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

This paper presents a blind analysis of seven independent mass models for the MACS J0138-2155 cluster, which uniquely strongly lenses two supernovae (Requiem and Encore), to predict future image appearances and derive a Hubble constant measurement of $H_0 = 66.9^{+11.2}_{-8.1}$ km s$^{-1}$ Mpc$^{-1}$ based on the time delay of SN Encore.

The Gist

Imagine the universe as a giant, cosmic funhouse. In this funhouse, massive clusters of galaxies act like funhouse mirrors. They don't just reflect light; they stretch, twist, and magnify it, acting as nature's most powerful telescopes. This phenomenon is called gravitational lensing.

This paper is about a specific "funhouse mirror" called MACS J0138, a massive galaxy cluster located billions of light-years away. What makes this mirror special is that it caught a rare, double act: two exploding stars (supernovae) from the same distant galaxy, happening at the same time, but appearing in different places and at different times because of the lensing.

Here is the story of how a team of astronomers used this cosmic trick to measure the speed of the universe's expansion, known as the Hubble Constant ($H_0$).

1. The Cosmic Time-Travelers: SN Requiem and SN Encore

Think of the distant galaxy behind the lens as a lighthouse. Usually, we see its light as one beam. But because of the MACS J0138 cluster, that light is bent into multiple beams, creating several "ghost images" of the same star.

• SN Requiem: This was the first "ghost" star found. It was discovered in old Hubble Telescope photos.
• SN Encore: This was the second "ghost" star, found later by the James Webb Space Telescope (JWST).

Here is the magic: Because the light takes different paths around the galaxy cluster to reach us, the images of these stars appear at different times. One image might show the star exploding today, while another image shows the same explosion happening 4,000 days later. It's like watching a movie where the same scene plays on four different screens, but each screen is delayed by a few years.

2. The Blind Taste Test: Seven Chefs, One Recipe

To measure the speed of the universe, the astronomers needed to know exactly how the galaxy cluster is bending the light. This requires building a "mass model"—a 3D map of the invisible dark matter holding the cluster together.

The problem? Different math software can build slightly different maps. To make sure they weren't just guessing or biasing their results, the team did something very clever: A Blind Analysis.

Imagine a cooking competition where seven different chefs are given the exact same ingredients (the telescope data) and asked to bake a cake (the mass model).

• The Rule: They cannot talk to each other. They cannot see each other's cakes while they are baking.
• The Goal: They must predict when the next "ghost" star will appear on the screens.
• The Reveal: Only after all seven cakes were baked and the predictions were locked in did they open the envelopes to compare results.

This ensured that no one was cheating or subconsciously tweaking their math to get a specific answer.

3. The Results: Do the Cakes Taste the Same?

When they compared the seven models, they found something amazing: They mostly agreed.
Even though the chefs used different recipes (different software and math approaches), they all predicted the positions and brightness of the stars with high accuracy. The models that fit the data best (the "best cakes") were very consistent.

This gave the team confidence that their map of the galaxy cluster was reliable.

4. The Big Prize: Measuring the Hubble Constant

Now, here is the main event. The astronomers measured the time delay between the two visible images of SN Encore. It turned out to be about 40 days.

Using their "blind" mass models and this 40-day delay, they calculated the Hubble Constant ($H_0$).

• The Result: They found the universe is expanding at a rate of roughly 67 km/s per Megaparsec.
• The Catch: The current measurement has a bit of uncertainty (about 14%) because the 40-day delay is a short time in cosmic terms. It's like trying to measure the speed of a car by only watching it for one second; a tiny error in timing makes a big difference in the speed calculation.

5. The Future: The Grand Finale

The paper's most exciting part is the prediction for the future. Because the light paths are so different, the "ghost" stars haven't finished their show yet.

• SN Requiem's Next Act: The models predict a fourth image of this star will appear very soon!
  • If the universe is expanding faster (a value of 73), it should appear between April and December 2026.
  • If it's expanding slower (a value of 67), it should appear between March and November 2027.
• SN Encore's Next Act: A new image of this star is predicted to appear around 2031.

Why does this matter?
The next appearance of SN Requiem will have a time delay of about 4,000 days (11 years). Measuring a delay that long is like timing a marathon runner instead of a sprinter. Even a tiny error in timing won't matter much. This future measurement could pin down the expansion rate of the universe with 2-3% precision, which is incredibly accurate.

Summary

This paper is a triumph of teamwork and scientific rigor. By treating the galaxy cluster like a cosmic lens and running a "blind taste test" with seven different modeling teams, they created a reliable map of the universe's structure. They used the time delay of a single exploding star to get a good estimate of the universe's speed, but they are saving the real precision for the future, when the next "ghost" star appears on the cosmic stage.

It's a reminder that in astronomy, sometimes you have to wait years (or decades) for the next scene of the movie to play out, but the payoff is a deeper understanding of how our universe works.

Technical Summary

1. Problem Statement

Strong gravitational lensing by massive galaxy clusters is a powerful tool for cosmology, particularly for measuring the Hubble constant ($H_0$) via time-delay cosmography. However, the accuracy of these measurements is limited by systematic uncertainties inherent in mass modeling (reconstructing the cluster's dark matter distribution).

• The Challenge: Different modeling software and assumptions (parametric vs. free-form) can yield varying mass distributions, leading to discrepancies in predicted image positions, magnifications, and time delays.
• The Specific Case: The galaxy cluster MACS J0138−2155 is unique because it strongly lenses two supernovae (SNe), SN Requiem and SN Encore, from the same host galaxy at $z=1.949$. This system offers a rare opportunity to measure $H_0$ with high precision, provided the lens mass model is robust and systematic errors are quantified.
• The Goal: To construct, compare, and validate multiple independent mass models of MACS J0138−2155 using a blind analysis to eliminate experimenter bias, and subsequently use these models to infer $H_0$ based on newly measured time delays.

2. Methodology

The authors employed a rigorous, controlled experimental design involving seven independent modeling teams and six different software packages.

• Data Assembly:

  • Imaging: High-quality data from Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) across multiple filters.
  • Spectroscopy: Data from the Multi Unit Spectroscopic Explorer (MUSE) and JWST NIRSpec.
  • Constraints: The teams identified 8 "gold" lensed-image systems (23 multiple images with secure spectroscopic redshifts) and 1 "silver" system. These span redshifts from $z=0.767$ to $3.420$.
  • Input: All teams received the same vetted photometric and spectroscopic catalogs (from Ertl et al. 2025 and Granata et al. 2025).

• Blind Analysis Protocol:

  • Seven teams constructed mass models independently without exchanging results.
  • Teams submitted predictions for the positions, magnifications, and time delays of SN Encore and SN Requiem.
  • The time delay between the first two images of SN Encore ($\Delta t_{1b,1a}$) was kept secret from the modeling teams until after the models were finalized.
  • An uninvolved co-author verified submissions before unblinding.

• Modeling Approaches:

  • Parametric Models (5 teams): Used software like glafic, GLEE, Lenstool, and Zitrin-analytic. These assume specific functional forms for mass distributions (e.g., NFW, dPIE) and often use scaling relations (Faber-Jackson) to link galaxy luminosity to mass.
  • Free-form/Hybrid Models (2 teams): Used MrMARTIAN and WSLAP+. These divide the lens plane into grids or cells, minimizing assumptions about the mass profile shape, though MrMARTIAN incorporates analytic nodes for flexibility.
  • Baseline Models: All teams constructed a "baseline" model using a single lens plane and circular positional uncertainties to ensure direct comparability.

• Statistical Framework:

  • Models were optimized to minimize $\chi^2_{im}$ (difference between observed and predicted image positions).
  • Bayesian Information Criterion (BIC) and likelihood weighting were used to compare models with different numbers of parameters.
  • $H_0$ was inferred by scaling the predicted time delays ($\Delta t \propto 1/H_0$) to match the measured delay.

3. Key Contributions

1. First Blind Lens Modeling Comparison for a Double-SN Cluster: This is the first study to perform a blind comparison of multiple mass models for a cluster hosting two strongly lensed supernovae.
2. Quantification of Systematic Uncertainties: By comparing seven independent models, the authors quantified the scatter in predictions arising solely from modeling choices and software differences.
3. Robust $H_0$ Measurement: The study provides a new, independent measurement of the Hubble constant using SN Encore, free from the "local distance ladder" and "CMB" systematics.
4. Forecasting Future Events: The paper provides precise predictions for the reappearance of future images of both SNe, which is critical for planning future observations to reduce $H_0$ uncertainty.

4. Key Results

• Model Consistency:

  • Four teams achieved excellent fits with $\chi^2_{im} \le 25$ (two teams reached $\chi^2_{im} < 11$).
  • Despite different methodologies, the models showed good consistency in predicting the positions, magnifications, and time delays of the observed images of SN Encore and SN Requiem, particularly for the teams with the best fits.
  • Discrepancies were largest in the innermost regions ($<10$ kpc) and outer regions ($>100$ kpc) where constraints are sparse.

• $H_0$ Inference (Current Data):

  • Using the newly measured time delay $\Delta t_{1b,1a} = -39.8^{+3.9}_{-3.3}$ days (Pierel et al. 2026) and the weighted combination of the seven mass models:
    $$H_0 = 66.9^{+11.2}_{-8.1} \text{ km s}^{-1} \text{ Mpc}^{-1}$$
  • The uncertainty is currently dominated by the time-delay measurement error (~9-10%) rather than the mass modeling systematics.
  • This result is statistically consistent with previous lensed SN measurements (SN Refsdal, SN H0pe), local distance ladders (SH0ES, CCHP), and CMB (Planck) measurements.

• Predictions for Future Images:

  • SN Encore: A new image (1d) is predicted to appear in mid-2031 with a time delay of $\sim3000$ days.
  • SN Requiem: A new image (2d) is predicted to appear much sooner, between April–December 2026 (if $H_0 \approx 73$) or March–November 2027 (if $H_0 \approx 67$).
  • Future Precision: Detecting these future images will provide time delays with $\sim1\%$ precision, potentially allowing an $H_0$ measurement with 2–3% uncertainty from this single cluster.

• Model Performance:

  • Parametric models (glafic, GLEE, Lenstool II) generally reproduced observed positions better than some free-form approaches.
  • The GLEE and glafic models achieved the lowest $\chi^2_{im}$ and BIC values, respectively.

5. Significance

• Resolving the Hubble Tension: This work demonstrates that strong lensing clusters with multiple lensed supernovae are viable, independent probes for $H_0$. The current result ($66.9 \pm 9.5$) sits between the high$H_0$of the local distance ladder and the low$H_0$ of the CMB, contributing to the ongoing debate on the Hubble tension.
• Validation of Modeling Techniques: The blind analysis confirms that diverse modeling approaches can converge on consistent predictions when high-quality data (JWST/MUSE) and robust constraints (gold systems) are used. This builds confidence in using these clusters for precision cosmology.
• Strategic Roadmap: The precise forecasts for the reappearance of SN Requiem (potentially within a year) and SN Encore allow the astronomical community to schedule critical HST and JWST observations to capture these events, which will be the key to achieving percent-level precision on $H_0$.
• Framework for Future Studies: The paper establishes a "gold standard" protocol for blind lens modeling comparisons, which can be applied to other lensing systems to further reduce systematic uncertainties in cosmological parameter estimation.