redshift of z = 1.949, providing an excellent probe of cosmology through time delays between their multiple images. Through the Hubble Space Telescope, James Webb Space Telescope, and Multi Unit Spectroscopic Explorer observations, we assembled high-quality data products, including eight sets of “gold” lensed-image systems consisting of 23 multiple images with secure spectroscopic redshifts. We further identified one “silver” lensed-image system with a likely but nonsecure redshift measurement. By restricting ourselves to high-quality gold images, we obtain overall good consistency in the model predictions of the positions, magnifications, and time delays of the multiple images of SN Encore and SN Requiem – especially from the teams whose models fit the observed image positions with χ_im² ≤ 25. We predict the next images of SNe Encore and Requiem to reappear with time delays ≳3000 days and ∼3700 to 4000 days, respectively, based on a fiducial cosmological model with H₀ = 70 km s⁻¹ Mpc⁻¹ and Ω_m = 1 − Ω_Λ = 0.3. By considering a range of hypothetical time-delay values with the same Ω_m = 1 − Ω_Λ = 0.3, we obtain relations between H₀ and the time delays of SN Encore and SN Requiem. In particular, for H₀ = 73 km s⁻¹ Mpc⁻¹, the four lowest χ_im² models forecast the next image of SN Requiem to appear approximately April–December 2026; for H₀ = 67 km s⁻¹ Mpc⁻¹, they predict it to appear approximately March–November 2027 (1σ uncertainties). Using the newly measured time delay between the two detected multiple images of SN Encore by Pierel et al. (2026, ApJ, 998, 219) and our mass modeling, we infer $H_0=66.9_{-8.1}^{+11.2}$ km s⁻¹ Mpc⁻¹, where the uncertainty is dominated by that of the short time delay between the existing pair of images. The long time delays of the next-appearing SN Requiem and SN Encore images provide excellent opportunities to measure H₀ with 2−3% uncertainty. Our mass models form the basis for cosmological inference from this unique lens cluster with two strongly lensed SNe.