{"id":"14b41e42-dd1b-4fd1-a00d-302ac1b5961f","arxiv_id":"2608.09014","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Cross-correlating CHIME fast radio burst dispersion measures with the Planck tSZ map, with galaxy clusters masked, detects diffuse warm-hot gas and suggests it holds about half of the cosmic baryons.","lead":"Astronomers have long been unable to account for a large share of the ordinary matter in the nearby universe. This paper detects that missing matter as warm thin gas stretched between galaxies, by combining radio flashes from distant sources with a subtle distortion of the cosmic microwave background.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported f_WHIM=0.48 is conditional on an unpropagated T_e=2.4e6 K anchor; the closure claim is not robust to the temperature degeneracy acknowledged in Sec. 4.","rationale":"The reader's weakest assumption—the unpropagated T_e/f_WSZ anchors in Eq. (5)—is also the most load-bearing one for the paper's central claim. If this anchor is wrong, f_WHIM is not 0.48 and the closure pie chart in Fig. 6 loses its basis. The paper is honest about the degeneracy in Sec. 4, but it does not let it enter the quoted uncertainty, so the central claim is conditional. I do not see a reason to move beyond the reader's CONDITIONAL verdict: the masked-signal stability (f≈0.49 with 3θ_500), the RA-shuffle null test, and the catalog-based NaMaster estimator are genuine supporting elements. The temperature concern does not invalidate the correlation measurement; it invalidates the quoted baryon fraction as a standalone result. If the check above shows the marginalized f_WHIM remains inside a physical range, the paper could be accepted as is; if not, the abstract and Fig. 6 must be recast as constraints on f_WHIM×T_e, not on the baryon budget.","tokens_in":14674,"tokens_out":7994,"duration_ms":83146,"concrete_test":"Re-run the MCMC of Sec. 2.4 with Eq. (5) modified to W_phys^SZ = (4.02×10^-10 Mpc^-1) × f_WHIM × f_WSZ × (T_e/2.4×10^6 K), assigning a log-uniform prior to T_e over [10^5,10^7] K and a prior to f_WSZ based on the Ibitoye et al. 2024 posterior; report the marginalized f_WHIM. If its 68% interval spans from <0.2 to >1 (or the posterior piles up at the prior boundary), the headline 0.48 and the closure statement are temperature-prior-dominated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—that f_WHIM≈0.48 closes the local baryon budget—is fixed by the adoption of T_e=2.4×10^6 K and f_WSZ≈3.09 in Eq. (5), with no uncertainty propagated from either anchor. The tSZ weight is proportional to n_e T_e while the FRB weight is proportional to n_e, so the measured cross-spectrum amplitude constrains f_WHIM×T_e, not f_WHIM alone; for fixed signal f_WHIM scales roughly as 1/T_e. Sec. 4 itself states that T_e≈10^5 K would require an unphysical f_WHIM>1 and T_e≈10^7 K would reduce f_WHIM below 20%. The paper nevertheless headlines 0.48 and presents a closure pie chart whose 13% error bars exclude the temperature systematic. Thus the 68% interval 0.27–0.61 is not a marginal posterior over the dominant nuisance parameter; the 'missing baryons located in the WHIM' claim holds only under a single assumed thermodynamic state.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents an angular cross-correlation measurement between the dispersion measures of 2,656 FRBs from CHIME/FRB Catalog 2 and the Planck PR4 NILC tSZ Compton-y map, after masking galaxy clusters. The authors report a positive cross-power spectrum at 3.05σ significance with the 1θ500 mask, a best-fit WHIM baryon fraction f_WHIM = 0.48 (68% interval 0.27–0.61) anchored at T_e = 2.4×10^6 K, and an effective localization scale ℓ_loc = 477 (68% interval 338–1321). They argue that the signal originates from diffuse WHIM because expanding the mask to 3θ500 leaves f_WHIM ≈ 0.494, and an RA-shuffle null test yields a mean spectrum consistent with zero. The paper concludes that the missing baryons reside in the WHIM and that the local baryon budget is statistically closed.","tokens_in":14947,"tokens_out":5235,"duration_ms":46027,"significance":"If correct, the measurement would be the first direct FRB–tSZ cross-correlation detection that isolates the WHIM, and it demonstrates a valuable observational route to the missing-baryon problem. The cleanest assets are the catalog-based pseudo-C_ℓ estimator, the RA-shuffle null test, and the stability of f_WHIM under cluster-mask expansion. However, the amplitude interpretation is conditional on an externally adopted temperature anchor, and the quoted baryon fraction does not yet provide a robust stand-alone census; the detection significance is modest and somewhat mask-dependent.","major_comments":[{"comment":"The headline f_WHIM = 0.48 is degenerate with the mean WHIM temperature because the tSZ weight is proportional to n_e T_e while the FRB weight is proportional to n_e; for a fixed measured cross-spectrum amplitude, f_WHIM scales approximately as 1/T_e. The authors adopt T_e = 2.4×10^6 K and f_WSZ ≈ 3.09 without propagating their uncertainties, and Section 4 itself notes that T_e ~ 10^5 K would require an unphysical f_WHIM > 1 while T_e ~ 10^7 K would lower f_WHIM below 20%. The quoted 68% confidence interval is therefore not a posterior over the dominant nuisance parameter. I recommend marginalizing over T_e with a physically motivated prior, reporting the result as a joint constraint on f_WHIM × T_e, or at minimum clearly framing 0.48 as a conditional estimate rather than a direct measurement of the baryon fraction.","section":"Section 2.3.1, Eq. (5); Section 4"},{"comment":"The detection significance falls from 3.05σ with the 1θ500 mask to 2.06σ with the 3θ500 mask. The abstract and conclusion headline the 99.77% significance and describe the 3θ500 result as confirming the WHIM origin, but at 2.06σ the more conservative measurement is only a marginal detection. The text should report both significances in the abstract and soften the \"confirms\" language to \"consistent with a diffuse origin,\" since the statistical evidence for a non-zero signal at the stricter mask is below the conventional 3σ threshold.","section":"Section 3.2"},{"comment":"The model assumes P_e(k,z) = P_m(k,z), i.e., a unit bias between the diffuse electron distribution and the matter distribution at the scales used. Because f_WHIM is fitted as the amplitude of this model, any non-unit or scale-dependent electron bias is absorbed into f_WHIM. This premise is not tested in the paper; a comparison with hydrodynamical simulations or a bias parameter marginalized over would make the amplitude claim more robust.","section":"Section 2.3, paragraph before Eq. (4)"},{"comment":"The FRB projection kernel is normalized using f_IGM = 0.84 as a fixed input and a p(z) derived from pseudo-redshift medians with a KDE smoothing bandwidth, and neither the uncertainty in f_IGM nor the pseudo-redshift systematics is propagated into the posterior. Since f_WHIM is the ratio of the measured cross-spectrum amplitude to the model normalization, these choices enter the headline value directly; the sensitivity of f_WHIM to the p(z) construction and to the lower and upper bounds of the redshift distribution should be quantified.","section":"Sections 2.3.2 and 2.3.3"}],"minor_comments":[{"comment":"The paper describes the result as the first detection, but a concurrent study (Sharma et al. 2026) already reports a positive FRB–tSZ correlation; please clarify that the novelty is isolating the WHIM via cluster masking.","section":"Abstract and Section 1"},{"comment":"The text refers to a C^1 apodization while the Figure 1 caption says \"cosine apodization\"; unify the terminology.","section":"Section 2.1.2 and Figure 1 caption"},{"comment":"The jackknife variance formula uses N in the prefactor, but the text specifies 53 valid patches; state explicitly that N=53 in this expression.","section":"Eq. (3)"},{"comment":"The likelihood uses only the diagonal of the jackknife covariance; given that nearby multipole bins are likely correlated through mode coupling, a short justification or a covariance-matrix test would strengthen the quoted Δχ² significance.","section":"Eq. (9)"},{"comment":"The significance is quoted as √Δχ² in units of Gaussian sigma; since the number of degrees of freedom is not stated, specify the dof for the null and best-fit χ² values.","section":"Section 2.4"},{"comment":"Typo \"wholistic\" should be \"holistic\".","section":"Section 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is promising and the null tests are clean, but the central quantitative claim depends on an unpropagated temperature anchor and the detection significance is marginal under the more conservative mask. A revision that propagates the temperature/systematics and recalibrates the abstract's closure and significance claims would make the paper publishable. I see no fatal internal inconsistency that warrants rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this is a real, carefully built measurement—the masked FRB–tSZ cross-power spectrum from CHIME/FRB Catalog 2—but the headline number, f_WHIM = 0.48, is not as robust as the abstract implies. The detection is plausible, the RA-shuffle null test is clean, and the f_WHIM stability between the 1θ500 and 3θ500 masks (0.48 vs 0.494) is genuinely reassuring. That part deserves credit.\n\nWhat’s new: the cluster-masking strategy to isolate diffuse WHIM from ICM is a sensible step, and the data-driven pseudo-redshift distribution avoids some of the model dependency that plagues FRB analyses. The paper is also honest enough to report that the significance drops to 2.06σ with the 3θ500 mask and that switching to a CIB-deprojected y-map reduces the detection to ~2.4σ. That transparency is good.\n\nThe soft spot is the thermodynamic anchor. The tSZ weight is proportional to neTe while the FRB weight is proportional to ne, so the cross-spectrum amplitude constrains f_WHIM × Te, not f_WHIM alone. The paper adopts Te = 2.4e6 K and f_WSZ = 3.09 from Ibitoye et al. (2024) without propagating their uncertainties, and then reports 0.27–0.61 as a 68% interval. That interval is conditional on a single temperature; as the paper’s own Sec. 4 states, Te ~ 1e5 K would require f_WHIM > 1 and Te ~ 1e7 K would push f_WHIM below 20%. So the 'closure' pie chart, with its ~13% error bars, overstates what is actually measured. Also, the assumption that the diffuse electron power spectrum traces the matter power spectrum with unit bias is untested; if that bias is not unity the amplitude interpretation shifts.\n\nI also think the 'first detection' framing is a beat too strong. Muñoz & Loeb proposed the statistic in 2018, and the concurrent Sharma et al. (2026) result uses the same CHIME catalog with tSZ. This paper’s specific contribution is the mask and the WHIM isolation, which is legitimate, but the 'first' should be hedged in the final version.\n\nBottom line: the measurement is worth taking seriously, and the null tests and mask stability give me reasonable confidence that the correlation is not an artifact. But the baryon fraction and the closure claim are prior-dominated, and the headline should be re-parameterized as f_WHIM × Te or clearly presented as conditional on Te. This deserves peer review—a good referee can push on the temperature prior and the bias assumption—but I’d want major revisions before endorsing the cosmological conclusion.","headline":"A careful masked FRB–tSZ cross-correlation measurement with a clean null test, but the headline f_WHIM = 0.48 and the 'baryon budget closed' claim are anchored to an unpropagated Te = 2.4e6 K assumption; the detection itself drops to ~2σ under the strictest mask.","tokens_in":15496,"tokens_out":2406,"would_cite":true,"duration_ms":21578,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A 99.77%-confidence cross-correlation locates the missing baryons in warm-hot cosmic-web gas.","keywords":["fast radio bursts","Sunyaev-Zel'dovich effect","warm-hot intergalactic medium","missing baryons","dispersion measure","cosmic web","angular cross-correlation","Compton y-map"],"falsifier":"Measure the actual mean electron temperature of the WHIM--for instance with X-ray absorption-line spectroscopy of cosmic filaments or with a simulation-calibrated temperature prior--and recompute $f_{\\rm WHIM}$ from the same cross-power spectrum: a temperature near $10^7$ K would push the fraction below 20%, and a temperature near $10^5$ K would require more baryons than exist, either of which would falsify the budget-closing interpretation.","tokens_in":14491,"feed_emoji":"📡","tokens_out":16663,"duration_ms":137139,"temperature":0.7,"pith_summary":"The paper tries to account for the universe's 'missing baryons'--the ordinary matter that late-time censuses cannot find--by cross-correlating the dispersion measures of 2,656 fast radio bursts with the Planck satellite's Compton-$y$ map, which traces the pressure of hot gas. After masking galaxy clusters to remove the bright cluster gas, it reports a positive angular cross-correlation at >99.77% confidence and fits a warm-hot intergalactic medium (WHIM) baryon fraction $f_{\\rm WHIM}=0.48$, with a 68% confidence interval of $0.27$--$0.61$, anchored at a mean gas temperature of $T_e=2.4\\times10^6$ K. If correct, this closes the local cosmic baryon budget: the missing baryons are hiding in diffuse warm-hot gas in the cosmic web rather than in any yet-unseen collapsed structure.","feed_headline":"Half the missing baryons hide in warm-hot cosmic gas","feed_subtitle":"A 99.77% cross-correlation between 2,656 fast radio bursts and the tSZ map places 48% of cosmic baryons in warm-hot gas.","key_machinery":"The load-bearing object is the angular cross-power spectrum $C_\\ell$ between the FRB dispersion-measure field and the tSZ Compton-$y$ map. It is measured with a catalog-based pseudo-$C_\\ell$ estimator on masked skies and compared with a theoretical model built from the Limber approximation: a line-of-sight integral of the three-dimensional electron power spectrum, assumed to trace dark matter, times two weight functions. The FRB weight function combines the IGM electron column and the data-driven redshift distribution of the FRB sample; the tSZ weight function is proportional to $f_{\\rm WHIM}$ times a fiducial pressure amplitude $f_{\\rm WSZ}$. Because the tSZ signal depends on electron pressure ($P_e\\propto n_e T_e$), the paper fixes the mean WHIM temperature at $2.4\\times10^6$ K and fits $f_{\\rm WHIM}$ together with the FRB localization scale $\\ell_{\\rm loc}$.","core_discovery":"The central claim is that the dispersion measures of extragalactic fast radio bursts and the thermal Sunyaev-Zel'dovich Compton-$y$ signal trace the same diffuse electron population, so their angular cross-power spectrum can isolate the WHIM. Masking clusters at $1\\theta_{500}$ and $3\\theta_{500}$ radii leaves a positive cross-correlation ($3.05\\sigma$, >99.77% confidence) whose amplitude, modeled with the Limber approximation and a tSZ weight function anchored at $T_e=2.4\\times10^6$ K with $f_{\\rm WSZ}\\approx3.09$, yields $f_{\\rm WHIM}=0.48$ ($0.27$--$0.61$ at 68%). The inferred fraction is nearly invariant ($f_{\\rm WHIM}\\approx0.494$) under the more aggressive cluster mask, which the authors take as evidence that the signal comes from diffuse cosmic-web gas rather than residual cluster halos. Adding this WHIM share to the baryons already counted in stars, cold gas, the circumgalactic and intracluster medium, and the Ly$\\alpha$ forest accounts for roughly 94% of the cosmological baryon budget, with the remaining ~6.4% covered by the 1$\\sigma$ uncertainties of the diffuse phases.","pith_inferences":["The paper leaves implicit that its headline fraction is essentially a temperature assumption in disguise; a direct measurement of the WHIM temperature would convert the same cross-correlation amplitude into a baryon census without the $f_{\\rm WHIM}$--$T_e$ degeneracy.","The same pipeline applied to future FRB samples with host-galaxy redshifts and to CIB-deprojected tSZ maps could sharpen the detection; the paper itself notes that the significance drops to about $2.4\\sigma$ on the CIB-deprojected map.","If FRB DMs are also cross-correlated with CMB lensing or the kinetic Sunyaev-Zel'dovich effect, the combination could map the WHIM's spatial distribution and temperature, and test the unit-bias assumption for the electron power spectrum that the paper does not test.","The WHIM fraction is likely redshift-dependent, so extending this measurement to higher-redshift FRB samples could trace the assembly of the cosmic web and test whether the local budget closure holds at earlier epochs."],"forward_implications":["The local cosmic baryon budget can be closed statistically: the measured 48% WHIM share, added to roughly 7% in stars and ISM, 1.7% in cold gas, 5% in the CGM, 4% in the ICM, and 28% in the Ly$\\alpha$ forest, reaches about 94%, with the residual covered by the 1$\\sigma$ uncertainties.","FRB-tSZ cross-correlation becomes a practical probe of diffuse gas that sidesteps the host-galaxy DM degeneracy and the cosmic infrared background contamination that dominate the auto-power spectra of either tracer.","The inferred WHIM fraction remains nearly unchanged when the cluster mask is widened from $1\\theta_{500}$ to $3\\theta_{500}$, indicating the signal is diffuse rather than cluster contamination.","The fitted FRB localization scale $\\ell_{\\rm loc}\\approx477$ with a 68% range of $338$--$1321$ is consistent with the expected CHIME localization range, which supports the modeling pipeline.","A baryon-rich WHIM near $2.4\\times10^6$ K is favored over a cold $10^5$ K WHIM, which would require more baryons than exist, and over a hot $10^7$ K WHIM, which would leave fewer than 20% of baryons in the WHIM."],"supporting_citations":[{"why":"Supplies the fiducial tSZ pressure amplitude and mean WHIM temperature that anchor the model weight function.","marker":"Ibitoye et al. 2024"},{"why":"Provides the NILC Compton-y map from Planck PR4 and the apodized masks that define the base tSZ sky coverage.","marker":"Chandran et al. 2023"},{"why":"Releases the second CHIME/FRB catalog from which the cleaned 2,656-FRB sample is drawn.","marker":"Chime/Frb Collaboration et al. 2026"},{"why":"PSZ2 cluster catalog used with MCXC-II to define the 1theta500 and 3theta500 exclusion masks.","marker":"Ade et al. 2016"},{"why":"Provides the pseudo-C_l estimator and mode-coupling formalism used to measure and decouple the cross-power spectrum.","marker":"Alonso et al. 2019"},{"why":"Gives the theoretical CHIME localization scale range used to set the prior on the localization parameter and to check the fitted value.","marker":"Rafiei-Ravandi et al. 2021"},{"why":"Supplies the pseudo-redshift posterior method used to build the data-driven FRB redshift distribution.","marker":"Gao et al. 2025"},{"why":"Defines the DM selection cuts, weight-function conventions, and localization-scale modeling adapted for this analysis.","marker":"Wang et al. 2025"},{"why":"Provides the stacked tSZ filament detection and the WHIM temperature scale cited to justify the 2.4 million kelvin anchor.","marker":"de Graaff et al. 2019"},{"why":"Provides the IGM baryon fraction used in the DM weight function and the photoionized Ly-alpha forest fraction used in the baryon budget.","marker":"Shull et al. 2012"}],"fun_headline_variants":["FRB-tSZ cross-correlation finds 48% of missing baryons","Missing baryons: warm-hot gas holds nearly half","Cosmic web's diffuse gas hides half of missing baryons","FRBs and Planck map reveal half the missing baryons"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire 48% number rests on the assumed mean WHIM temperature of 2.4 million kelvin, together with the assumption that diffuse free electrons trace dark matter with unit bias: at $10^5$ K the same signal would require more than the total baryon budget, and at $10^7$ K it would leave less than 20% of baryons in the WHIM.","fun_headline_variants_meta":{"raw":{"variants":["FRB-tSZ cross-correlation finds 48% of missing baryons","Missing baryons: warm-hot gas holds nearly half","Cosmic web's diffuse gas hides half of missing baryons","FRBs and Planck map reveal half the missing baryons"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000344,"raw_usage":{"total_tokens":1973,"prompt_tokens":1109,"completion_tokens":864,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":725,"completion_tokens_details":{"reasoning_tokens":793}},"tokens_in":725,"tokens_out":864,"duration_ms":9052,"temperature":1.0,"reasoning_tokens":793,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:18:28.833914+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the actual mean electron temperature of the WHIM--for instance with X-ray absorption-line spectroscopy of cosmic filaments or with a simulation-calibrated temperature prior--and recompute $f_{\\rm WHIM}$ from the same cross-power spectrum: a temperature near $10^7$ K would push the fraction below 20%, and a temperature near $10^5$ K would require more baryons than exist, either of which would falsify the budget-closing interpretation.","supporting_citations":[{"cited_title":"2024, The Astrophysical Journal Supplement Series, 270, doi: 10.3847/1538-4365/ad08c5","cited_arxiv_id":null,"evidence_quote":"Supplies the fiducial tSZ pressure amplitude and mean WHIM temperature that anchor the model weight function."}],"review_version":1}