{"id":"ba7dce6b-5f6d-43a6-ae04-3eae3fc5ba61","arxiv_id":"2607.02654","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"At z≈2, Magneticum protoclusters show moderate self-similarity deviations, double-β density profiles, and hot ionised gas dominant only beyond ~0.1–0.5 R500c, with clear mass, merger and AGN trends.","lead":"A large Magneticum simulation sample of 3818 protoclusters at z≈2 yields non-parametric gas and electron-density profiles that deviate moderately from self-similarity and show a strong double-β shape. The maps of density, ionisation and secondary dependences on mass, mergers and AGN activity give observers a practical prior for interpreting sparse X-ray and SZ data on the nascent ICM.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the Reader's already-flagged CIE/photoionisation caveat.","rationale":"The paper delivers exactly what it claims: a large-sample (N=3818), non-parametric characterisation of gas and electron-density profiles at z≈2 inside Magneticum Box2b/hr, with secondary dependences on M12 and fEdd. The strongest claim (moderate departures from self-similarity, double-β structure, hot ionised gas dominant only at intermediate radii) is directly supported by the stacked profiles and Spearman maps in §§3.1–3.3. The Reader already identified the single most load-bearing assumption (CIE + neglect of AGN photoionisation). That assumption is discussed honestly in §4.1 and does not invalidate the characterisation within the simulation framework; it simply limits how far the ionisation fractions can be taken as universal. No additional load-bearing concern (e.g., centre-matching systematics, M12 definition, or variance-decomposition methodology) rises to the same level. Therefore the CONDITIONAL verdict and HIGH confidence remain appropriate; no adjustment is required.","tokens_in":33162,"tokens_out":563,"duration_ms":6957,"concrete_test":"Recompute the stacked ne(r) and ionisation-fraction profiles of Fig. 3 after applying a simple local AGN photoionisation correction (e.g., a radially declining ionisation boost scaled to the central SMBH luminosity and duty cycle already available in the snapshots) inside 0.05–0.2 R500c; if the ~70 ckpc dip in ne/nfully-ionised fills by more than ~30 % or the double-β shape disappears for the high-fEdd bin, the reported ionisation structure is sensitive to the neglected radiation field.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Reader correctly isolates the most load-bearing soft spot: ne is derived under CIE and neglecting local AGN photoionisation (§2.3, validity §4.1), which directly shapes the reported ionisation fractions and the double-β electron-density feature near ~70 ckpc. The paper already quantifies CIE timescales (4–6 orders of magnitude shorter than dynamical/cooling times) and notes self-shielding inside ~0.1–0.2 R500c, so the assumption is not unexamined. No stronger internal inconsistency or hidden assumption that would overturn the non-parametric characterisation itself is present. The purely thermal AGN feedback and Spiderweb tension (§4.3) are openly discussed model limitations, not unacknowledged flaws in the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper presents a non-parametric characterisation of gas mass density, temperature structure, ionisation degree and electron number density profiles for 3818 protocluster cores at z ≃ 2 (M500c > 10^13 M⊙) drawn from Magneticum Box2b/hr. After re-centring with ASOHF, multiphase correction (Eq. 1), and CIE-based electron densities, the authors stack profiles versus mass and secondary indicators of assembly state (M12) and central AGN activity (integrated Eddington ratio f̄Edd). They report moderate departures from self-similarity, a ubiquitous double-β morphology that strengthens with mass and AGN accretion, and the dominance of hot, ionised gas only at intermediate radii (r ≳ [0.1–0.5] R500c). The work also supplies X-ray exposure-time estimates, a comparison to Spiderweb measurements, and an ANOVA-style variance decomposition showing that M500c, M12 and f̄Edd together explain up to ~30 % of the logarithmic scatter in ne(r).","tokens_in":33360,"tokens_out":1079,"duration_ms":9837,"significance":"If the reported trends hold, the paper supplies the first statistically large, simulation-based map of proto-ICM density and ionisation structure at z ≃ 2, directly usable for interpreting Faraday rotation, SZ and forthcoming X-ray constraints on high-redshift systems. Strengths include the carefully documented sample construction (ASOHF re-centring, multiphase treatment, CIE tables), robust stacking with bootstrap uncertainties, explicit Spearman correlations, and an open discussion of model limitations (thermal AGN feedback, Spiderweb tension). The non-parametric results are intended as the foundation for a forthcoming parametric calibration, which would be of clear practical value to observers.","major_comments":[{"comment":"§2.3 and §4.1: Electron densities rest on CIE and the neglect of local AGN photoionisation. The CIE timescale argument (4–6 orders of magnitude shorter than dynamical/cooling times) is persuasive for the bulk mass, and self-shielding is invoked inside ~0.1–0.2 R500c. However, the ~70 ckpc ionisation dip—central to the reported double-β ne shape and its correlation with f̄Edd—lies precisely where AGN radiation could raise the ionisation fraction. A quantitative upper bound (even a simple Strömgren-sphere or optically-thin estimate using the same SMBH accretion rates already measured) is needed to show that the dip and the secondary trends survive this uncertainty; without it the ionisation-structure claim remains only partially stress-tested.","section":null},{"comment":"§4.3 and Fig. 7: The systematic under-prediction of Spiderweb central densities is acknowledged and partially mitigated by aperture and homogeneity corrections, yet none of the 3818 systems reach the observed mean ne inside 0.44 R500c. Given that the paper’s stated motivation is to provide density templates for interpreting high-z observables, the authors should either (i) quantify how much of the discrepancy is attributable to the purely thermal AGN feedback implementation (e.g., by citing or performing a controlled comparison with a kinetic-feedback run) or (ii) clearly demarcate the mass/radius regime in which the Magneticum profiles can be used as templates versus the regime in which they are known to be biased low.","section":null}],"minor_comments":[{"comment":"Fig. 1 (right) and Fig. 3 (bottom-right): Spearman coefficients are shown without indicating whether they are mass-corrected; the later panels of Fig. 4 do make this distinction. A uniform statement would improve clarity.","section":null},{"comment":"§2.5: The integrated Eddington ratio averages over ~500 Myr between snapshots. A short sensitivity test (or at least a statement) using the instantaneous rate would reassure readers that the reported central-density correlations are not window-dependent.","section":null},{"comment":"Appendix A / Fig. A.1: The example of Subfind–ASOHF centre mismatch is helpful; stating the median and 95th-percentile offsets in the main text (rather than only in the appendix) would strengthen the methods section.","section":null},{"comment":"Fig. 6: The exposure-time forecast assumes Aeff = 500 cm2 and a fixed background; a brief note on how the contours scale with NewAthena’s larger effective area (even if angular resolution remains a limiting factor) would make the figure more forward-looking.","section":null},{"comment":"Typographical: “ASOHF” is introduced with a footnote URL; a standard citation to Vallés-Pérez et al. (2022) in the main text would be cleaner. Occasional missing spaces after commas and inconsistent use of “ckpc” versus “kpc” appear in §§3.1–3.2.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is solid, carefully written and appropriately cautious about model limitations. The two major points are fixable with modest additional analysis or clearer demarcation of applicability; neither undermines the non-parametric characterisation itself. I see no reason to delay publication beyond a standard minor revision cycle. Fit for A&A is excellent."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is the first large-sample (N=3818) non-parametric characterisation of gas and electron-density profiles for z≈2 protocluster cores, stacked by mass and by two secondary indicators (M12 and integrated fEdd). That is the actual new result. The double-β morphology, the non-self-similar ionisation dip near 70 ckpc, the moderate mass trends, and the ANOVA-style variance decomposition (up to ~30% of the log-ne scatter) are quantitative findings that earlier smaller-volume or purely qualitative Magneticum papers did not deliver.\n\nMethods are careful: ASOHF re-centring, multiphase correction, CIE tables, robust stacking with bootstrap errors, and clear Spearman coefficients. The Spiderweb comparison is handled honestly—they show the tension, test the constant-density bias and aperture choice, and leave open whether the object is rare or the thermal AGN model is too ejective. Appendices on temperature bins, baryon depletion, and X-ray exposure estimates are useful rather than decorative.\n\nSoft spots are real but already named. ne rests on CIE plus neglect of local AGN photoionisation; the paper checks that CIE timescales are short and that cores are self-shielded, yet the ~70 ckpc feature sits exactly where residual photoionisation could matter. Purely thermal feedback is a known Magneticum limitation and may suppress central densities relative to kinetic models. Neither issue overturns the non-parametric maps themselves; they bound how far one should export the numbers to Faraday or SZ work without multi-model checks. Free parameters (500 Myr averaging window, binning thresholds) are minor.\n\nWho it is for: anyone interpreting sparse high-z X-ray/SZ/RM data or building parametric proto-ICM models. Citation pattern is normal for a Magneticum paper. Math and data handling look solid. I would send it to referees; the central claims hold inside the simulation framework and the caveats are proportionate. Worth reading and, for the right applications, citing.","headline":"Solid large-N non-parametric maps of z≈2 proto-ICM density and ionisation from Magneticum; the double-β shape, ~70 ckpc dip, and secondary trends are real within the model, with the usual thermal-feedback and CIE caveats already flagged by the authors.","tokens_in":33993,"tokens_out":538,"would_cite":true,"duration_ms":6712,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"At z~2, hot ionised gas in protocluster cores only dominates outside ~0.1–0.5 R500c and shows a strong double-β density shape that grows with mass and AGN activity.","keywords":["protoclusters","intracluster medium","electron density profiles","self-similarity","AGN feedback","cosmological simulations","z~2"],"falsifier":"A statistically significant sample of z≃2 protoclusters with measured electron-density profiles (via deep X-ray or joint SZ+X-ray analysis) that lack the central double-β steepening or that show hot-ionised gas already dominant well inside 0.1 R500c would contradict the stacked simulation result.","tokens_in":34087,"feed_emoji":"🌌","tokens_out":733,"duration_ms":7360,"temperature":0.7,"pith_summary":"Protoclusters are the earliest sites where gas is shock-heated into a nascent intracluster medium, but their small angular size and cosmological dimming make the hot phase hard to observe. This paper uses a large cosmological simulation to map the gas-mass and electron-number-density profiles of more than 3800 protocluster cores at z≃2, spanning masses above 10^13 solar masses. The stacked profiles deviate moderately from pure self-similarity: they display a pronounced double-β shape that steepens toward the centre, especially in the most massive systems and those with strong central black-hole accretion. Cold, largely neutral gas still dominates the very centre (r ≲ 70 ckpc), while hot, fully ionised plasma only becomes the majority component at intermediate radii that themselves scale with mass. Both the density and the ionisation fraction also correlate with a simple merger indicator and with the time-averaged Eddington ratio of the central black hole. The resulting non-parametric maps are offered as the foundation for future parametric models that observers can use to interpret X-ray, Sunyaev–Zeldovich and Faraday-rotation data of high-redshift systems.","feed_headline":"Hot gas in z~2 protoclusters only dominates outside 0.1 R500c","feed_subtitle":"Stacked simulation profiles show a double-β shape that grows with mass and central black-hole accretion","key_machinery":"Non-parametric stacked radial profiles of gas density, temperature-binned mass fractions and electron number density, constructed for 3818 simulated protocluster cores and further stratified by M500c, the stellar mass ratio M12 of the two brightest galaxies, and the time-averaged Eddington ratio of the central black hole.","core_discovery":"Protoclusters at z≃2 exhibit moderate departures from self-similar gas density and temperature structure, featuring a strong double-β profile that is most pronounced at high mass and high central AGN accretion; hot, ionised gas only dominates outside roughly 0.1–0.5 R500c, and its density at those radii correlates with both halo mass and dynamical disturbance.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Hot gas only dominates z~2 protoclusters outside 0.1 R500c","Double-β gas profiles grow with mass and AGN at z≃2","Proto-ICM at z~2: hot ionised gas peaks beyond 0.1-0.5 R500c","z~2 protoclusters show non-self-similar density and temperature","Ionised gas density links to mass and disturbance past 0.1 R500c"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"Electron densities rest on the assumption of collisional ionisation equilibrium with photo-ionisation neglected, so any substantial non-equilibrium or local AGN radiation field would reshape the reported ionisation fractions and the double-β electron-density profile.","fun_headline_variants_meta":{"raw":{"variants":["Hot gas only dominates z~2 protoclusters outside 0.1 R500c","Double-β gas profiles grow with mass and AGN at z≃2","Proto-ICM at z~2: hot ionised gas peaks beyond 0.1-0.5 R500c","z~2 protoclusters show non-self-similar density and temperature","Ionised gas density links to mass and disturbance past 0.1 R500c"]},"model":"grok-4.5","effort":"low","cost_usd":0.008178,"raw_usage":{"total_tokens":2031,"prompt_tokens":906,"num_sources_used":0,"completion_tokens":120,"cost_in_usd_ticks":81780000,"prompt_tokens_details":{"text_tokens":906,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1005,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":906,"tokens_out":120,"duration_ms":6848,"temperature":1.0,"reasoning_tokens":1005,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T07:55:11.879198+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A statistically significant sample of z≃2 protoclusters with measured electron-density profiles (via deep X-ray or joint SZ+X-ray analysis) that lack the central double-β steepening or that show hot-ionised gas already dominant well inside 0.1 R500c would contradict the stacked simulation result.","supporting_citations":[],"review_version":1}