{"id":"0da9c65b-89fe-4696-9017-3bd950ffc1da","arxiv_id":"2412.09864","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In 324 simulated galaxy clusters, the gas shock radius is 1.4 to 1.9 times the dark-matter splashback radius, and the ratio grows with recent mass accretion.","lead":"This paper measures how the shock radius, where infalling gas crashes into a galaxy cluster, compares with the splashback radius, where dark matter stops falling in and starts orbiting. Using 324 simulated clusters, it finds the shock radius is typically 1.4 to 1.9 times larger than the splashback radius, and this ratio grows for clusters that recently gained mass.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The entropy-peak/min-slope proxy for rshock is imported from non-radiative simulations and never validated against actual shock jumps in GIZMO-Simba-7k; if feedback or substructure creates spurious entropy extrema, Eqs. 5-12 do not measure the accretion shock.","rationale":"The paper is a careful empirical study on a large mass-complete sample, and its headline result agrees with previous non-radiative work (Aung et al. 2021: rshock,m/rsplash≈1.89 vs 1.91) and is broadly stable across GIZMO-Simba-3k, 7k, and GadgetX (Appendix 1). That cross-code consistency is genuine support for the empirical correlation, but it does not validate the physical label 'shock': all runs use the same entropy-extremum definition. The most load-bearing assumption is that the entropy maximum/minimum-slope radius in a full-physics simulation is the accretion shock. The manuscript provides no independent shock identification (temperature jump, velocity jump, Mach number), so an alternative explanation—e.g., an entropy feature produced by feedback, sloshing, or pre-shock density fluctuations—cannot be excluded. The reader's weakest_assumption identifies exactly this concern, and my independent reading agrees. The abstract's 'rshock ∝ 0.65 rsplash' phrasing is also an overstatement given the large intercepts in Eqs. 5-6, but that is secondary. I therefore see no reason to move the verdict away from CONDITIONAL.","tokens_in":17247,"tokens_out":5541,"duration_ms":61083,"concrete_test":"On a random subset of ~20 GIZMO-Simba-7k clusters, run a standard shock finder on gas cells that identifies the outermost accretion shock from temperature, density, and velocity jumps and Mach number (e.g., the algorithm used by Vazza/Böss or an equivalent independent implementation). Compare the resulting shock radius with rshock,p and rshock,m computed from the same snapshots and radial binning. Accept the proxy if the median absolute difference is <10% and the Spearman correlations with M200 and ΔM/M are preserved; if the median offset is comparable to the 0.5-0.8 R200 separation between rshock,p and rshock,m, or if the accretion-rate trend disappears, Eqs. 5-12 should be refit to the true shock radius.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The quantitative claims—median rshock,p/rsplash=1.38 and rshock,m/rsplash=1.91, plus Eqs. 5-12—inherit their physical meaning entirely from identifying rshock with the maximum of K or the minimum of d lnK/d lnr (§2, Fig. 3). This identification was established in non-radiative simulations (Lau et al. 2015; Shi 2016), but GIZMO-Simba-7k includes radiative cooling, star formation, and AGN feedback; these processes can alter the entropy profile in cluster outskirts through metal cooling, turbulent mixing, and clumpy accretion, and the paper presents no check against direct shock diagnostics such as temperature or velocity jumps. The median over 48 angular segments and Gaussian smoothing used to suppress substructure could also shift or create extrema. Appendix 1 checks sensitivity to resolution and galaxy-formation model, but not the proxy itself, so it cannot certify that rshock,p/rshock,m corresponds to the physical accretion shock. If the entropy feature is unrelated to the shock, the central claim degrades to a correlation between splashback and a generic entropy-feature radius.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses 324 galaxy clusters from The Three Hundred GIZMO-Simba-7k simulations to measure the shock radius, defined by an entropy maximum (rshock,p) or a minimum of the entropy logarithmic slope (rshock,m), and the dark-matter splashback radius (rsplash). The authors find median ratios rshock,p/rsplash = 1.38 and rshock,m/rsplash = 1.91, best-fit linear relations rshock ~ 0.65 rsplash + offset (Eqs. 5-6), and weak-to-moderate anti-correlations of rshock/R200 and rsplash/R200 with M200 and recent accretion rate. The results are compared with non-radiative simulations and observational tSZ/X-ray studies, and the paper discusses implications for locating the accretion shock in observations.","tokens_in":17435,"tokens_out":4981,"duration_ms":48055,"significance":"If the entropy-based shock radius is a faithful tracer of the physical accretion shock in full-physics simulations, this is a valuable statistical calibration: it is the largest sample (324 clusters) used for such a measurement, it spans multiple simulation codes and resolutions, and it provides quantitative relations that can guide stacking searches in tSZ, X-ray, and radio data. The agreement with Aung et al. (2021) in the median ratio (1.91 vs 1.89) is a useful cross-check, and the explicit bootstrap uncertainties and the sensitivity appendix are strengths. However, the physical interpretation of the central relations hinges on the unvalidated assumption that the entropy extremum marks the accretion shock in the presence of cooling, star formation, and AGN feedback.","major_comments":[{"comment":"The identification of rshock with the maximum of K or the minimum of d lnK/d lnr is imported from non-radiative simulations (Lau et al. 2015; Shi 2016) and is applied to GIZMO-Simba-7k without validation against direct shock diagnostics. Since this run includes radiative cooling, star formation, and AGN feedback, processes that can alter the entropy profile in cluster outskirts, the paper should demonstrate that the entropy extremum actually coincides with a genuine gas shock. A concrete check would be to measure temperature or velocity jumps, or to compare with a shock-finding algorithm, in a subset of clusters. Without such validation, Eqs. 5-12 and the median ratios are measurements of an entropy-feature radius, and their physical interpretation as the accretion-shock radius is not secured.","section":"Section 2, Figure 3"},{"comment":"The description of the angular-segment binning is ambiguous and could introduce a systematic bias in rshock. The text states that the median density and median mass-weighted temperature are evaluated in each radial bin and used to estimate the entropy via Eq. 1. Because K = k_B T / n_e^{2/3} is nonlinear, the entropy of the median temperature and median density is not generally equal to the median of the per-segment entropy values. If the latter was not used, the location of the entropy maximum or slope minimum can be shifted. The authors should clarify the exact procedure and test the sensitivity of rshock,p and rshock,m to whether the median is taken before or after computing K.","section":"Section 2, radial-profile construction"},{"comment":"The sensitivity check for Eq. 11 (rshock,m/R200 versus ΔM/M) lists the GIZMO-Simba-7k coefficients as (-1.05, 3.13), which is identical to the pair quoted for Eq. 10 and inconsistent with the fiducial values (-1.34, 4.27) stated in the main text. This appears to be a transcription error, but it undermines the reader's ability to assess the robustness of the rshock,m versus accretion-rate relation. The authors should correct the appendix and re-check the listed coefficients for all runs.","section":"Appendix 1, Eq. 11 coefficients"}],"minor_comments":[{"comment":"The abstract and conclusions quote rshock,m/R200 = 3.54, while the text around Figure 3 reports 3.58; these values should be reconciled.","section":"Abstract and Section 5"},{"comment":"The phrase 'the best-fit linear relation increases as rshock ∝ 0.65 rsplash' is misleading because Eqs. 5 and 6 have non-zero intercepts (1.39 and 2.38 h^-1 Mpc); a proportional relation would have zero intercept. Please refer to the slope rather than using the proportionality symbol.","section":"Abstract, Eqs. 5-6"},{"comment":"The Gaussian smoothing applied to the density and entropy profiles is mentioned but its width is not specified; since the location of maxima and minima can depend on the smoothing scale, the authors should state the smoothing length and test its impact on the measured radii.","section":"Section 2"},{"comment":"The Spearman correlation coefficients for Eqs. 5 and 6 are reported, but the corresponding p-values, although described as 'vanishingly small', are not given; please provide numeric values.","section":"Section 3, Figure 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well within the journal's scope and the core dataset is a strength. The main issue is the lack of direct validation of the entropy-based shock proxy in the full-physics runs; this should be addressed before publication. The appendix typo in the Eq. 11 coefficients should also be corrected. If the authors add a validation test (e.g., temperature/velocity jumps in a subsample) and clarify the median-binning procedure, the paper would be suitable for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a careful, useful calibration paper, and the central result—rshock larger than rsplash, ratio roughly 1.4–1.9, modulated by accretion history—holds up as far as the measurements go. The main caveat is that the shock radius is never checked against actual shock jumps; if you want to use Eqs. 5–12 to plan observations, that is the thing to press on.\n\nWhat's actually new: Aung, Nagai, and Lau (2021) had rshock,m/rsplash ~ 1.89 from 65 non-radiative clusters. This paper confirms that in 324 full-physics GIZMO-Simba-7k clusters, adds the rshock,p definition, and provides explicit best-fit linear relations with bootstrap uncertainties (Eqs. 5–12), plus mass and accretion-rate scalings. The robustness check across three simulation codes and two resolutions is genuinely useful; slopes and intercepts vary somewhat, but the qualitative trends hold. The paper also does the right thing by comparing with external prior work rather than leaning only on self-citations.\n\nSoft spots, in order of importance:\n\n1. The entropy-extremum proxy for rshock is imported from non-radiative simulations and never validated in the full-physics runs. The 48-segment median and Gaussian smoothing could plausibly shift or create extrema; cooling, star formation, and AGN feedback can alter the entropy profile in cluster outskirts. The paper needs at least one direct check—temperature or velocity jumps, or comparison against an actual shock finder—before Eqs. 5–12 can be read as measuring the accretion shock rather than a generic entropy-feature radius. This is a legitimate concern, not manufactured; but it is fixable and probably does not overturn the central claim, because the qualitative result matches non-radiative work and the ratio is physically plausible.\n\n2. The abstract says the best-fit linear relation increases as rshock ∝ 0.65 rsplash, which is misleading: Eq. 5 has an intercept of 1.39 h−1 Mpc, so this is not a proportionality. A reader could easily over-interpret. This should be rephrased.\n\n3. Data availability is thin: all data come from The Three Hundred collaboration, and the GIZMO-Simba-7k run itself is cited as in preparation. That is common for simulation papers, but it does limit independent verification.\n\nWho this is for: observers planning stacked tSZ, X-ray, or radio searches of cluster outskirts, and simulators working on shock and splashback boundaries. It deserves a serious referee; the analysis is transparent and the claims are mostly proportional to the evidence. I would send it out, with a request to address the proxy validation.","headline":"Solid, useful calibration of the shock–splashback relation in full-physics clusters; the entropy-proxy validation gap is real but addressable.","tokens_in":18100,"tokens_out":2087,"would_cite":true,"duration_ms":20870,"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":"Using 324 simulated galaxy clusters, this paper shows that the accretion shock radius is systematically larger than the splashback radius, with median ratios of 1.38 and 1.91 and a linear relation $r_\\mathrm{shock} \\simeq…","keywords":["splashback radius","accretion shock","intracluster medium entropy","galaxy cluster outskirts","cosmological hydrodynamical simulations","thermal Sunyaev-Zeldovich effect","mass accretion history","cluster boundary"],"falsifier":"If, in the same simulated clusters, direct shock diagnostics such as temperature jumps or velocity discontinuities fail to coincide with $r_\\mathrm{shock,p}$ or $r_\\mathrm{shock,m}$ within the scatter, then the entropy-extremum definition does not trace the physical shock and the calibrated relations would not describe the shock boundary. Observationally, a stacked thermal Sunyaev-Zeldovich or X-ray profile of clusters with weak-lensing splashback measurements would test the claim: a shock feature appearing at $r_\\mathrm{splash}$ rather than near $1.4$–$1.9\\,r_\\mathrm{splash}$ would falsify the predicted offset.","tokens_in":16963,"feed_emoji":"🌌","tokens_out":14677,"duration_ms":127501,"temperature":0.7,"pith_summary":"This paper sets out to quantify how the accretion shock radius of a galaxy cluster's gas, $r_\\mathrm{shock}$, relates to the splashback radius, $r_\\mathrm{splash}$, where dark matter and galaxies complete their first orbit. Using 324 clusters from full-physics cosmological simulations that include cooling, star formation, and black-hole feedback, it finds that the shock radius is almost always outside the splashback radius. Depending on how the shock is defined from the gas entropy profile, the median ratio is about 1.38 or 1.91, and the best-fit relation is $r_\\mathrm{shock} \\simeq 0.65\\,r_\\mathrm{splash}$ plus a constant offset. Both radii shrink relative to $R_{200}$ for more massive and more recently accreting clusters, while the ratio $r_\\mathrm{shock}/r_\\mathrm{splash}$ grows with recent accretion rate. The result matters because it gives observers a quantitative target: searches for shocks in radio, X-ray, and thermal Sunyaev-Zeldovich data should expect the boundary to lie well beyond the splashback radius.","feed_headline":"Shock radius sits 1.4–1.9 times splashback in simulated clusters","feed_subtitle":"The ratio grows with recent mass accretion, giving radio, X-ray, and microwave surveys a predicted scale to search.","key_machinery":"The load-bearing objects are the two boundary radii and the gas-entropy feature used to define one of them. The entropy $K \\equiv k_\\mathrm{B}T/n_\\mathrm{e}^{2/3}$ is computed from the simulated gas temperature and electron density; the shock radius is identified either where $K$ reaches its maximum ($r_\\mathrm{shock,p}$) or where its logarithmic slope $\\mathrm{d}\\ln K/\\mathrm{d}\\ln r$ reaches its minimum ($r_\\mathrm{shock,m}$). The splashback radius is identified, by convention, where the logarithmic slope of the spherically averaged dark-matter density profile reaches its minimum. To make these identifications reliable in the presence of substructure, profiles are built from angular median filtering within each of 100 logarithmic radial bins, then smoothed with a Gaussian filter; the reported uncertainties and correlations come from bootstrap resampling and Spearman rank coefficients.","core_discovery":"The paper's central claim is that the accretion shock and the splashback boundary are not the same surface. In the median cluster, the dark-matter splashback radius is $r_\\mathrm{splash}=1.87\\,R_{200}$, while the shock radius from the entropy maximum is $r_\\mathrm{shock,p}=2.58\\,R_{200}$ and from the minimum entropy slope $r_\\mathrm{shock,m}=3.54\\,R_{200}$. This gives median ratios $r_\\mathrm{shock,p}/r_\\mathrm{splash}=1.38$ and $r_\\mathrm{shock,m}/r_\\mathrm{splash}=1.91$, and the best-fit relations $r_\\mathrm{shock,p}=0.64\\,r_\\mathrm{splash}+1.39\\,h^{-1}\\mathrm{Mpc}$ and $r_\\mathrm{shock,m}=0.65\\,r_\\mathrm{splash}+2.38\\,h^{-1}\\mathrm{Mpc}$. Both radii, normalized by $R_{200}$, anticorrelate with virial mass and with the fractional mass increase since $z=0.5$, while the ratio $r_\\mathrm{shock}/r_\\mathrm{splash}$ is larger for clusters with higher recent accretion rates. The authors take this as evidence that the shock radius is a separate, outer boundary whose location in observations can be predicted from a measured splashback radius and an estimate of recent accretion.","pith_inferences":["If the entropy feature truly marks the accretion shock, then combining a measured splashback radius with the accretion-rate dependence of the ratio gives an observational prior: a cluster with a given $r_\\mathrm{splash}$ and recent accretion history has a predictable radius where shock emission should appear.","A natural next test inside the same simulation volume would compare the entropy-defined shock radii against direct temperature-jump and velocity-jump shock finders; the paper does not run that comparison, so the physical interpretation of $r_\\mathrm{shock}$ remains an open question.","The consistency of the relation across different galaxy formation implementations suggests the offset may be a generic feature of cluster accretion, but verifying it against observed stacked thermal Sunyaev-Zeldovich profiles with measured splashback radii would connect the prediction to data.","Since $r_\\mathrm{splash}$ can be measured from galaxy density and weak lensing, the ratio could in principle serve as a dynamical-age indicator, tagging clusters that have recently accreted a large fraction of their mass."],"forward_implications":["For a typical cluster, the accretion shock should be sought at about $1.38$–$1.91$ times the splashback radius, i.e. near $2.6$–$3.5\\,R_{200}$, not at the splashback radius itself.","Because both $r_\\mathrm{shock}/R_{200}$ and $r_\\mathrm{splash}/R_{200}$ decrease with $M_{200}$ and with recent accretion, stacks used to detect the shock should be split by mass and accretion rate; mixing populations will blur the signal.","The ratio $r_\\mathrm{shock}/r_\\mathrm{splash}$ is not universal: it grows for clusters that have accreted a larger fraction of their mass since $z=0.5$, and this dependence is dominated by how strongly $r_\\mathrm{splash}/R_{200}$ responds to accretion history.","Observational splashback measurements from galaxy density or weak lensing, combined with these relations, give a predicted radial window for non-thermal radio, X-ray, and thermal Sunyaev-Zeldovich shock searches."],"supporting_citations":[{"why":"Defines $r_\\mathrm{shock,p}$ as the radius where the gas entropy profile peaks, the first of the two shock definitions used here.","marker":"Lau et al. 2015"},{"why":"Defines $r_\\mathrm{shock,m}$ as the radius where the entropy logarithmic slope is minimal, the second shock definition used here.","marker":"Shi 2016"},{"why":"Non-radiative simulation study reporting $r_\\mathrm{shock,m}/r_\\mathrm{splash}\\simeq1.89$, the prior measurement this paper extends to a full-physics sample.","marker":"Aung, Nagai, and Lau 2021"},{"why":"Introduces the splashback radius as the physical boundary of dark matter halos, providing the concept behind $r_\\mathrm{splash}$.","marker":"More, Diemer, and Kravtsov 2015"},{"why":"Establishes the practical convention of locating $r_\\mathrm{splash}$ at the minimum logarithmic slope of the density profile.","marker":"Mansfield, Kravtsov, and Diemer 2017"},{"why":"Analytical model that assumes $r_\\mathrm{shock}$ and $r_\\mathrm{splash}$ coincide, the assumption this paper's measured offset contradicts.","marker":"Patej and Loeb 2015"},{"why":"Simulation study linking stacked thermal Sunyaev-Zeldovich shock features to cluster accretion state, the observational template the paper's predictions are aimed at.","marker":"Baxter et al. 2021"},{"why":"Describes the galaxy formation simulations and calibration underlying the 324-cluster sample.","marker":"Cui et al. 2022"}],"fun_headline_variants":["Shock radius 1.4–1.9× splashback in clusters","Accretion shock outruns splashback by up to 1.9×","Cluster shock beyond splashback: simulations quantify gap","Shock and splashback radii diverge in galaxy clusters","Simulations show shock radius far outside splashback"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the entropy maximum (or minimum slope) actually marks the accretion shock in these full-physics runs, an identification imported from non-radiative simulations and not checked against direct temperature or velocity jumps in this paper.","fun_headline_variants_meta":{"raw":{"variants":["Shock radius 1.4–1.9× splashback in clusters","Accretion shock outruns splashback by up to 1.9×","Cluster shock beyond splashback: simulations quantify gap","Shock and splashback radii diverge in galaxy clusters","Simulations show shock radius far outside splashback"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001202,"raw_usage":{"total_tokens":5134,"prompt_tokens":1304,"completion_tokens":3830,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":920,"completion_tokens_details":{"reasoning_tokens":3742}},"tokens_in":920,"tokens_out":3830,"duration_ms":30096,"temperature":1.0,"reasoning_tokens":3742,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:38:45.905376+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If, in the same simulated clusters, direct shock diagnostics such as temperature jumps or velocity discontinuities fail to coincide with $r_\\mathrm{shock,p}$ or $r_\\mathrm{shock,m}$ within the scatter, then the entropy-extremum definition does not trace the physical shock and the calibrated relations would not describe the shock boundary. Observationally, a stacked thermal Sunyaev-Zeldovich or X-ray profile of clusters with weak-lensing splashback measurements would test the claim: a shock feature appearing at $r_\\mathrm{splash}$ rather than near $1.4$–$1.9\\,r_\\mathrm{splash}$ would falsify the predicted offset.","supporting_citations":[],"review_version":1}