Pith. sign in

REVIEW 3 major objections 5 minor 81 references

A view of the CIZA J2242.8+5301 galaxy cluster at very low radio frequencies

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper's 45 MHz LOFAR observations of CIZA J2242.8+5301 reveal a symmetric surface brightness profile across the eastern northern relic, challenging the standard single-shock downstream-advection model and suggesting comparable Mach…

desk verdict Solid new 45 MHz data on the Sausage cluster, but the headline symmetric-profile claim rests on a profile that still contains the overlapping source R5 and is not statistically symmetric. read the letter →

arxiv 2505.23402 v1 pith:LCKU5TE6 submitted 2025-05-29 astro-ph.CO

G. Lusetti , M. Brüggen , H. W. Edler , F. de Gasperin , M. Hoeft , G. Di Gennaro , D. Hoang , T. Pasini
show 4 more authors
R. van Weeren V. Cuciti H. Rottgering G. Brunetti
This is my paper · ORCID
classification astro-ph.CO
keywords galaxyclustersradiorelicsdiffusiveshockaccelerationlow-frequencyobservationsLOFARspectralindexMachnumbermagneticfields
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 presents the first observations below 100 MHz (45 MHz) of the Sausage cluster CIZA J2242.8+5301, a merging galaxy cluster with two large radio relics, using the LOw Frequency ARray (LOFAR). Its main finding is that the eastern half of the northern radio relic has a symmetric surface brightness profile, with wings of emission extending on both sides of the peak. That shape is not what the standard model predicts: a single, sharp, edge-on shock should produce a sharp rise at the shock front and a one-sided downstream decay as electrons cool. The paper derives Mach numbers from the local injection spectral index at the relic edges, finding $M_N=2.9\pm0.5$ and $M_S=2.9\pm0.8$ for the northern and southern relics, and models the profile with projection, magnetic-field variation, and shock-surface wiggles. If correct, the symmetric profile means the standard single-shock diffusive shock acceleration (DSA) picture needs additional ingredients to explain low-frequency relic morphology.

What carries the argument

The argument is carried by the deconvolved surface brightness profile of the northern relic, extracted from the 45 MHz image in 70″×15″ boxes along the relic, and by a toy model that generates the profile from a spherical-cap shock. The model includes line-of-sight projection with opening angle $\Psi=12^\circ$, a log-normal distribution of the downstream magnetic field (best fit $B_0=0.3\,\mu$G, scatter $\log(\sigma)=1.65$), and Gaussian 'wiggles' of the shock radius with $\sigma=15$ kpc. Comparing this model against 45 MHz and higher-frequency profiles shows it can match the downstream side but always leaves an excess of emission upstream, which is the load-bearing discrepancy. The Mach-number analysis uses the injection spectral index measured in beam-sized boxes along the relic edges, with Gaussian-mixture classification to separate statistically distinct spectral-index populations.

What would settle it

Subtract a model of R5, built from higher-frequency images where R5 is more clearly separated, from the 45 MHz eastern profile and recompute its shape; if the profile becomes asymmetric like the western half, the claimed symmetry is a superposition effect. Alternatively, low-frequency imaging at higher resolution that separates R5 from the relic would settle whether the upstream wing is part of the relic or a separate structure.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that LOFAR's Low Band Antenna (LBA) 45 MHz imaging resolves the eastern part of the northern relic into a surface brightness distribution that is symmetric about its peak, with significant upstream and downstream wings, whereas the western part shows the usual asymmetric rise-and-cool profile. This contradicts the expectation of particle acceleration at a single sharp shock followed by downstream advection of the accelerated electrons, and the paper argues that the symmetry must be produced by a combination of projection, spatial variation of the magnetic field (modeled as log-normal), and small-scale corrugation of the shock surface. The modeling reproduces the downstream decline at 45, 145, 1500, and 3000 MHz but leaves a systematic excess upstream, which the paper interprets as evidence that the simple picture is incomplete. The same low-frequency data give injection spectral indices that translate to very similar Mach numbers for the two relics, $M_N=2.9\pm0.5$ and $M_S=2.9\pm0.8$, suggesting the two shocks are comparably strong.

Load-bearing premise

The symmetric profile is treated as belonging to the northern relic itself, but a faint, separate patch of radio emission called R5 overlaps the same region and is not subtracted from the profile, so it could be supplying part of the upstream wing.

Editorial extensions

If this is right

  • The eastern half of the northern relic cannot be explained by the standard single-shock, downstream-advection model; projection, magnetic-field variation, or additional structure such as R5 must contribute.
  • The two relics have comparable shock strengths, $M_N=2.9\pm0.5$ and $M_S=2.9\pm0.8$, when Mach numbers are derived from the local injection spectral index rather than from the integrated spectrum.
  • Integrated spectra of both relics are close to single power laws from 45 MHz to 3 GHz, consistent with DSA from the thermal pool, but the local-injection Mach numbers are lower than those from integrated indices and reduce the usual radio/X-ray Mach discrepancy.
  • Low-frequency observations trace faint, steep-spectrum regions that are invisible at higher frequencies, such as the north-western part of the southern relic, and reveal connections between substructures that appear disconnected at higher frequencies.

Reading between the lines

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

  • If the eastern profile's symmetry survives after subtracting R5, the standard single-shock DSA picture needs additional ingredients, such as substantial magnetic-field fluctuations or large-scale shock corrugation, to explain low-frequency relic morphology.
  • The near-equal Mach numbers from local injection indices suggest that opposing relics in a roughly 1:1 merger may have comparable strengths when measured at the shock front, which could reduce the apparent radio/X-ray Mach discrepancy in other systems too.
  • The systematic upstream excess that resists the toy model may indicate that part of the emission comes from a separate structure projected onto the main relic; higher-resolution low-frequency imaging could separate these components.
  • Because 45 MHz emission is less affected by radiative losses, comparing injection indices derived at low frequency with higher-frequency maps isolates the cooling history; this approach could be applied to other double-relic systems.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper presents the first LOFAR LBA 45 MHz observations of the Sausage cluster CIZA J2242.8+5301, reaching a thermal-noise-limited rms of 1.5 mJy/beam at 15'' resolution. Combining these data with existing 145 MHz to 3 GHz images, the authors measure integrated spectra, spectral index and curvature maps, local injection indices along the relic edges, and derive Mach numbers for the northern (RN) and southern (RS) relics. They report M_N = 2.9 ± 0.4 and M_S = 2.9 ± 0.8 from the flatter GMM-selected injection-index components, and they claim a 'remarkably symmetric' 45 MHz surface-brightness profile across the eastern part of RN, which they model with a spherical-cap shock, projection, a log-normal magnetic field, and Gaussian shock-surface wiggles. The model leaves a systematic upstream excess, which is discussed as a remaining discrepancy.

Significance. The 45 MHz images and the multi-frequency spectral products constitute a useful observational contribution to a benchmark cluster, and the data reduction appears carefully executed. If the symmetric eastern profile is intrinsic to RN, the result would be significant because it challenges the standard edge-on single-shock plus downstream-advection interpretation of radio relics. However, the central claim is not yet established: the profile extraction does not subtract or mask R5, a known extended steep-spectrum source overlapping the same region, and the paper's own skewness test (p≈3×10^-14 for the full 45 MHz profile) does not support the 'remarkably symmetric' wording. With a quantitative, R5-subtracted profile the claim could become a durable falsifiable result; in the present form it is an interesting but unproven superposition candidate.

major comments (3)
  1. [Sec. 4.2, Fig. 9 (right); Sec. 4.3] The symmetry claim rests on a profile from which only compact sources were blanked, while R5—an extended, steep-spectrum source (α_R5_int = −0.90 ± 0.03) that Sec. 3.1 places north of the eastern edge of RN and Sec. 4.3 describes as a ~716 kpc-long, ~100 kpc-wide structure in the north-west part of RN—is not subtracted. Because R5 is clearly detected at 45 MHz and appears more diffuse at low frequencies, its unsubtracted emission can produce the upstream wing that makes the eastern profile look symmetric. The authors should re-extract the eastern profile after masking or modelling R5 (or, at minimum, quantify the contribution of R5 to each profile bin); without this step, the headline claim may be a superposition of two distinct structures rather than an intrinsic property of the relic shock. The contradiction between the two reported locations of R5 (north of the eastern edge vs. north-west) also needs to be resolved.
  2. [Appendix A, Table A.1] The quantitative test contradicts the 'remarkably symmetric' claim. For the full 45 MHz deconvolved profile, the reported skewness is 0.63 with p = 3.25 × 10^-14, so Gaussianity (zero skewness) is rejected at overwhelming significance; the text's statement that 'the 45 MHz profile is more symmetric, with a skewness between −0.5 and 0.5' is numerically inconsistent with the tabulated value. The authors should either report a symmetry metric for the eastern half alone, with uncertainties, or rephrase the claim as 'less asymmetric than at 610 MHz.'
  3. [Fig. 9 (right) and Sec. 4.2 modelling] The deconvolved profiles are plotted without error bars, and the 'symmetry' is assessed visually. These same profiles are used to derive the FWHM of 138 kpc, the magnetic-field range of 5–10 μG, and the comparison with the spherical-cap model, so without uncertainties the significance of the symmetry and the resulting parameter constraints cannot be evaluated. Error bars obtained, for example, from bootstrapping the clean-component model or from the image rms and beam correlation should be shown.
minor comments (5)
  1. [Sec. 3.4, after Eq. (2)] The two sentences defining C<0 for a concave spectrum and 'Conversely, C<0' for an inverted spectrum are mutually inconsistent; for the inverted case defined by |α_high|<|α_low|, C = α_high − α_low is positive.
  2. [Sec. 4.2] The spherical-cap curvature radius is quoted as 'R = 1.5 kpc', which appears to be a typo for Mpc; with R = 1.5 kpc and Ψ = 12°, the projected injection distance would be ~0.3 kpc, not the 33 kpc quoted in the text.
  3. [Abstract vs. Sec. 4.1 and Table 4] The abstract reports M_N = 2.9 ± 0.5 while Sec. 4.1 and Table 4 report M_N = 2.9 ± 0.4 for the same local-injection-index measurement; the values should agree.
  4. [Sec. 3.1 and Conclusions] Section 3.1 reports the 15''-resolution size of RN as ~2 Mpc × 450 kpc, while the Conclusions quote 2.2 Mpc × 760 kpc (the 30'' value) as the northern relic's size; the resolution used in the summary should be stated explicitly.
  5. [Fig. 9 and Fig. 11 captions] The Fig. 11 caption contains a typo ('emission regio'), and the Fig. 9 caption uses 'FMHW' instead of 'FWHM'; the caption of Fig. 9 also says 15''-spaced extraction regions while the text says 70×15'' boxes, and the notation should be unified.

Circularity Check

0 steps flagged · score 1.0 of 10

No meaningful circularity: Mach numbers are measured from spectral indices via standard DSA relations, and the symmetric-profile claim is an observational extraction, not a model output.

full rationale

The paper's derivation chain is not circular. Mach numbers come from measured spectral indices inserted into the standard DSA equations (Eqs. 3-5), not from fitting M to a pre-chosen result; the GMM clustering selects populations, but the values are data-driven. The headline claim of a symmetric 45 MHz profile across the eastern northern relic is an observational measurement from deconvolved images (Sect. 4.2, Fig. 9), not an output of the toy model; in fact, the model leaves a systematic upstream discrepancy, so the profile claim is not forced by the model. The magnetic-field modelling parameters (B0 = 0.3 microG, log sigma = 1.65) are fitted to the profiles, but the paper's B-field conclusions rest on FWHM/cooling-length reasoning and external constraints, so this is model dependence rather than circularity. The main unresolved concern is physical rather than circular: R5 overlaps the eastern profile and is not subtracted in the Sect. 4.2 extraction, so part of the 'symmetric wing' could be a superposition with R5 (Sect. 4.3). That is a contamination and interpretation limitation, not a case of a prediction being equivalent to its input by construction. Self-citations to prior work by the same groups supply data and a model framework, but the key numbers are independently measured and compared against external benchmarks, including previous spectral index and Mach number estimates.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central observational claims rest on standard radio astronomy calibration and DSA theory. The interpretive SB model introduces four fitted parameters (B_0, log σ, Ψ, σ_wiggles) and the Mach number estimates depend on a model choice between two statistically distinct spectral index populations. No new physical entities are introduced.

free parameters (6)
  • B_0 (log-normal median magnetic field) = 0.3 µG
    Fitted in the surface brightness model of the northern relic (Sect. 4.2).
  • log σ (log-normal scatter) = 1.65
    Fitted in the same model; produces B range from about 3e-3 to 16 µG.
  • Ψ (spherical cap opening angle) = 12 degrees
    Constrained from the 3 GHz high-resolution profile; used in the toy model.
  • σ_wiggles (Gaussian shock-surface scatter) = 15 kpc
    Ad hoc parameter added to smooth the upstream profile; still leaves excess.
  • Injection spectral index (north, selected) = -0.76 ± 0.08
    Chosen as the flatter of two GMM clusters along the relic edge; directly sets M_N.
  • Injection spectral index (south, selected) = -0.77 ± 0.16
    Chosen as the flatter of two GMM clusters; directly sets M_S.
assumptions (6)
  • domain assumption DSA relation between injection spectral index and Mach number (Eq. 5: M = sqrt((2 α_inj - 3)/(2 α_inj + 1)))
    Used to convert measured spectral indices to Mach numbers; standard theory from Drury 1983 and Blandford & Eichler 1987.
  • domain assumption Integrated spectral index equals injection index plus 0.5 (Eq. 4)
    Used for integrated Mach numbers; Kardashev 1962.
  • domain assumption Spectral index measured at the relic edge is the injection index because cooling is negligible over the beam
    Sect. 4.1: 50 Myr travel time across the beam vs 360 Myr cooling time.
  • domain assumption Synchrotron and IC cooling length formula for relic width
    Sect. 4.2: used to infer B from the FWHM of the relic profile.
  • ad hoc to paper Spherical cap shock model with uniform Mach number, log-normal B field, and Gaussian wiggles
    Toy model in Sect. 4.2 and Appendix B; not independently validated.
  • domain assumption 3σ rms threshold defines source boundaries
    Used for flux extraction and profile definition; standard practice in radio astronomy.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A view of the CIZA J2242.8+5301 galaxy cluster at very low radio frequencies." pith.science (2026). https://pith.science/paper/LCKU5TE6

@misc{pith2026250523402,
  author       = {Pith},
  title        = {Pith review of: A view of the CIZA J2242.8+5301 galaxy cluster at very low radio frequencies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LCKU5TE6}},
  note         = {Machine review of arXiv:2505.23402}
}
read the original abstract

The galaxy cluster CIZA J2242.8+5301 is a well-studied merging galaxy cluster that hosts prominent double radio relics including the famous sausage relic, as well as other diffuse radio sources. Observations at frequencies below 100 MHz are essential for investigating the physics of radio relics as they provide unique access to the low-energy population of cosmic-ray electrons. We aim to study the morphology, spectral characteristics, and physical processes that produce relics. We present the first observations of the Sausage cluster at 45 MHz, the lowest radio frequency at which this cluster has been studied to date, using the Low Band Antenna (LBA) of the LOFAR radio interferometer. We made use of ten hours of LOFAR LBA observations, from which we achieved a thermal-noise limited radio image with a noise level of 1.5 mJy/beam at a resolution of 15 arcsec. These data were combined with existing multi-frequency measurements at higher frequencies: LOFAR High Band Antenna, Giant Metrewave Radio Telescope, Westerbork Synthesis Radio Telescope, and Karl G. Jansky Very Large Array. This broad frequency coverage allowed us to derive integrated spectral indices, spectral index and curvature maps, and Mach number distributions across the relics. We derived Mach numbers from the local injection index measure using low-frequency data with M_N = 2.9 +-0.5 for the northern relic and M_S = 2.9+-0.8 for the southern relic. LOFAR LBA observations reveal a remarkably symmetric surface brightness profile across the eastern part of the northern relic, with wings extending on either side of the peak. This discovery is contrary to the expectation of particle acceleration at a single, sharp shock and the subsequent downstream advection of accelerated electrons. We modelled the surface brightness profile, including the effects of projection, magnetic field variation, and shock deformation.

Figures

Figures reproduced from arXiv: 2505.23402 by the authors.

Figure 1
Figure 1. Results of the demix without considering (left) and considering (right) the target field sky model. The red circle indicates the location of Cassiopeia A while the arrow points towards the location of Cygnus A outside the FoV. The Sausage cluster resides at the centre of the image, the two bright radio galaxies NVSS J224133+531105 and NVSS J223950+525346 are highlighted with white squares. The insets show zoom-in im… view at source ↗
Figure 2
Figure 2. Image of CIZA J2242.8+5301 at 45 MHz, shown at the LBA nominal resolution (15′′ beam). The contour levels are [−3, 2, 3, 6, 12, 24, 48, 96] × σ 45 rms, where σ 45 rms = 1.5 mJy/beam, with additional dashed 3σrms level from 45′′ image ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Final images at different resolutions. Left: 15′′−beam, σrms = 1.59 mJy/beam; Centre: 30′′−beam, σrms = 2.05 mJy/beam; Right: 45′′−beam, σrms = 3.23 mJy/beam; Contours are drawn at [-3,3,...]×σrms with √ 2 steps. radial-like source (R2), which extends for 760 kpc. We note that, unlike in higher-frequency observations where these sub￾structures appear fragmented and disconnected from each other —even when compared at… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Integrated radio spectrum of RN, RS, R1, R2, and R2 from 45 MHz to 3 GHz. Extraction regions are shown in the bottom left corner. Values obtained in this work at 45 MHz are highlighted in red, while extra points are at 145, 323, 608, 1230, 1380 MHz (Hoang et al. 2017),…
Figure 5
Figure 5. Figure 5: Top panel: Spectral index map between 45 and 145 MHz at a spatial resolution of 13′′ × 13′′ (left), 23′′ × 23′′ (middle) and 37′′ × 37′′ (right). Bottom panel: Relative spectral index error ∆α 45 MHz 145 MHz. Pixels with surface brightness values below 2σrms in the two…
Figure 6
Figure 6. Figure 6: Four-frequency (45, 145, 1500, 3000 MHz) spectral curvature map. Pixels with surface brightness values below 2σrms in the two images were blanked and [3, 6, 12, 24, 48, 96] × σ 45 MHz rms contours are over-plotted. by these energy losses, providing a more reliable prox…
Figure 7
Figure 7. Figure 7: Injection spectral index calculated in 15′′-box (∼ 48 kpc separation) along the relics’ edges. Left: Zoom-in over the RN (top) and RS (bot￾tom). Right: Injection spectral index profiles extracted from 45-145 MHz 15′′-resolution images. The right panels display the dens…
Figure 8
Figure 8. Figure 8: Mach number estimates for northern (RN) and southern (RS) radio shocks in CIZA J2242.8+5301, derived from the radio spectral index (MR, teal) and the ICM X-ray analysis (MX, orange). The violin plots illustrate the distribution of Mach number estimates from the liter￾a…
Figure 9
Figure 9. Figure 9: Theoretical relic cooling lengths compared with the deconvolved surface brightness profile of RN. Left: Relationship between the cooling length (i.e. the relic thickness under ideal conditions of no projection effects and pure radiative losses), magnetic field strength…
Figure 10
Figure 10. Figure 10: Surface brightness profile across the western half of RN. We applied the model to different frequencies at different resolutions: 3 GHz at 3.5 ′′ (orange), 1.5 GHz at 8′′ (blue), 150 MHz at 8′′ (red), and 45 MHz at 15′′. Left: Log-normal magnetic field distribution (B…
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

81 extracted references · 65 canonical work pages

  1. [1]

    1974, IEEE Transactions on Automatic Control, 19, 716

    Akaike , H. 1974, IEEE Transactions on Automatic Control, 19, 716

    1974

  2. [2]

    & Kawahara , H

    Akamatsu , H. & Kawahara , H. 2013, , 65, 16

    work page 2013

  3. [3]

    J., Ogrean , G

    Akamatsu , H., van Weeren , R. J., Ogrean , G. A., et al. 2015, , 582, A87

    work page 2015

  4. [4]

    & Eichler , D

    Blandford , R. & Eichler , D. 1987, , 154, 1

    work page 1987

  5. [5]

    Blandford , R. D. & Ostriker , J. P. 1978, , 221, L29

    work page 1978

  6. [6]

    2009, , 494, 429

    Bonafede , A., Giovannini , G., Feretti , L., Govoni , F., & Murgia , M. 2009, , 494, 429

    work page 2009

  7. [7]

    2020, , 634, A64

    Botteon , A., Brunetti , G., Ryu , D., & Roh , S. 2020, , 634, A64

    work page 2020

  8. [8]

    & Jones , T

    Brunetti , G. & Jones , T. W. 2014, International Journal of Modern Physics D, 23, 1430007

    2014

Show all 81 references
  1. [9]

    J., Cotton , W

    Condon , J. J., Cotton , W. D., Greisen , E. W., et al. 1998, , 115, 1693

    1998

  2. [10]

    A., Jee , M

    Dawson , W. A., Jee , M. J., Stroe , A., et al. 2015, , 805, 143

    2015

  3. [11]

    2020 a , , 642, A85

    de Gasperin , F., Brunetti , G., Br \"u ggen , M., et al. 2020 a , , 642, A85

    2020

  4. [12]

    J., Drabent , A., et al

    de Gasperin , F., Dijkema , T. J., Drabent , A., et al. 2019, , 622, A5

    2019

  5. [13]

    W., Williams , W

    de Gasperin , F., Edler , H. W., Williams , W. L., et al. 2023, , 673, A165

    2023

  6. [14]

    T., van Weeren , R

    de Gasperin , F., Intema , H. T., van Weeren , R. J., et al. 2015, , 453, 3483

    2015

  7. [15]

    2022, , 659, A146

    de Gasperin , F., Rudnick , L., Finoguenov , A., et al. 2022, , 659, A146

    2022

  8. [16]

    P., et al

    de Gasperin , F., Vink , J., McKean , J. P., et al. 2020 b , , 635, A150

    2020

  9. [17]

    L., Best , P., et al

    de Gasperin , F., Williams , W. L., Best , P., et al. 2021, , 648, A104

    2021

  10. [18]

    J., Hoeft , M., et al

    Di Gennaro , G., van Weeren , R. J., Hoeft , M., et al. 2018, , 865, 24

    2018

  11. [19]

    J., Rudnick , L., et al

    Di Gennaro , G., van Weeren , R. J., Rudnick , L., et al. 2021, , 911, 3

    2021

  12. [20]

    2021, , 500, 795

    Dominguez-Fernandez , P., Bruggen , M., Vazza , F., et al. 2021, , 500, 795

    2021

  13. [21]

    2024 a , , 685, A68

    Dom \' nguez-Fern \'a ndez , P., Ryu , D., & Kang , H. 2024 a , , 685, A68

    2024

  14. [22]

    2024 b , , 685, A68

    Dom \' nguez-Fern \'a ndez , P., Ryu , D., & Kang , H. 2024 b , , 685, A68

    2024

  15. [23]

    Donnert , J. M. F., Stroe , A., Brunetti , G., Hoang , D., & Roettgering , H. 2016, , 462, 2014

    2016

  16. [24]

    Drury , L. O. 1983, Reports on Progress in Physics, 46, 973

    1983

  17. [25]

    W., de Gasperin , F., Brunetti , G., et al

    Edler , H. W., de Gasperin , F., Brunetti , G., et al. 2022, , 666, A3

    2022

  18. [26]

    A., Biermann , P

    Ensslin , T. A., Biermann , P. L., Klein , U., & Kohle , S. 1998, , 332, 395

    1998

  19. [27]

    2021, , 915, 18

    Ha , J.-H., Kim , S., Ryu , D., & Kang , H. 2021, , 915, 18

    2021

  20. [28]

    N., Shimwell , T

    Hoang , D. N., Shimwell , T. W., Stroe , A., et al. 2017, , 471, 1107

    2017

  21. [29]

    N., Shimwell , T

    Hoang , D. N., Shimwell , T. W., van Weeren , R. J., et al. 2018, , 478, 2218

    2018

  22. [30]

    & Br \"u ggen , M

    Hoeft , M. & Br \"u ggen , M. 2007, , 375, 77

    2007

  23. [31]

    E., Gottl \"o ber , S., et al

    Hoeft , M., Nuza , S. E., Gottl \"o ber , S., et al. 2011, Journal of Astrophysics and Astronomy, 32, 509

    2011

  24. [32]

    2022, , 509, 1160

    Inchingolo , G., Wittor , D., Rajpurohit , K., & Vazza , F. 2022, , 509, 1160

    2022

  25. [33]

    T., Jagannathan , P., Mooley , K

    Intema , H. T., Jagannathan , P., Mooley , K. P., & Frail , D. A. 2017, , 598, A78

    2017

  26. [34]

    J., Stroe , A., Dawson , W., et al

    Jee , M. J., Stroe , A., Dawson , W., et al. 2015, , 802, 46

    2015

  27. [35]

    2012, Journal of Korean Astronomical Society, 45, 127

    Kang , H. 2012, Journal of Korean Astronomical Society, 45, 127

    2012

  28. [36]

    2016, Journal of Korean Astronomical Society, 49, 145

    Kang , H. 2016, Journal of Korean Astronomical Society, 49, 145

    2016

  29. [37]

    & Ryu , D

    Kang , H. & Ryu , D. 2011, , 734, 18

    2011

  30. [38]

    Kardashev , N. S. 1962, , 6, 317

    1962

  31. [39]

    2017, , 600, A18

    Kierdorf , M., Beck , R., Hoeft , M., et al. 2017, , 600, A18

    2017

  32. [40]

    D., Ebeling , H., Mullis , C

    Kocevski , D. D., Ebeling , H., Mullis , C. R., & Tully , R. B. 2007, , 662, 224

    2007

  33. [41]

    M., Cotton , W

    Lane , W. M., Cotton , W. D., van Velzen , S., et al. 2014, , 440, 327

    2014

  34. [42]

    Leahy , D. A. & Roger , R. S. 1998, , 505, 784

    1998

  35. [43]

    2024, , 686, A55

    Lee , W., Pillepich , A., ZuHone , J., et al. 2024, , 686, A55

    2024

  36. [44]

    2017, , 472, 3605

    Loi , F., Murgia , M., Govoni , F., et al. 2017, , 472, 3605

    2017

  37. [45]

    2020, , 498, 1628

    Loi , F., Murgia , M., Vacca , V., et al. 2020, , 498, 1628

    2020

  38. [46]

    2005, , 627, 733

    Markevitch , M., Govoni , F., Brunetti , G., & Jerius , D. 2005, , 627, 733

    2005

  39. [47]

    Massey , F. J. J. 1951, Journal of the American Statistical Association, 46, 68

    1951

  40. [48]

    & Rafferty , D

    Mohan , N. & Rafferty , D. 2015, PyBDSF: Python Blob Detection and Source Finder , Astrophysics Source Code Library, record ascl:1502.007

    2015

  41. [49]

    R., McKinley , B., Hurley-Walker , N., et al

    Offringa , A. R., McKinley , B., Hurley-Walker , N., et al. 2014, , 444, 606

    2014

  42. [50]

    u ggen , M., R \

    Ogrean , G. A., Br \"u ggen , M., R \"o ttgering , H., et al. 2013, , 429, 2617

    2013

  43. [51]

    A., Br \"u ggen , M., van Weeren , R., et al

    Ogrean , G. A., Br \"u ggen , M., van Weeren , R., et al. 2014, , 440, 3416

    2014

  44. [52]

    W., Br \"u ggen , M., et al

    Pasini , T., Edler , H. W., Br \"u ggen , M., et al. 2022, , 663, A105

    2022

  45. [53]

    P., & Pfrommer , C

    Pinzke , A., Oh , S. P., & Pfrommer , C. 2013, , 435, 1061

    2013

  46. [54]

    M., Venturi , T., Rahaman , M., & Yang , H

    Raja , R., Smirnov , O. M., Venturi , T., Rahaman , M., & Yang , H. Y. K. 2024, , 977, 83

    2024

  47. [55]

    J., Hoeft , M., et al

    Rajpurohit , K., van Weeren , R. J., Hoeft , M., et al. 2022, , 927, 80

    2022

  48. [56]

    2020, , 642, L13

    Rajpurohit , K., Vazza , F., Hoeft , M., et al. 2020, , 642, L13

    2020

  49. [57]

    J., Bonnassieux , E., Vernstrom , T., et al

    Riseley , C. J., Bonnassieux , E., Vernstrom , T., et al. 2022, , 515, 1871

    2022

  50. [58]

    1978, Annals of Statistics, 6, 461

    Schwarz , G. 1978, Annals of Statistics, 6, 461

    1978

  51. [59]

    W., Xu , H., Hallman , E

    Skillman , S. W., Xu , H., Hallman , E. J., et al. 2013, , 765, 21

    2013

  52. [60]

    J., Hardcastle , M

    Stroe , A., Harwood , J. J., Hardcastle , M. J., & R \"o ttgering , H. J. A. 2014 a , , 445, 1213

    2014

  53. [61]

    J., et al

    Stroe , A., Rumsey , C., Harwood , J. J., et al. 2014 b , , 441, L41

    2014

  54. [62]

    2016, , 455, 2402

    Stroe , A., Shimwell , T., Rumsey , C., et al. 2016, , 455, 2402

    2016

  55. [63]

    J., Intema , H

    Stroe , A., van Weeren , R. J., Intema , H. T., et al. 2013 a , , 555, A110

    2013

  56. [64]

    J., Intema , H

    Stroe , A., van Weeren , R. J., Intema , H. T., et al. 2013 b , , 555, A110

    2013

  57. [65]

    2009, PhD thesis, Technical University of Delft, Netherlands

    Van der Tol , S. 2009, PhD thesis, Technical University of Delft, Netherlands

    2009

  58. [66]

    P., Wise , M

    van Haarlem , M. P., Wise , M. W., Gunst , A. W., et al. 2013, , 556, A2

    2013

  59. [67]

    J., Andrade-Santos , F., Dawson , W

    van Weeren , R. J., Andrade-Santos , F., Dawson , W. A., et al. 2017, Nature Astronomy, 1, 0005

    2017

  60. [68]

    J., de Gasperin , F., Akamatsu , H., et al

    van Weeren , R. J., de Gasperin , F., Akamatsu , H., et al. 2019, , 215, 16

    2019

  61. [69]

    J., Hoeft , M., R \"o ttgering , H

    van Weeren , R. J., Hoeft , M., R \"o ttgering , H. J. A., et al. 2011 a , , 528, A38

    2011

  62. [70]

    o ttgering , H. J. A., Br \

    van Weeren , R. J., Intema , H. T., R \"o ttgering , H. J. A., Br \"u ggen , M., & Hoeft , M. 2011 b , , 82, 569

    2011

  63. [71]

    o ttgering , H. J. A., Br \

    van Weeren , R. J., R \"o ttgering , H. J. A., Br \"u ggen , M., & Hoeft , M. 2010, Science, 330, 347

    2010

  64. [72]

    J., R \"o ttgering , H

    van Weeren , R. J., R \"o ttgering , H. J. A., Intema , H. T., et al. 2012, , 546, A124

    2012

  65. [73]

    J., Shimwell , T

    van Weeren , R. J., Shimwell , T. W., Botteon , A., et al. 2021, , 651, A115

    2021

  66. [74]

    & Botteon , A

    Vazza , F. & Botteon , A. 2024, Galaxies, 12, 19

    2024

  67. [75]

    2024, arXiv e-prints, arXiv:2411.11947

    Whittingham , J., Pfrommer , C., Werhahn , M., Jlassi , L., & Girichidis , P. 2024, arXiv e-prints, arXiv:2411.11947

    2024

  68. [76]

    2023, Universe, 9, 319

    Wittor , D. 2023, Universe, 9, 319

    2023

  69. [77]

    2021, , 506, 396

    Wittor , D., Ettori , S., Vazza , F., et al. 2021, , 506, 396

    2021

  70. [78]

    2019, , 490, 3987

    Wittor , D., Hoeft , M., Vazza , F., Br \"u ggen , M., & Dom \' nguez-Fern \'a ndez , P. 2019, , 490, 3987

    2019

  71. [79]

    2016, Galaxies, 4, 71

    Wittor , D., Vazza , F., & Br \"u ggen , M. 2016, Galaxies, 4, 71

    2016

  72. [80]

    , " * 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.sent...

  73. [81]

    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 gl...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.