{"id":"c03bb734-07e0-44dd-a12f-91e70df2071d","arxiv_id":"2412.00988","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A catalog of 31 polarized radio galaxies in ELAIS-N1 with host redshifts shows a residual rotation measure distribution centered near zero, independent of redshift and polarization degree.","lead":"A deep LOFAR polarization survey of the ELAIS-N1 field yields 31 polarized radio galaxies, with host redshifts and rotation measures cataloged. The paper finds that their residual rotation measures are consistent with zero on average and do not change with redshift or source morphology, offering a small but precise RM grid for cosmic magnetism studies.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The near-zero RRM median may be partly built in because the Galactic RM map used for subtraction was fitted to 8 of the same LoTSS-DR2 RMs in this field; the independence claims need a leave-out test.","rationale":"The reader's weakest_assumption identifies exactly the load-bearing issue: the GRM map of Hutschenreuter et al. (2022) is partly constructed from LoTSS-DR2 RMs, and 8 of the 9 such RMs in ELAIS-N1 are in the present sample. The central claims, quoted in the abstract, are that RRM values have a median close to zero, are independent of redshift and degree of polarization, and that sources behind clusters and superclusters are indistinguishable from the rest. All of these claims are filtered through Eq. (3), so if the GRM estimate at the source positions is not independent, the RRM distribution is narrowed and centered by construction. The paper itself acknowledges the overlap in Sect. 3 and also notes in the Conclusions that part of the GRM gradient remains in the RRM grid, indicating imperfect subtraction. My proposed test, refitting the map without the overlapping LoTSS RMs, would settle whether this concern changes the results. I credit the paper for the new catalog, the careful host-galaxy identification, and the morphological analysis, which do not depend on the GRM map and remain valuable regardless of the RRM outcome. The sample of 31 sources is small, and the cluster-comparison null results are underpowered, but those were already explicit limitations in the paper and are secondary to the circularity issue. Because the reader's conditional verdict already captures this concern, I see no need to change the verdict; the recommended action is to run the leave-out test before the interpretive claims are taken as established.","tokens_in":24983,"tokens_out":3852,"duration_ms":37439,"concrete_test":"Recompute the RRM values in Table A.1 using a GRM map that deliberately excludes the 9 LoTSS-DR2 RM entries in ELAIS-N1 from the Hutschenreuter et al. (2022) reconstruction, either by refitting the public map with those inputs removed or by running a local leave-one-out cross-validation with the same Gaussian-process kernel. Then re-evaluate Table 4 and Table 5. If the median RRM remains within about 2 rad m−2 of zero and the RRM-vs-redshift and RRM-vs-polarization Spearman tests stay non-significant, the overlap is not load-bearing; if the median shifts by more than about 2 rad m−2 or any p-value drops below 0.05, the near-zero median and independence claims are contaminated by the circular use of the same data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (3) defines RRM = RM − GRM using the Hutschenreuter et al. (2022) Galactic Faraday depth map, averaged over a 1-degree circle. That map is a Gaussian-process reconstruction trained on input RM catalogs, including the LoTSS-DR2 RM catalog. In the 25 deg^2 field the LoTSS-DR2 catalog contributes 9 RMs, and 8 of these are also in the 33-component sample analyzed here, as the paper states explicitly in Sect. 3 before Fig. 5. At those positions, the 'Galactic' estimate is not an independent constraint: the map will tend to reproduce the observed RM, so subtracting it forces RRM toward zero and shrinks its scatter. The near-zero median, the narrow RRM distribution in Table 4, and the null Spearman tests in Table 5 could therefore reflect the overlap rather than an intergalactic random walk. The paper's own conclusion that part of the GRM gradient remains in the RRM map is a separate, supporting sign that the subtraction is incomplete. Since the headline results depend on RRM, this circularity is the most load-bearing weakness.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper analyzes 31 polarized radio galaxies (33 polarized components) detected in the ELAIS-N1 LOFAR Deep Field at 146 MHz, following the catalog paper (Piras et al. 2024). The authors identify host galaxies and redshifts for all sources, classify radio morphologies, compute rest-frame luminosities and projected linear sizes, and compare these properties with the LoTSS-DR2 RM sample. Using Eq. (3), they subtract the Galactic RM from the Hutschenreuter et al. (2022) map to form residual rotation measures (RRMs). They report that the RRM distribution has a median close to zero and an rms of about 7 rad/m^2, find no significant Spearman correlations between |RRM| and redshift or degree of polarization, and compare the RRM properties of sources behind galaxy clusters and superclusters with the rest of the sample, concluding that foreground large-scale structure contributes little at 146 MHz. The paper is careful to note the small sample and a residual GRM gradient.","tokens_in":25307,"tokens_out":8134,"duration_ms":72280,"significance":"If the results hold, this is one of the deepest LOFAR RM grids at 146 MHz in a 25 deg^2 field, with complete host-galaxy redshift information for all sources. The comparison with LoTSS-DR2 shows that the deep-field sample reaches fainter and more distant polarized sources, and the null correlations with redshift and polarization would support the view that at 144-146 MHz the RRM is dominated by large-scale intergalactic contributions rather than by the source environment. The catalog and the explicit discussion of limitations are strengths; the paper does not rely on fitted free parameters, and the data products are to be made available via CDS and Zenodo. The main weakness is that the Galactic RM subtraction is not fully independent of the data: the Hutschenreuter et al. (2022) map used the LoTSS-DR2 RM catalog, and 8 of the 33 components in this field are also in that catalog, so the near-zero RRM median and the null correlations may be partly built in.","major_comments":[{"comment":"The central RRM result is not fully independent of the Galactic foreground model. The Hutschenreuter et al. (2022) map is a Gaussian-process reconstruction of RM catalogs that include LoTSS-DR2, and the paper states in Sect. 3 that 8 of the 33 ELAIS-N1 components are also in that input catalog. At those positions the GRM estimate will tend to reproduce the observed RM, so computing RRM = RM - GRM forces part of the signal toward zero and narrows the RRM distribution in Table 4. The null Spearman tests in Table 5 and the \"median close to zero\" claim could therefore be partly built in. I ask the authors to quantify the effect by recomputing the GRM values (or the local foreground fit) with the overlapping LoTSS-DR2 entries removed, and to report the RRM statistics and correlation coefficients for the 25 non-overlapping components as a cross-check.","section":"Sect. 3, Eq. (3)"},{"comment":"The authors acknowledge that \"the gradient seen in the GRM map remains in the RRM grid\" and call it a possible sign of residual GRM contamination. This residual gradient is in tension with the interpretation of the near-zero RRM median and the rms of 7.03 rad/m^2 as a clean extragalactic signal. Please quantify the residual: for example, fit and subtract a linear or low-order polynomial foreground across the field and report how the RRM mean, rms, and the Spearman statistics change, or compare the RRM gradient with the GRM gradient explicitly. This would also address whether the 25 non-overlapping sources show the same behavior.","section":"Sect. 3, Fig. 5, Table 4"},{"comment":"The cluster comparison rests on 11 versus 22 components and yields mean |RRM| values of 8.6 +/- 2.0 and 4.4 +/- 0.6 rad/m^2, a difference of about 2 sigma. With this sample size and the heterogeneous cluster definitions (and with three of the \"behind-cluster\" sources actually embedded in clusters), the statement that clusters and superclusters contribute little to the observed Faraday rotation is not strongly supported. Please report a permutation or bootstrap p-value for the difference, and state the 95% upper limit on the excess RRM that this sample can exclude. The current wording in the abstract (\"indistinguishable\") is too strong for a 2-sigma null result.","section":"Sect. 3.2, Table 7"}],"minor_comments":[{"comment":"The phrase \"sub-mJy regime\" should be defined explicitly as referring to polarized flux density or to the noise level, since the total flux densities in Table A.1 are all well above 1 mJy.","section":"Title, Abstract"},{"comment":"For sources 03 and 20, conflicting redshifts are listed in the source notes; please state explicitly how the adopted value was selected, since these choices affect the derived luminosities and linear sizes.","section":"Sect. 2.2, Table A.1"},{"comment":"The definition of sigma_GRM as the mean of the GRM uncertainty map within a 1-degree circle should be justified; if the map uncertainties are spatially correlated, this may not correctly represent the uncertainty of the averaged GRM.","section":"Sect. 3"},{"comment":"There is a typo in \"featuers\" (should be \"features\"), and throughout the text there are spacing artifacts such as \"di fferent\" and \"Fanaro ff-Riley\" that should be cleaned in the journal proof.","section":"Sect. 4 (Conclusions)"},{"comment":"The symbols <X> and rms are defined in the text but not in the table caption; please add a brief definition in the table notes for the general reader.","section":"Table 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is well-structured and honestly hedged. The main risk is the circularity of the GRM subtraction: the foreground map was trained partly on the same LoTSS-DR2 RMs used in this field, so the near-zero RRM median and the null correlations may be partially built in. I would like to see a leave-out test and a softened cluster conclusion before acceptance. If the leave-out test confirms the null results, the paper would be a useful contribution to low-frequency RM-grid studies."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a workmanlike catalog paper, and the workman part is the value. Piras et al. present 31 polarized radio galaxies (33 components) in the ELAIS-N1 LOFAR Deep Field, with host identifications, redshifts (100% complete: 26 spectroscopic, 5 photometric), morphologies, linear sizes, and luminosities. That alone is a step up from the 9 LoTSS-DR2 RMs and 10 Herrera Ruiz detections previously in this field. The catalog is on CDS, so it is reproducible, and the morphology statistics are given with Poisson errors. The paper also produces an RRM grid for the field, which is what anyone wanting a denser RM grid in this sky area will use.\n\nThe analysis is careful and the claims are generally hedged. The Spearman results have high p-values, the cluster comparison is flagged as underpowered, and they admit the residual GRM gradient in the RRM map might signal contamination. So the paper does not oversell.\n\nThe main soft spot is the RRM circularity the stress test flagged. The Galactic RM map of Hutschenreuter et al. (2022) was fitted using LoTSS-DR2 RMs, and 8 of the 33 components here come from that catalog. Subtracting a smoothed version of your own data will pull RRM toward zero. The paper mentions the overlap but never quantifies how much of the zero median and narrow scatter is built in. A leave-out test—or at least a statement of the fractional variance attributable to the overlap—should be added. My reading is that the effect is probably modest: the map smooths over a degree, and there are 27 NVSS RMs in the field as well, so the GRM is not determined by these eight points alone. But \"probably modest\" is not a number, and the authors can do better.\n\nThe sample size is also small. No correlation between RRM and redshift or polarization degree at n=31 is weak evidence, not strong evidence. The cluster comparison (11 vs 22) agrees within 2 sigma, which the authors interpret as \"no effect.\" That's an honest statement of a null result with low power, and they say a larger sample is needed.\n\nVerdict: send it to a referee. The catalog deserves to exist and be used. The referee should push on the leave-out test and ask for the overlap analysis. Once that is in place, the interpretive claims will be properly supported. This is not a breakthrough, but it is a useful brick in the wall of low-frequency RM grids.","headline":"A useful new polarized-source catalog in ELAIS-N1, whose RRM statistics carry a real but non-fatal circularity from the Galactic RM map; worth refereeing.","tokens_in":25797,"tokens_out":3803,"would_cite":true,"duration_ms":32313,"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 paper argues that residual rotation measures of 31 faint polarized radio galaxies are near zero, independent of redshift and fractional polarization, and unaffected by foreground clusters and superclusters.","keywords":["polarization","Faraday rotation measures","radio galaxies","LOFAR","ELAIS-N1","cosmic magnetism","residual rotation measure","sub-mJy sources"],"falsifier":"Recompute the RRMs with a Galactic foreground map that excludes all in-field LoTSS-DR2 and ELAIS-N1 entries; if the median RRM and its Spearman correlations with redshift and fractional polarization remain consistent with zero, the paper's central claim is confirmed, and if they shift significantly, the near-zero result was at least partly forced by the foreground model.","tokens_in":24772,"feed_emoji":"🧲","tokens_out":10981,"duration_ms":89042,"temperature":0.7,"pith_summary":"This paper characterizes the 31 faint, sub-millijansky polarized radio galaxies discovered in the ELAIS-N1 deep field with LOFAR at 146 MHz, the deepest polarization dataset at that frequency to date, and builds a rotation measure grid of the field. After identifying host galaxies and obtaining redshifts for all of them (range 0.06 to about 1.9), it computes residual rotation measures by subtracting a model of the Galactic foreground and finds that the median RRM is consistent with zero ($-1.78\\,\\mathrm{rad\\,m^{-2}}$) and shows no correlation with redshift or with degree of polarization. It also finds that sources whose lines of sight pass through galaxy clusters or a supercluster are statistically indistinguishable from the rest of the sample. If correct, this means that at 146 MHz the Faraday rotation of these faint sources is dominated by fluctuations in the intergalactic magneto-ionic medium rather than by the source surroundings or by foreground large-scale structure, and it demonstrates that deep low-frequency surveys can extend RM-grid cosmic magnetism studies into a regime that is fainter and more distant than the current largest catalogs.","feed_headline":"31 faint radio galaxies show zero residual Faraday rotation","feed_subtitle":"Deep 146 MHz data point to intergalactic fields, not clusters, as the source of rotation.","key_machinery":"The central object is the residual rotation measure, $\\mathrm{RRM}=\\mathrm{RM}-\\mathrm{GRM}$, where $\\mathrm{GRM}$ is the Galactic rotation measure averaged over a one-degree circle from a published reconstruction of the Galactic Faraday-depth sky; the paper assembles these values into an RRM grid covering the 25 square-degree field. The argument then turns on Spearman rank correlations between $|\\mathrm{RRM}|$, redshift, and fractional polarization, and on a comparison of the $|\\mathrm{RRM}|$ distribution for sources behind clusters and a supercluster versus sources on unobstructed sight lines. The detection itself rests on the stacked 6-arcsecond-resolution LOFAR polarization data from the companion catalog paper, which provides the observed RMs and the sub-mJy flux densities.","core_discovery":"The paper claims that the residual rotation measures of the 31 sub-mJy radio galaxies in the ELAIS-N1 field, computed as $\\mathrm{RRM} = \\mathrm{RM} - \\mathrm{GRM}$ with the Galactic component averaged from a published all-sky Faraday-depth map, have a median close to zero and are statistically independent of both redshift and fractional polarization (Spearman coefficients $r = -0.09$ and $r = +0.02$, with $p = 0.60$ and $p = 0.89$). It further claims that the nine polarized components whose sight lines pass through galaxy clusters or a supercluster show the same distribution of RRM and fractional polarization as the rest of the sample, and it interprets this as evidence that these foreground structures contribute very little to the observed Faraday rotation at 146 MHz. The radio galaxies themselves are mostly large systems (median projected size of about 317 kpc), and the higher median redshift and lower median luminosity relative to the LoTSS-DR2 RM catalog are presented as the expected result of a deeper, fainter survey.","pith_inferences":["A natural extension the authors do not pursue is to recompute the RRMs with a foreground map built without any in-field entries; if the near-zero median survives, the result would constrain the cosmological magnetic field to even lower strengths than the current 4 nG upper limit on megaparsec scales.","The sample includes compact, high-redshift sources (a blazar at $z=1.95$) whose RM could be followed up at multiple frequencies to separate source-intrinsic Faraday rotation from intergalactic contributions epoch by epoch.","The apparent contrast between this 146 MHz result and the strong RRM-versus-polarization anticorrelation seen at 1.4 GHz could be tested directly by matching these sources against 1.4 GHz RM catalogs; the paper's interpretation predicts that the 1.4 GHz signal would correlate with the local environment while the 146 MHz signal would not.","If the same zero-median, cluster-independent RRM pattern appears in the other LOFAR Deep Fields when they are analyzed with the same stacking method, the conclusion would rest on a much larger sample and the residual-foreground caveat would carry less weight."],"forward_implications":["If the near-zero median RRM holds, then at 146 MHz the Faraday rotation of faint extragalactic sources tracks fluctuations of the intergalactic magneto-ionic medium rather than the immediate source environment.","A denser RM grid built from sub-mJy sources would sample many more sight lines per square degree, improving statistical probes of cosmic magnetic fields at megaparsec scales.","The indistinguishability of sources behind clusters and superclusters implies that cluster magnetic fields at the probed radii (around $r_{200}$) are weak or low-density enough not to measurably rotate or depolarize 146 MHz emission.","The residual gradient in the RRM grid indicates that part of the Galactic foreground model may still contaminate the residuals, so future deep surveys with improved Galactic RM reconstructions should tighten the zero-median result.","Because FRII sources dominate the polarized detections, future deep surveys at these frequencies can expect to detect polarization preferentially from large, edge-brightened radio galaxies and giant radio galaxies."],"supporting_citations":[{"why":"Provided the 31-source polarized catalog and 33 RM components that this analysis characterizes; the central sample.","marker":"Piras et al. (2024)"},{"why":"Supplied the Galactic RM map from which GRM is averaged within a 1-degree circle to compute RRM; the foreground model whose overlap with the sample is the paper's acknowledged weak point.","marker":"Hutschenreuter et al. (2022)"},{"why":"Gives the LoTSS-DR2 RM catalog, the comparison sample for morphology, redshift, luminosity, and polarization trends, and a constituent of the Galactic RM map causing the overlap.","marker":"O'Sullivan et al. (2023)"},{"why":"Established the RRM method at 144 MHz and the interpretation that the RRM origin is likely the intergalactic medium at low frequencies.","marker":"Carretti et al. (2022)"},{"why":"Supplied host-galaxy identifications, redshifts, sizes, and flux densities for 16 of the 31 radio galaxies.","marker":"Simonte et al. (2024)"},{"why":"Provided the FRI/FRII morphological classifications in the multiwavelength region used for the sample's morphological fractions.","marker":"Mingo et al. (2022)"},{"why":"Gave the deep 6-arcsecond Stokes I image of ELAIS-N1 from which flux densities and angular sizes were measured.","marker":"Sabater et al. (2021)"},{"why":"One of the two cluster catalogs used to identify lines of sight crossing clusters in the field.","marker":"Wen & Han (2024)"},{"why":"The second cluster catalog (CFSFDP) used to compare polarized sources behind clusters with the rest of the sample.","marker":"Zou et al. (2022)"},{"why":"Cataloged the two superclusters (MSCC 473 and 476) behind which sources 8 and 12 lie; used for the supercluster comparison.","marker":"Chow-Martínez et al. (2014)"}],"fun_headline_variants":["31 faint galaxies show no cluster effect on Faraday rotation","No cluster-induced rotation in 31 faint radio galaxies","Residual Faraday rotation vanishes for faint radio galaxies","Deep LOFAR: cluster sightlines don't alter Faraday rotation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central claim assumes the Galactic rotation measure map used for the subtraction is correct in this field, but that map was built in part from the same data being analyzed — nine LoTSS-DR2 entries in the field, eight of which are also in this sample — so the near-zero residual median is not fully independent of the foreground model.","fun_headline_variants_meta":{"raw":{"variants":["31 faint galaxies show no cluster effect on Faraday rotation","No cluster-induced rotation in 31 faint radio galaxies","Residual Faraday rotation vanishes for faint radio galaxies","Deep LOFAR: cluster sightlines don't alter Faraday rotation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000648,"raw_usage":{"total_tokens":3066,"prompt_tokens":1128,"completion_tokens":1938,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":744,"completion_tokens_details":{"reasoning_tokens":1873}},"tokens_in":744,"tokens_out":1938,"duration_ms":14531,"temperature":1.0,"reasoning_tokens":1873,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:46:25.076957+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the RRMs with a Galactic foreground map that excludes all in-field LoTSS-DR2 and ELAIS-N1 entries; if the median RRM and its Spearman correlations with redshift and fractional polarization remain consistent with zero, the paper's central claim is confirmed, and if they shift significantly, the near-zero result was at least partly forced by the foreground model.","supporting_citations":[{"cited_title":"S., Betti , S., et al","cited_arxiv_id":null,"evidence_quote":"Supplied the Galactic RM map from which GRM is averaged within a 1-degree circle to compute RRM; the foreground model whose overlap with the sample is the paper's acknowledged weak point."},{"cited_title":"P., et al","cited_arxiv_id":null,"evidence_quote":"Established the RRM method at 144 MHz and the interpretation that the RRM origin is likely the intergalactic medium at low frequencies."},{"cited_title":"N., Tasse , C., et al","cited_arxiv_id":null,"evidence_quote":"Gave the deep 6-arcsecond Stokes I image of ELAIS-N1 from which flux densities and angular sizes were measured."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"One of the two cluster catalogs used to identify lines of sight crossing clusters in the field."},{"cited_title":"A., & Trejo-Alonso , J","cited_arxiv_id":null,"evidence_quote":"Cataloged the two superclusters (MSCC 473 and 476) behind which sources 8 and 12 lie; used for the supercluster comparison."}],"review_version":1}