LOFAR Deep Fields: Probing the sub-mJy regime of polarized extragalactic sources in ELAIS-N1. II. Analysis

A. Bonafede; C. Horellou; E. Carretti; I. Prandoni; J. Conway; M. Thomasson; S. Piras; S.P. O'Sullivan; T.W. Shimwell; V. Vacca

REVIEW 3 major objections 5 minor 1 cited by

LOFAR Deep Fields: Probing the sub-mJy regime of polarized extragalactic sources in ELAIS-N1. II. Analysis

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2412.00988 v1 pith:HXHKNZCK submitted 2024-12-01 astro-ph.GA

S. Piras , C. Horellou , J. Conway , M. Thomasson , T.W. Shimwell , S.P. O'Sullivan , E. Carretti , V. Vacca

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A. Bonafede I. Prandoni

This is my paper · ORCID

classification astro-ph.GA

keywords polarizationFaradayrotationmeasuresradiogalaxiesLOFARELAIS-N1cosmicmagnetismresidualmeasuresub-mJysources

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

The 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.

The 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.

Verdict: 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.

Referee Report

3 major / 5 minor

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.

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 (3)

[Sect. 3, Eq. (3)] 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.
[Sect. 3, Fig. 5, Table 4] 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.
[Sect. 3.2, Table 7] 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.

minor comments (5)

[Title, Abstract] 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.
[Sect. 2.2, Table A.1] 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.
[Sect. 3] 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.
[Sect. 4 (Conclusions)] 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.
[Table 4] 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.

Circularity Check

1 steps flagged · score 4.0 of 10

The near-zero RRM median is partly built in: the Galactic RM map used in Eq. (3) was fitted to a catalog containing 8 of the 33 RMs analyzed here, so the residual is not fully independent; the paper acknowledges but does not quantify this overlap.

fitted input called prediction [Sect. 3, Eq. (3) and the paragraph before Fig. 5; echoed in Conclusions]
"The extragalactic RM, called residual rotation measure (RRM), is obtained by subtracting the foreground Galactic RM (GRM) from the observed RM, RRM = RM− GRM. (3) ... Hutschenreuter et al. (2022) used a number of RM catalogs, the largest of which were the NVSS RM catalog of Taylor et al. (2009) and the LoTSS-DR2 RM catalog of O’Sullivan et al. (2023). ... the LoTSS-DR2 RM catalog has 9 entries (8 of these polarized sources are in our catalog..."

Eq. (3) defines RRM by subtracting a Galactic RM term that, for 8 of the 33 components, is not independent of the RM being subtracted. The paper reports that Hutschenreuter et al. (2022) built their GRM map from RM catalogs including LoTSS-DR2 RM, and that the LoTSS-DR2 catalog has 9 entries in ELAIS-N1, 8 of which are in this sample. The map is a fit to those RMs, so at those positions GRM already contains information about the observed RM; the residual is pulled toward zero. The near-zero median (Table 4: -1.78 rad m-2) and the null Spearman tests (Table 5) are therefore partly forced by the overlap, not purely an intergalactic signal.

full rationale

The paper's main numerical chain—RM measurements from Paper I, host identification, redshifts, luminosities, linear sizes, and morphological classes—is self-contained and does not reduce to its inputs: luminosities use the standard distance formula with fixed cosmology, sizes use angular-size distances, and the RRM correlation tests are computed directly from the measured values. The only load-bearing external input that is not independent of the sample is the Galactic RM map of Hutschenreuter et al. (2022). The paper itself reports that the LoTSS-DR2 RM catalog used in that map has 9 entries in the ELAIS-N1 field, 8 of which are also in the 33-component sample. For those lines of sight the subtraction in Eq. (3) removes a foreground estimate that was partly fitted to the same observed RM; this pulls the RRM residuals toward zero and narrows their distribution. The near-zero median (Table 4) and the absence of Spearman correlations (Table 5) are therefore not fully independent results, and the conclusion that the map is 'a reasonable estimate' is partly a validation on training data. The effect is partial: the map is a global, smoothed Gaussian-process reconstruction and only 24% of the sample overlaps, so the remaining 25 components and the global fit provide independent content. A leave-out test (excluding the 8 overlapping LoTSS-DR2 RMs from the map) would be needed to establish how much of the RRM result survives. No other self-citation is load-bearing: the cited LoTSS-DR2 RM and Carretti et al. (2022) comparisons are used as external benchmarks, not to define the paper's quantities. Overall, this is a moderate, data-overlap circularity rather than a constructional identity, so the score is 4.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted in this paper; the analysis rests on external catalogs and assumed physical relations. The main burden is that the Galactic RM map used to build RRMs partly contains the very LoTSS RM values being analyzed, and the host/redshift identifications are taken from heterogeneous sources with some known conflicts.

assumptions (5)

domain assumption Flat Lambda CDM cosmology with H0 = 67.8 km/s/Mpc and Omega_m = 0.308.
Used in Section 1 to compute luminosity distances and linear sizes from angular sizes; values from Planck Collaboration et al. (2016b).
domain assumption Spectral index alpha = -0.7 for all sources in the k-correction.
Rest-frame luminosities in Eq. (2) assume S proportional to nu^alpha with alpha = -0.7. No uncertainty is propagated, and the value is taken from prior literature.
domain assumption RRM = RM - GRM, with GRM from the Hutschenreuter et al. (2022) sky map averaged in a 1-degree circle.
Eq. (3). The GRM map is partly constructed from the LoTSS-DR2 RM catalog, which contains 8 of the 33 polarized components analyzed here, so the subtraction is not fully external.
domain assumption r500/r200 = 0.7 conversion to define cluster radii.
Sect. 3.2 uses this relation from Ettori & Balestra (2009) to convert catalog r500 values to r200, which determines which sources are considered behind clusters.
domain assumption Redshifts and host galaxy identifications from SDSS, DESI, Simonte et al. (2024), and NED are correct.
Sect. 2.2 relies on external catalogs for all 31 sources. For several sources, conflicting values exist in the literature (e.g., sources 03 and 20), so host association and redshift are not uniformly secure.

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Cite this review

Pith. "Pith review of LOFAR Deep Fields: Probing the sub-mJy regime of polarized extragalactic sources in ELAIS-N1. II. Analysis." pith.science (2026). https://pith.science/paper/HXHKNZCK

@misc{pith2026241200988,
  author       = {Pith},
  title        = {Pith review of: LOFAR Deep Fields: Probing the sub-mJy regime of polarized extragalactic sources in ELAIS-N1. II. Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HXHKNZCK}},
  note         = {Machine review of arXiv:2412.00988}
}

read the original abstract

Deep polarization surveys at low radio frequencies are key to cosmic magnetism studies: Larger catalogs of polarized extragalactic sources and increased precision on Faraday rotation measures (RMs) make it possible to probe the magneto-ionic medium along the lines of sight of the sources and to construct denser RM grids. In a first paper, we presented a search for polarized sources in deep observations of the 25 square degree area of the European Large Area ISO Survey North 1 (ELAIS-N1) field with the LOw Frequency ARray (LOFAR) in the range 114.9 to 177.4 MHz. In this paper, we investigate the properties of the polarized radio galaxies and use the catalog to produce an RM grid of the field. After identifying the host galaxies and collecting redshift information, we characterized the radio galaxies in terms of their radio morphologies, rest frame radio luminosities, and linear sizes. We calculated residual rotation measures (RRMs) by removing the Galactic RM and studied the variation in the RRMs with redshift and degree of polarization. We produced an RRM grid of the field and compared the positions of the polarized sources with those of galaxy clusters and superclusters. The radio galaxies show a variety of morphologies, including diffuse emission; Fanaroff Riley type II sources make up about half of the sample. Using available multiband catalogs, we found redshifts for the hosts of all polarized sources in the range of 0.06 to 1.9. Polarized emission is detected mainly from large radio galaxies. The RRM values have a median close to zero, and they appear to be independent of redshift and degree of polarization. The sources in the lines of sight of clusters of galaxies and of a supercluster are indistinguishable in their polarization and RRM properties from the population of sources that are not behind these structures.

Figures

Figures reproduced from arXiv: 2412.00988 by the authors.

**Figure 2.** Distribution of the projected linear sizes of the subset of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Comparison of the variations of the degrees of polarization with linear size and with projected distance from the host in the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Histograms of the GRM, RM, and RRM distributions for [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Images of the GRM, RM, and RRM values. Top panel: Galactic RM map from Hutschenreuter et al. (2022). Other panels: Distribution of polarized sources in the ELAIS-N1 LOFAR Deep Field. The size of the markers is proportional to the magnitude of the RM values (middle pa…

**Figure 6.** Figure 6: Variations of degrees of polarization, RRM and redshift values. Left and middle panels: Degree of polarization and |RRM| as a function of redshift. The sample was split to have a roughly equal number of sources in each redshift bin. Data points from sources with spectr…

**Figure 7.** Figure 7: Galaxy clusters (shaded circles), superclusters, and po [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Helical radio jets as probes of magnetised cluster environments: Periodic Faraday Rotation Revealed in the Corkscrew Galaxy by POSSUM
astro-ph.GA 2026-07 conditional novelty 6.5 of 10

Periodic RM oscillations matching the Corkscrew jet's lateral deviations reveal a transition from jet/sheath to local-ICM Faraday media along the flow.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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