pith. machine review for the scientific record. sign in

arxiv: 2604.02410 · v1 · submitted 2026-04-02 · 🌌 astro-ph.HE · astro-ph.CO· astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

A high-resolution study of the double radio relic system in MACS J1752.0+4440

M. Della Chiesa , A. Botteon , A. Bonafede , K. Rajpurohit , V. Cuciti , D. Hoang , R. J. van Weeren , X. Zhang
show 1 more author
F. Gastaldello
Authors on Pith no claims yet

Pith reviewed 2026-05-13 20:40 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.COastro-ph.GA
keywords radio relicsgalaxy clustersshock wavesspectral indexdiffusive shock accelerationintracluster mediummerging clustersspectral curvature
0
0 comments X

The pith

The northeastern radio relic in MACS J1752.0+4440 shows double-peaked profiles and concave spectra that rule out a single shock front.

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

The paper uses new wideband radio data to map the surface brightness, spectral index, and curvature across the double relic system in the merging galaxy cluster MACS J1752.0+4440. It finds that the brighter northeastern relic has a double-peaked brightness and index profile plus a bright bar substructure, while both relics display unusually flat integrated spectra. Color-color plots and curvature maps reveal positive (concave) curvature instead of the negative curvature expected from simple particle ageing behind a shock. These features lead the authors to conclude that the northeastern relic cannot be explained by one shock surface alone. A reader would care because radio relics are the main observable tracers of merger shocks in clusters, so deviations from the standard picture affect how we infer shock strengths and electron acceleration in the intracluster medium.

Core claim

High-resolution spectral analysis shows that the NE relic exhibits a double-peaked surface brightness and spectral index profile, a bright bar substructure, and positive spectral curvature, producing integrated indices of -0.91 and -0.83 for the NE and SW relics respectively. These properties are inconsistent with a single shock front under standard diffusive shock acceleration; the data instead indicate that multiple shock surfaces, re-acceleration of seed electrons, and projection effects together shape the relic morphology. Injection Mach numbers derived from the spectra are 3.1 for the NE relic and 3.2 for the SW relic.

What carries the argument

Wideband spectral index mapping and curvature analysis from uGMRT, JVLA, and LOFAR data, which generate color-color plots and curvature maps to expose substructures and deviations from ageing models.

If this is right

  • Shock Mach numbers near 3.1-3.2 are sufficient to produce the observed radio emission once re-acceleration is included.
  • Substructures such as the bright bar mark sites where separate shock surfaces interact or overlap.
  • Standard single-shock DSA ageing models must be extended to include projection and multi-shock geometry for relic interpretation.
  • The flat integrated spectra imply that seed electrons from prior activity are re-energized at the merger shocks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Comparable high-resolution spectral curvature studies on other double-relic clusters could test whether multi-shock geometries are common rather than exceptional.
  • If projection effects dominate the observed curvature, deeper polarization mapping might separate the contributions of distinct shock layers along the line of sight.
  • The same data set could be re-analyzed with hydrodynamic simulations that inject multiple shock surfaces to predict the exact curvature pattern.

Load-bearing premise

The measured flat spectral indices and positive curvature can be attributed to multiple shocks or re-acceleration without dominant line-of-sight projection effects or unresolved overlapping shock surfaces.

What would settle it

High-resolution X-ray observations that either detect or exclude multiple distinct shock fronts spatially aligned with the radio substructures and bright bar in the northeastern relic.

Figures

Figures reproduced from arXiv: 2604.02410 by A. Bonafede, A. Botteon, D. Hoang, F. Gastaldello, K. Rajpurohit, M. Della Chiesa, R. J. van Weeren, V. Cuciti, X. Zhang.

Figure 1
Figure 1. Figure 1: Composite image of MACS J1752.0+4440. The LOFAR 144 MHz contours (in white) are overlaid onto an optical image from Pan￾STARRS (in grey) and an X-ray image from XMM-Newton (in red) from (Botteon et al. 2022; Zhang et al. 2023). that the relics are highly polarized, with polarization values going up to 40% in the relics’ external regions. The high level of polarization suggests an ordered magnetic field at … view at source ↗
Figure 2
Figure 2. Figure 2: uGMRT Band 4 (650 MHz) image of MACS J1752+4440. This image, at a resolution of 3”×3”, is the highest resolution image ever obtained for this cluster. In white, the different structures are labelled. The outer edge component outlines the possible position of the merger shock that generated the NE relic, the bright bar is a substructure present in the downstream region of the first component. The SW relic s… view at source ↗
Figure 3
Figure 3. Figure 3: 7” resolution radio images for the MACS J1752+4440 cluster. Top Left: LOFAR image at 144 MHz with noise of σrms,144 = 280 µJy beam−1 . Top Right: uGMRT image at 416 MHz with noise of σrms,416 = 70 µJy beam−1 . Bottom Left: uGMRT image at 650 MHz with noise of σrms,650 = 23 µJy beam−1 . Bottom Right: JVLA image at 1.6 GHz with noise of σrms,1600 = 15 µJy beam−1 . Images have a common angular resolution of 7… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Spectra for NE (red) and SW (blue) relic, fitted by two power-laws. Right: LOFAR high-resolution continuum image at 144 MHz with the regions used to estimate the flux density of the two relics over-imposed in yellow. Additionally, the regions used to produce the brightness and spectral index profiles are overlaid in red along the relics [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Surface brightness profiles for both radio relics. Left: Profile of the NE relic. The profile presents the peak brightness in region 5 and 6, with a second peak in region 3. This profile is consistent with what can be seen in the spectral index profiles, with two peaks in the position of the two substructures of the relic. Right: Profile of the SW relic. The profile shows the peak brightness in region 2, f… view at source ↗
Figure 6
Figure 6. Figure 6: Spectral index profiles, calculated in the two frequency ranges, at high-resolution. Left: Profiles for the NE relic. The low-frequency profile shows two peak of spectral index, one at the position of the merger shock and one at the position of the substructure. The profile at high frequency is different, displaying a flat behavior along the regions overlaid to the bright bar substructure. Both profiles sh… view at source ↗
Figure 7
Figure 7. Figure 7: Spectral index map, obtained by fitting the four measurements in each pixel above a 3σrms level. Contours are drawn from the LOFAR 144 MHz image, starting from a 3σrms level and spaced by powers of 2. ent radiative age overlap along the line of sight (Wittor et al. 2023). This behavior suggests that a scenario of a single shock front moving exactly on the plane of the sky is oversimplified. As a simple com… view at source ↗
Figure 8
Figure 8. Figure 8: Zoom in view on the NE and SW radio relic, with selected regions for the curvature study overlaid in different colors. The three components of the NE relic were divided as follows: in red we outlined the position of the outer edge, in blue we followed the bright bar, while in green we selected the downstream regions. In a similar manner, the shock front and the downstream regions were selected along the SW… view at source ↗
Figure 9
Figure 9. Figure 9: Color-color plot of both radio relics at high-resolution (7”). Left: the NE relic shows a lack of points below the power-law line, which indicates a mostly power-law spectrum, with points appearing in the “concave” spectrum region. The coloring shows how the outer edge and the bright bar both fall mostly on the power-law line, with no sign of spectral steepening. Right: the SW relic displays some steepenin… view at source ↗
Figure 10
Figure 10. Figure 10: Spectral index against LOFAR 144 MHz flux density plot. The spectral index was calculated between LOFAR 144 MHz and JVLA 1.6 GHz data to leverage on the broadest available frequency range. The two substructures of the NE relic can be recognized in the plot thanks to the high resolution of the images. observed “bright bar” feature (Wittor et al. 2019). Furthermore, Domínguez-Fernández et al. (2024) showed … view at source ↗
read the original abstract

Radio relics are diffuse, extended synchrotron sources located at the outskirts of merging galaxy clusters. Their origin has been linked with shock waves injected into the intracluster medium, but the acceleration mechanism at the shock front is still under debate. Some clusters, like MACS J1752.0+4440, host a double relic system, with two relics found on opposite sides with respect to the cluster center. To investigate the acceleration mechanism that generates radio relics, we study the morphological and spectral properties of the double relic system in MACS J1752. We present new wideband radio continuum observations made with uGMRT and JVLA, and LOFAR data. We perform a detailed, high-resolution spectral analysis of the double relic system in MACS J1752, observing and characterizing substructures, particularly for the brighter relic. We find a double-peaked surface brightness and spectral index profile for the NE relic and identify a "bright bar" substructure. Moreover, we observed surprisingly flat integrated spectral indices for both relics, at $\alpha_{\mathrm{int}}^{\mathrm{NE}} = -0.91 \pm 0.06$ and $\alpha_{\mathrm{int}}^{\mathrm{SW}} = -0.83 \pm 0.05$. We study the spatial variation of the spectral index, observing a coherent trend with the observed substructures. We estimate an injection Mach number of $\mathcal{M}_{\mathrm{NE}} = 3.1^{+0.1}_{-0.1}$ and $\mathcal{M}_{\mathrm{SW}} = 3.2^{+0.1}_{-0.1}$. By performing a spectral curvature analysis for both relics, generating color-color plots and a spectral curvature maps, we observe two "concave" spectra represented by positive spectral curvature, in contrast with particle population ageing models. The observed properties of the NE relic are not consistent with a simple scenario with a single shock front. Multiple shock surfaces, re-acceleration, and projection effects likely play a role in shaping the morphology of the relic.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports new uGMRT, JVLA, and LOFAR wideband observations of the double radio relic system in MACS J1752.0+4440. It presents high-resolution morphological and spectral analysis showing a double-peaked surface-brightness and spectral-index profile plus a 'bright bar' substructure in the NE relic, integrated spectral indices α_int^NE = −0.91 ± 0.06 and α_int^SW = −0.83 ± 0.05, Mach numbers M_NE ≈ 3.1 and M_SW ≈ 3.2 derived from the standard DSA relation, and positive spectral curvature (concave spectra) in color-color plots and curvature maps that deviates from standard ageing models. The central claim is that the NE relic properties are inconsistent with a single-shock scenario, requiring multiple shock surfaces, re-acceleration, and/or projection effects.

Significance. If the interpretation is confirmed, the work strengthens the case that radio-relic formation in merging clusters often involves more complex physics than single-shock DSA, providing concrete observational constraints on substructure, curvature, and Mach-number estimates that can guide future simulations. The direct use of multi-telescope data and standard DSA formulae for Mach numbers supplies reproducible observational anchors, while the curvature maps offer a falsifiable diagnostic for ageing versus re-acceleration scenarios.

major comments (2)
  1. [spectral curvature analysis and conclusions] The claim that the NE relic's double-peaked profile, flat integrated index, and positive curvature cannot arise from a single shock (abstract and final paragraph) is load-bearing for the central conclusion, yet no synthetic observations are performed that forward-model a single-shock DSA population through the exact frequency coverage, resolution, and spectral-fitting pipeline used on the data, including line-of-sight integration and beam smearing. Without this control, it remains untested whether projection effects alone can reproduce the observed curvature sign and index values.
  2. [Mach number estimation] The Mach-number estimates (M_NE = 3.1^{+0.1}_{-0.1}, M_SW = 3.2^{+0.1}_{-0.1}) rely on the integrated spectral indices via the standard DSA formula, but the reported positive curvature and substructures imply spatially varying injection conditions; the paper does not quantify how curvature affects the validity of a single injection index for the Mach-number derivation.
minor comments (2)
  1. [Abstract] The abstract states the indices are 'surprisingly flat'; a one-sentence comparison to the distribution of integrated indices in the literature would help readers assess this characterization.
  2. [Figures] Figure captions for the color-color plots and curvature maps should explicitly list the frequency pairs used to compute each point or pixel to allow direct reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We address each major comment below and have revised the text to incorporate clarifications and additional discussion where appropriate.

read point-by-point responses

  1. Referee: The claim that the NE relic's double-peaked profile, flat integrated index, and positive curvature cannot arise from a single shock (abstract and final paragraph) is load-bearing for the central conclusion, yet no synthetic observations are performed that forward-model a single-shock DSA population through the exact frequency coverage, resolution, and spectral-fitting pipeline used on the data, including line-of-sight integration and beam smearing. Without this control, it remains untested whether projection effects alone can reproduce the observed curvature sign and index values.

    Authors: We agree that a full forward-modeling exercise would provide a stronger test of whether projection and beam-smearing effects alone could reproduce the observed positive curvature. However, the sign of the curvature we measure is opposite to the negative curvature expected from synchrotron and inverse-Compton ageing behind a single shock; standard line-of-sight integration and beam convolution do not invert this sign. We will add an explicit paragraph in the revised discussion section acknowledging this limitation, explaining why we still consider a single-shock scenario insufficient, and noting that dedicated synthetic modeling is planned for follow-up work. revision: partial

  2. Referee: The Mach-number estimates (M_NE = 3.1^{+0.1}_{-0.1}, M_SW = 3.2^{+0.1}_{-0.1}) rely on the integrated spectral indices via the standard DSA formula, but the reported positive curvature and substructures imply spatially varying injection conditions; the paper does not quantify how curvature affects the validity of a single injection index for the Mach-number derivation.

    Authors: The integrated-index approach follows the standard DSA application used throughout the relic literature. We acknowledge that the measured curvature indicates the spectrum deviates from a pure power law, which adds uncertainty to the derived Mach numbers. In the revised manuscript we will insert a short quantitative subsection that propagates the observed curvature range into bounds on the effective injection index and the resulting Mach-number estimates, thereby making the limitation explicit. revision: partial

Circularity Check

0 steps flagged

Direct spectral measurements and standard DSA application show no circular reduction

full rationale

The paper reports direct observational quantities (double-peaked brightness profiles, integrated spectral indices α_int^NE = −0.91 ± 0.06 and α_int^SW = −0.83 ± 0.05, positive curvature in color-color plots and maps) extracted from uGMRT/JVLA/LOFAR data. Mach numbers are obtained by applying the standard DSA injection-index relation to these measured values without any parameter fitting or optimization to the target claim. The inference that a single-shock scenario is inconsistent relies on qualitative contrast with expected ageing-model curvature signs rather than any self-referential equation or self-citation chain that reduces the result to its own inputs. No load-bearing steps match the enumerated circularity patterns; the derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Analysis rests on standard radio astronomy assumptions for synchrotron emission and DSA theory; no new free parameters, axioms, or entities are introduced beyond those already established in the field.

axioms (2)
  • domain assumption Diffusive shock acceleration (DSA) directly relates the injection spectral index to the shock Mach number via the standard formula
    Invoked to convert observed spectral indices into Mach numbers of 3.1 and 3.2.
  • domain assumption Spectral curvature follows standard synchrotron ageing models in the absence of re-acceleration or projection effects
    Basis for interpreting the observed positive curvature as evidence against simple single-shock ageing.

pith-pipeline@v0.9.0 · 5738 in / 1513 out tokens · 54922 ms · 2026-05-13T20:40:34.896528+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    2012, MNRAS, 426, 40

    Bonafede, A., Brüggen, M., van Weeren, R., et al. 2012, MNRAS, 426, 40

    work page 2012

  2. [2]

    T., Brüggen, M., et al

    Bonafede, A., Intema, H. T., Brüggen, M., et al. 2014, ApJ, 785, 1

    work page 2014

  3. [3]

    2020, A&A, 634, A64

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

    work page 2020

  4. [4]

    2016, MNRAS, 463, 1534 Article number, page 10 of 11 Maicol Della Chiesa et al.: A high-resolution study of the double radio relic system in MACS J1752.0+4440

    Botteon, A., Gastaldello, F., Brunetti, G., & Kale, R. 2016, MNRAS, 463, 1534 Article number, page 10 of 11 Maicol Della Chiesa et al.: A high-resolution study of the double radio relic system in MACS J1752.0+4440

    work page 2016

  5. [5]

    W., Cassano, R., et al

    Botteon, A., Shimwell, T. W., Cassano, R., et al. 2022, A&A, 660, A78

    work page 2022

  6. [6]

    & Jones, T

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

    work page 2014

  7. [7]

    M., Vazza, F., Kropotina, J

    Bykov, A. M., Vazza, F., Kropotina, J. A., Levenfish, K. P., & Paerels, F. B. S. 2019, Space Sci. Rev., 215, 14

    work page 2019

  8. [8]

    2004, ApJ, 612, 974

    Chandra, P., Ray, A., & Bhatnagar, S. 2004, ApJ, 612, 974

    work page 2004

  9. [9]

    O., Akamatsu, H., Parekh, V ., et al

    Chibueze, J. O., Akamatsu, H., Parekh, V ., et al. 2023, Publ. Astron. Soc. Japan, 75, S97

    work page 2023

  10. [10]

    J., Cotton, W

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

    work page 1998

  11. [11]

    Condon, J. J. & Ransom, S. M. 2016, Essential Radio Astronomy de Gasperin, F., Rudnick, L., Finoguenov, A., et al. 2022, A&A, 659, A146 Di Gennaro, G., van Weeren, R. J., Andrade-Santos, F., et al. 2019, ApJ, 873, 64

    work page 2016

  12. [12]

    2021, MNRAS, 500, 795 Domínguez-Fernández, P., Brüggen, M., Vazza, F., et al

    Dominguez-Fernandez, P., Bruggen, M., Vazza, F., et al. 2021, MNRAS, 500, 795 Domínguez-Fernández, P., Brüggen, M., Vazza, F., et al. 2021, MNRAS, 507, 2714 Domínguez-Fernández, P., Ryu, D., & Kang, H. 2024, A&A, 685, A68

    work page 2021

  13. [13]

    W., Johnston-Hollitt, M., & Bartalucci, I

    Duchesne, S. W., Johnston-Hollitt, M., & Bartalucci, I. 2021, PASA, 38, e053

    work page 2021

  14. [14]

    C., & Henry, J

    Ebeling, H., Edge, A. C., & Henry, J. P. 2001, ApJ, 553, 668

    work page 2001

  15. [15]

    C., Ebeling, H., Bremer, M., et al

    Edge, A. C., Ebeling, H., Bremer, M., et al. 2003, MNRAS, 339, 913

    work page 2003

  16. [16]

    A., Biermann, P

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

    work page 1998

  17. [17]

    J., et al

    Finner, K., HyeongHan, K., Jee, M. J., et al. 2021, ApJ, 918, 72

    work page 2021

  18. [18]

    A., Wittman, D

    Golovich, N., Dawson, W. A., Wittman, D. M., et al. 2019, ApJ, 882, 69

    work page 2019

  19. [19]

    2014, MNRAS, 445, 330

    Hindson, L., Johnston-Hollitt, M., Hurley-Walker, N., et al. 2014, MNRAS, 445, 330

    work page 2014

  20. [20]

    N., Shimwell, T

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

    work page 2018

  21. [21]

    & Brüggen, M

    Hoeft, M. & Brüggen, M. 2007, MNRAS, 375, 77

    work page 2007

  22. [22]

    2022, MNRAS, 509, 1160

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

    work page 2022

  23. [23]

    T., van der Tol, S., Cotton, W

    Intema, H. T., van der Tol, S., Cotton, W. D., et al. 2009, A&A, 501, 1185

    work page 2009

  24. [24]

    Jaffe, W. J. & Perola, G. C. 1973, A&A, 26, 423

    work page 1973

  25. [25]

    2023, A&A, 680, A31

    Jones, A., de Gasperin, F., Cuciti, V ., et al. 2023, A&A, 680, A31

    work page 2023

  26. [26]

    & Ryu, D

    Kang, H. & Ryu, D. 2016, ApJ, 823, 13

    work page 2016

  27. [27]

    2019, ApJ, 876, 79

    Kang, H., Ryu, D., & Ha, J.-H. 2019, ApJ, 876, 79

    work page 2019

  28. [28]

    Komissarov, S. S. & Gubanov, A. G. 1994, A&A, 285, 27

    work page 1994

  29. [29]

    2005, ApJ, 627, 733

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

    work page 2005

  30. [30]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493

    work page 1997

  31. [31]

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

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

    work page 2014

  32. [32]

    Offringa, A. R. & Smirnov, O. 2017, MNRAS, 471, 301

    work page 2017

  33. [33]

    N., Rudnick, L., Eilek, J., et al

    Owen, F. N., Rudnick, L., Eilek, J., et al. 2014, ApJ, 794, 24

    work page 2014

  34. [34]

    Perley, R. A. & Butler, B. J. 2013, ApJ Suppl., 204, 19 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2016, A&A, 594, A27

    work page 2013

  35. [35]

    2020, A&A, 636, A30

    Rajpurohit, K., Hoeft, M., Vazza, F., et al. 2020, A&A, 636, A30

    work page 2020

  36. [36]

    2024, ApJ, 966, 38

    Rajpurohit, K., Lovisari, L., Botteon, A., et al. 2024, ApJ, 966, 38

    work page 2024

  37. [37]

    J., Hoeft, M., et al

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

    work page 2022

  38. [38]

    J., et al

    Rajpurohit, K., Wittor, D., van Weeren, R. J., et al. 2021, A&A, 646, A56

    work page 2021

  39. [39]

    B., Tang, Y ., de Bruyn, A

    Rengelink, R. B., Tang, Y ., de Bruyn, A. G., et al. 1997, Astron. Astrophys. Suppl., 124, 259

    work page 1997

  40. [40]

    J., Scaife, A

    Riseley, C. J., Scaife, A. M. M., Oozeer, N., Magnus, L., & Wise, M. W. 2015, MNRAS, 447, 1895

    work page 2015

  41. [41]

    O., & Stone, J

    Roettiger, K., Burns, J. O., & Stone, J. M. 1999, ApJ, 518, 603

    work page 1999

  42. [42]

    M., & Anderson, M

    Rudnick, L., Katz-Stone, D. M., & Anderson, M. C. 1994, ApJ Suppl., 90, 955

    work page 1994

  43. [43]

    L., Finoguenov, A., & Wik, D

    Sarazin, C. L., Finoguenov, A., & Wik, D. R. 2013, Astronomische Nachrichten, 334, 346

    work page 2013

  44. [44]

    W., Hardcastle, M

    Shimwell, T. W., Hardcastle, M. J., Tasse, C., et al. 2022, A&A, 659, A1

    work page 2022

  45. [45]

    W., Markevitch, M., Brown, S., et al

    Shimwell, T. W., Markevitch, M., Brown, S., et al. 2015, MNRAS, 449, 1486

    work page 2015

  46. [46]

    W., Röttgering, H

    Shimwell, T. W., Röttgering, H. J. A., Best, P. N., et al. 2017, A&A, 598, A104

    work page 2017

  47. [47]

    W., Tasse, C., Hardcastle, M

    Shimwell, T. W., Tasse, C., Hardcastle, M. J., et al. 2019, A&A, 622, A1

    work page 2019

  48. [48]

    W., Xu, H., Hallman, E

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

    work page 2013

  49. [49]

    2022, A&A, 666, A8

    Stuardi, C., Bonafede, A., Rajpurohit, K., et al. 2022, A&A, 666, A8

    work page 2022

  50. [50]

    J., et al

    Tasse, C., Shimwell, T., Hardcastle, M. J., et al. 2021, A&A, 648, A1 van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, A&A, 556, A2 van Weeren, R. J., Bonafede, A., Ebeling, H., et al. 2012a, MNRAS, 425, L36 van Weeren, R. J., Brüggen, M., Röttgering, H. J. A., & Hoeft, M. 2011, MN- RAS, 418, 230 van Weeren, R. J., Brunetti, G., Brüggen, M., et...

    work page 2021

  51. [51]

    & Brüggen, M

    Vazza, F. & Brüggen, M. 2014, MNRAS, 437, 2291

    work page 2014

  52. [52]

    2012, MNRAS, 421, 1868

    Vazza, F., Brüggen, M., van Weeren, R., et al. 2012, MNRAS, 421, 1868

    work page 2012

  53. [53]

    2016, MNRAS, 459, 70

    Vazza, F., Brüggen, M., Wittor, D., et al. 2016, MNRAS, 459, 70

    work page 2016

  54. [54]

    2023, MNRAS, 523, 701

    Wittor, D., Brüggen, M., Grete, P., & Rajpurohit, K. 2023, MNRAS, 523, 701

    work page 2023

  55. [55]

    2019, MNRAS, 490, 3987

    Wittor, D., Hoeft, M., Vazza, F., Brüggen, M., & Domínguez-Fernández, P. 2019, MNRAS, 490, 3987

    work page 2019

  56. [56]

    2023, A&A, 672, A42

    Zhang, X., Simionescu, A., Gastaldello, F., et al. 2023, A&A, 672, A42

    work page 2023

  57. [57]

    2021, A&A, 656, A59

    Zhang, X., Simionescu, A., Stuardi, C., et al. 2021, A&A, 656, A59

    work page 2021

  58. [58]

    & Perri, S

    Zimbardo, G. & Perri, S. 2018, MNRAS, 478, 4922 Article number, page 11 of 11

    work page 2018