The z=1.03 Merging Cluster SPT-CL J0356-5337: New Strong Lensing Analysis with HST and MUSE

Benjamin Floyd; Bradford Benson; Gourav Khullar; Grace Smith; Guillaume Mahler; Kate Napier; Keren Sharon; Lindsey Bleem; Matthew Bayliss; Michael D. Gladders

REVIEW 2 major objections 4 minor 1 cited by

The z=1.03 Merging Cluster SPT-CL J0356-5337: New Strong Lensing Analysis with HST and MUSE

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Strong lensing resolves two cluster cores with a 1.35 mass ratio, supporting a plane-of-sky major merger.

desk verdict Solid incremental lensing update with genuinely new data; the 1.35 mass ratio is plausible, but the 80-kpc aperture masses are inward extrapolations from constraints that all lie outside that radius. read the letter →

arxiv 2507.07404 v2 pith:UYNYNNH2 submitted 2025-07-10 astro-ph.CO astro-ph.GA

Grace Smith , Guillaume Mahler , Kate Napier , Keren Sharon , Matthew Bayliss , Bradford Benson , Lindsey Bleem , Benjamin Floyd

show 3 more authors

Michael D. Gladders Gourav Khullar Tim Schrabback

This is my paper

classification astro-ph.COastro-ph.GA

keywords galaxyclustersstronggravitationallensingclustermergersdarkmatterdistributionhigh-redshiftuniverseMUSEspectroscopyHubbleSpaceTelescopeLyman-alphaemitters

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 aims to determine whether the z=1.034 galaxy cluster SPT-CL J0356-5337 is a major merger and to weigh its two mass components. With new multiband HST imaging and VLT/MUSE spectroscopy, the authors identify five strongly lensed background galaxies (twelve sets of multiple images) and grow the cluster member catalog from 45 to 149 galaxies. Their lens models split the projected mass into a core around the brightest cluster galaxy and a western core around a compact group of luminous red galaxies, giving $M_{\mathrm{BCG}}(<80\,\mathrm{kpc}) = 3.93^{+0.21}_{-0.14}\times 10^{13}\,M_\odot$ and $M_{\mathrm{LRG}}(<80\,\mathrm{kpc}) = 2.92^{+0.16}_{-0.23}\times 10^{13}\,M_\odot$, a mass ratio of $1.35^{+0.16}_{-0.08}$. Because that ratio, the ~170 kpc sky separation, and the ~135 km/s radial velocity offset all agree, the authors conclude the system is a major merger seen largely on the plane of the sky. Such near-plane mergers of massive halos at high redshift are rare, and this one now has a mass map sharp enough to compare galaxies, dark matter, and hot gas during the collision.

What carries the argument

The machinery is parametric strong-lens mass reconstruction: multiply imaged background galaxies act as natural rulers, and the lens plane is modeled as a superposition of pseudo-isothermal elliptical mass distributions (dPIE halos). Cluster-scale halos have free position, ellipticity, orientation, velocity dispersion, and core radius; the 149 cluster member galaxies contribute halos whose sizes and velocities scale with their F110W/F160W luminosities, with two normalization parameters shared by the whole population. A Markov Chain Monte Carlo sampler varies these parameters until the predicted positions of the 32 multiple images match the observed ones, and the resulting projected mass maps are summed in 80-kpc apertures around each core to obtain the subcluster masses and their ratio. New multiband colors and MUSE redshifts, including two newly confirmed lensed sources at $z=3.0205$ and $z=5.3288$, are what let the constraints extend east and west of the two cores instead of only between them.

What would settle it

A model-independent projected mass map—for example, a deep weak-lensing shear analysis outside the strong-lensing region or a free-form strong-lens reconstruction without fixed halo profiles—that yields an 80-kpc mass ratio below about 1.1, or Chandra X-ray imaging that shows a single gas peak coincident with one of the two cores rather than between them, would call the major-merger and plane-of-sky conclusions into question.

Watch

Extended reading notes

Core claim

The central claim is that the projected mass distribution of SPT-CL J0356-5337 contains two dominant components within 80 kpc apertures: the BCG core and the LRG core. The best-fit model (two cluster-scale halos plus galaxy-scale halos) yields $M_{\mathrm{BCG}}(<80\,\mathrm{kpc}) = 3.93^{+0.21}_{-0.14}\times 10^{13}\,M_\odot$ and $M_{\mathrm{LRG}}(<80\,\mathrm{kpc}) = 2.92^{+0.16}_{-0.23}\times 10^{13}\,M_\odot$, a ratio of $1.35^{+0.16}_{-0.08}$, and the total projected mass within 500 kpc is $3.75^{+0.40}_{-0.34}\times 10^{14}\,M_\odot$. The same aperture masses and ratios are recovered across all five model variants—one, two, or three cluster-scale halos, with galaxy scaling relations free or fixed—so the paper argues this measurement is robust to modeling assumptions. Combined with the small separation (~170 kpc) and small radial velocity difference (135 km/s), the two-component mass map corroborates the earlier suggestion that SPT-0356 is a major merger occurring close to the plane of the sky.

Load-bearing premise

The load-bearing assumption is that the cluster's mass is well represented by a sum of smooth elliptical (dPIE) halos, with galaxy-scale halos scaled from red-sequence luminosities; if significant mass sits in unmodeled substructure or follows a very different inner profile, the 80-kpc aperture masses and the 1.35 ratio could shift.

Editorial extensions

If this is right

If SPT-0356 is a major merger on the plane of the sky, it becomes a rare high-redshift example where two dark matter halos of comparable mass can be weighed during the collision, complementing local analogs like the Bullet Cluster.
The 80-kpc aperture masses, with roughly 5-7% statistical uncertainties, provide a strong-lensing benchmark for merger simulations and for calibrating SZ-selected cluster mass estimates at $z\sim1$.
The new western constraints localize the LRG-group dark matter halo to a much smaller region than before, making the predicted offset between gas, galaxies, and dark matter directly testable with the Chandra X-ray data already in hand.
The measured total mass profile is nearly identical across models even though the galaxy mass fraction varies between 10% and 18%, so the overall cluster mass budget is secure even where the decomposition into galaxies and dark matter is not.

Reading between the lines

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

A natural extension the authors do not carry out is to calibrate the measured 1.35 aperture mass ratio against simulated major mergers at $z\sim1$; projection and the 80-kpc apertures can each bias the ratio relative to the true 3D mass, and only simulations can quantify that bias.
If the Chandra X-ray data show a single gas peak between the two dark matter halos, SPT-0356 would qualify as a dissociative merger at $z>1$, joining a short list of systems that separate baryons from dark matter and can be used to constrain dark-matter self-interactions at high redshift.
The newly confirmed lensed source at $z=5.3288$ is a pointed probe of the inner mass profile: treating its extended Ly$\alpha$ emission as an extended source, rather than a single compact knot, could either tighten the model or reveal small-scale substructure that the smooth-halo superposition misses.
The three double-peaked Ly$\alpha$ emitters at $z=4.1448$, ruled out as multiple images of one source, are likely a magnified background group; their line profiles could serve as kinematic tracers of circumgalactic gas in an early overdensity.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a competent, genuinely useful update of the Mahler et al. (2020) lens model for SPT-CL J0356-5337, with new HST and MUSE data. The headline measurement—two subcluster masses within 80 kpc and a 1.35 mass ratio—is plausible and robust across a reasonable set of parametric models. But the 80-kpc numbers are extrapolations from constraints that all sit outside that radius, so the quoted statistical errors understate the systematic uncertainty from the assumed dPIE inner profile.

What's new: two new spectroscopically confirmed lensed sources (z=3.0205 from a single Ly-alpha line, z=5.3288 also Ly-alpha), a tripled member catalog (149 galaxies vs 45), and better constraint geometry, with system 7 east and system 4 west. The improvement in the LRG halo position is real and driven by system 4. The model comparison (A-E) is honest, and the paper explicitly tests one- vs two- vs three-halo models and free vs fixed galaxy scaling relations. That is the right way to do this. Also good: they do not oversell the 'deconstructed' H1/H2 ratio of 3.2±1.2, and they flag it as degenerate.

Soft spots, in order:

1. The 80-kpc aperture masses. Every multiple-image constraint in Table 1 is outside 80 kpc from the respective core; the innermost is system 1 at ~130 kpc and system 4 at ~97 kpc. The model therefore pins the enclosed mass and deflection field outside the apertures, while the mass inside 80 kpc is set by the assumed dPIE core shape, with H1's core radius in model B ~68 kpc, comparable to the aperture. The consistency across models A-E is consistency within one profile family, not a test of the inner slope. The ratio could shift by more than the quoted errors if the true profile is cuspier. The authors actually give a hint of this themselves with the deconstructed estimate, which yields 3.2±1.2. I would want a sentence acknowledging that the 80-kpc aperture masses inherit this model dependence, and ideally a cored vs cusped profile check.

2. The two new MUSE redshifts rest on single Ly-alpha lines. The paper has a confidence classification but doesn't state it for these two. Given Ly-alpha can be asymmetric and offset from systemic, this is a minor concern; system 7 is at z~5.33 and could matter for critical curve placement. Still minor.

3. BIC is used but then overridden by physical arguments. That is fine, but the selection of model B as fiducial is somewhat subjective. Not a flaw; they show all models.

The central argument—that this is a two-component merger with comparable masses—holds up. The mass ratio within 80 kpc is stable at ~1.3-1.4 across models, and the velocity offset is small. This is a good example of careful parametric lensing work and deserves serious refereeing. The extrapolation issue is addressable with a non-parametric or cusped-profile test, and the single-line redshifts deserve a check.

Recommendation: send to peer review. A good referee will ask for a robustness check on the inner profile, but this is a solid dataset and a fair claim.

Referee Report

2 major / 4 minor

Summary. The paper presents a new strong-lensing analysis of the z=1.034 cluster SPT-CL J0356-5337 based on new multiband HST imaging and MUSE spectroscopy. The authors identify 12 sets of multiple images in five spectroscopically confirmed lensed sources, increase the cluster member catalog from 45 to 149 galaxies, and construct a sequence of five parametric (dPIE) lens models with increasing complexity. From the models they measure the projected mass enclosed within 80 kpc apertures around the BCG and the LRG subcluster, obtaining M_BCG(<80 kpc)=3.93+0.21-0.14 x 10^13 Msun and M_LRG(<80 kpc)=2.92+0.16-0.23 x 10^13 Msun, a ratio of 1.35+0.16-0.08. They conclude that the cluster is dominated by two comparable-mass components and is likely undergoing a major merger on the plane of the sky, consistent with the earlier analysis of Mahler et al. (2020).

Significance. If the mass ratio is robust, the paper is a valuable addition to the small set of high-redshift merging clusters with strong-lensing mass maps. The new HST and MUSE data clearly improve the observational basis: the number of spectroscopically confirmed lensed sources increases from three to five, the cluster member catalog is tripled, and the new constraints east and west of the two cores reduce the statistical uncertainties on the halo positions and total mass compared with Mahler et al. (2020). The authors also report interesting serendipitous detections of extended Ly-alpha emission and a candidate background group of LAEs. The modeling is careful: five model variants are compared, MCMC uncertainties are propagated to the mass ratio in each chain step, and the authors explicitly discuss model degeneracies. However, the central claim of a robust 1.35 mass ratio rests on a single parametric family for the cluster-scale halos, and the paper's own 'deconstructed' mass estimate (3.2+-1.2) and its discussion of component degeneracies indicate that this ratio is less robust than the total projected mass.

major comments (2)

[Section 5.1, Table 2, Table 3, Section 4.1] The 80-kpc aperture masses are measured from best-fit dPIE halos whose core radii are comparable to the aperture size: in model B, H1 has r_c=68+10-27 kpc and H2 has r_c=37+62-11 kpc. I verified that the apertures are not entirely unconstrained: system 4 lies at about 60 kpc from the LRG core and system 1 at about 74-76 kpc from the BCG, so the aperture boundary is directly probed by image positions. However, the mass interior to those radii is not directly sampled; the dPIE core shape determines how the enclosed mass is distributed inside the core, and the image positions mainly fix the enclosed mass at or outside the aperture edge. The agreement among models A-E in Table 3 tests the number of cluster-scale halos and the treatment of galaxy scaling relations, but every model uses the same dPIE family for the cluster halos (Section 4.1). The abstract's statement that the lensing constraints give 'a robust estimate of the projected mass density regardless of modeling assumptions' is therefore stronger than what the model comparison demonstrates. I recommend adding a systematic test with an alternative radial profile family (e.g., NFW-like or cuspy halos) for the cluster-scale components, or explicitly qualifying the 80-kpc masses and the mass ratio as conditional on the dPIE parametrization.
[Section 5.1 and Section 6.3] The paper reports a 'deconstructed' mass ratio of 3.2+-1.2 within 160 kpc, compared with 1.35+0.16-0.08 within 80 kpc. The authors caution that single-component masses are degenerate and that this estimate should be treated with caution, but the large difference is not reconciled in the text. Section 6.3 states that the lensing analysis cannot tightly constrain the relative contributions of mass components and that the shape of the model outside the strong-lensing constraints is unconstrained. Because the central conclusion is the classification as a major merger, which depends on the subcluster mass ratio, the paper should either quantify the effect of the component-assignment degeneracy on the 80-kpc ratio (the fixed versus free galaxy scaling-relation models D/E are a partial step in this direction) or soften the concluding claim that the ratio is robust to modeling assumptions. As written, the reader cannot tell whether the 1.35 ratio is a property of the total projected mass distribution or an artifact of the 80-kpc aperture and the dPIE decomposition.

minor comments (4)

[Equation (1), Section 5] The BIC definition uses n=40 as the sample size; please state explicitly that n is the number of constraints and clarify how the k=number-of-free-parameters enters, since the text refers to both 'sample size' and 'number of constraints' without a definition of the likelihood's data points.
[Section 3.2] The text reads 'The double peak emission is observed at 6254.35 Å and 6254.35 Å'; one of these should be the blue peak at 6243.80 Å, as given earlier in the same paragraph.
[Table 1] The magnification uncertainties for system 4 and candidate 5 are extremely asymmetric and large (e.g., mu=12.3+167.7-5.6 for 4.3c). Consider reporting these in a separate table or noting that the magnification posterior is poorly constrained, to avoid giving the impression of well-measured values.
[Section 6.4] The BIC strongly favors model A (BIC=32.9) over the fiducial model B (BIC=50.9), yet model B is selected based on physical alignment arguments. This is a defensible choice, but the criteria for preferring model B over model A should be stated more quantitatively (e.g., what level of H1-BCG misalignment is considered unphysical).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the 80-kpc subcluster masses are integrals of a model fit to independent lensing constraints, not fitted parameters renamed as predictions.

full rationale

SPT-0356's central mass measurements are not circular. The derivation chain is: new HST/MUSE observations -> identification of 12 sets of multiple images from five spectroscopically confirmed sources -> Lenstool parametric fits (models A-E) to image positions and redshifts -> integration of the best-fit projected mass density inside 80 kpc apertures centered on the BCG and LRG group. The aperture masses and their ratio are outputs of the fit, not constraints used in the fit; no parameter is fitted to M_BCG(<80kpc) or M_LRG(<80kpc) and then presented as a prediction. The Mahler et al. (2020) model is used only as a starting point and for comparison, and the final models are re-optimized against the new, independent constraints (systems 4 and 7, MUSE redshifts, expanded member catalog), with the authors explicitly testing one-, two-, and three-halo models and fixed versus free galaxy scaling relations. Robustness across these models, despite the shared dPIE parameterization, is a model-consistency check rather than a circular reduction. The skeptic's observation that all image constraints lie outside 80 kpc is a valid caveat about inner-profile extrapolation and systematic uncertainty, but it does not make the aperture-mass estimate equivalent to an input by construction. Self-citations to Mahler et al. (2020) provide previously published redshifts and methodological precedent, but are not load-bearing for the new fit.

Assumptions & free parameters 19 free parameters · 5 assumptions · 0 invented entities

These are the key fitted parameters of the fiducial model B that determine the projected mass density within 80 kpc of the two subcluster cores. The full parameter list is in Table 2; additional free parameters in models C-E (e.g., H4) are not listed here.

free parameters (19)

H1 sigma0 (BCG subcluster velocity dispersion normalization) = 884+30-166 km/s (model B)
Cluster-scale dPIE halo near the BCG; directly sets the mass of the dominant component in the 80 kpc aperture.
H1 core radius rc = 68+10-27 kpc (model B)
dPIE core radius of H1; affects inner mass profile.
H1 ellipticity e = 0.73+0.07-0.12 (model B)
Ellipticity of H1; optimized by Lenstool.
H1 position (Delta RA, Delta Dec) = -0.20+2.95-0.88, 1.12+0.68-1.57 arcsec (model B)
Position relative to reference coordinate; affects mass distribution alignment.
H1 position angle theta = 27.4+2.8-2.8 deg (model B)
Orientation of H1.
H2 sigma0 (LRG subcluster velocity dispersion normalization) = 373+186-20 km/s (model B)
Cluster-scale halo near the LRG group; determines the western mass component.
H2 core radius rc = 37+62-11 kpc (model B)
dPIE core radius of H2.
H2 ellipticity e = 0.26+0.60-0.23 (model B)
Ellipticity of H2.
H2 position (Delta RA, Delta Dec) = -28.9+13.6-1.6, 6.2+3.6-3.9 arcsec (model B)
Position of the western halo relative to reference.
H2 position angle theta = 243+30-137 deg (model B)
Orientation of H2.
L* sigma0 (pivot velocity dispersion of galaxy scaling relation) = 246.5+2.7-51.5 km/s (model B)
Normalizes masses of all cluster member galaxies via luminosity scaling.
L* rcut (pivot truncation radius) = 43.1+34.7-6.8 kpc (model B)
Sets truncation radius for galaxy-scale halos.
System 33 redshift = 3.06+0.12-0.11
The redshift of the candidate knot family 33 was left free in the optimization because no unique spectroscopic redshift could be extracted.
H3 sigma0 (galaxy-scale halo near system 4) = 51+142-13 km/s (model B)
Galaxy-scale halo near lensed system 4; freed slope and normalization to account for local perturbations.
H3 rcut = 81+16-80 kpc (model B)
Truncation radius for H3.
H3 rc = 0.15+0.33-0.14 kpc (model B)
Core radius for H3.
H5 sigma0 (jellyfish galaxy halo) = 150+95-96 km/s (model B)
Independent galaxy-scale halo for the star-forming jellyfish member, decoupled from scaling relations.
H5 rcut = 14+35-12 kpc (model B)
Truncation radius for H5.
H5 rc = 0.01+0.08-0.01 kpc (model B)
Core radius for H5.

assumptions (5)

domain assumption Flat LambdaCDM cosmology with Omega_m=0.3, Omega_Lambda=0.7, H0=70 km/s/Mpc is assumed for distance and mass conversions.
Section 1 states this cosmology; all physical scales (kpc, mass) depend on it.
standard math Strong lensing is described by the standard thin-lens approximation and the deflector can be modeled as a linear sum of dPIE halos.
Section 4.1; the dPIE profile is adopted from prior literature (Eliasdottir et al. 2007) and not independently justified.
domain assumption Cluster member galaxy masses scale with luminosity according to the Jullo et al. (2007) relations.
Section 4.2 and 4.3; all 149 member galaxies are included using these scaling relations with only a few free pivot parameters.
domain assumption The new redshifts of systems 4 (z=3.0205) and 7 (z=5.3288) derived from single Ly-alpha emission lines are correct.
Section 3.1; these are used as hard constraints in the lens model without error bars or explicit confidence flags.
domain assumption The red-sequence selection (F110W-F160W vs F110W) identifies cluster members without significant contamination or incompleteness.
Section 4.2; the red-sequence fit is extrapolated to faint magnitudes and outside the MUSE field.

how reviews work

0 comments

Cite this review

Pith. "Pith review of The z=1.03 Merging Cluster SPT-CL J0356-5337: New Strong Lensing Analysis with HST and MUSE." pith.science (2026). https://pith.science/paper/UYNYNNH2

@misc{pith2026250707404,
  author       = {Pith},
  title        = {Pith review of: The z=1.03 Merging Cluster SPT-CL J0356-5337: New Strong Lensing Analysis with HST and MUSE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UYNYNNH2}},
  note         = {Machine review of arXiv:2507.07404}
}

read the original abstract

We present a strong lensing analysis and reconstruct the mass distribution of SPT-CL J0356-5337, a galaxy cluster at redshift z = 1.034. Our model supersedes previous models by making use of new multi-band HST data and MUSE spectroscopy. We identify two additional lensed galaxies to inform a more well-constrained model using 12 sets of multiple images in 5 separate lensed sources. The three previously-known sources were spectroscopically confirmed by Mahler et al. (2020) at redshifts of z = 2.363, z = 2.364, and z = 3.048. We measured the spectroscopic redshifts of two of the newly-discovered arcs using MUSE data, at z = 3.0205 and z = 5.3288. We increase the number of cluster member galaxies by a factor of three compared to previous work. We also report the detection of extended Lya emission from several background galaxies. We measure the total projected mass density of the two major sub-cluster components, one dominated by the BCG, and the other by a compact group of luminous red galaxies. We find M_BCG(< 80kpc) = 3.93+0.21-0.14 * 10^13Msun and M_LRG(< 80kpc) = 2.92+0.16 -0.23 * 10^13Msun, yielding a mass ratio of 1.35+0.16 -0.08. The strong lensing constraints offer a robust estimate of the projected mass density regardless of modelling assumptions; allowing more substructure in this line of sight does not change the results or conclusions. Our results corroborate the conclusion that SPT-CL J0356-5337 is dominated by two mass components, and is likely undergoing a major merger on the plane of the sky

Figures

Figures reproduced from arXiv: 2507.07404 by the authors.

**Figure 1.** HST imaging of SPT-0356 using WFC3/F160W (red), ACS/F814W (green) and ACS/F606W (blue). Cluster components are labeled in white. The different instrument footprints are labeled in white (MUSE), orange (HST WFC3), and cyan (HST ACS mosaic). band HST imaging that was available at the time to use the substructure of each source as an individual constraint, multiplexing two of the systems into three sets of constraints… view at source ↗

**Figure 2.** HST image of SPT-0356 with lens model constraints labeled. The critical curve at z = 3 is shown for model B. Arcs and arc candidates are labeled and color-coded by system; their coordinates are listed in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Zoom-in on three strongly lensed galaxies with multiple images, showing Lyα emission in the MUSE Integral Field Unit (IFU). The Lyα emission is represented with green contours overplotted on the HST imaging. The top two systems show extended Lyα emission with peaked emission offset from the HST continuum. The bottom row shows three images of a very compact Lyα emitter. Contour levels are at 250, 500, 2500, and 5000… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Left: HST imaging and Lyα contours of three LAEs ∼ 30′′ southeast of the BCG. Contours of the Lyα levels from MUSE are plotted at 250, 500, 2500, and 5000 ×10−20ergs s −1 cm−2 arcsec−2 . The critical curve for the redshift of these galaxies is overplotted as a solid re…

**Figure 5.** Figure 5: The three LAEs at z = 4.1448, ray-traced to the source plane (Lyα contours from MUSE overplotted on the HST imaging). The galaxies are separated by ∼ 40 kpc when unlensed and likely form a small background group. H5 is a galaxy-scale halo that accounts for the mass of …

**Figure 6.** Figure 6: Color-magnitude diagram of galaxies in the HST/WFC3 field of view. The F110W-F160W color is plotted against F110W magnitude. Cluster member galaxies form a red sequence in this parameter space, highlighted by spectroscopically-selected cluster members (green datapoin…

**Figure 7.** Figure 7: Image of the field with cluster member galaxies identified. Magenta ellipses denote cluster member galaxies spectroscopically confirmed using MUSE data. Yellow ellipses denote cluster member galaxies identified by color (see Section 4.2). The dark matter halos describ…

**Figure 8.** Figure 8: Mass and mass fraction from the different lens models presented in this work. From left to right: the total mass of the cluster measured as projected (cylindrical) mass within 500 kpc from the BCG; the mass measured within 80 kpc from the BCG, the mass measured within …

**Figure 9.** Figure 9: Mass contours overlaid on the HST imaging for models A, B, C, and D in blue, red, green, and orange, respectively. The contours are plotted at projected mass densities of 0.25, 0.5, 1 and 2×109M⊙kpc−2 . The magenta cross marks the centroid the X-ray emission (Mahler …

**Figure 10.** Figure 10: The projected mass density profile of the individual contributions of the major cluster halos and the galaxy component. The average mass densities are measured in annuli centered on the BCG. Uncertainties are on the order of ∼10%, but are omitted for clarity. Each pan…

**Figure 11.** Figure 11: Total projected mass density profiles for the range of models investigated in this paper. The average mass densities are measured in annuli centered on the BCG. The “bump” at ∼ 200 kpc corresponds to the LRG structure. Uncertainties are 95% confidence interval, derive…

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

SLICE: SPT-CL J0546-5345 -- A prominent strong-lensing cluster at $z=1.07$
astro-ph.CO 2025-07 conditional novelty 5.0 of 10

SPT-CL J0546-5345 is a prominent strong-lensing galaxy cluster at z=1.07, with Einstein radii up to about 28 arcseconds and a projected mass of about 2e14 solar masses within 200 kpc, comparable to Hubble Frontier Fie...

Reference graph

Works this paper leans on

35 extracted references · 5 canonical work pages · cited by 1 Pith paper

[1]

2022, A&A, 668, A142, doi: 10.1051/0004-6361/202244836 Astropy Collaboration, Price-Whelan, A

Acebron, A., Grillo, C., Bergamini, P., et al. 2022, A&A, 668, A142, doi: 10.1051/0004-6361/202244836 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f

doi:10.1051/0004-6361/202244836 2022
[2]

2016, MPDAF: MUSE Python Data Analysis Framework, Astrophysics Source Code Library, record ascl:1611.003

Shepherd, M. 2016, MPDAF: MUSE Python Data Analysis Framework, Astrophysics Source Code Library, record ascl:1611.003

work page 2016
[3]

2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 773508, doi: 10.1117/12.856027

doi:10.1117/12.856027 2010
[4]

2017, A&A, 608, A1, doi: 10.1051/0004-6361/201730833

Bacon, R., Conseil, S., Mary, D., et al. 2017, A&A, 608, A1, doi: 10.1051/0004-6361/201730833

doi:10.1051/0004-6361/201730833 2017
[5]

1996, A&AS, 117, 393, doi: 10.1051/aas:1996164 19

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164 19

doi:10.1051/aas:1996164 1996
[6]

2023, ApJ, 958, 148, doi: 10.3847/1538-4357/acf832

Biviano, A., Pizzuti, L., Mercurio, A., et al. 2023, ApJ, 958, 148, doi: 10.3847/1538-4357/acf832

doi:10.3847/1538-4357/acf832 2023
[7]

E., Stalder, B., de Haan, T., et al

Bleem, L. E., Stalder, B., de Haan, T., et al. 2015, ApJS, 216, 27, doi: 10.1088/0067-0049/216/2/27

doi:10.1088/0067-0049/216/2/27 2015
[8]

E., Bocquet, S., Stalder, B., et al

Bleem, L. E., Bocquet, S., Stalder, B., et al. 2020, ApJS, 247, 25, doi: 10.3847/1538-4365/ab6993

doi:10.3847/1538-4365/ab6993 2020

Show all 35 references

[9]

P., Schrabback, T., et al

Bocquet, S., Dietrich, J. P., Schrabback, T., et al. 2019, ApJ, 878, 55, doi: 10.3847/1538-4357/ab1f10 Bradaˇ c, M., Allen, S. W., Treu, T., et al. 2008, ApJ, 687, 959, doi: 10.1086/591246 Bradaˇ c, M., Clowe, D., Gonzalez, A. H., et al. 2006, ApJ, 652, 937, doi: 10.1086/508601

2019 doi
[10]

B., Grillo, C., Rosati, P., et al

Caminha, G. B., Grillo, C., Rosati, P., et al. 2023, A&A, 678, A3, doi: 10.1051/0004-6361/202244897

2023 doi
[11]

H., et al

Clowe, D., Bradaˇ c, M., Gonzalez, A. H., et al. 2006, ApJL, 648, L109, doi: 10.1086/508162

2006 doi
[12]

A., Wittman, D., Jee, M

Dawson, W. A., Wittman, D., Jee, M. J., et al. 2012, ApJL, 747, L42, doi: 10.1088/2041-8205/747/2/L42 El ´ ıasd´ ottir,´A., Limousin, M., Richard, J., et al. 2007, arXiv e-prints, arXiv:0710.5636, doi: 10.48550/arXiv.0710.5636

2012 doi arXiv
[13]

2008, MNRAS, 386, 577, doi: 10.1111/j.1365-2966.2008.13075.x

Fakhouri, O., & Ma, C.-P. 2008, MNRAS, 386, 577, doi: 10.1111/j.1365-2966.2008.13075.x

2008
[14]

S., & et al

Fruchter, A. S., & et al. 2010, in 2010 Space Telescope Science Institute Calibration Workshop, 382–387

2010
[15]

2016, MNRAS, 462, 1978, doi: 10.1093/mnras/stw1782

Fumagalli, M., Cantalupo, S., Dekel, A., et al. 2016, MNRAS, 462, 1978, doi: 10.1093/mnras/stw1782

2016 doi
[16]

2017, MNRAS, 471, 3686, doi: 10.1093/mnras/stx1896

Fumagalli, M., Mackenzie, R., Trayford, J., et al. 2017, MNRAS, 471, 3686, doi: 10.1093/mnras/stx1896

2017 doi
[17]

D., & Yee, H

Gladders, M. D., & Yee, H. K. C. 2000, AJ, 120, 2148, doi: 10.1086/301557

2000 doi
[18]

2015, Science, 347, 1462, doi: 10.1126/science.1261381 Inc., T

Harvey, D., Massey, R., Kitching, T., Taylor, A., & Tittley, E. 2015, Science, 347, 1462, doi: 10.1126/science.1261381 Inc., T. M. 2022, MATLAB version: 9.13.0 (R2022b),

2015 doi
[19]

L., & Sharon, K

Johnson, T. L., & Sharon, K. 2016, ApJ, 832, 82, doi: 10.3847/0004-637X/832/1/82

2016 doi
[20]

P., Limousin, M., et al

Jullo, E., Kneib, J. P., Limousin, M., et al. 2007, New Journal of Physics, 9, 447, doi: 10.1088/1367-2630/9/12/447

2007 doi
[21]

E., & Raftery, A

Kass, R. E., & Raftery, A. E. 1995, Journal of the American Statistical Association, 90, 773, doi: 10.1080/01621459.1995.10476572

1995
[22]

G., Groth, E

Lambas, D. G., Groth, E. J., & Peebles, P. J. E. 1988, AJ, 95, 996, doi: 10.1086/114695

1988 doi
[23]

2019, Behavior Research Methods, 51, 440, doi: 10.3758/s13428-018-1188-3

Lorah, J., & Womack, A. 2019, Behavior Research Methods, 51, 440, doi: 10.3758/s13428-018-1188-3

2019 doi
[24]

2018, MNRAS, 473, 663, doi: 10.1093/mnras/stx1971

Mahler, G., Richard, J., Cl´ ement, B., et al. 2018, MNRAS, 473, 663, doi: 10.1093/mnras/stx1971

2018 doi
[25]

D., et al

Mahler, G., Sharon, K., Gladders, M. D., et al. 2020, ApJ, 894, 150, doi: 10.3847/1538-4357/ab886b

2020 doi
[26]

H., Clowe, D., et al

Markevitch, M., Gonzalez, A. H., Clowe, D., et al. 2004, ApJ, 606, 819, doi: 10.1086/383178

2004 doi
[27]

P., Sif´ on, C., et al

Menanteau, F., Hughes, J. P., Sif´ on, C., et al. 2012, ApJ, 748, 7, doi: 10.1088/0004-637X/748/1/7

2012 doi
[28]

2020, MNRAS, 493, 3331, doi: 10.1093/mnras/staa473

Niemiec, A., Jauzac, M., Jullo, E., et al. 2020, MNRAS, 493, 3331, doi: 10.1093/mnras/staa473

2020 doi
[29]

Ofek, E. O. 2014, MAAT: MATLAB Astronomy and Astrophysics Toolbox, Astrophysics Source Code Library, record ascl:1407.005. http://ascl.net/1407.005

2014
[30]

L., Borgani, S., et al

Ragone-Figueroa, C., Granato, G. L., Borgani, S., et al. 2020, MNRAS, 495, 2436, doi: 10.1093/mnras/staa1389

2020 doi
[31]

W., Markevitch, M., Clowe, D., Gonzalez, A

Randall, S. W., Markevitch, M., Clowe, D., Gonzalez, A. H., & Bradaˇ c, M. 2008, ApJ, 679, 1173, doi: 10.1086/587859

2008 doi
[32]

1978, The Annals of Statistics, 6, 461 , doi: 10.1214/aos/1176344136

Schwarz, G. 1978, The Annals of Statistics, 6, 461 , doi: 10.1214/aos/1176344136

1978
[33]

T., Lilly, S

Soto, K. T., Lilly, S. J., Bacon, R., Richard, J., & Conseil, S. 2016, MNRAS, 458, 3210, doi: 10.1093/mnras/stw474

2016 doi
[34]

2015, in Science Operations 2015: Science Data Management, 1, doi: 10.5281/zenodo.34658

Weilbacher, P. 2015, in Science Operations 2015: Science Data Management, 1, doi: 10.5281/zenodo.34658

2015 doi
[35]

Wittman, D., Golovich, N., & Dawson, W. A. 2018, ApJ, 869, 104, doi: 10.3847/1538-4357/aaee77

2018 doi

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

2022, A&A, 668, A142, doi: 10.1051/0004-6361/202244836 Astropy Collaboration, Price-Whelan, A

Acebron, A., Grillo, C., Bergamini, P., et al. 2022, A&A, 668, A142, doi: 10.1051/0004-6361/202244836 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: 10.3847/1538-3881/aabc4f

doi:10.1051/0004-6361/202244836 2022

[2] [2]

2016, MPDAF: MUSE Python Data Analysis Framework, Astrophysics Source Code Library, record ascl:1611.003

Shepherd, M. 2016, MPDAF: MUSE Python Data Analysis Framework, Astrophysics Source Code Library, record ascl:1611.003

work page 2016

[3] [3]

2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol

Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 773508, doi: 10.1117/12.856027

doi:10.1117/12.856027 2010

[4] [4]

2017, A&A, 608, A1, doi: 10.1051/0004-6361/201730833

Bacon, R., Conseil, S., Mary, D., et al. 2017, A&A, 608, A1, doi: 10.1051/0004-6361/201730833

doi:10.1051/0004-6361/201730833 2017

[5] [5]

1996, A&AS, 117, 393, doi: 10.1051/aas:1996164 19

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393, doi: 10.1051/aas:1996164 19

doi:10.1051/aas:1996164 1996

[6] [6]

2023, ApJ, 958, 148, doi: 10.3847/1538-4357/acf832

Biviano, A., Pizzuti, L., Mercurio, A., et al. 2023, ApJ, 958, 148, doi: 10.3847/1538-4357/acf832

doi:10.3847/1538-4357/acf832 2023

[7] [7]

E., Stalder, B., de Haan, T., et al

Bleem, L. E., Stalder, B., de Haan, T., et al. 2015, ApJS, 216, 27, doi: 10.1088/0067-0049/216/2/27

doi:10.1088/0067-0049/216/2/27 2015

[8] [8]

E., Bocquet, S., Stalder, B., et al

Bleem, L. E., Bocquet, S., Stalder, B., et al. 2020, ApJS, 247, 25, doi: 10.3847/1538-4365/ab6993

doi:10.3847/1538-4365/ab6993 2020