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REVIEW 2 major objections 6 minor 37 references

Spectroscopic and X-ray Modeling of the Strong Lensing Galaxy Cluster MACS J0138.0-2155

T0 review · 2 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Two independent mass estimates — one from X-ray gas temperature, one from galaxy velocities — put the strong lensing cluster MACS J0138.0-2155 at roughly 5e14 solar masses and show it is round and relaxed.

desk verdict A careful cluster characterization with a real systematics strength, undercut by an abstract that silently drops the unknown velocity-bias factor from the mass claim. read the letter →

arxiv 2412.19955 v2 pith:5RMO2SG3 submitted 2024-12-27 astro-ph.CO

Abigail Flowers , Jackson H. O'Donnell , Tesla E. Jeltema , Vernon Wetzell , M. Grant Roberts This is my paper · ORCID
classification astro-ph.CO
keywords galaxyclustersstronggravitationallensingX-rayastronomyFaber-JacksonrelationvelocitydispersionclustermassestimationMACSJ0138.0-2155lensedsupernovae
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

This paper characterizes the mass and galactic substructure of MACS J0138.0-2155, the galaxy cluster that lenses a $z=1.95$ source hosting two observed supernovae, Requiem and Encore. Using X-ray data and optical spectroscopy of member galaxies, it finds a cluster mass of roughly $5\times10^{14}$ solar masses through two independent channels: the hot gas temperature gives $M_{500}=5.2^{+1.5}_{-1.2}\times10^{14}\,M_\odot$, and the galaxy velocity dispersion gives $b_v^{1/\alpha}M_{200}\approx3.6^{+2.0}_{-2.7}\times10^{14}\,M_\odot$. It also finds the cluster is round and relaxed, with an ellipticity of $0.12\pm0.03$ within the lensing region, and measures a cluster-specific Faber-Jackson relation between galaxy luminosity and stellar velocity dispersion, with slope $\alpha=0.26\pm0.06$ (stat.) $\pm0.03$ (sys.). These measurements matter because accurate strong-lensing mass models of this cluster require knowing both the total mass and how much the individual member galaxies contribute, and the paper supplies that calibration directly.

What carries the argument

The machinery is three coordinated datasets: Chandra X-ray spectra and images for the hot intra-cluster medium, integral-field optical spectroscopy for individual galaxy redshifts and stellar velocity dispersions, and Hubble imaging for galaxy luminosities. Masses are obtained by plugging the measured X-ray temperature into a temperature-mass scaling relation and the line-of-sight velocity dispersion into a velocity dispersion-mass scaling relation. The cluster velocity dispersion is estimated with biweight and gapper statistics on 23 member galaxies, each bootstrap-resampled. The cluster-specific Faber-Jackson relation $\sigma=\sigma_{\rm ref}(L/L_0)^\alpha$, fit with an MCMC and an explicit intrinsic scatter $\Delta\sigma$, is the device that turns the measured luminosities into stellar velocity dispersion predictions; the paper runs 81 variations of the spectral fitting choices to gauge systematic uncertainty in the galaxy dispersions.

What would settle it

A direct strong-lensing model of the $z=1.95$ arcs that includes the measured member-galaxy dispersions would give an independent $M_{200}$; if that mass falls outside $3.6^{+2.0}_{-2.7}\times10^{14}\,M_\odot$, the scaling-relation-based mass estimate is falsified.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that MACS0138 is a massive, relaxed cluster whose total mass can be pinned down by two independent observables, and whose member galaxies obey a well-measured cluster-specific Faber-Jackson relation. The X-ray temperature of $6.7\pm0.4$ keV and round emission morphology ($e=0.12\pm0.03$) support a relaxed, likely cool-core cluster with $M_{500}=5.2^{+1.5}_{-1.2}\times10^{14}\,M_\odot$. The cluster velocity dispersion (gapper bootstrap median $718^{+132}_{-182}$ km s$^{-1}$) gives $b_v^{1/\alpha}M_{200}=3.6^{+2.0}_{-2.7}\times10^{14}\,M_\odot$, where $b_v$ is an unknown velocity bias, and this is consistent with the X-ray mass once the different overdensity radii are accounted for. The Faber-Jackson fit over 18 bright, quiescent member galaxies gives $\alpha=0.26\pm0.06$ (stat.) $\pm0.03$ (sys.) with intrinsic scatter $\Delta\sigma=31^{+8}_{-6}$ km s$^{-1}$ at a reference velocity dispersion near 220 km s$^{-1}$, matching independent analyses and providing a direct calibration of the galaxy subhalo population for the forthcoming lens model. The paper also flags a small group at $z\approx0.37$, including a massive galaxy with stellar velocity dispersion $236\pm3$ km s$^{-1}$ close in projection to the cluster center, as a line-of-sight structure that must be included in lens modeling.

Load-bearing premise

The mass numbers are not direct measurements; they come from external scaling relations that assume MACS0138 is a relaxed, self-similar cluster, and the velocity-dispersion mass is only the biased quantity $b_v^{1/\alpha}M_{200}$, with the velocity bias $b_v$ left unmeasured.

Editorial extensions

If this is right

  • The measured Faber-Jackson relation ($\alpha=0.26$) gives lens modelers a cluster-specific way to assign stellar velocity dispersions to member galaxies from their F555W luminosities, including the mass contribution of the galaxy subhalo population within the lensing region.
  • The round X-ray morphology and small core radius suggest MACS0138 is a relaxed, likely cool-core cluster, supporting the use of self-similar scaling relations in its mass and lens modeling.
  • The consistency of the X-ray and velocity-dispersion masses means the cluster's total mass is robustly near $5\times10^{14}\,M_\odot$ within uncertainties, providing a strong prior for upcoming strong-lensing work with Requiem and Encore.
  • The identification of a foreground group at $z\approx0.37$ containing a massive galaxy ($\sigma_*\approx236$ km s$^{-1}$) near the cluster center means any lens model of the $z=1.95$ source must include an extra deflector plane, and the paper provides the redshifts and velocity dispersions needed to do so.
  • The 81-variation systematics suite shows that statistical errors dominate over analysis choices for the Faber-Jackson slope, but the systematic uncertainty of about $0.03$ should be propagated into lens models that adopt the relation.

Reading between the lines

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

  • The paper does not pursue this, but the same two mass estimates could be combined to measure the unknown velocity bias $b_v$ for this cluster: comparing the velocity-dispersion mass to the X-ray mass at a common overdensity radius would calibrate the factor $b_v^{1/\alpha}$.
  • The low intrinsic scatter in the Faber-Jackson relation hints that the satellite population is dynamically regular; a testable extension is to apply the same 81-variation systematics analysis to other strong lensing clusters to see whether the slope and scatter vary with cluster mass or redshift.
  • The foreground group at $z\approx0.37$ may be a second deflector plane for the $z=1.95$ source; if so, including it in the lens model could resolve part of the tension between the round X-ray ellipticity ($e=0.12$) and the more elliptical dark matter halo inferred by prior lens models.
  • A direct implication for the lensed supernovae Requiem and Encore is that future time-delay cosmography from these supernovae would start with the galaxy subhalo contribution to the lensing potential already quantified by the cluster-specific Faber-Jackson calibration.
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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

2 major / 6 minor

Summary. The paper analyzes the strong lensing cluster MACS J0138.0-2155 using Chandra X-ray data, MUSE integral-field spectroscopy, and HST imaging. It reports an X-ray temperature of 6.7 +/- 0.4 keV, a cluster galaxy velocity dispersion of 718^{+132}_{-182} km/s, an X-ray-derived M500 = 5.2^{+1.5}_{-1.2} x 10^14 M_sun, and a velocity-dispersion-derived b_v^{1/alpha} M200 = 3.6^{+2.0}_{-2.7} x 10^14 M_sun. It also fits a cluster-specific Faber-Jackson relation with slope alpha = 0.26 +/- 0.06 (stat.) +/- 0.03 (sys.), intrinsic scatter 31^{+8}_{-6} (stat.) +/- 4 (sys.) km/s, and reference dispersion about 223 km/s, and identifies a small group at z ~ 0.37 whose most massive member, galaxy A, is close in projection to the cluster center. The results are cross-checked against independent analyses by Granata et al. and Acebron et al.

Significance. If the results hold, the paper provides a useful mass calibration and substructure characterization for an important cluster that hosts two lensed supernovae. The analysis is careful and uses standard tools, and the agreement with independent teams, especially on the Faber-Jackson slope and the X-ray temperature, is a genuine strength. The explicit 81-run systematics protocol for the stellar velocity dispersions is also a strong feature, and I found no circular reasoning: the Faber-Jackson fit is data-driven and the masses come from external scaling relations. The main caveat is that the velocity-dispersion mass is only measured in combination with an unknown galaxy velocity bias, a point that is handled correctly in the body and conclusion but not in the abstract.

major comments (2)
  1. [Abstract and Section 5 (Discussion), with Eq. (2) in Section 4.2] The abstract reports 'M200 approx 3.6^{+2.0}_{-2.7} x 10^{14} M_sun' from the velocity dispersion results, but Eq. (2) defines the observable as b_v^{1/alpha} M200, where b_v is the unknown galaxy velocity bias relative to dark matter. With alpha = 0.3361, M200 scales as b_v^{-1/alpha} = b_v^{-2.98}; for b_v in 0.8-1.2 the implied M200 ranges from about 2.1 x 10^{14} to 7.0 x 10^{14} M_sun, which is substantially wider than the quoted asymmetric errors. Section 5 repeats the omission by stating 'the velocity dispersion estimate of M200 = 3.6...' without the b_v^{1/alpha} factor, while the conclusion correctly carries the factor and the caveat. Because the abstract and discussion present the primary mass claim, they should state the product b_v^{1/alpha} M200 explicitly, or fold a quoted range of b_v into the mass uncertainty.
  2. [Table 1, Section 4.3, and Section 6] Galaxy A's stellar velocity dispersion is listed as 236 +/- 3 km/s in Table 1 and in Section 4.3, but the Conclusion states 291 +/- 3 km/s. This internal inconsistency concerns a measurement that matters for the paper's line-of-sight group and lens-model contamination discussion. The authors should correct the value and ensure it is consistent throughout the manuscript.
minor comments (6)
  1. [Section 6, first paragraph] The text reads 'MASCJ0138'; this is a typographical error for 'MACS0138'.
  2. [Figure 1 caption] The caption contains a duplicated word: 'HST F555W image with with galaxies'.
  3. [Section 5, first paragraph] The phrase 'compared the the velocity dispersion estimate' has a duplicated 'the'.
  4. [Section 3.2 and Section 5] The manuscript uses 'affects' where 'effects' is meant, e.g., 'test the affects of our analysis choices' in Section 3.2 and 'investigate the affects of signal-to-noise' in Section 5.
  5. [Section 4.2 and Section 6] The bias factor is typeset inconsistently as b_v in Section 4.2 and as b_nu in the conclusion (e.g., 'b1/alpha_nu M200'); a single notation should be used throughout.
  6. [Table 1 footnote] The footnote reads 'the 18 galaxies used modeling the Faber-Jackson relation'; this should read 'used in modeling the Faber-Jackson relation'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: cluster masses come from externally calibrated scaling relations and the Faber-Jackson slope is a direct fit to the measured galaxy data.

full rationale

The paper's central results are empirical measurements from the data: the X-ray temperature is fit from Chandra spectra (Section 4.4), the cluster velocity dispersion is computed from MUSE galaxy redshifts using biweight and gapper estimators (Section 4.2), and the Faber-Jackson slope alpha is fit with MCMC from measured stellar velocity dispersions and HST photometry (Sections 3.2 and 4.1). None of these quantities is defined in terms of the cluster mass it later implies. The masses are obtained by inserting these independently measured observables into external scaling relations: Eq. (2) uses the Evrard et al. (2008) velocity dispersion-mass relation, and Section 4.4 uses the Mantz et al. (2016) temperature-mass relation. These relations are not derived in the paper and are not fitted to the cluster data, so there is no reduction of a prediction to an input. The velocity-dispersion mass is explicitly labeled as b_v^{1/alpha} M200 in Eq. (2) and in the Conclusion, with the text stating that b_v represents 'the unknown biases in the galactic velocities relative to the dark matter'; the abstract's omission of the b_v factor is a presentation concern, not a circularity. The 81 systematics runs vary spectral fitting choices and do not target any final cluster property. Self-citations (e.g., Wetzell et al. 2022, Hollowood et al. 2019) point to methods whose original sources are external (Beers et al. 1990; CIAO/MATCha pipeline development), and they are not used to justify a loaded premise or forbid alternatives. Independent agreement with Granata et al. (2024) and Acebron et al. (2025) provides external benchmark support. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is smuggled in via citation. Therefore the derivation chain is self-contained with no circular steps.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central mass estimates rest on published scaling relations rather than a first-principles derivation; the only new modeling assumption is the power-law form of the Faber-Jackson relation, which is standard in the field. No new physical entities are introduced.

free parameters (4)
  • X-ray metal abundance = 0.3 Z_sun (fixed)
    Fixed in the wabs*mekal spectral model; affects the derived temperature and luminosity.
  • Faber-Jackson sample selection thresholds = m_F555W < 23.5, pPXF chi2 < 2.5, dispersion error < 75 km/s
    Hand-chosen quality cuts that determine the 18-galaxy sample used to fit the scaling relation.
  • Nominal template galaxy for pPXF = galaxy W
    The template used for all nominal fits; systematics runs iterate over W, AB, AI.
  • Reference magnitude for Faber-Jackson relation = m_F555W = 20
    Chosen reference point defining L0 and sigma_ref; does not affect the slope.
assumptions (6)
  • domain assumption Flat Lambda-CDM cosmology with Omega_M=0.3, Omega_L=0.7, h0=0.69
    Used to compute h(z) when converting velocity dispersion to M200 in Eq. 2 (Section 4.2).
  • domain assumption Evrard et al. (2008) velocity dispersion-mass relation
    Input scaling used to estimate M200 from galaxy velocity dispersion (Section 4.2).
  • domain assumption Mantz et al. (2016) X-ray temperature-mass relation
    Input scaling used to estimate M500 from X-ray temperature (Section 4.4).
  • domain assumption Faber-Jackson relation is a single power law with intrinsic scatter
    Functional form assumed in Eq. 1 and the MCMC likelihood (Section 3.2).
  • standard math Biweight location/scale and gapper estimators are unbiased for small samples
    Statistical estimators adopted from Beers et al. (1990) for the cluster velocity dispersion (Section 3.3).
  • domain assumption X-ray surface brightness follows an elliptical beta model
    Used to fit ellipticity within the lensing region (Section 4.4).

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Cite this review

Pith. "Pith review of Spectroscopic and X-ray Modeling of the Strong Lensing Galaxy Cluster MACS J0138.0-2155." pith.science (2026). https://pith.science/paper/5RMO2SG3

@misc{pith2026241219955,
  author       = {Pith},
  title        = {Pith review of: Spectroscopic and X-ray Modeling of the Strong Lensing Galaxy Cluster MACS J0138.0-2155},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5RMO2SG3}},
  note         = {Machine review of arXiv:2412.19955}
}
abstract

We model the total mass and galactic substructure in the strong lensing galaxy cluster MACS J0138.0-2155 using a combination of Chandra X-ray data, Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy, and Hubble Space Telescope imaging. MACS J0138.0-2155 lenses a source galaxy at $z=1.95$ which hosts two strongly lensed supernovae, Requiem and Encore. We find MACS J0138.0-2155 to have an X-ray temperature of $6.7\pm0.4$ keV and a velocity dispersion of cluster member galaxies of $718^{+132}_{-182}$ km s$^{-1}$. These lead to the mass estimates for the cluster of $M_{500} = 5.2^{+1.5}_{-1.2} \times 10^{14} M_\odot$ from the X-ray results and $M_{200} \approx 3.6^{+2.0}_{-2.7} \times 10 ^{14} M_{\odot}$ from the velocity dispersion results. The round morphology of the X-ray emission indicates that this cluster is relaxed with an ellipticity within the lensing region of $e=0.12\pm0.03$. Using 18 of the brightest, non-blended, quiescent galaxies, we fit the cluster specific Faber-Jackson relation, including a set of 81 variations in the analysis choices to estimate the systematic uncertainties in our results. We find a slope of $\alpha = 0.26 \pm 0.06 (\mathrm{stat.}) \pm 0.03 (\mathrm{sys.})$ with an intrinsic scatter of $\Delta \sigma = 31^{+8}_{-6} (\mathrm{stat.}) \pm 4 (\mathrm{sys.})$ km s$^{-1}$ at a reference velocity dispersion of $\sim 220$ km s$^{-1}$. We also report on significant galaxies along the line-of-sight potentially impacting the lens modeling, including a massive galaxy with stellar velocity dispersion of $236 \pm 3$ km s$^{-1}$ which lies close in projection to the central cluster galaxy. This galaxy is part of a small group at a slightly higher redshift than the cluster.

Figures

Figures reproduced from arXiv: 2412.19955 by the authors.

Figure 1
Figure 1. — HST F555W image with with galaxies in our spectro￾scopic sample listed in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. — Histogram of confident redshifts of galaxies in the MUSE field as fit by MARZ with redshifts near the cluster redshift. where they were visually inspected, assigned redshifts, and assigned quality flags from 0 to 4. This work utilizes objects with quality flags of 3 and 4. We do not use the central galaxy in the analysis in this paper, and we also do not include four, blue jellyfish galaxies (galaxies un￾dergoing … view at source ↗
Figure 1
Figure 1. Columns 2-4 list the positions and magnitudes in the HST F555W imaging. Column 5 gives the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figures from the paper (8 more)
Figure 3
Figure 3. Figure 3: — MUSE spectrum of the template galaxy used in the nominal Faber-Jackson fit, galaxy W (black), overlaid with pPXF’s best fitting model (red) and residuals (green). The spectrum is shown from 3850˚A to 4500˚A and includes visible Calcium H & K and G-band absorption fea…
Figure 5
Figure 5. Figure 5: — Corner plot showing the results of the MCMC fitting of the Faber-Jackson relation for the variables σref (reference disper￾sion for m = 20), α (power-law slope), and ∆σ (intrinsic scatter); the histograms show the median values and the 68% confidence interval. Variab…
Figure 6
Figure 6. Figure 6: — Histogram of bootstrap results for the biweight (top) and gapper (bottom) methods of determining the cluster velocity dispersion, including vertical lines indicating the nominal result, median of the bootstrap results, and the 68% confidence interval. Dispersion Nomi…
Figure 7
Figure 7. Figure 7: — MUSE spectrum of galaxy A (black) overlaid with pPXF’s best fitting model (red) and residuals (green). The spectrum is shown from 3850˚A to 4500˚A and includes visible Calcium H & K and G-band absorption features. with h(z) = h0 p ΩM(1 + z) 3 + ΩΛ and take ΩM = 0.3, …
Figure 8
Figure 8. Figure 8: — Contours of X-ray emission overlaid on the JWST F200W image of MACS0138. X-ray contours are log spaced and based on the Chandra 0.5-2 keV image which has been adaptively smoothed. where rc is the core radius, Σ0 is the central surface brightness, and r is the appropr…
Figure 9
Figure 9. Figure 9: — Histogram showing the distribution of best-fit values for σref, the reference velocity dispersion in the Faber-Jackson relation, derived from the systematics tests [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: — Histogram showing the distribution of best-fit values for α, the slope of the Faber-Jackson relation, derived from the systematics tests. REFERENCES Acebron, A., Bergamini, P., Rosati, P., et al. 2025, Enhanced strong lensing model of MACS J0138.0−2155 thanks to new…
Figure 11
Figure 11. Figure 11: — Histogram showing the distribution of best-fit values for ∆σ, the intrinsic scatter in the Faber-Jackson relation, derived from the systematics tests. Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067 Fruscione, A., M…

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