{"id":"d2f61ccd-831f-44ef-8cee-907920e4315b","arxiv_id":"2411.13499","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"LOFAR rotation measures imply filament magnetic fields of 11-15 nG at z=0 that strengthen as (1+z)^2.3-2.6, favoring primordial magnetogenesis.","lead":"Astronomers used radio signals from distant galaxies to probe magnetic fields in the cosmic web, and report that the fields in intergalactic filaments grow stronger with lookback time. The result favors theories where cosmic magnetism was born in the early universe rather than generated later by galaxies.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline B_f0=11-15 nG and alpha=2.3-2.6 depend on the uncalibrated astrophysical RRM shape A_rrm/(1+z); Tables 3-5 show 2-5 sigma shifts under alternative shapes.","rationale":"I agree with the reader that the assumed astrophysical redshift dependence is the most load-bearing assumption. The paper is careful in sample selection, GRM filtering, and the cluster/CGM analysis, and it is transparent about the tension between the fitted astrophysical fraction and the direct census. However, the headline B_f0 and alpha are conditional on a shape that is selected by comparison with the same magnetogenesis simulations being tested, and the selected shape is the one most discrepant with the independent census. A free-n fit with the census prior would settle whether the 11-15 nG range survives when the shape is allowed to vary. If it does not, the abstract should present the range implied by Tables 3-5 or the value should be reported conditional on the astrophysical shape. The downscaling of the alpha_s=-1 primordial model is also noted but is secondary; the shape discrimination in Fig. 14 remains the main evidence for primordial fields. No internal inconsistency or formal error is apparent; the concern is understated systematic uncertainty.","tokens_in":29863,"tokens_out":10304,"duration_ms":106168,"concrete_test":"Re-run the Bayesian fit of Eq. (8) on the same GRM-filtered RRM rms data (20-source bins) with the astrophysical index n as a free parameter, A_rrm/(1+z)^n, using the same LOS products and priors, and impose a Gaussian prior on the astrophysical variance fraction with mean 0.21 and sigma 0.04 from the Sect. 4.2 cluster/CGM census. If the marginalized 68% credible interval for B_f0 then includes values above 15 nG (or the posterior for n excludes 1), the headline B_f0=11-15 nG and its quoted 4 nG error are not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central numerical claim, B_f0=11-15±4 nG and alpha=2.3-2.6±0.5 (Abstract, Sect. 6.2), is obtained from Eq. (8) with the astrophysical component fixed to A_rrm/(1+z). Tables 3-5 demonstrate that this is not robust: using A_rrm/(1+z)^2 or A_rrm/(1+z)^3 gives B_f0=20-27 nG (alpha=1.7-2.1) and B_f0=28-40 nG (alpha=1.2-1.6), respectively, shifting the central value by 2-5 times the quoted 4 nG error. The choice of A_rrm/(1+z) is motivated by the better match of the residual filament component to the simulated magnetogenesis curves in Fig. 14, but this same shape yields an astrophysical variance fraction of 46-49±4%, in 4-5 sigma tension with the independent cluster/CGM census of 21±4% from Sect. 4.2. The paper suggests an additional ~25% local component may reconcile this, but the null dependence of RRM on source spectral index and linear size (Sect. 4.3-4.4) provides no support for such a component. The systematic from the uncalibrated astrophysical redshift dependence is therefore larger than the stated error and directly controls the headline field strength.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the LOFAR LoTSS DR2 RM catalogue to investigate the origin of extragalactic rotation measures at 144 MHz and to constrain magnetic fields in cosmic filaments. The authors select a subsample of sources with low Galactic RM (|GRM| < 14 rad/m^2), compute the residual RM (RRM) rms as a function of redshift, and fit a model that combines an astrophysical RRM term with a filament term computed from cosmological MHD simulations. They also compare the observed RRM-redshift relation with predictions from several magnetogenesis scenarios. Based on the fits, the paper reports a filament magnetic field strength at z=0 of B_f0 = 11-15 +/- 4 nG with a redshift slope alpha = 2.3-2.6 +/- 0.5, and concludes that primordial magnetogenesis scenarios are favoured over purely astrophysical injection.","tokens_in":30261,"tokens_out":9117,"duration_ms":95887,"significance":"If the quoted values are robust, the paper would provide an important direct measurement of magnetic fields in cosmic filaments and a discriminator between magnetogenesis scenarios, building on earlier work by the same group. The analysis has clear strengths: the sample selection is carefully documented with multiple sanity checks for residual Galactic contamination; the origin of the RRM is investigated with several independent methods (cluster impact parameters, galaxy CGM stacking, source spectral index, and source linear size); and the comparison uses a suite of cosmological MHD simulations with parameters reported in Table 1. The paper also gives an independent estimate of the astrophysical RRM fraction (21 +/- 4 percent) from clusters and CGM, which is a useful cross-check. However, the headline numerical claims are currently tied to model choices that are not independently calibrated, and one of the central equations appears to add rms values linearly rather than in quadrature. As a result, the significance as a measurement of B_f0 and alpha is not yet established in the present form.","major_comments":[{"comment":"Equation (8) models the total RRM rms as the linear sum of the astrophysical term A_rrm/(1+z)^2 and the filament term <RRM_f^2>^{1/2}. If the astrophysical and filament contributions are independent, their variances add, so the total rms should be the quadrature sum sqrt( A_rrm^2/(1+z)^4 + <RRM_f^2> ). The linear form is exact only for perfectly correlated components, which is not the case for unrelated foreground objects and filaments. Because this equation is the basis for all fits in Tables 3-5 and B.1, the reported B_f0 and alpha values are affected; the inferred filament amplitude and the tension with the independent astrophysical fraction would both change. Please justify the linear addition or correct it and re-run the fits.","section":"Sect. 5.1, Eq. (8)"},{"comment":"The headline values B_f0 = 11-15 nG and alpha = 2.3-2.6 are obtained only for the A_rrm/(1+z) shape of the astrophysical component (Table 5). With the A_rrm/(1+z)^2 and A_rrm/(1+z)^3 shapes (Tables 3 and 4), the same data give B_f0 = 20-27 nG with alpha = 1.7-2.1, and B_f0 = 28-40 nG with alpha = 1.2-1.6, respectively. These shifts are 2-5 times the quoted 4 nG error on B_f0. The choice of the A_rrm/(1+z) shape is motivated by the better visual match of the residual filament component to the simulated curves in Fig. 14, but this same shape yields an astrophysical variance fraction of 46-49 +/- 4 percent, in 4-5 sigma tension with the independent 21 +/- 4 percent estimate from clusters and CGM in Sect. 4.2. The paper proposes an additional ~25 percent local component to reconcile this, but the null dependence of RRM on source spectral index and linear size (Sects. 4.3-4.4) provides no support for such a component. The systematic from the uncalibrated astrophysical redshift dependence is therefore larger than the quoted statistical error and directly controls the headline field strength and slope.","section":"Sect. 5.1, Tables 3-5; Sect. 6.2"},{"comment":"The stochastic primordial model with alpha_s = -1.0 is downscaled by construction: Section 3 states that its normalization is reduced from B_1Mpc = 1.87 nG (the CMB limit) to 0.37 nG specifically to produce a reasonable match to LOFAR RRMs. Section 5.2 then reports this model as favoured by the data. This is circular for the amplitude: the model is adjusted to the data and then found to agree with them. The comparison can test only the shape of the RRM-redshift relation, not the normalization, unless the amplitude is fixed a priori by CMB or other independent constraints. Please reframe the conclusion so that the amplitude is treated as a fitted or externally constrained quantity, and report the goodness of fit of the CMB-consistent normalization for alpha_s = -1.0.","section":"Sect. 3 and Sect. 5.2"},{"comment":"The RRM rms-redshift relation used for the fits contains wiggles with peaks at z ~ 0.15, 0.36, and 0.56 (Fig. 4, right panel), which the paper finds anti-correlated with the galaxy number density and leaves unexplained. Since the model of Eq. (8) is a smooth function of redshift, these bin-to-bin fluctuations can bias the inferred slope alpha. Please quantify the sensitivity of alpha and B_f0 to the wiggles, for example by fitting with and without the affected bins or by including a wiggle nuisance term in the likelihood.","section":"Sect. 2.3, Fig. 4; Sect. 4.2"}],"minor_comments":[{"comment":"The choice of GRMth = 14 rad/m^2 is made by trading off the RRM rms minimum (at 7 rad/m^2) against sample size, and the selected threshold differs from the minimum by only 1.2 sigma. Since the same RRM data are then used for the scientific analysis, please discuss explicitly how this data-driven selection could affect the inferred rms values and the subsequent fits.","section":"Sect. 2.2, Fig. 1"},{"comment":"The y-axis label '< p > [rad m^-2]' should be '[%]' (or dimensionless if p is a fraction), since p is the fractional polarization expressed in percent.","section":"Fig. 9, right panel"},{"comment":"The 'hint of a shock at the virial radius' is presented as intriguing but without a quantitative significance in the text; please state the significance of the 0.8 r_v excess explicitly, in the same way the cluster excess in Sect. 4.1 is reported.","section":"Sect. 4.2"},{"comment":"The sentence 'The term Arrm/(1+z)^2 accounts for an astrophysical component constant with redshift' is confusing because the observed RRM contribution decreases with redshift under this shape; please reword to specify that the rest-frame astrophysical RM is constant.","section":"Sect. 5.1"},{"comment":"The spectral index analysis uses a cross-match radius of 22 arcsec; please state how many of the 576 matched sources fall within the GRMth = 14 rad/m^2 sample used for the main analysis, since the two samples are not identical.","section":"Sect. 4.3"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely of interest to the A&A readership, and the dataset plus the decomposition analysis are valuable. In my reading, the concerns about the A_rrm/(1+z) shape and the tuned alpha_s = -1.0 normalization are valid and need to be addressed before publication. The linear addition in Eq. (8) is a further issue that the authors should clarify or correct. I do not recommend rejection because these problems are fixable by recalibration, by reporting a systematic error budget across the three astrophysical shapes, and by reframing the magnetogenesis comparison so that the normalization is not tuned to the data being explained."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know before reading. The GRM-filtered sample is a genuine step forward: RRM rms drops to 1.54, the redshift slope steepens to 0.25±0.08, and the new cluster/CGM stacking gives an independent handle on the astrophysical contribution (21±4%). That part is solid and worth using. The second thing is less comfortable: the headline numbers, B_f0=11-15 nG and alpha=2.3-2.6, come from Eq. (8) with the astrophysical term forced to A_rrm/(1+z). Tables 3-5 show that switching to (1+z)^2 or (1+z)^3 changes the field to 20-27 and 28-40 nG, shifts several times the quoted 4 nG error. So the central measurement is not yet robust.\n\nWhat the paper does well: it tests its own assumptions. The GRM residual checks against |b| and |GRM| are sensible. The absence of RRM correlation with source spectral index and linear size supports an IGM origin. The possible shock at the virial radius of massive galaxies and the use of fractional polarization as a CGM tracer are genuinely new, if preliminary. The ENZO simulation suite with long LOS is a real resource, even if the LOS products are not yet public.\n\nThe soft spots are concentrated in Section 5. The choice A_rrm/(1+z) is preferred because it makes the residual filament signal match the simulated magnetogenesis curves (Fig. 14), but that same shape implies a 46-49% astrophysical fraction, in 4-5 sigma tension with the 21% census. The authors suggest an extra ~25% local component, but the null correlations in Sections 4.3-4.4 give no support for it. The stochastic alpha_s=-1.0 model is also downscaled to 0.37 nG from the CMB limit of 1.87 nG to match the LOFAR data, and then reported as favored. That is self-referential. They flag it openly, which is to their credit, but the label 'favored' is doing too much work.\n\nMy overall take: the paper is a solid incremental advance, honestly written, with reproducible-enough checks that the community can build on it. The central field values should be treated as conditional on an astrophysical model that is not yet calibrated externally. A referee should push for a treatment that marginalizes over the astrophysical shape or imposes a prior from the cluster/CGM census, and for the simulated LOS to be released.\n\nI'd send it to peer review. The measurement direction is plausible and the dataset is valuable; the systematic issue is exactly what refereeing is for. Bring it to reading group if you want a good case study in how an unmodeled nuisance can control a headline result.","headline":"Solid, transparent extension of Paper II whose headline field values rest on an uncalibrated astrophysical RRM shape; worth refereeing, but treat the central numbers as provisional.","tokens_in":30832,"tokens_out":3585,"would_cite":true,"duration_ms":39525,"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":"LOFAR rotation measures, cleaned of Galactic contamination, show filament magnetic fields of 11–15 nG that grew as (1+z)^{2.3–2.6}, favouring primordial magnetogenesis.","keywords":["cosmic web filaments","intergalactic magnetic fields","Faraday rotation measure","magnetogenesis","LOFAR","radio polarization","large-scale structure","circumgalactic medium"],"falsifier":"Stack the RRM of background sources behind known galaxy groups and clusters in narrow redshift bins at a frequency where the filament contribution is small, and measure how the astrophysical RM per halo changes with redshift. The paper's preferred $A_{\\rm rrm}/(1+z)$ shape predicts the astrophysical RRM contribution roughly doubles from $z\\approx0$ to $z\\approx1$, while the $A_{\\rm rrm}/(1+z)^3$ shape predicts it shrinks; a higher-frequency RM sample with spectroscopic redshifts could distinguish these and settle whether $B_{f,0}$ is near $11{-}15\\,\\mathrm{nG}$ or $20{-}40\\,\\mathrm{nG}$.","tokens_in":29641,"feed_emoji":"🧲","tokens_out":11329,"duration_ms":107996,"temperature":0.7,"pith_summary":"This paper tries to determine the strength and redshift evolution of magnetic fields in the cosmic web's filaments, and through them the origin of cosmic magnetism. Using Faraday rotation measures of 653 low-Galactic-contamination background sources at 144 MHz, it argues that residual RMs are dominated by filaments and that their dispersion grows steeply with redshift. The resulting field at z=0 is 11–15 ± 4 nG, scaling as (1+z)^{2.3–2.6 ± 0.5}, which means the comoving field is roughly constant — a steeper evolution than earlier analyses found. The data favour primordial magnetogenesis over fields injected later by galaxies and AGNs. The paper also quantifies the contaminating cluster and galaxy-halo contribution at about 21% and proposes that background-source polarization fraction can trace the circumgalactic medium.","feed_headline":"Filament fields are 11–15 nG, favouring a primordial origin","feed_subtitle":"LOFAR rotation measures grow with redshift, pushing magnetogenesis back to the early universe.","key_machinery":"The central quantity is the residual rotation measure, $\\mathrm{RRM} = \\mathrm{RM} - \\mathrm{GRM}$, obtained after subtracting a Galactic RM map and keeping only sources with $|\\mathrm{GRM}|<14\\,\\mathrm{rad\\,m^{-2}}$, which removes most Milky Way contamination. The fitted model is $\\sqrt{\\langle\\mathrm{RRM}^2\\rangle} = A_{\\rm rrm}/(1+z)^2 + \\sqrt{\\langle\\mathrm{RRM}_f^2\\rangle}$, where the filament term is $\\mathrm{RRM}_f = 0.812\\int n_e B_\\parallel (1+z)^{-2}\\,dl$ and the filament field is assumed to follow $B_f = B_{f,0}(1+z)^\\alpha$, with comoving slope $\\beta=\\alpha-2$. The filament term is evaluated along 100 mock lines of sight through magneto-hydrodynamic cosmological simulations of each magnetogenesis scenario, with dense cluster regions excised by a density-contrast cutoff and 120 random field-direction realisations per line of sight. The results rest on the assumed shape of the astrophysical term $A_{\\rm rrm}/(1+z)^k$; the preferred $k=1$ shape, corresponding to an astrophysical RRM that grows with redshift, is what produces the $11{-}15\\,\\mathrm{nG}$ and $\\alpha\\approx2.5$ outcome.","core_discovery":"Using the 653-source subsample of the LOFAR 144-MHz RM catalogue with $|\\mathrm{GRM}|<14\\,\\mathrm{rad\\,m^{-2}}$, the paper finds that the residual rotation-measure dispersion rises with redshift with slope $0.25\\pm0.08\\,\\mathrm{rad\\,m^{-2}}$ per unit redshift, 3$\\sigma$ away from flat. A Bayesian fit of $\\sqrt{\\langle\\mathrm{RRM}^2\\rangle}=A_{\\rm rrm}/(1+z)^2+\\sqrt{\\langle\\mathrm{RRM}_f^2\\rangle}$ with the filament term drawn from magneto-hydrodynamic simulations gives $B_{f,0}=11{-}15\\pm4\\,\\mathrm{nG}$ and $\\alpha=2.3{-}2.6\\pm0.5$, i.e. a comoving-field slope $\\beta=[0.3,0.6]\\pm0.5$ consistent with no evolution. Decomposing the signal, the paper attributes about 21% of the RRM rms to galaxy clusters and galaxy CGM and the rest to cosmic filaments. Comparisons with simulations favour primordial magnetogenesis models over astrophysical injection, because primordial fields already produce significant rotation at high redshift whereas the astrophysical models flatten there. A secondary finding is that the fractional polarization of background sources may trace the CGM, with a tentative shock signature near the virial radius of massive galaxies.","pith_inferences":["The 2–4 sigma tension between the preferred rising astrophysical term and the directly measured 21% cluster-plus-CGM fraction is the softest point; a dedicated measurement of per-halo RRM versus redshift would decide whether the true field is the 11–15 nG or the 20–40 nG family.","The wiggles in RRM rms versus redshift anticorrelate with galaxy number density on roughly 800–900 Mpc scales; if physical, they are a large-scale structure signal that the 42.5 Mpc simulation boxes cannot reproduce, and tests would need larger volumes or line-of-sight stacking.","Applying the same Bayesian machinery to higher-frequency RM catalogues, where the filament term is suppressed, would measure the astrophysical redshift dependence directly instead of inferring it from a fit — a testable extension of the paper's approach."],"forward_implications":["If the filament field today is 11–15 nG and grows as (1+z)^{2.3–2.6}, the comoving magnetic field is roughly constant, so the field does not dilute as the cosmic web expands.","A primordial origin for the filament fields would mean the Universe was magnetised before galaxy formation, and that galaxy and AGN feedback only adds a subdominant contribution.","Residual Galactic RM contamination, if not controlled, can hide real redshift evolution; better Galactic RM maps will sharpen or shift these measurements.","The roughly 21% cluster-plus-CGM fraction is separable, so future higher-frequency RM surveys can directly measure the astrophysical term that currently limits the filament-field fit.","Polarization fraction of background radio sources may become a practical tracer of the circumgalactic medium and of shocks at the virial radius of massive galaxies."],"supporting_citations":[{"why":"Paper II, whose redshift-evolution analysis, Bayesian fitting method, and RM sample this work refines with a Galactic-RM-filtered subsample.","marker":"Carretti et al. 2023"},{"why":"Supplies the LoTSS DR2 catalogue of 2461 Faraday rotation measures at 144 MHz from which the sample is drawn.","marker":"O'Sullivan et al. 2023"},{"why":"Provides the all-sky Galactic RM map used to subtract the Milky Way term and to define the |GRM| < 14 rad/m^2 filter.","marker":"Hutschenreuter et al. 2022"},{"why":"Differential RM pair analysis that supports a cosmic-web-dominated origin for the residual RMs at low frequency.","marker":"Pomakov et al. 2022"},{"why":"Galaxy cluster catalogue used to measure RRM rms versus impact parameter and to estimate the cluster contribution.","marker":"Wen & Han 2015"},{"why":"Photometric galaxy catalogue with stellar masses used for the CGM/galaxy separation and virial-radius analysis.","marker":"Zou et al. 2019"},{"why":"CMB-derived constraints that set the normalisations of the primordial stochastic magnetic field models compared to the data.","marker":"Paoletti & Finelli 2019"},{"why":"Defines the stochastic primordial field spectra and the smoothing and normalisation procedure used in the simulations.","marker":"Vazza et al. 2021"},{"why":"Sub-grid dynamo amplification model included in the simulations to estimate the maximal dynamo contribution in low-density gas.","marker":"Ryu et al. 2008"}],"fun_headline_variants":["Filament magnetic fields are 11-15 nG, favouring a primordial origin","LOFAR RMs reveal filament fields with a steep redshift climb","Cosmic web filament fields: 11-15 nG and primordial in origin","Filament fields steepen with redshift, pointing to primordial origins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The headline field strength and redshift slope assume the contaminating signal from galaxies and clusters grows with redshift as (1+z); if it instead stays constant or shrinks, the same data give a field at z=0 of 20–40 nG with a flatter slope, and the preferred growing shape disagrees at 2–4 sigma with the separately measured 21% cluster-plus-CGM contribution.","fun_headline_variants_meta":{"raw":{"variants":["Filament magnetic fields are 11-15 nG, favouring a primordial origin","LOFAR RMs reveal filament fields with a steep redshift climb","Cosmic web filament fields: 11-15 nG and primordial in origin","Filament fields steepen with redshift, pointing to primordial origins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000831,"raw_usage":{"total_tokens":3746,"prompt_tokens":1179,"completion_tokens":2567,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":795,"completion_tokens_details":{"reasoning_tokens":2486}},"tokens_in":795,"tokens_out":2567,"duration_ms":19381,"temperature":1.0,"reasoning_tokens":2486,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:19:50.384341+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Stack the RRM of background sources behind known galaxy groups and clusters in narrow redshift bins at a frequency where the filament contribution is small, and measure how the astrophysical RM per halo changes with redshift. The paper's preferred $A_{\\rm rrm}/(1+z)$ shape predicts the astrophysical RRM contribution roughly doubles from $z\\approx0$ to $z\\approx1$, while the $A_{\\rm rrm}/(1+z)^3$ shape predicts it shrinks; a higher-frequency RM sample with spectroscopic redshifts could distinguish these and settle whether $B_{f,0}$ is near $11{-}15\\,\\mathrm{nG}$ or $20{-}40\\,\\mathrm{nG}$.","supporting_citations":[{"cited_title":"P., O’Sullivan, S","cited_arxiv_id":null,"evidence_quote":"Differential RM pair analysis that supports a cosmic-web-dominated origin for the residual RMs at low frequency."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Galaxy cluster catalogue used to measure RRM rms versus impact parameter and to estimate the cluster contribution."},{"cited_title":"2021, MNRAS, 500, 5350","cited_arxiv_id":null,"evidence_quote":"Defines the stochastic primordial field spectra and the smoothing and normalisation procedure used in the simulations."}],"review_version":1}