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Cosmology with Supernova Encore in the lensing cluster MACS J0138$-$2155 -- Spectroscopy with MUSE

T0 review · 3 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper establishes the spectroscopic and kinematic groundwork that turns the two strongly lensed supernovae in the cluster MACS J0138–2155 into a Hubble-constant measurement.

desk verdict A solid, honest data paper that moves the SN Encore/Requiem H0 program forward; the two unresolved sigma_v discrepancies and unpublished error calibration are real but not fatal. read the letter →

arxiv 2412.13250 v3 pith:5AWW7KXJ submitted 2024-12-17 astro-ph.GA astro-ph.CO

G. Granata , G. B. Caminha , S. Ertl , C. Grillo , S. Schuldt , S. H. Suyu , A. Acebron , P. Bergamini
show 4 more authors
R. Cañameras A. M. Koekemoer P. Rosati S. Taubenberger
This is my paper · ORCID
classification astro-ph.GAastro-ph.CO
keywords galaxyclusters:individual(MACSJ0138.0−2155)gravitationallensing:stronggalaxies:distancesandredshiftskinematicsdynamicsellipticallenticularcDsupernovatimedelaysHubbleconstantFaber-Jacksonrelation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Gravitational lensing by the galaxy cluster MACS J0138–2155 produces multiple images of background sources, including four images of the host galaxy of the two supernovae Requiem and Encore; the time delays among those images depend on the Hubble constant, but only if the cluster's total mass distribution is modelled accurately. This paper supplies the observational ingredients that make such a model possible. From 3.7 hours of MUSE integral-field spectroscopy it builds a catalogue of 107 reliable redshifts, identifying 50 cluster members and 13 lensed images from four background sources, and it measures line-of-sight stellar velocity dispersions for 14 bright cluster members. Combining those kinematics with HST F160W magnitudes, it calibrates the Faber–Jackson relation, $L \propto \sigma^{1/\alpha}$, finding $\alpha = 0.25^{+0.05}_{-0.05}$ with an intrinsic scatter of $25^{+6}_{-4}$ km/s. That relation sets the velocity-dispersion parameter of every member galaxy in the strong-lensing mass model, breaking the degeneracy between member velocity dispersion and truncation radius. The result is a cluster mass model from which the Requiem–Encore time delays can be converted into an $H_0$ measurement.

What carries the argument

The load-bearing mechanism is the Faber–Jackson relation, $L \propto \sigma^{1/\alpha}$, calibrated by a Markov-chain Monte Carlo fit from 13 early-type cluster members whose line-of-sight velocity dispersions $\sigma_v$ come from pPXF full-spectrum fits of MUSE spectra, and whose luminosities come from HST F160W magnitudes. A dual pseudo-isothermal elliptical mass distribution (a dPIE, a truncated mass profile with a velocity-dispersion parameter and a half-mass radius) is the standard model component used for cluster members; for vanishing core radius its velocity-dispersion parameter is well approximated by the central stellar velocity dispersion. The calibrated relation sets that parameter from observed magnitude for every member, so the strong-lensing model no longer has to explore the degenerate velocity-dispersion/truncation-radius plane freely. The companion strong-lensing models adopt exactly this prior, which is how the kinematics enter the time-delay prediction.

What would settle it

Take the 14 cluster members with measured velocity dispersions and re-observe them at higher spectral resolution and S/N with an independent instrument and fitting code. If the recovered dispersions differ from the published values by more than the quoted uncertainties (as two of the values already differ from an independent shallower catalogue), then the Faber–Jackson calibration and the lens-model priors built on it are biased. A cheaper intermediate check is to re-run pPXF on the same spectra with the single-template approach used by that shallower catalogue and see whether the two discrepant galaxies move toward its values.

Watch

Extended reading notes

Core claim

The paper's central claim is that the new MUSE data yield a pure, complete spectroscopic sample of the cluster and a reliably calibrated Faber–Jackson relation for its early-type members, and that these are what make the upcoming $H_0$ measurement from the two lensed supernovae trustworthy. The catalogue contains 107 secure or likely redshifts, with 50 cluster members in the narrow range $0.324<z<0.349$ and 13 lensed images from four background sources spanning $0.767 \le z \le 3.420$, including the four images of the SN host at $z=1.95$; two of the background sources are new Lyman-$\alpha$ emitters found by scanning the cube. For the kinematics, pPXF full-spectrum fits on surface-brightness-weighted apertures give velocity dispersions for 14 cluster members and two background galaxies. Fitting $L \propto \sigma^{1/\alpha}$ to 13 early-type members yields $\alpha = 0.25^{+0.05}_{-0.05}$, $\sigma_{v,\mathrm{ref}} = 206^{+14}_{-13}$ km/s at the reference magnitude, and an intrinsic scatter of $25^{+6}_{-4}$ km/s. The slope is consistent with Faber–Jackson calibrations in six other lensing clusters at $0.31\le z \le 0.59$, so the paper concludes there is no statistically significant redshift evolution of the relation in that range. Because the dPIE velocity-dispersion parameter of a member is well approximated by its central stellar velocity dispersion, this calibrated relation gives the lens model an observational prior for every member's mass, which is what breaks the velocity-dispersion/truncation-radius degeneracy that would otherwise bias the predicted time delays.

Load-bearing premise

The load-bearing premise is that the velocity dispersions recovered from pPXF fits to MUSE spectra are unbiased estimates of the dPIE velocity-dispersion parameter that the lens model assigns to each cluster member; if those kinematics are biased, the Faber–Jackson relation and every strong-lensing model that uses it inherit that bias.

Editorial extensions

If this is right

  • The 107-object redshift catalogue pins down which galaxies are cluster members and which are lensed background objects, so the strong-lensing model of MACS0138 no longer has to fit the member list and image redshifts as free unknowns.
  • With the Faber–Jackson prior assigning a velocity dispersion to every member from its F160W magnitude, the lens model can predict the time delays between the four images of the SN host with a controlled member-mass uncertainty, making the subsequent $H_0$ measurement from Requiem and Encore possible.
  • The two newly discovered Lyman-$\alpha$ sources at $z=3.152$ and $z=3.420$ add multiple-image constraints at high redshift, strengthening the model against the mass-sheet degeneracy.
  • The consistency of the calibrated slope with six other clusters at $0.31\le z\le 0.59$ implies the same mass-luminosity scaling can be used as a prior for other cluster lenses in that redshift range without independent kinematics for every member.
  • The quoted intrinsic scatter of 25 km/s around the relation gives a direct estimate of how much member mass varies at fixed luminosity, which can be propagated into the final $H_0$ uncertainty budget.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Faber–Jackson prior is as informative as claimed, the resulting $H_0$ from Requiem–Encore should be systematically more precise than it would be with the member masses left free; this can be tested by comparing the $H_0$ posterior with and without the kinematic prior in the same lens model.
  • The reported tens-of-km/s disagreements for two objects with an independent shallower catalogue suggest the systematic floor of the kinematic measurements is not yet fully settled, so a targeted re-observation of those two galaxies at higher S/N with a different template set would be a decisive check.
  • The S/N $\ge 10$ threshold and the quoted uncertainties rest on 16,000 simulated spectra described in a companion paper that has not yet appeared; publishing those simulations would let other groups reproduce the error budget and extend the method to shallower data.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper presents VLT/MUSE spectroscopy of the galaxy cluster MACS J0138−2155, totalling 3.7 hours, and uses it to build a spectroscopic catalogue of 107 objects with reliable redshifts, including 50 cluster members and 13 multiply lensed images from four background sources (among them four images of the host galaxy of SNe Requiem and Encore). It measures line-of-sight stellar velocity dispersions for 14 cluster members and two background galaxies from pPXF fits with a carefully selected stellar template library, and calibrates the Faber-Jackson relation L ∝ σ^{1/α} for 13 early-type cluster members using F160W magnitudes from a companion paper, finding α = 0.25 ± 0.05 and intrinsic scatter 25 km/s. The calibrated relation is compared with six other strong-lensing clusters and found to be consistent with no significant redshift evolution. The kinematic catalogue and scaling relation are intended as priors for strong lensing models used for H0 measurement from the two lensed supernovae.

Significance. If the measured velocity dispersions and the resulting Faber-Jackson calibration are reliable, this paper provides a valuable data product for cluster lensing cosmology: a complete spectroscopic member sample, new multiply imaged background sources, and a direct kinematic prior on the dPIE velocity dispersion parameters that break a known degeneracy in cluster lens models. The data reduction is careful and the redshift catalogue is a concrete deliverable. The main weakness is that the two load-bearing ingredients for the FJ claim, the velocity dispersion error calibration and the FJ fit, rest on materials that are either unpublished or disputed by an independent measurement, so the paper's central reliability claim is not yet fully supported.

major comments (3)
  1. [Section 4.1, Table 1] The velocity dispersion for ID MUSE 930 (97 ± 5 km/s) differs by ~70 km/s from the independent measurement of Flowers et al. (2024) (167 ± 15 km/s), and ID MUSE 873 differs by ~50 km/s (238 ± 2 vs 291 ± 3 km/s). Because ID 930 is one of the 13 points used to fit the Faber-Jackson relation, the authors should demonstrate that the fitted parameters (α, σ_v,ref, Δσ_v) are robust to this possible systematic. A straightforward sensitivity test would be to refit the relation without ID 930 (or using the Flowers et al. value) and report the resulting parameters; without such a test, the claim that the calibrated slope is reliable is not yet established.
  2. [Section 4.1] The uncertainty on each σ_v value is derived from a calibration based on 16,000 simulated spectra that is described only in the unpublished Granata et al. (in prep.) paper. Since these error bars enter directly into the Faber-Jackson likelihood and the quoted intrinsic scatter, the paper should either provide the essential elements of the simulation (input galaxy models, noise recipes, the fitted relative-uncertainty versus S/N relation) or include them in an appendix, so that the error estimates are reproducible and can be assessed by the reader.
  3. [Section 4.2, Eq. (1) and Table 2] The Faber-Jackson fit treats the F160W magnitudes from Ertl et al. (2025) as fixed (not explicitly including their uncertainties). If magnitude errors are non-negligible, the fitted slope α could be biased. Please clarify whether the likelihood adopted from Bergamini et al. (2019) includes errors on both variables, and if not, provide a quantitative statement of the impact of magnitude uncertainties on α and σ_v,ref.
minor comments (3)
  1. [Section 5] In the Summary, the paper states 'we report 4 lensed images of the host of SN Encore and SN Requiem, and 11 images from three other lensed background sources', which sums to 15, but the catalogue in Section 3.2 and Table A.1 lists 13 multiply lensed images in total, with 9 images from the three other sources. Please correct the count.
  2. [Section 2] There are typographical issues, e.g., 'reduced e ffective exposure time' and 'James WebbSpace Telescope'; please fix the spacing.
  3. [Section 4.1] The sentence 'we probed the relative uncertainty on the value of sigma as a function of S/N from the 1σ scatter of the recovered σv values about the input velocity dispersion of the 16,000 simulated spectra' could be reworded for clarity, e.g., 'we measured the relative uncertainty as a function of S/N from the 1σ scatter of the recovered σv values about the input values.'

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the redshifts, velocity dispersions, and Faber-Jackson slope are direct measurements or explicit fits; companion-paper dependencies affect calibration provenance, not derivation.

full rationale

The paper's central results are not derived from the model they are meant to constrain. Redshifts come from direct spectral-line identification in MUSE data (Section 3), with quality flags assigned from template matching and emission-line shapes. The stellar velocity dispersions come from pPXF full-spectrum fits shown in Appendix B, and the Faber-Jackson relation is an explicit MCMC fit of Equation (1) to the measured sigma values and F160W magnitudes, not a prediction from the relation itself. The recovered normalization being consistent with the reference galaxy's measured sigma is expected from the definition of the reference magnitude in Equation (1), but it is presented only as a consistency note, not as an independent prediction. The reliance on Granata et al. (in prep.) for the 16,000 simulated spectra calibrating the S/N threshold and uncertainties is a verifiability or provenance concern, since that companion paper is unpublished and partly overlaps in authorship; however, the actual sigma values are measured, not imported from that paper, and the uncertainities are the only part resting on the simulations. Similarly, the dPIE approximation and Faber-Jackson prior methodology are cited from published work (Bergamini et al. 2019), which provides methodological support rather than a reduction of this paper's outputs to its inputs. The disagreements with Flowers et al. (2024) on two sigma values are a systematic-bias risk that belongs to correctness assessment, not circularity. No step in the paper derives a target quantity from that same quantity by construction or via a self-citation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims are measurements and a fitted scaling relation; no new physical entities are introduced. The fitted Faber-Jackson parameters are outputs, not ad hoc inputs, but they are listed for completeness. The main unstated support comes from the dPIE-based identification of stellar with total velocity dispersion, the proxy use of F160W luminosity, the unpublished simulation calibration, and the GALEV K-corrections.

free parameters (3)
  • Faber-Jackson slope alpha = 0.25 (+0.05, -0.05)
    Fitted by MCMC to 13 early-type cluster members using Eq. (1); this is the calibrated scaling relation, not a hidden input.
  • Velocity dispersion normalization sigma_v,ref = 206 (+14, -13) km/s
    Normalization of Eq. (1) at the reference magnitude mF160W=17.985; determined from the same MCMC fit.
  • Intrinsic scatter Delta_sigma_v = 25 (+6, -4) km/s
    Second parameter of the scaling relation posterior, quantifying scatter about the Faber-Jackson relation.
assumptions (4)
  • domain assumption Member galaxy halos are described by truncated dPIE profiles with vanishing core radius, and the dPIE velocity dispersion parameter equals the central stellar velocity dispersion.
    Invoked in Section 4.2 via Bergamini et al. (2019); this identification is what lets the measured stellar kinematics serve as a mass prior in lens models.
  • domain assumption Total luminosity in F160W is a good proxy for total stellar mass and follows a single power-law Faber-Jackson relation for early-type cluster members.
    Used in Section 4.2 to link luminosity to velocity dispersion; the BCG is excluded because it may not follow the same relation.
  • domain assumption The pPXF fitting configuration (462 XSL templates, 12th-degree additive polynomials, Gaussian LOSVD) recovers unbiased velocity dispersions when S/N >= 10.
    Relies on 16,000 simulated MUSE spectra in the unpublished Granata et al. (in prep.); the threshold is not independently verifiable from this paper.
  • domain assumption GALEV synthetic early-type spectra provide adequate K-corrections to compare magnitudes across seven clusters in the rest-frame J band.
    Used in Section 4.2 and Figure 7 for the comparison of Faber-Jackson relations; systematic errors from this choice are not quantified.

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Cite this review

Pith. "Pith review of Cosmology with Supernova Encore in the lensing cluster MACS J0138$-$2155 -- Spectroscopy with MUSE." pith.science (2026). https://pith.science/paper/5AWW7KXJ

@misc{pith2026241213250,
  author       = {Pith},
  title        = {Pith review of: Cosmology with Supernova Encore in the lensing cluster MACS J0138$-$2155 -- Spectroscopy with MUSE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5AWW7KXJ}},
  note         = {Machine review of arXiv:2412.13250}
}
abstract

We present a spectroscopic analysis of MACS J0138$-$2155, at $z=0.336$, the first galaxy cluster hosting two strongly-lensed supernovae (SNe), Requiem and Encore, providing us with a chance to obtain a reliable $H_0$ measurement from the time delays between the multiple images. We take advantage of new data from the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope, covering a central $1 \rm \, arcmin^2$ of the lensing cluster, for a total depth of 3.7 hours, including 2.9 hours recently obtained by our Target of Opportunity programme. Our new spectroscopic catalogue contains reliable redshifts for 107 objects, including 50 galaxy cluster members with secure redshift values in the range $0.324 < z < 0.349$, and 13 lensed multiple images from four background sources between $0.767\leq z \leq 3.420$, including four images of the host galaxy of the two SNe. We exploit the MUSE data to study the stellar kinematics of 14 bright cluster members and two background galaxies, obtaining reliable measurements of their line-of-sight velocity dispersion. Finally, we combine these results with measurements of the total magnitude of the cluster members in the Hubble Space Telescope F160W band to calibrate the Faber-Jackson relation between luminosity and stellar velocity dispersion ($L \propto \sigma^{1/\alpha}$) for the early-type cluster member galaxies, measuring a slope $\alpha=0.25^{+0.05}_{-0.05}$. A pure and complete sample of cluster member galaxies and a reliable characterisation of their total mass structure are key to building accurate total mass maps of the cluster, mitigating the impact of parametric degeneracies, which is necessary for inferring the value of $H_0$ from the measured time delays between the lensed images of the two SNe.

Figures

Figures reproduced from arXiv: 2412.13250 by the authors.

Figure 1
Figure 1. MUSE FoV of MACS0138 overlaid on a colour image built from JWST NIRCam images (red: F277W, F356W, F444W; [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Redshift distribution around the cluster redshift ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. MUSE FoV of MACS0138 overlaid on a colour image built from the JWST NIRCam images (the bands used are the same [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Spectra of the secure multiple images (QF [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: VLT/MUSE mean stacked spectrum of the 13 cluster members, all except the BCG, for which we obtained a line-of￾sight stellar velocity dispersion measurement. The shaded region shows the standard deviation of each spectral pixel. The spectra were smoothed by applying a G…
Figure 6
Figure 6. Figure 6: Faber-Jackson relation for the members of MACS0138. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Faber-Jackson relation for the members of MACS0138 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Forward citations

Cited by 3 Pith papers

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.