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This paper presents the first multi-probe mass modelling method that separates dark matter from baryonic mass at both cluster and galaxy scales, and applies it to Abell S1063.

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A multi-probe model of Abell S1063 separates dark matter, gas, and stellar mass, and gives a stellar-to-subhalo relation consistent with IllustrisTNG.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection A genuinely serious and unusually transparent multi-probe cluster model, but the abstract's 'accurately reproduced' BCG/ICL kinematics are contradicted by the paper's own chi-square, and that probe is the one carrying the core disentangling. the 3 major comments →

arxiv 2509.07777 v2 pith:ZHAKWUUS submitted 2025-09-09 astro-ph.CO astro-ph.GA

A comprehensive separation of dark matter and baryonic mass components in galaxy clusters II: an overview of the mass distribution in Abell S1063

Benjamin Beauchesne , Benjamin Cl\'ement , Marceau Limousin , Anna Niemiec , Mathilde Jauzac , Bel\'en Alcalde Pampliega , Johan Richard , Guillaume Mahler
show 6 more authors
Jose M. Diego Pascale Hibon Anton M. Koekemoer Thomas Connor Jean-Paul Kneib Andreas L. Faisst
This is my paper
classification astro-ph.CO astro-ph.GA
keywords galaxy clustersdark matterbaryonic mass componentsstrong gravitational lensingX-ray surface brightnessstellar kinematicsstellar-to-subhalo mass relationAbell S1063
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 claims to have built the first mass-modelling method that separates dark matter from every baryonic mass component in a massive galaxy cluster, and to have demonstrated it on Abell S1063. The method combines strong lensing, X-ray surface brightness, cluster member velocity dispersions, and the stellar kinematics of the brightest cluster galaxy plus intra-cluster light in one self-consistent model. Each cluster member is split into a stellar profile fixed by the observed light and a dark-matter profile scaled from it by a global spatial factor and a double power-law stellar-to-subhalo relation. The best model reproduces multiple-image positions to 0.50 arcsec RMS, fits the X-ray and BCG/ICL kinematics within uncertainties, and requires an additional 35 km/s scatter in cluster member dispersions. If correct, it provides a complete census of where each mass component sits in a cluster core, making the dark-matter-only profile directly comparable to cosmological simulations.

Core claim

The central claim is that a single parametric mass model can reproduce almost every available mass probe of a massive cluster while explicitly separating dark matter from gas, cluster member stars, and the BCG/ICL component, at cluster and galaxy scales. Applied to Abell S1063, the best-fitting model achieves an RMS of 0.50 arcsec on strong-lensing image positions, including a central image near the BCG reproduced at 0.23 arcsec; it matches the X-ray surface brightness and the BCG/ICL stellar kinematic profiles within observational uncertainties, at the cost of a 35 km/s intrinsic scatter in cluster member line-of-sight dispersions. The inferred stellar-to-subhalo mass relation agrees at 1σ

What carries the argument

The load-bearing object is the fully parametrised multi-probe mass model, in which each component has its own physical profile. The intra-cluster gas is a set of dPIE (smoothly cored elliptical) potentials fitted to X-ray surface brightness; cluster-scale dark matter is two dPIE haloes; the BCG and intra-cluster light form a multi-Gaussian expansion with two free mass-to-light coefficients; and every cluster member is a pair of dPIEs, baryons fixed to the observed light and dark matter obtained by scaling the light radii by a single global factor α_c with velocity dispersion set by a double power-law stellar-to-subhalo relation. The likelihoods from strong lensing, X-rays, member kinematics,

Load-bearing premise

For every cluster member, the dark matter distribution is tied to the starlight by a single spatial scaling and a double power-law stellar-to-subhalo relation; if that scaling is wrong for the real galaxy population, the inferred subhalo masses and the comparison to simulations shift even when all the data are fitted.

What would settle it

Take a cluster with galaxies in a wide range of tidal states and apply the method: if it cannot reproduce image positions and velocity dispersions without a scatter well above 35 km/s, or if the recovered stellar-to-subhalo relation disagrees with independent weak-lensing measurements around the same galaxies, the tied light-to-DM scaling is falsified.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Total mass inside 250 kpc is recovered with 20–30% smaller statistical uncertainty than the previous joint lensing+X-ray model, and the DM-only profile to better than 5% across the constrained radii.
  • The method produces a stellar-to-subhalo mass relation measured at cluster-centric radii where stacked weak lensing cannot reach, directly comparable to hydrodynamical simulations.
  • Resolving the baryonic components improves strong-lensing reproduction near the cluster centre: the central-image system improves from 0.50 to 0.26 arcsec RMS relative to the prior model.
  • The BCG & ICL stellar mass estimate is 48–133% higher than SED-based estimates, implying a radial IMF variation that can be tested with higher-resolution stellar kinematics.

Where Pith is reading between the lines

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

  • If the single global spatial scaling were replaced by a cluster-centric radial dependence, the same data could map tidal stripping of subhaloes; the 35 km/s scatter may be the signature of that variation.
  • The high accuracy on the central image suggests this modelling can also constrain central supermassive black holes in BCGs if the right data are added; the paper's SMBH tests are too weak to be conclusive.
  • The BCG/ICL mass-to-light mismatch could also reflect the assumed orbital anisotropy in the kinematic model; a more general orbit-superposition kinematic model would separate that degeneracy.
  • Applying the same multi-probe separation to a sample of relaxed clusters would allow measurement of dark-matter core sizes, distinguishing cuspy cold dark matter from self-interacting or fuzzy dark matter.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript presents a parametric mass model of Abell S1063 in which dark matter and baryons are modelled separately for the cluster-scale DM halo, the intra-cluster medium, cluster member galaxies, and the BCG+ICL component. The model is constrained jointly by strong lensing image positions, X-ray surface brightness, cluster member velocity dispersions, and BCG/ICL stellar kinematics. The best model achieves an RMS of 0.50 arcsec on the multiple image positions, and the authors report reduced uncertainties on the total and DM-only mass profiles. They also compare the inferred stellar-to-subhalo mass relation (SsHMR) with IllustrisTNG and find 1σ agreement. The paper is the second in a series and builds on the mass constraints presented in the companion paper B25a.

Significance. This is a substantial technical step: combining four independent mass probes in a single parametric model with explicit separation of baryonic and dark components is ambitious and potentially very useful. The lensing RMS improvement over the B24 model and the reported factor-of-four reduction in core mass-profile uncertainty are concrete achievements. The model also produces component-by-component mass profiles that are directly comparable to hydrodynamical simulations, which is a valuable feature. However, the validation of the central claim is weakened by two issues: the BCG/ICL kinematics are not reproduced within the observational uncertainties, and the SsHMR comparison is not an independent test because the relation is a fitted model component.

major comments (3)
  1. [Abstract and §4.2.4] The abstract states that the BCG & ICL kinematic profiles are 'accurately reproduced within observational uncertainties', but §4.2.4 reports a reduced chi-squared of 3.86 (+0.33/−0.23), a minimum of 3.40, and a best-fit value of 4.50, with two data points at 2.9σ and 3.8σ. The text itself concedes that 'it does not include a model that agrees with the measurement uncertainties'. Since §4.3 attributes the factor-of-four reduction in core mass-profile uncertainty to L_BCG-kin, this is a load-bearing inconsistency. Please revise the abstract and discuss how the poor kinematic fit affects the posterior estimates of Υ_BCG* and the BCG DM profile, rather than treating the fit as a validation.
  2. [§5.4 and Eq. (4)] The SsHMR is imposed as a double power-law (Eq. 4) with parameters N, M1, δ and γ optimized inside the model. The subsequent claim of 1σ agreement with IllustrisTNG is therefore a comparison between a fitted model ingredient and a simulation, not an independent estimate of the relation. This is especially consequential because the 35 km/s intrinsic scatter added to the cluster member kinematics (§3.3) is calibrated to force reduced chi-squared near unity, so the kinematics do not independently validate the SsHMR. Please reframe the comparison as a posterior predictive consistency check, or show explicitly that the simulation's SsHMR lies within the posterior of the fitted relation under the assumed functional form.
  3. [§3.5 and §4.3] The final posterior is obtained through importance sampling with weights proportional to L_BCG-kin (Eq. 23), and §4.2.4 notes that the poor chi-squared 'may highlight ... undersampling of the posterior due to our two-step optimisation procedure'. All quoted credible intervals for the mass profiles in §4.3 come from this approximate posterior. Please report diagnostics for the importance sampling step (e.g., effective sample size, number of unique particles) and a sensitivity test, for instance with more inclination samples or an alternative inference scheme. Without this, the claimed factor-of-four reduction in core profile uncertainty is not fully supported.
minor comments (6)
  1. [Eq. (21)] The likelihood label in Eq. (21) is written as L_CM−kin, but from context it should be L_BCG−kin. Please correct.
  2. [Fig. 5] The x-axis tick labels in Fig. 5 appear garbled ('0 100 101' instead of 10^0, 10^1). Please fix the typesetting.
  3. [§4.2.4] The sentence 'mass models are already in good agreement with the observed stellar kinematics' is difficult to reconcile with the reduced chi-squared of 3.86 reported in the same section. Please clarify what definition of 'good agreement' is intended.
  4. [§6] The claim of 'the most complex parametric mass model' is subjective. Please provide a quantitative comparison with the model complexity of previously published cluster mass models, or soften the wording.
  5. [§5.5] The IMF correction is computed using model-predicted σ_e from the best-fitting model, but the model is then rejected because the best-fit σ_e changes when M* is corrected. This circularity is acknowledged only implicitly. Please state it as a limitation and discuss possible ways to break the loop (e.g., joint fitting of M* and the correction factor).
  6. [Data availability] The data availability statement says mass models are available at 'the following repository' but does not give a URL or DOI. Please provide a resolvable link.

Circularity Check

0 steps flagged

No circular reduction in the central disentangling; the fitted SsHMR comparison is a benchmark, not a prediction, though self-calibrated systematics and a self-cited simulation relation weaken validation claims.

full rationale

The core mass decomposition is not circular: strong lensing, X-ray surface brightness, cluster-member velocity dispersions, and BCG/ICL kinematics enter as independent likelihoods (Sects. 3.1–3.4) and the DM/baryon components are separate dPIE/MGE profiles with parameters optimized against those data. The stellar-to-subhalo mass relation is introduced as the parametrization of cluster-member DM (Eqs. 4–5) and its parameters are fit inside the model; but the paper calls its later comparison to IllustrisTNG a 'measurement' and an 'estimate' (Sect. 5.4), not a prediction. The double power-law form is borrowed from Niemiec et al. (2022), which includes a co-author, so the comparison target is self-adjacent; nevertheless the simulation values are external and not derived from the present fit, so this is not a circular reduction. The abstract's 'accurately reproduced within observational uncertainties' is contradicted by the BCG/ICL kinematics reduced chi2 of 3.86 reported in Sect. 4.2.4, but that is a fit-quality/correctness issue rather than a definitional circularity. Similarly, the 0.55 arcsec lensing error and 35 km/s cluster-member scatter are tuned to make reduced chi2 ~1 (Sects. 3.2 and 3.3), which limits the strength of those 'reproduction' claims but does not make the derivation equivalent to its inputs. Overall the central claim has independent content grounded in the data; the self-citations are not load-bearing circularity.

Axiom & Free-Parameter Ledger

10 free parameters · 7 axioms · 0 invented entities

The model's central decomposition rests on a large set of assumed profile shapes and scaling laws. The most consequential are the cluster member scaling assumptions (alpha_c, SsHMR), the chosen error terms (0.55 arcsec, 35 km/s), and the BCG/ICL mass-to-light freedom. No new physical entities such as particles or forces are introduced.

free parameters (10)
  • alpha_c = 16.9 to 18.9 (Tables A1-A3)
    Universal spatial scaling of cluster member DM radii relative to their baryonic dPIEs; fitted by the model and assumed identical for all members.
  • SsHMR normalization N = 2.1 to 3.1
    Normalization of the double power-law stellar-to-subhalo relation fitted in Eq. (4).
  • SsHMR turnoff mass M1 = 4.6e10 to 8.4e10 Msun
    Fitted turnoff mass in Eq. (4); controls the stellar-to-subhalo relation used to set cluster member DM velocity dispersions.
  • SsHMR low-mass slope delta = 0.26 to 0.43
    Fitted low-mass slope in Eq. (4).
  • SsHMR high-mass slope gamma = 0.71 to 0.99
    Fitted high-mass slope in Eq. (4).
  • BCG mass-to-light ratio Upsilon_BCG,2_lt1 = 30.6 to 34.5
    MGE normalization coefficient for the inner, BCG-dominated Gaussians.
  • ICL mass-to-light ratio Upsilon_BCG,2_lt2 = 7.8 to 13.4
    MGE normalization coefficient for the wider, ICL-dominated Gaussians.
  • Cluster member LOSVD intrinsic scatter = 35 km/s
    Added by hand, based on a preliminary maximum-likelihood estimate, so that the reduced chi-squared of the cluster member kinematics is approximately 1.
  • Lensing positional error = 0.55 arcsec
    Chosen by maximum likelihood to absorb observational and systematic errors so the best model reaches reduced chi-squared near 1.
  • X-ray intrinsic error parameter a = optimized, value not stated in excerpt
    Defines sigma_X = a * mu_i in the Negative Binomial X-ray likelihood; optimized as part of the model.
axioms (7)
  • domain assumption All mass components are represented by dPIE potentials with fixed analytic forms.
    Invoked throughout Section 2; the entire mass model is built on this profile choice.
  • domain assumption Cluster member baryonic mass follows the light distribution and the stellar mass from SED fitting.
    Section 2.2: baryonic dPIE parameters are fixed to the light profile and the velocity dispersion is rescaled to match the SED stellar mass.
  • domain assumption Cluster member DM radii scale with a single global alpha_c and velocity dispersions follow a double power-law SsHMR.
    Eqs. (1)-(4); this assumption directly produces the SsHMR that is later compared to IllustrisTNG.
  • domain assumption Stellar orbits in cluster members are isotropic.
    Section 3.3, Eq. (10): beta_aniso is set to 0 to compute LOSVDs.
  • domain assumption JAM axisymmetric modelling applies to the BCG and ICL, with light and mass sharing the same position angle and Gaussian LOSVDs.
    Section 3.4: required by JamPy implementation, including fixed q_min and inclination marginalization.
  • domain assumption Cluster members inside the BCG kinematics extraction region lie on the same mass plane as the BCG and are included in the spherical-shell mass profile.
    Section 3.4: the authors state this is correct only under the assumption of a single mass plane.
  • standard math Importance sampling from the biased posterior to the target posterior is valid because the two distributions are sufficiently close.
    Section 3.5: the procedure relies on the biased and target posteriors not being too different, and the authors note undersampling risks.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of A comprehensive separation of dark matter and baryonic mass components in galaxy clusters II: an overview of the mass distribution in Abell S1063." pith.science (2026). https://pith.science/paper/ZHAKWUUS

@misc{pith2026250907777,
  author       = {Pith},
  title        = {Pith review of: A comprehensive separation of dark matter and baryonic mass components in galaxy clusters II: an overview of the mass distribution in Abell S1063},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZHAKWUUS}},
  note         = {Machine review of arXiv:2509.07777}
}
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abstract

In the first paper of this series, we derived mass constraints on the total mass and the baryonic components of the galaxy cluster Abell S1063. The main focus was to recover stellar masses and kinematics for cluster members, the brightest cluster galaxy (BCG) and the intra-cluster light (ICL). In this second paper, we introduce a multi-probe mass modelling approach that incorporates constraints on both the total mass and the individual baryonic components. We obtain comprehensive mass models of Abell S1063, in which the dark matter distribution is disentangled from the baryonic mass at both cluster and galaxy scales. The best-fitting mass model achieves an RMS of $0.50"$ on the multiple image positions. The kinematic profiles of the BCG \& ICL, as well as the X-ray surface brightness of the intra-cluster gas, are accurately reproduced within observational uncertainties. However, a $35~\mathrm{km/s}$ scatter is required for the cluster member line-of-sight dispersions. This method yields the most complex parametric mass model with consistency among almost all available mass constraints. We find a $1\sigma$ agreement between the inferred stellar-to-subhalo mass relation and that predicted by large-scale cosmological simulations. The ICL stellar mass derived from our model is consistent with estimates from stellar population modelling. We present the first multi-probe mass modelling method capable of disentangling the dark matter from the baryonic mass distributions in massive galaxy clusters. Its results, such as the stellar-to-subhalo mass relation or the distribution of each mass component, can be directly compared to hydrodynamical cosmological simulations such as illustrisTNG.

Figures

Figures reproduced from arXiv: 2509.07777 by Andreas L. Faisst, Anna Niemiec, Anton M. Koekemoer, Bel\'en Alcalde Pampliega, Benjamin Beauchesne, Benjamin Cl\'ement, Guillaume Mahler, Jean-Paul Kneib, Johan Richard, Jose M. Diego, Marceau Limousin, Mathilde Jauzac, Pascale Hibon, Thomas Connor.

Figure 1
Figure 1. Figure 1: The BUFFALO colour composite image of AS1063 with the following HST filters: F435W (blue), F606W (green) and F814W (red). The X-ray surface brightness from the Chandra X-ray Observatory is shown by the green dashed contours. The set of multiple images used in this work is highlighted by the cyan circles. The white contours present the BCG & ICL light distribution as fitted in B25a. Cluster members for whic… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of each model component. Each one of them is associated with a set of analytical profiles and the likelihood that they are affecting. to its associated electron density, and then its surface brightness. We refer the reader to B24 and the references within for a detailed procedure description. To define the likelihood and to take into account the limitations of our modelling choices, we incorporate… view at source ↗
Figure 3
Figure 3. Figure 3: Diagram of the inference workflow in two steps. A biased posterior distribution is obtained on the combined likelihood excluding the BCG & ICL kinematics. In the second step, we resample the biased posterior through importance sampling to obtain the final posterior estimate. similar to the Bayesian Information Criterion (BIC Schwarz 1978) or Akaike Information Criterion (AIC Akaike 1998), and is a readapta… view at source ↗
Figure 4
Figure 4. Figure 4: Model predicted 𝜎𝑒 as a function of the observed one, for each SED model. The uncertainties for the observed 𝜎𝑒 are the measurement standard deviations. For the model predicted 𝜎𝑒, the uncertainties show the 1𝜎 CI from the mass model posterior. The top left, top right and bottom left panels present the results from the mass model with LePhare, the double power-law SFH and the delayed SFH SED models, respec… view at source ↗
Figure 5
Figure 5. Figure 5: Stellar kinematic data and model of the BCG & ICL component as a function of the elliptical radius in kpc. The cyan distribution represents the biased posterior before the importance sampling step, while the magenta one is the approximated posterior after the resampling procedure. The scattered points represent the observational data points. The elliptical radius is defined with the same ellipticity as use… view at source ↗
Figure 6
Figure 6. Figure 6: 2D normalised surface mass density (convergence) associated with the total mass distribution. Each cluster-scale mass component is highlighted by contours. The BCG & ICL baryons are highlighted in dashed black, while the intra-cluster gas and DM are in dotted red and solid pink contours, respectively. 101 102 R (kpc) 10−3 10−2 10−1 100 Surface mass density (10 9M kpc −2 ) BCG & ICL Total Gas DM Σ ∝ R −2.77… view at source ↗
Figure 7
Figure 7. Figure 7: Left panel: Surface mass density of the whole cluster (red) and each of its components: the cluster-scale DM component (black), the BCG & ICL baryons (blue) and the gas (green). The plain lines represent the median of each distribution among the model posterior while the shaded area shows its 3𝜎 CI. As a qualitative comparison to BCG & ICL profile slope, we present two power-law profiles with a slope of −2… view at source ↗
Figure 8
Figure 8. Figure 8: Left panel: Mass density of the whole cluster (red) and each of its components: the cluster-scale DM component (black), the BCG & ICL baryons (blue) and the gas (green). A gNFW fit to the total mass distribution is presented as a comparison to model the mass slope. Plain lines represent the median of each distribution among the model posterior, while the shaded area shows its 3𝜎 CI. Right panel: Fraction o… view at source ↗
Figure 9
Figure 9. Figure 9: Stellar-mass-to-light ratio of the BCG & ICL component, Υ BCG ∗,lt for the three models with a “BCG - ML 2” parametrisation with their equivalent estimated through SED fitting, Υ BCG ∗,SED as a function of the elliptical radii defined in B25a (section 5.2). Error bars represent the 1𝜎 CI for both Υ BCG ∗ estimates, while errors on the radius represent the width of the elliptical bins in which it is average… view at source ↗
Figure 10
Figure 10. Figure 10: Stellar-mass-to-light ratio mismatch parameter 𝛼 as a function of the elliptical radius defined in B25a (section 5.2). In each plot, we highlight the BCG size using its half-light radius, represented by the dashed black line. The shaded brown area represents the expected mismatch due to IMF variation in early-type galaxies as reported by Lu et al. (2024). The width of this area represents 3 times the stan… view at source ↗
Figure 11
Figure 11. Figure 11: Stellar-to-subhalo mass relation measured in this work compared to the results from the illustrisTNG simulations as reported in Niemiec et al. (2022). We represent our estimate through each cluster member. The position of the colour points represents the median of their stellar masses as given by the SED fitting or the total mass from the model posterior distribution. The error bars show the 1𝜎 CI for tho… view at source ↗

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Forward citations

Cited by 3 Pith papers

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

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.