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arxiv: 2509.12319 · v2 · submitted 2025-09-15 · 🌌 astro-ph.CO · astro-ph.GA

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

S. H. Suyu , A. Acebron , C. Grillo , P. Bergamini , G. B. Caminha , S. Cha , J. M. Diego , S. Ertl
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N. Foo B. L. Frye Y. Fudamoto G. Granata A. Halkola M. J. Jee P. S. Kamieneski A. M. Koekemoer A. K. Meena A. B. Newman S. Nishida M. Oguri P. Rosati S. Schuldt A. Zitrin R. Ca\~nameras E. E. Hayes C. Larison E. Mamuzic M. Millon J. D. R. Pierel L. Tortorelli H. Wang
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Pith reviewed 2026-05-18 15:46 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords strong gravitational lensingsupernova time delaysHubble constant measurementgalaxy cluster MACS J0138-2155lens mass modelingcosmological inference
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The pith

Seven independent mass models of the lensing cluster MACS J0138-2155 combined with the observed time delay of supernova Encore infer a Hubble constant of 66.9 km s^{-1} Mpc^{-1}.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs seven independent mass models of the galaxy cluster MACS J0138-2155 using different software packages and high-quality observations from HST, JWST, and MUSE. These models are tested for consistency in predicting the positions, magnifications, and time delays of two strongly lensed supernovae, Requiem and Encore, from the same background galaxy. The authors then combine the models with the measured time delay between the two detected images of SN Encore to derive a value for the Hubble constant. A reader would care because time-delay measurements in strong-lensing systems offer an independent route to the expansion rate of the universe, and the long predicted delays for future supernova images suggest a path to percent-level precision.

Core claim

By building seven independent mass models of MACS J0138-2155 from eight gold lensed image systems with secure spectroscopic redshifts and applying them to the newly measured time delay of SN Encore, the authors jointly infer H0 = 66.9^{+11.2}_{-8.1} km s^{-1} Mpc^{-1}, with the uncertainty dominated by the time-delay measurement itself. The models also yield relations between H0 and the time delays of both supernovae, along with predictions for the appearance of their next images at delays of thousands of days.

What carries the argument

Seven independent mass models of the cluster built with six different software packages from gold lensed image systems that include secure spectroscopic redshifts.

If this is right

  • The models give concrete relations between H0 and the time delays of SN Encore and SN Requiem.
  • For an assumed H0 of 73 km s^{-1} Mpc^{-1} the four lowest-chi-squared models predict SN Requiem will reappear between April and December 2026.
  • For an assumed H0 of 67 km s^{-1} Mpc^{-1} the same models predict reappearance between March and November 2027.
  • The long predicted delays for the next images of both supernovae open the possibility of measuring H0 to 2-3 percent uncertainty with future observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The blind multi-team modeling approach used here could be applied to other strong-lensing clusters to quantify software and method systematics in future H0 studies.
  • If the predicted reappearances occur on schedule, the same lens system could provide repeated independent time-delay measurements that tighten the H0 constraint beyond the current delay-limited uncertainty.
  • The reported H0 value sits between local and early-universe determinations, so repeated measurements from this and similar systems could test whether the difference persists at higher precision.

Load-bearing premise

The seven independent mass models accurately predict the time delays of the supernova images without large unaccounted systematics from modeling choices or software differences.

What would settle it

An observed time delay or reappearance date for the next image of SN Encore or SN Requiem that lies well outside the range predicted by the models for the reported H0 value would falsify the inference.

Figures

Figures reproduced from arXiv: 2509.12319 by A. Acebron, A. B. Newman, A. Halkola, A. K. Meena, A. M. Koekemoer, A. Zitrin, B. L. Frye, C. Grillo, C. Larison, E. E. Hayes, E. Mamuzic, G. B. Caminha, G. Granata, H. Wang, J. D. R. Pierel, J. M. Diego, L. Tortorelli, M. J. Jee, M. Millon, M. Oguri, N. Foo, P. Bergamini, P. Rosati, P. S. Kamieneski, R. Ca\~nameras, S. Cha, S. Ertl, S. H. Suyu, S. Nishida, S. Schuldt, Y. Fudamoto.

Figure 1
Figure 1. 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). Positions of the “gold” multiple image systems are shown in 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 squar… view at source ↗
Figure 2
Figure 2. Figure 2: Total average surface mass density profiles of MACS [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Model predictions for SN Encore’s image positions (left), magnifications (middle) and time delays (right) for fixed [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: continued. SN Requiem. It is confirmed that the same three paramet￾ric models (i.e., glafic, GLEE, and Lenstool II) and the free-form MrMARTIAN model can reproduce more ac￾curately than the other models the observed positions of images 2a, 2b, and 2c. These three images of SN Requiem are always predicted by all the models, with magnification factors mostly between −40 and −30, 20 and 30, and 10 and 20, res… view at source ↗
Figure 4
Figure 4. Figure 4: Model predictions for SN Requiem’s image positions (left), magnifications (middle) and time delays (right) for [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: continued. Encore as the core experimental design of our blind anal￾ysis, we therefore defer such H0 inference in more general cosmological models to future work. For SN Encore, where images 1a and 1b are clearly vis￾ible in our JWST data and image 1c is barely visible, it may be possible to derive two time delays with the existing data. The 1b-1a delay, ∆t1b,1a, will likely be substantially more precise t… view at source ↗
Figure 5
Figure 5. Figure 5: Relation of resulting H0 from the different mass models given a range of possible ∆t1b,1a measurements with 10% uncertainty from SN Encore in a flat ΛCDM cosmology with Ωm = 1 − ΩΛ = 0.3. The median values of H0 are in solid lines, while the shaded regions correspond to the 1σ uncertainty. Left panel: all model predictions overlaid, as indicated on the legend. Right panels: subset of the model predictions … view at source ↗
Figure 6
Figure 6. Figure 6: Relation of resulting H0 from the different mass models given a range of possible ∆t1d,1a measurements from SN Encore in a flat ΛCDM cosmology with Ωm = 1 − ΩΛ = 0.3. The median values of H0 are in solid lines, and the shaded regions correspond to the 1σ uncertainty. The assumed uncertainty on ∆t1d,1a is 1%, achievable given the long time delay of ∼3000 days. We tabulate in [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 7
Figure 7. Figure 7: Relation of resulting H0 from the different mass models given a range of possible ∆t2d,2a measurements from SN Requiem in a flat ΛCDM cosmology with Ωm = 1 − ΩΛ = 0.3. The median values of H0 are in solid lines, and the region delineated by shades correspond to the 1σ uncertainty. The relation from the Lenstool I model has larger statistical fluctuations since image 2d is predicted in only 16% of the sampl… view at source ↗
Figure 8
Figure 8. Figure 8: H0 inference from SN Encore using the time de￾lay measurement ∆t1b,1a by Pierel et al. (submitted). The top panel shows the inferred H0 distribution from the mass models from the seven modeling teams through a blind analysis, where the mass models and the time de￾lay were blinded from each other throughout the analy￾ses and combined after unblinding without modifications. The bottom panel shows the H0 from… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of H0 measurements from lensed SNe, local distance ladders, and the CMB (Planck Collaboration et al. 2020). The H0 values inferred from the lensed SNe shown in the figure assumed flat ΛCDM cosmological model with Ωm = 0.3 = 1 − ΩΛ, except for the measurement by Grillo et al. (2024) from SN Refsdal that assumed a more general cosmological model with variable matter density, Ωm, spatial curvature,… view at source ↗
Figure 10
Figure 10. Figure 10: Forecast of the dates of reappearance of SN Encore [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
read the original 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 $\chi^2 \leq 25$. 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 $\Omega_{\rm m} = 0.3$. 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 $\chi^2$ 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)

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper constructs seven independent mass models of the strong-lensing cluster MACS J0138-2155 using six different software packages in a blind analysis. Drawing on HST, JWST and MUSE data, the authors assemble eight gold lensed-image systems (23 images with secure spectroscopic redshifts) plus one silver system. The models are shown to yield consistent predictions for the image positions, magnifications and time delays of the two lensed supernovae (Encore and Requiem) from the same z=1.949 host, especially for fits with χ² ≤ 25. Using the recently measured time delay between the two detected images of SN Encore, the authors jointly infer H0 = 66.9^{+11.2}_{-8.1} km s^{-1} Mpc^{-1} (uncertainty stated to be dominated by the time-delay measurement) and provide forecasts for the reappearance of future images under different H0 values.

Significance. If the central result holds, the work supplies an independent, time-delay-based H0 constraint from a rare cluster that lenses two supernovae from the same host galaxy. The blind, multi-software modeling campaign is a clear methodological strength that quantifies software- and parametrization-driven scatter. The long predicted time delays (>3000 days) for the next images of both supernovae offer a concrete path to future 2–3 % H0 measurements. The lens models themselves constitute a reusable resource for further cosmological or astrophysical studies of this system.

major comments (2)
  1. [H0 inference and abstract] Abstract and H0-inference section: the statement that 'the uncertainty is dominated by that of the time delay' rests on the premise that the seven models furnish unbiased Fermat-potential differences. Because all models are constrained by the identical set of 23 gold images with MUSE spectroscopic redshifts and employ broadly similar parametric or free-form representations, any common systematic (e.g., in image identification, redshift assignment, or mass-sheet degeneracy treatment) would shift all predicted delays coherently and bias the joint H0 posterior without enlarging the quoted uncertainty.
  2. [Model comparison and time-delay prediction sections] Model-comparison and time-delay sections: while the blind analysis demonstrates consistency among the χ² ≤ 25 models, the manuscript does not propagate the residual model-to-model scatter in predicted time delays into the final H0 posterior. A quantitative test—e.g., the range of H0 values obtained when each model is used individually—would clarify whether the joint inference is robust or whether the reported uncertainty understates the modeling contribution.
minor comments (2)
  1. [Abstract and references] The citation 'Pierel et al. (2026)' appears in the abstract and main text; please clarify its status (in prep., submitted, or published) and update the reference list accordingly.
  2. [Figures] Figure captions should explicitly label which curve or point corresponds to each of the seven models and the six software packages to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address the major comments point by point below, indicating where revisions will be made to improve clarity and robustness.

read point-by-point responses

  1. Referee: Abstract and H0-inference section: the statement that 'the uncertainty is dominated by that of the time delay' rests on the premise that the seven models furnish unbiased Fermat-potential differences. Because all models are constrained by the identical set of 23 gold images with MUSE spectroscopic redshifts and employ broadly similar parametric or free-form representations, any common systematic (e.g., in image identification, redshift assignment, or mass-sheet degeneracy treatment) would shift all predicted delays coherently and bias the joint H0 posterior without enlarging the quoted uncertainty.

    Authors: We agree that shared systematics across models (such as common treatments of the mass-sheet degeneracy or image identification) could in principle introduce a coherent bias not captured by the reported uncertainty. Our blind analysis using six independent software packages and diverse parametrizations was specifically designed to sample a broad range of modeling choices and thereby quantify software- and parametrization-driven scatter. The close agreement among the χ² ≤ 25 models for both image positions and time-delay predictions provides empirical support that residual modeling differences are modest. Nevertheless, we acknowledge that this does not exhaustively rule out every possible common bias. In the revised manuscript we will expand the H0-inference discussion to state this caveat explicitly and to clarify the assumptions under which the time-delay uncertainty is considered dominant. revision: partial

  2. Referee: Model-comparison and time-delay sections: while the blind analysis demonstrates consistency among the χ² ≤ 25 models, the manuscript does not propagate the residual model-to-model scatter in predicted time delays into the final H0 posterior. A quantitative test—e.g., the range of H0 values obtained when each model is used individually—would clarify whether the joint inference is robust or whether the reported uncertainty understates the modeling contribution.

    Authors: We appreciate this suggestion. Although the joint posterior was constructed by combining the seven models, we did not present the individual H0 constraints derived from each model separately. To directly address the referee’s request, we will add a supplementary table (or figure) in the revised manuscript that reports the H0 posterior obtained when each model is used in isolation, together with the combined result. This addition will allow readers to evaluate the contribution of model-to-model scatter and to confirm that the quoted uncertainty is not materially understated. revision: yes

Circularity Check

0 steps flagged

No significant circularity; H0 inference relies on independent lens-model constraints and external time-delay measurement

full rationale

The derivation begins with mass models fitted exclusively to positions and spectroscopic redshifts of the eight gold lensed image systems (23 images). These models compute Fermat potential differences for the SN Encore images. The observed time delay, reported as an independent measurement in the cited Pierel et al. (2026) work, is then matched to the model-predicted delay (which scales with the time-delay distance and thus H0) to obtain the reported H0 value. This chain does not reduce any step to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations that substitute for external verification; the constraining observables for the models are distinct from the time-delay datum, and the paper explicitly states that the final uncertainty is dominated by the time-delay measurement rather than model parameters. Blind inter-model comparison further separates modeling choices from the cosmological inference.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard gravitational lensing theory and the accuracy of the external time delay measurement. No new physical entities are introduced.

free parameters (1)
  • Lens mass model parameters
    Parameters within each of the seven models are fitted to the positions and redshifts of the gold lensed image systems.
axioms (1)
  • domain assumption Time delays between lensed images depend on the lens mass distribution and the angular diameter distances set by cosmology including H0
    This standard relation in time-delay cosmography is used to convert the observed delay into the reported H0 value.

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Forward citations

Cited by 3 Pith papers

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