{"id":"e480a181-218a-4ae6-b656-116d86cb6d2a","arxiv_id":"2507.05404","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A simulation-calibrated power law between intracluster light and total mass is used to estimate cluster mass profiles; it works for deep Euclid data of Perseus but fails on shallower Hubble Frontier Fields clusters.","lead":"This paper shows that the faint intracluster light around galaxies in a cluster can, in principle, be converted into a measurement of the cluster's total mass using a relation calibrated on simulations. Applied to the deep Euclid image of Perseus it gives a mass consistent with galaxy dynamics, while shallower Hubble data produce unphysical results.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing deprojection step: the projected Σ⋆/Σtot calibration yields Σ_tot, not spherical M200; without the Abel inversion that is never shown, the reported Perseus mass and comparisons to 3D tracers are unsupported.","rationale":"The reader's weakest assumption is the universality of the z<0.5 power-law calibration, which is indeed a real limitation supported by the broader z=0.54 scatter and the unphysical HFF masses. However, the most load-bearing concern for the central claim is more fundamental and internal: the paper never shows how the projected Σ_tot profile from Equation 1 is converted into the spherical M200 quoted for Perseus. Without a correct deprojection, the method does not actually deliver a cluster mass profile in the standard sense, even under perfect calibration. The heuristic scaling in Section 3 suggests a cylindrical mass proxy rather than a spherical overdensity mass, so the comparison to X-ray and dynamical masses may be apples-to-oranges. The reader did mention the deprojection step as missing in their rationale, but did not make it the weakest assumption, so my agreement is partial. A focused check—rederiving the Perseus mass with Abel inversion—would settle whether this gap is fatal or merely a documentation issue. Since the paper can be made correct by adding and validating the deprojection, the appropriate verdict remains CONDITIONAL, unchanged from the reader's assessment.","tokens_in":10526,"tokens_out":6198,"duration_ms":74371,"concrete_test":"Reproduce the Perseus mass estimate from the published Sigma_tot profile using a standard Abel inversion under spherical symmetry to obtain the 3D density and then the spherical M200 and R200. If the Abel-inverted M200 differs from the reported 2.4(+1.3/-0.9)e15 M⊙ by more than the quoted uncertainties, or if the resulting R200 does not match the value implied by the paper, the missing deprojection step is load-bearing and the comparisons to velocity-dispersion and X-ray masses are invalid. If the Abel-inverted mass agrees, the concern is resolved and the authors should simply document the deprojection explicitly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires converting an observed ICL surface density into a spherical overdensity mass M200. Equation 1 calibrates the ratio of projected densities: log10 Sigma_tot = log10 Sigma_star - a log10 r - b. This directly yields a projected total-matter surface density, not a 3D density. To recover M200 and R200, which are spherical quantities, one must deproject Sigma_tot via Abel inversion or an equivalent model assumption, but Section 3 contains no deprojection equation. The only mass expression in the text is the heuristic 'mass ∝ Σtot(r) r^2 ∝ Σ⋆ r^{3.1}' used to justify the slope cutoff; this resembles a cylindrical cumulative-mass approximation, not the standard spherical enclosed mass. If the authors used this crude estimator, the Perseus M200 = 2.4e15 M⊙ and the comparison to X-ray and dynamical masses are not meaningful because those tracers use spherical mass definitions. The paper also does not describe how R200 is identified from the projected profile. This is an internal gap that affects the one successful application, not just the HFF failures, and it is independent of the calibration's universality.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper calibrates, using 30 C-EAGLE zoom-in cluster simulations, a power-law relation between the projected ICL+BCG stellar mass density and the projected total matter density (Eq. 1), and it provides fit parameters and covariances at several redshifts (Table A.1). The authors then apply this relation to the Euclid Early Release Observations of the Perseus cluster and to four Hubble Frontier Fields clusters, claiming to recover cluster mass profiles and M200 values. For Perseus they report M200 = 2.4(+1.3/-0.9) x 10^15 M_sun, which is compatible with velocity-dispersion estimates but a factor of two above the X-ray value; for the HFF clusters the recovered M200 values are unphysically large, which the authors attribute to insufficient radial extent of the observed ICL profiles.","tokens_in":10766,"tokens_out":7830,"duration_ms":90882,"significance":"If the missing deprojection step is supplied and the Perseus result survives, the method would be a useful complement to traditional cluster mass estimators, particularly given Euclid's ability to measure ICL to large radii. The paper's strengths are its use of high-resolution simulations, the explicit propagation of calibration scatter through a multivariate normal distribution and bootstrap, and the honest reporting of the HFF failures. However, the method is currently demonstrated for only one cluster, the four HFF applications do not produce meaningful M200 values, and the redshift and dynamical-state dependence of the calibration is not quantified. The authors are transparent about these limitations, which is commendable, but the abstract and conclusions overstate the current demonstration.","major_comments":[{"comment":"The paper calibrates a relation between projected surface densities but never shows how Sigma_tot(R) is converted into the spherical enclosed mass M(<r), M200, and R200. The only mass expression in the text, 'mass ∝ Σtot(r) r^2 ∝ Σ⋆ r^{3.1}' (Section 3), is a cylindrical cumulative-mass approximation and is used only for the slope-cutoff argument; it does not define the profiles plotted in Figures 3 and 4. As written, the comparison of the Perseus M200 = 2.4e15 M_sun with X-ray and dynamical masses, which use spherical mass definitions, is unsupported. Please specify the deprojection (Abel inversion or an equivalent model assumption), state how R200 is identified from the projected profile, and label the mass definition on the figure axes.","section":"Section 3, Eq. (1)"},{"comment":"The HFF applications do not support the method as presented: the recovered M200 values for A2744, AS1063, A370, and MACSJ0717.5+3745 are 3.5e16, 1.1e16, 1.8e15, and 5.8e17 M_sun, respectively, and the paper's own note says only Perseus can provide an accurate mass estimation. Since four of five applications fail at the level of the headline quantity, the abstract and conclusions should be qualified to state that the method is presently demonstrated only for clusters with ICL profiles measured beyond the radius where the logarithmic slope falls below about -3.1, rather than claiming a general independent approach.","section":"Section 4.2, Table 1"},{"comment":"The universality of the calibration is not established beyond the C-EAGLE mass range [10^14, 10^15.4] M200/M_sun and redshifts z<0.5. The z=0.54 row of Table A.1 has a substantially different mean intercept (b=0.165 vs 0.316) and larger covariance, and Section 5 states that the relaxation-state dependence is unexplored. The application to MACSJ0717.5+3745 at z=0.545 uses the z<0.5 calibration despite this evidence, and the poor agreement for that cluster is attributed to redshift without a quantitative test. A statement of the domain of validity, or a sensitivity test to the calibration choice, is needed for the central claim.","section":"Appendix A, Section 5"}],"minor_comments":[{"comment":"The notation log10(r[kpc]) is dimensionally sloppy; write log10(r/1 kpc) or define r as dimensionless in units of kpc.","section":"Section 2, Eq. (1)"},{"comment":"The fICL values (e.g., 7.7±3.1) are reported without a definition or units; please specify what fraction is being measured.","section":"Section 4.2"},{"comment":"The cluster label 'MACS07017' does not match the text and Figure 4, which use 'MACSJ0717.5+3745'.","section":"Table 1"},{"comment":"The text quotes n=-4.4 while the legend shows n=-4.43; make the values consistent.","section":"Section 3, Figure 2"},{"comment":"The assumed M/L = 1.02 from Vazdekis et al. (2016) is quoted without stating the wavelength band or IMF; a brief justification would improve reproducibility.","section":"Section 4.1"},{"comment":"The conclusion that there is no redshift evolution for z<0.5 rests on overlapping 1σ contours; a quantitative test (e.g., likelihood ratio) would be more convincing, especially given the differing covariance matrices.","section":"Appendix A"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the missing deprojection is a genuine internal gap, not merely a disagreement with consensus; it can be fixed within the manuscript's scope by adding the Abel inversion and recomputing the Perseus and HFF comparisons. I do not see circularity: the mass comes from a simulation-calibrated relation and is compared against external estimates. The paper is honest about the HFF failures, which supports the authors' credibility. If the deprojection step is supplied and the domain of validity is stated, I would support publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Isaac and Ana have put together a useful extension of the ICL-based mass estimator they introduced in 2020. The main additions are real: a multivariate error model for the power-law fit parameters, more independent projections, and the first applications to Euclid's Perseus data and to four Hubble Frontier Fields clusters. The paper is also refreshingly honest. It says outright when the method fails, and why, and it flags the redshift dependence and the unexplored dependence on relaxation state.\n\nThe weak spot is not the calibration itself; it's the step that turns a projected density ratio into a spherical mass. Equation 1 calibrates the ratio of projected surface densities, giving log Σ_tot. To recover M200 and R200 you need to deproject Σ_tot into a 3D density profile, via Abel inversion or an equivalent assumption. That step never appears. The only mass expression in the text is the heuristic M ∝ Σ_tot(r) r^2, which is a cylindrical cumulative mass, not the spherical enclosed mass used by X-ray, lensing, and velocity-dispersion estimates. If that approximation is what produced the Perseus numbers, the factor of two agreement with X-ray is coincidence, and the comparison to dynamical masses is comparing different mass definitions. This gap affects the one successful application, not just the HFF failures. The authors themselves note the HFF masses are unphysical unless the ICL profile is steep enough, so the method's utility hinges on getting the Perseus case right.\n\nThe error treatment is a step up from the earlier paper, but it still omits systematic terms like the M/L conversion and the extrapolation prior; those are secondary next to the deprojection issue.\n\nThis paper is for people who want to use Euclid ICL data for cluster masses. It deserves a serious referee: the idea is new, the data are real, and the authors are upfront about limitations. My recommendation is to send it out, but with a referee brief that explicitly asks for the deprojection step or, failing that, a clear statement that the mass profile is a cylindrical approximation and the comparison to spherical mass tracers is accordingly limited.","headline":"A genuinely useful extension of the ICL-mass idea, but the missing deprojection step means the Perseus mass profile and its comparison to other tracers are on shaky ground.","tokens_in":11328,"tokens_out":3591,"would_cite":false,"duration_ms":41928,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The intracluster light alone, converted through a simulation-calibrated power law, recovers a galaxy cluster's total mass profile.","keywords":["intracluster light","galaxy cluster mass profiles","C-EAGLE simulations","Perseus cluster","Hubble Frontier Fields","power-law mass estimator","Euclid observations","ICL surface brightness"],"falsifier":"For a cluster with an ICL profile measured beyond r200, compare the projected total mass profile predicted by the calibrated power law with an independent weak-lensing shear profile: a deviation larger than the quoted covariance, or an M200 mismatch beyond 2σ, would falsify the central claim. A second test is to apply the calibration to matched samples of relaxed and merging clusters at the same redshift and mass and check whether the recovered masses scatter symmetrically around the lensing values; a systematic offset with dynamical state would indicate the relation is not universal.","tokens_in":10289,"feed_emoji":"🌌","tokens_out":9227,"duration_ms":94468,"temperature":0.7,"pith_summary":"This paper proposes that the intracluster light (ICL)—the diffuse starlight from stars stripped out of their galaxies—can serve as a standalone tracer of a galaxy cluster's total mass distribution. In the C-EAGLE simulations, the ratio of projected ICL stellar mass to projected total matter density follows a power law, and the authors calibrate that relation with realistic scatter using 30 simulated clusters at z<0.5. Applying it to the Euclid observations of Perseus recovers M200 = 2.4(+1.3/-0.9) × $10^{15}$ solar masses, matching velocity-dispersion estimates while sitting roughly twice the X-ray value. The paper concludes that ICL profiles alone can give cluster mass profiles whenever the observed ICL steepens past a logarithmic slope of about -3; shallower profiles leave the recovered mass formally unbounded.","feed_headline":"Intracluster light alone can estimate cluster mass profiles","feed_subtitle":"Simulation-calibrated power law turns ICL profiles into masses; Perseus gets 2.4 × 10^15 solar masses.","key_machinery":"The load-bearing object is the power-law ratio between the projected intracluster stellar mass density Σ⋆ (including the brightest central galaxy) and the projected total matter density Σtot, written as log10 Σtot = log10 Σ⋆ - a log10 r - b. It is calibrated from three projections of each of 30 C-EAGLE clusters at several redshifts below z = 0.5, with the scatter described by a multivariate normal distribution in (a, b) rather than the unrealistically small errors of the earlier fit. The same relation also defines the method's practical limit: because total mass within radius r grows as Σtot(r) $r^{2}$, a power-law extrapolation of an observed ICL profile with logarithmic slope n only gives a finite cluster mass if the slope is steeper than about -3.1, which is exactly why Perseus works and the shallower HFF profiles do not.","core_discovery":"The central discovery is that the projected intracluster stellar mass density and the projected total matter density are related by log10 Σtot = log10 Σ⋆ - a log10 r - b, with the simulation-calibrated parameters a = -1.139 and b = 0.316, plus a covariance matrix that encodes cluster-to-cluster and projection scatter. This turns any observed ICL+BCG surface-density profile into a total mass profile without lensing, X-ray, or dynamical data. The paper shows the method works for Perseus—recovering M200 = 2.4(+1.3/-0.9) × $10^{15}$ solar masses in agreement with velocity-dispersion estimates—and fails in a controlled way for the four Hubble Frontier Fields clusters, whose shallow ICL slopes force power-law extrapolations that leave the mass unbounded. It presents the relation as an observationally accessible, independent mass estimator whose error budget is dominated by the simulated scatter in the calibration.","pith_inferences":["If the calibrated power law holds in the outskirts, single-band deep imaging could become a cheap mass estimator for clusters, bypassing the expensive spectroscopy, lensing, and X-ray campaigns that other tracers require.","The factor-of-two excess over the Perseus X-ray mass could indicate hydrostatic bias in X-ray estimates or an overestimate from the simulation calibration; a sample of clusters with both deep ICL and X-ray data would separate the two.","The markedly wider scatter in the z = 0.54 calibration suggests the relation should be redshift-dependent, and Euclid data to z = 0.7 could produce a stratified calibration.","The slope criterion n ≲ -3.1 might double as a dynamical-state indicator: clusters with shallow observed ICL profiles are plausibly still assembling their ICL, which would make the criterion a physical selection effect rather than a purely technical one."],"forward_implications":["Deep ICL observations that reach a logarithmic slope of -3 or steeper can yield a full cluster mass profile to the virial radius using no other tracer.","For Perseus, the ICL-based M200 = 2.4(+1.3/-0.9) × 10^15 solar masses agrees with velocity-dispersion estimates while exceeding the X-ray value by roughly a factor of two, positioning the ICL as an independent arbiter in the disagreement between mass tracers.","When the observed ICL profile stops at a shallow slope, a power-law extrapolation leaves the total mass unbounded, so those clusters cannot yet be measured this way.","All four Hubble Frontier Fields clusters yield unphysically large masses from the extrapolation, indicating that the method's current limitation is observational depth rather than the calibration itself.","Euclid's planned sample of hundreds of clusters with ICL detected beyond 500 kpc out to z = 0.7 is the dataset that can test and exploit this estimator at scale."],"supporting_citations":[{"why":"Establishes the power-law relation between projected ICL stellar mass and total matter density in C-EAGLE simulations that this paper extends with realistic scatter estimates.","marker":"Alonso Asensio et al. (2020)"},{"why":"Presents the C-EAGLE cluster simulation suite from which the 30 clusters' profiles are drawn.","marker":"Barnes et al. (2017)"},{"why":"Describes the cluster sample and simulation setup used to calibrate the ICL-total mass relation.","marker":"Bahé et al. (2017)"},{"why":"Defines the EAGLE galaxy formation model and AGNdT9 calibration used in the simulations.","marker":"Schaye et al. (2015)"},{"why":"Provides the Euclid Early Release Observations of Perseus, including the ICL+BCG surface brightness profile to one-third of the virial radius.","marker":"Kluge et al. (2025)"},{"why":"Supplies the Hubble Frontier Fields ICL+BCG surface density profiles used for the four additional clusters.","marker":"Montes & Trujillo (2018)"},{"why":"Provides the surface-brightness to stellar-mass conversion used to turn the Perseus ICL profile into a mass density.","marker":"Montes & Trujillo (2014)"},{"why":"Gives the velocity-dispersion mass estimate of Perseus against which the ICL-based mass is compared.","marker":"Meusinger et al. (2020)"},{"why":"Gives the X-ray mass estimate of Perseus that the ICL result overestimates by a factor of two.","marker":"Simionescu et al. (2011)"}],"fun_headline_variants":["ICL alone unveils galaxy cluster mass profiles","Cluster masses from stray starlight, no lensing required","Intracluster light alone estimates cluster mass profiles","ICL power law turns cluster starlight into mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire method rests on assuming that the power-law ratio of intracluster stellar mass to total matter density calibrated from 30 simulated clusters at z<0.5—with parameters a = -1.139 and b = 0.316—applies unchanged to every real cluster, regardless of mass, redshift, or dynamical state, and continues to hold beyond the observed ICL radius; the paper's own z = 0.54 fit is much wider, and the HFF clusters with shallow slopes return unphysical masses.","fun_headline_variants_meta":{"raw":{"variants":["ICL alone unveils galaxy cluster mass profiles","Cluster masses from stray starlight, no lensing required","Intracluster light alone estimates cluster mass profiles","ICL power law turns cluster starlight into mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000713,"raw_usage":{"total_tokens":3213,"prompt_tokens":957,"completion_tokens":2256,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":573,"completion_tokens_details":{"reasoning_tokens":2192}},"tokens_in":573,"tokens_out":2256,"duration_ms":19816,"temperature":1.0,"reasoning_tokens":2192,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:27:24.122493+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a cluster with an ICL profile measured beyond r200, compare the projected total mass profile predicted by the calibrated power law with an independent weak-lensing shear profile: a deviation larger than the quoted covariance, or an M200 mismatch beyond 2σ, would falsify the central claim. A second test is to apply the calibration to matched samples of relaxed and merging clusters at the same redshift and mass and check whether the recovered masses scatter symmetrically around the lensing values; a systematic offset with dynamical state would indicate the relation is not universal.","supporting_citations":[{"cited_title":"& Trujillo, I","cited_arxiv_id":null,"evidence_quote":"Provides the surface-brightness to stellar-mass conversion used to turn the Perseus ICL profile into a mass density."},{"cited_title":"2020, A&A, 640, A30","cited_arxiv_id":null,"evidence_quote":"Gives the velocity-dispersion mass estimate of Perseus against which the ICL-based mass is compared."}],"review_version":1}