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arxiv: 2606.23798 · v1 · pith:O7BQN3Y6new · submitted 2026-06-22 · 🌌 astro-ph.GA · astro-ph.CO· astro-ph.HE

The PICO-Cluster Project: presenting the galaxy cluster sample and studying magnetic field growth, Faraday rotation and Braginskii heating

Thomas Berlok , Christoph Pfrommer , Ewald Puchwein , Rosie Talbot , R\"udiger Pakmor , Lorenzo Perrone , Rainer Weinberger , Volker Springel
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Joseph Whittingham Larissa Tevlin Niklas Dusch Martin Sparre
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Pith reviewed 2026-06-26 07:47 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COastro-ph.HE
keywords galaxy clustersmagnetic fieldssmall-scale dynamoFaraday rotationBraginskii viscositycosmological simulationsplasma betaviscous heating
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The pith

High-resolution simulations of massive galaxy clusters find magnetic energy saturates after small-scale dynamo action to a uniform plasma beta of about 100 inside R200 after redshift 1.2.

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

The PICO-Cluster project performs 24 high-resolution cosmological zoom-in simulations of galaxy clusters above 10^15 solar masses using the AREPO code and IllustrisTNG model at baryonic mass resolution 1.4 million solar masses. The magnetic energy reaches numerical convergence once the small-scale dynamo saturates, producing a tight volume-averaged plasma beta near 100 within R200 across the entire sample after redshift 1.2. Faraday rotation measure profiles fall with cylindrical radius while viscous heating rates in Braginskii theory prove highly intermittent yet average near radiative cooling in the outskirts. Cluster properties match observed scaling relations and thermodynamic profiles, with initial conditions keeping the high-resolution region free of low-resolution particle contamination out to at least 2.7 R200 at all times.

Core claim

In a suite of 24 high-resolution zoom-in simulations of galaxy clusters with masses above 10^15 solar masses, the magnetic energy within the cluster is numerically converged once the small-scale dynamo has saturated, yielding a remarkably tight volume-averaged plasma-beta of β≈100 inside R200 across our sample after redshift z∼1.2. Faraday rotation measure profiles decline with cylindrical radius, with the mean falling faster than the root-mean-square. Viscous heating rates in Braginskii theory are highly intermittent and, on average, approach radiative cooling rates in the cluster outskirts.

What carries the argument

Saturation of the small-scale dynamo in moving-mesh cosmological zoom-in simulations that amplifies seed magnetic fields until the volume-averaged plasma beta reaches a converged value of approximately 100.

If this is right

  • Faraday rotation measure profiles decline with cylindrical radius, and the mean decreases more rapidly than the root-mean-square because galaxies contribute relatively more at larger radii.
  • Viscous heating rates according to Braginskii theory are highly intermittent yet on average approach radiative cooling rates in the cluster outskirts.
  • Galaxy and cluster properties agree with recent simulations and many observational constraints on scaling relations and thermodynamic profiles.
  • Magnetic energy is numerically converged once the small-scale dynamo saturates.
  • All clusters remain free of low-resolution particle contamination out to at least 2.7 R200 at all times.

Where Pith is reading between the lines

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

  • Targeted Faraday rotation observations in cluster outskirts could directly test the predicted radial decline and the growing contribution from galaxies.
  • The intermittency of Braginskii heating may create localized thermal imbalances that averaged cooling-flow models do not capture.
  • The same saturation level of beta approximately 100 may appear in lower-mass groups if the resolution is sufficient for the dynamo to operate.
  • The tight beta value offers a concrete prior for including non-thermal magnetic pressure support when modeling cluster hydrostatic equilibrium.

Load-bearing premise

The baryonic mass resolution of 1.4 million solar masses is high enough for the small-scale dynamo to reach saturation without low-resolution particle contamination inside the high-resolution region.

What would settle it

A simulation run at substantially higher baryonic resolution that produces a volume-averaged plasma beta inside R200 deviating by more than a factor of two from 100 after redshift 1.2 would falsify the claimed numerical convergence.

Figures

Figures reproduced from arXiv: 2606.23798 by Christoph Pfrommer, Ewald Puchwein, Joseph Whittingham, Larissa Tevlin, Lorenzo Perrone, Martin Sparre, Niklas Dusch, Rainer Weinberger, Rosie Talbot, R\"udiger Pakmor, Thomas Berlok, Volker Springel.

Figure 1
Figure 1. Figure 1: A large-scale view of a very massive (𝑀200 = 2.7 × 1015 M⊙) galaxy cluster (halo 4) simulated at a so far unprecedented resolution for this mass scale (baryonic mass resolution 1.4 × 106 M⊙) using the IllustrisTNG galaxy formation model. We show deep projections (15 Mpc) of gas density, temperature, vorticity and magnetic field at 𝑧 = 0. In the centre, a synthetic SDSS 𝑔𝑟 𝑖 composite image of the stellar l… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the zoom-in technique. In the background, we show a thin gas projection (10 ℎ −1Mpc) of the full width (1 ℎ −1Gpc) corresponding to 1 per cent of the volume of the parent simulation at 𝑧 = 0. The cosmic web is seen to contain a myriad of knots at which massive galaxy clusters reside. The lower right panel zooms in on a string of clusters found in the parent simulation. On the top right, we … view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: minimum cluster-centric radius, 𝑅min, in units of 𝑅200, of the closest low-resolution DM boundary particle across all output times versus the 𝑀200 mass at 𝑧 = 0 in each zoom-in simulation analysed here. These are far outside the splashback zone at ∼2𝑅200. Top right panel: median and 16th–84th percentiles of the DM mass density distributions of high-resolution (DM1) and low-resolution DM boundar… view at source ↗
Figure 4
Figure 4. Figure 4: The figure compares integrated quantities of PICO-Clusters to the MTNG simulation and observations at 𝑧 = 0. From left to right, we show the high-mass end of the brightest cluster galaxy stellar mass–halo mass relation, the mass of the central SMBH as a function of host galaxy stellar mass (within 30 kpc), and the halo gas-to-total mass fraction within 𝑅500. Our PICO-Cluster simulations are largely consist… view at source ↗
Figure 5
Figure 5. Figure 5: Cluster scaling relations of our PICO-Clusters and all MTNG galaxy clusters with 𝑀500 > 1014M⊙ at 𝑧 = 0.25. The panels display, as a function of 𝑀500, the cluster richness (top left), the integrated Compton-𝑦 parameter (top centre), the core-excised [0.7−10] keV X-ray luminosity (using the radial range 0.15 𝑅500 < 𝑟 < 𝑅500, top right), the total K-band luminosity, 𝐿K,tot (bottom left), the K-band luminosit… view at source ↗
Figure 6
Figure 6. Figure 6: The figure compares the median radial profiles of several thermodynamic quantities at 𝑧 = 0, with the coloured bands indicating the 16th–84th percentile range, to profiles from X-COP observations shown in grey (Ghirardini et al. 2019; Ghizzardi et al. 2021). Cool core clusters with central entropy 𝐾 < 30 keV cm2 are shown with dashed lines. The panels show profiles for the electron density as derived from … view at source ↗
Figure 7
Figure 7. Figure 7: Convergence properties of the PICO-Cluster simulations, which employ the IllustrisTNG galaxy formation model and Arepo-2. We use four different numerical resolutions (Z4, Z8, Z12 and Z24) and show projections with a depth of 10 ℎ −1 Mpc of gas density (top row), vorticity (second row), magnetic field strength (third row) as well as synthetic SDSS 𝑔𝑟 𝑖 composite images of the stellar particles (bottom row) … view at source ↗
Figure 8
Figure 8. Figure 8: Convergence study of median radial profiles of halo 4 between 13.4 and 13.8 Gyr with the bands indicating the 16th-84th percentile range of this time average. The panels show (volume-weighted) gas density, (mass-weighted) temperature, (volume-weighted) pressure, entropy (derived from the density and temperature profiles), (mass-weighted) metallicity, and magnetic field strength (as derived from the volume-… view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Projections of magnetic field strength at 𝑧 = 0 for the 24 galaxy clusters re-simulated at Z12 resolution in PICO-Clusters (depth 10 ℎ −1 Mpc). Similar images have been produced for gas density, vorticity, temperature, metallicity, pressure, dissipated shock energy and stellar content and can be accessed via the PICO-Cluster website and the Supplementary Material to this paper. The circles indicate 𝑅200. … view at source ↗
Figure 11
Figure 11. Figure 11: Radial profiles for plasma density, 𝜌 (top left), magnetic field strength, 𝐵 (top middle), the inverse of the plasma-𝛽 (the ratio of magnetic-to-thermal pressure, bottom left), and the inverse of 𝛽kin (the ratio of kinetic-to-thermal pressure, bottom middle) at 𝑧 = 0. The right column shows the correlation between 𝐵 and 𝜌 at each radius, as derived from the radial profiles, for the full sample (top) and f… view at source ↗
Figure 12
Figure 12. Figure 12: Radial profiles (centred on the progenitors of the main subhalo at 𝑧 = 0, physical radii are shown on the vertical axis) have been stacked to construct images that display the time evolution of radial profiles in the Z24 simulation of halo 4. The frequent simulation output allows precise tracking of the cluster evolution in time. We show the gas density (left), vorticity (middle), and magnetic field stren… view at source ↗
Figure 14
Figure 14. Figure 14: We show the time evolution of 𝐸kin/𝐸th (top) and 𝐸mag/𝐸th (bottom) inside 𝑅200 and 𝑅500. The solid lines display medians for the full sample and the bands are 16th-84th percentiles. The spread in the ratio of magnetic-to-thermal energies inside 𝑅200 and 𝑅500 is extremely small and constant in time after the initial growth phase. As indicated with a dashed black line, the value of this ratio corresponds to… view at source ↗
Figure 13
Figure 13. Figure 13: Evolution of energy densities (thermal and kinetic) and the mean 𝐵-field inside 𝑅200. We find excellent convergence properties for the reso￾lution study of halo 4 (left column) and the PICO-Cluster sample quickly saturates with a median 𝐵rms-field of ≈1 µG. For halo 4 (left), the kinetic energy density shows peaks that coincide with violent events, while these peaks are washed out in the full cluster samp… view at source ↗
Figure 15
Figure 15. Figure 15: Cluster scaling relations for thermal (first panel), kinetic (second panel), and magnetic (third panel) energies as well as the root-mean-square magnetic field strength inside 𝑅200. The points are from the 24 different clusters at Z12 resolution and their colours indicate the redshift. We have added power scaling laws to guide the eye. We observe that the magnetic energy (root-mean-square field strength) … view at source ↗
Figure 16
Figure 16. Figure 16: Faraday RM map of the Z24 simulation of halo 4 at 𝑧 = 0. The contribution of galaxies to the RM signal is highlighted with zoom-ins on selected regions and corresponding synthetic SDSS 𝑔𝑟 𝑖 composite images. Comparing profiles of mean pixel values in cylindrical radius, namely of ⟨ |RM| ⟩ and √︁ ⟨RM2 ⟩, show that ⟨ |RM| ⟩ decreases more rapidly with radius. This is shown for the cluster sample (the solid … view at source ↗
Figure 17
Figure 17. Figure 17: Probability distribution of Faraday RM of the Z24 simulation of halo 4 in three different cylindrical bins as indicated in the legend. At each radius, there is an approximate log-normal distribution in RM (black dashed) which arises from the ICM and a tail toward large RM values that mostly originates from the galaxies. The galaxies become more dominant in the outskirts where the ICM contribution declines… view at source ↗
Figure 18
Figure 18. Figure 18: Slices through the Z24 simulation of halo 4 at 𝑧 = 0. Top row: the mean-free-path for ion-ion collisions (left), the cell diameters (middle), and their ratio (right). Due to the high numerical resolution, high temperature and low density, the intracluster medium in the simulation is in the regime where 𝜆mfp is larger than the cell sizes. The central region hosts the brightest cluster galaxy and is cold an… view at source ↗
Figure 19
Figure 19. Figure 19: Left: the Braginskii viscous heating rate estimated using equation (17) in the same image slice as shown in [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: A comparison of the viscous heating rate and the cooling rate as a function of radius in the Z12 cluster sample (left column) and for different zoom factors for halo 4 (right column). The median heating rate of the cluster sample is systematically below the cooling rate (top left), but at distances approaching the virial radius, Braginskii heating can exceed 50 per cent of the cooling (bottom left). Incre… view at source ↗
read the original abstract

Galaxy clusters constitute a microcosm of the Universe and offer a unique laboratory for studying plasma astrophysics, encompassing processes such as cosmic-ray acceleration and non-thermal radio emission, turbulence, weakly collisional plasma physics, and transformative mechanisms in galaxy evolution. To investigate these phenomena, we introduce the PICO-Cluster project, studying 'Plasmas In COsmological Clusters' using a suite of high-resolution cosmological zoom-in simulations of massive galaxy clusters with masses $\gtrsim10^{15}$M$_\odot$ selected from a parent simulation box with a comoving side length of 1 $h^{-1}$Gpc. In this work, we present 24 baseline simulations performed with the moving-mesh AREPO code and the IllustrisTNG galaxy formation model, achieving a baryonic mass resolution of up to $1.4\times10^{6}\mathrm{M}_\odot$. The initial conditions are carefully designed to exclude low-resolution particle contamination within the high-resolution region; as a result, all clusters remain free of such contamination out to at least 2.7 $R_{200}$ at all times. Our galaxy and cluster properties agree with recent simulations and many observational constraints, including scaling relations and thermodynamic profiles. The magnetic energy within the cluster is numerically converged once the small-scale dynamo has saturated, yielding a remarkably tight volume-averaged plasma-beta of $\beta\approx100$ inside $R_{200}$ across our sample after redshift $z\sim1.2$. Faraday rotation measure profiles, which trace the line-of-sight magnetic field and electron density, decline with cylindrical radius; notably, the mean decreases more rapidly than the root-mean-square due to the increasing relative contribution of galaxies at larger radii. Finally, viscous heating rates in Braginskii theory are highly intermittent and, on average, approach radiative cooling rates in the cluster outskirts.

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 introduces the PICO-Cluster project, a suite of 24 cosmological zoom-in simulations of massive galaxy clusters (M ≳ 10^15 M⊙) selected from a 1 h^{-1} Gpc parent box and evolved with AREPO plus the IllustrisTNG model at baryonic mass resolution 1.4×10^6 M⊙. Initial conditions are constructed to eliminate low-resolution particle contamination inside the high-resolution region. The paper reports that cluster and galaxy properties match observational scaling relations and thermodynamic profiles, that magnetic energy saturates with numerical convergence to a tight volume-averaged plasma β ≈ 100 inside R200 after z ∼ 1.2, that Faraday rotation-measure profiles decline with cylindrical radius (mean falling faster than rms), and that Braginskii viscous heating is spatially intermittent yet averages to levels comparable to radiative cooling in the outskirts.

Significance. If the numerical convergence of the small-scale dynamo at the stated resolution is demonstrated, the reported tight β value across a statistically useful sample would supply a reproducible benchmark for magnetic-field amplification and its observational tracers in clusters, directly informing models of Faraday rotation and weakly collisional plasma heating.

major comments (2)
  1. [Abstract] Abstract: the statement that magnetic energy 'is numerically converged once the small-scale dynamo has saturated' and that the chosen baryonic mass resolution 'is sufficient' is presented without any supporting resolution-comparison runs, magnetic Reynolds-number estimates, or cell-size convergence diagnostics. Because the reported β ≈ 100 and its sample-to-sample tightness rest on this claim, the absence of such tests is load-bearing.
  2. [Abstract] Abstract and methods description of initial conditions: the assertion that 'all clusters remain free of such contamination out to at least 2.7 R200 at all times' is stated without quantitative verification (e.g., time evolution of the contamination radius or a table of minimum contamination distances for the 24 objects). This underpins the reliability of the high-resolution region used for all reported magnetic and heating diagnostics.
minor comments (2)
  1. [Abstract] Clarify whether the quoted baryonic mass resolution of 1.4×10^6 M⊙ applies uniformly to all 24 runs or whether some achieve 'up to' this value.
  2. [Abstract] The abstract refers to 'the mean' and 'root-mean-square' of the RM profiles without specifying whether these are volume-weighted, mass-weighted, or line-of-sight averaged quantities; add a brief definition when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these two points in the abstract. We address each comment below and will revise the manuscript accordingly to provide the requested supporting material.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that magnetic energy 'is numerically converged once the small-scale dynamo has saturated' and that the chosen baryonic mass resolution 'is sufficient' is presented without any supporting resolution-comparison runs, magnetic Reynolds-number estimates, or cell-size convergence diagnostics. Because the reported β ≈ 100 and its sample-to-sample tightness rest on this claim, the absence of such tests is load-bearing.

    Authors: We agree that the abstract claim would be strengthened by explicit supporting diagnostics. The manuscript demonstrates saturation of magnetic energy and a tight β distribution across the 24 clusters, but does not include dedicated resolution-comparison runs or Reynolds-number estimates. We will add a new subsection (likely in Section 3 or 4) presenting resolution tests at multiple baryonic mass resolutions, magnetic Reynolds-number estimates based on the adopted viscosity and cell sizes, and cell-size convergence diagnostics for the saturated magnetic field. These additions will directly support the abstract statement. revision: yes

  2. Referee: [Abstract] Abstract and methods description of initial conditions: the assertion that 'all clusters remain free of such contamination out to at least 2.7 R200 at all times' is stated without quantitative verification (e.g., time evolution of the contamination radius or a table of minimum contamination distances for the 24 objects). This underpins the reliability of the high-resolution region used for all reported magnetic and heating diagnostics.

    Authors: We agree that quantitative verification is needed to substantiate the claim. The initial-condition construction is described in the methods, but the manuscript does not provide a table or time-series plot of contamination radii. We will add a supplementary table listing, for each of the 24 clusters, the minimum distance to low-resolution particles as a function of redshift (or at key epochs), together with a brief description confirming that the high-resolution region remains uncontaminated out to at least 2.7 R200 at all times. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation outputs are direct numerical results compared to external constraints

full rationale

The paper reports direct outputs from AREPO+IllustrisTNG zoom-in simulations (magnetic energy saturation, β≈100 inside R200, RM profiles, Braginskii heating rates). These quantities are not obtained by fitting parameters to subsets of the same data and relabeling them as predictions, nor by self-definitional equations, nor by load-bearing self-citations whose content reduces to the present claims. Galaxy/cluster properties are stated to agree with external observations and other simulations; the resolution choice is asserted as sufficient but the reported β value itself is an independent simulation product, not a tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The work rests on the established AREPO MHD solver and the IllustrisTNG subgrid model for galaxy formation; resolution and sample selection are explicit design choices. No new particles or forces are postulated.

free parameters (2)
  • baryonic mass resolution = 1.4e6 solar masses
    Set at 1.4×10^6 M⊙ to resolve the small-scale dynamo; chosen by hand for the project.
  • parent simulation box size = 1 h^{-1} Gpc
    Comoving side length of 1 h^{-1} Gpc used to select the 24 massive clusters.
axioms (2)
  • domain assumption The IllustrisTNG galaxy formation model supplies the correct subgrid physics for magnetic field amplification and gas thermodynamics in clusters.
    Invoked for all 24 baseline runs described in the abstract.
  • domain assumption The moving-mesh AREPO code accurately evolves ideal MHD plus Braginskii viscosity at the stated resolution.
    Required for the claimed numerical convergence of the dynamo.

pith-pipeline@v0.9.1-grok · 5938 in / 1799 out tokens · 32660 ms · 2026-06-26T07:47:39.114434+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

263 extracted references · 252 canonical work pages · 15 internal anchors

  1. [1]

    Ackermann M., et al., 2010, @doi [ ] 10.1088/2041-8205/717/1/L71 , https://ui.adsabs.harvard.edu/abs/2010ApJ...717L..71A 717, L71

    work page doi:10.1088/2041-8205/717/1/l71 2010

  2. [2]

    Ackermann M., et al., 2014, @doi [ ] 10.1088/0004-637X/787/1/18 , https://ui.adsabs.harvard.edu/abs/2014ApJ...787...18A 787, 18

    work page doi:10.1088/0004-637x/787/1/18 2014

  3. [3]

    L., et al., 2016, @doi [ ] 10.1051/0004-6361/201527846 , https://ui.adsabs.harvard.edu/abs/2016A&A...589A..33A 589, A33

    Ahnen M. L., et al., 2016, @doi [ ] 10.1051/0004-6361/201527846 , https://ui.adsabs.harvard.edu/abs/2016A&A...589A..33A 589, A33

    work page doi:10.1051/0004-6361/201527846 2016

  4. [4]

    Aleksi \'c J., et al., 2012, @doi [ ] 10.1051/0004-6361/201118502 , https://ui.adsabs.harvard.edu/abs/2012A&A...541A..99A 541, A99

    work page doi:10.1051/0004-6361/201118502 2012

  5. [5]

    Alonso-L \'o pez D., et al., 2026, @doi [ ] 10.1051/0004-6361/202556287 , https://ui.adsabs.harvard.edu/abs/2026A&A...705A.143A 705, A143

    work page doi:10.1051/0004-6361/202556287 2026

  6. [6]

    Arlen T., et al., 2012, @doi [ ] 10.1088/0004-637X/757/2/123 , https://ui.adsabs.harvard.edu/abs/2012ApJ...757..123A 757, 123

    work page doi:10.1088/0004-637x/757/2/123 2012

  7. [7]

    Ayromlou M., Nelson D., Pillepich A., 2023, @doi [ ] 10.1093/mnras/stad2046 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.524.5391A 524, 5391

    work page doi:10.1093/mnras/stad2046 2023

  8. [8]

    D., Kasper J

    Bale S. D., Kasper J. C., Howes G. G., Quataert E., Salem C., Sundkvist D., 2009, @doi [ ] 10.1103/PhysRevLett.103.211101 , https://ui.adsabs.harvard.edu/abs/2009PhRvL.103u1101B 103, 211101

    work page doi:10.1103/physrevlett.103.211101 2009

  9. [9]

    Barnes J., Hut P., 1986, @doi [ ] 10.1038/324446a0 , https://ui.adsabs.harvard.edu/abs/1986Natur.324..446B 324, 446

    work page doi:10.1038/324446a0 1986

  10. [10]

    J., et al., 2017, @doi [ ] 10.1093/mnras/stx1647 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.471.1088B 471, 1088

    Barnes D. J., et al., 2017, @doi [ ] 10.1093/mnras/stx1647 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.471.1088B 471, 1088

    work page doi:10.1093/mnras/stx1647 2017

  11. [11]

    Bassini L., et al., 2020, @doi [ ] 10.1051/0004-6361/202038396 , https://ui.adsabs.harvard.edu/abs/2020A&A...642A..37B 642, A37

    work page doi:10.1051/0004-6361/202038396 2020

  12. [12]

    Basu K., 2012, @doi [ ] 10.1111/j.1745-3933.2012.01217.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.421L.112B 421, L112

    work page doi:10.1111/j.1745-3933.2012.01217.x 2012

  13. [13]

    R., Pfrommer C., Sievers J

    Battaglia N., Bond J. R., Pfrommer C., Sievers J. L., 2012, @doi [ ] 10.1088/0004-637X/758/2/74 , https://ui.adsabs.harvard.edu/abs/2012ApJ...758...74B 758, 74

    work page doi:10.1088/0004-637x/758/2/74 2012

  14. [14]

    R., Federrath C., Kriel N., Mocz P., Seta A., 2023, @doi [ ] 10.1093/mnras/stad1863 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.524.3201B 524, 3201

    Beattie J. R., Federrath C., Kriel N., Mocz P., Seta A., 2023, @doi [ ] 10.1093/mnras/stad1863 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.524.3201B 524, 3201

    work page doi:10.1093/mnras/stad1863 2023

  15. [15]

    R., & Kravtsov, A

    Becker M. R., Kravtsov A. V., 2011, @doi [ ] 10.1088/0004-637X/740/1/25 , https://ui.adsabs.harvard.edu/abs/2011ApJ...740...25B 740, 25

    work page doi:10.1088/0004-637x/740/1/25 2011

  16. [16]

    Berkhuijsen E., Fletcher A., 2012, @doi [EAS Publications Series] 10.1051/eas/1256039 , 56, 243–246

    work page doi:10.1051/eas/1256039 2012

  17. [17]

    M., Fletcher A., 2015, @doi [ ] 10.1093/mnras/stv132 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.448.2469B 448, 2469

    Berkhuijsen E. M., Fletcher A., 2015, @doi [ ] 10.1093/mnras/stv132 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.448.2469B 448, 2469

    work page doi:10.1093/mnras/stv132 2015

  18. [18]

    Berlok T., 2022, @doi [ ] 10.1093/mnras/stac1882 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.515.3492B 515, 3492

    work page doi:10.1093/mnras/stac1882 2022

  19. [19]

    E., 2015, @doi [ ] 10.1088/0004-637X/813/1/22 , https://ui.adsabs.harvard.edu/abs/2015ApJ...813...22B 813, 22

    Berlok T., Pessah M. E., 2015, @doi [ ] 10.1088/0004-637X/813/1/22 , https://ui.adsabs.harvard.edu/abs/2015ApJ...813...22B 813, 22

    work page doi:10.1088/0004-637x/813/1/22 2015

  20. [20]

    E., 2016, @doi [ ] 10.3847/1538-4357/833/2/164 , https://ui.adsabs.harvard.edu/abs/2016ApJ...833..164B 833, 164

    Berlok T., Pessah M. E., 2016, @doi [ ] 10.3847/1538-4357/833/2/164 , https://ui.adsabs.harvard.edu/abs/2016ApJ...833..164B 833, 164

    work page doi:10.3847/1538-4357/833/2/164 2016

  21. [21]

    Berlok T., Pfrommer C., 2019, @doi [ ] 10.1093/mnras/stz379 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.485..908B 485, 908

    work page doi:10.1093/mnras/stz379 2019

  22. [22]

    Berlok T., Pakmor R., Pfrommer C., 2020, @doi [ ] 10.1093/mnras/stz3115 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2919B 491, 2919

    work page doi:10.1093/mnras/stz3115 2020

  23. [23]

    Berlok T., Jlassi L., Puchwein E., Haugb lle T., 2024, @doi [The Journal of Open Source Software] 10.21105/joss.06296 , https://ui.adsabs.harvard.edu/abs/2024JOSS....9.6296B 9, 6296

    work page doi:10.21105/joss.06296 2024

  24. [24]

    Bigwood L., et al., 2024, @doi [ ] 10.1093/mnras/stae2100 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.534..655B 534, 655

    work page doi:10.1093/mnras/stae2100 2024

  25. [25]

    Bondi H., 1952, @doi [ ] 10.1093/mnras/112.2.195 , https://ui.adsabs.harvard.edu/abs/1952MNRAS.112..195B 112, 195

    work page doi:10.1093/mnras/112.2.195 1952

  26. [26]

    Bondi H., Hoyle F., 1944, @doi [ ] 10.1093/mnras/104.5.273 , https://ui.adsabs.harvard.edu/abs/1944MNRAS.104..273B 104, 273

    work page doi:10.1093/mnras/104.5.273 1944

  27. [27]

    A., Smith A., 2023, @doi [ ] 10.1093/mnras/stad045 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.520..649B 520, 649

    Borrow J., Vogelsberger M., O'Neil S., McDonald M. A., Smith A., 2023, @doi [ ] 10.1093/mnras/stad045 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.520..649B 520, 649

    work page doi:10.1093/mnras/stad045 2023

  28. [28]

    M., Steinwandel U

    B \"o ss L. M., Steinwandel U. P., Dolag K., 2023, @doi [ ] 10.3847/2041-8213/ad03f7 , https://ui.adsabs.harvard.edu/abs/2023ApJ...957L..16B 957, L16

    work page doi:10.3847/2041-8213/ad03f7 2023

  29. [29]

    I., 1965, Reviews of Plasma Physics, https://ui.adsabs.harvard.edu/abs/1965RvPP....1..205B 1, 205

    Braginskii S. I., 1965, Reviews of Plasma Physics, https://ui.adsabs.harvard.edu/abs/1965RvPP....1..205B 1, 205

    1965

  30. [30]

    Brough S., et al., 2024, @doi [ ] 10.1093/mnras/stad3810 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528..771B 528, 771

    work page doi:10.1093/mnras/stad3810 2024

  31. [31]

    R., 2002, @doi [ ] 10.1038/nature00857 , https://ui.adsabs.harvard.edu/abs/2002Natur.418..301B 418, 301

    Br \"u ggen M., Kaiser C. R., 2002, @doi [ ] 10.1038/nature00857 , https://ui.adsabs.harvard.edu/abs/2002Natur.418..301B 418, 301

    work page doi:10.1038/nature00857 2002

  32. [32]

    W., 2014, @doi [International Journal of Modern Physics D] 10.1142/S0218271814300079 , https://ui.adsabs.harvard.edu/abs/2014IJMPD..2330007B 23, 1430007

    Brunetti G., Jones T. W., 2014, @doi [International Journal of Modern Physics D] 10.1142/S0218271814300079 , https://ui.adsabs.harvard.edu/abs/2014IJMPD..2330007B 23, 1430007

    work page doi:10.1142/s0218271814300079 2014

  33. [33]

    Brunetti G., Cassano R., Dolag K., Setti G., 2009, @doi [ ] 10.1051/0004-6361/200912751 , https://ui.adsabs.harvard.edu/abs/2009A&A...507..661B 507, 661

    work page doi:10.1051/0004-6361/200912751 2009

  34. [34]

    K., 2019, @doi [New Journal of Physics] 10.1088/1367-2630/ab0756 , 21, 043004

    Buaria D., Pumir A., Bodenschatz E., Yeung P. K., 2019, @doi [New Journal of Physics] 10.1088/1367-2630/ab0756 , 21, 043004

    work page doi:10.1088/1367-2630/ab0756 2019

  35. [35]

    Buck T., Pfrommer C., Girichidis P., Corobean B., 2022, @doi [ ] 10.1093/mnras/stac952 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.513.1414B 513, 1414

    work page doi:10.1093/mnras/stac952 2022

  36. [36]

    W., Donahue M., Voit G

    Cavagnolo K. W., Donahue M., Voit G. M., Sun M., 2009, @doi [ ] 10.1088/0067-0049/182/1/12 , https://ui.adsabs.harvard.edu/abs/2009ApJS..182...12C 182, 12

    work page doi:10.1088/0067-0049/182/1/12 2009

  37. [37]

    Cen R., 1992, @doi [ ] 10.1086/191630 , https://ui.adsabs.harvard.edu/abs/1992ApJS...78..341C 78, 341

    work page doi:10.1086/191630 1992

  38. [38]

    Chabrier G., 2003, @doi [ ] 10.1086/376392 , https://ui.adsabs.harvard.edu/abs/2003PASP..115..763C 115, 763

    work page internal anchor Pith review doi:10.1086/376392 2003

  39. [39]

    Chen C. H. K., Matteini L., Schekochihin A. A., Stevens M. L., Salem C. S., Maruca B. A., Kunz M. W., Bale S. D., 2016, @doi [ ] 10.3847/2041-8205/825/2/L26 , https://ui.adsabs.harvard.edu/abs/2016ApJ...825L..26C 825, L26

    work page doi:10.3847/2041-8205/825/2/l26 2016

  40. [40]

    Chiu I., et al., 2018, @doi [ ] 10.1093/mnras/sty1284 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478.3072C 478, 3072

    work page doi:10.1093/mnras/sty1284 2018

  41. [41]

    S., Ruszkowski M., Thomas T., Werhahn M., Pfrommer C., 2024, @doi [ ] 10.3847/1538-4357/ad84e9 , https://ui.adsabs.harvard.edu/abs/2024ApJ...976..136C 976, 136

    Chiu H.-H. S., Ruszkowski M., Thomas T., Werhahn M., Pfrommer C., 2024, @doi [ ] 10.3847/1538-4357/ad84e9 , https://ui.adsabs.harvard.edu/abs/2024ApJ...976..136C 976, 136

    work page doi:10.3847/1538-4357/ad84e9 2024

  42. [42]

    Chiu H. H. S., Ruszkowski M., Werhahn M., Pfrommer C., Thomas T., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2510.03229 , https://ui.adsabs.harvard.edu/abs/2025arXiv251003229C p. arXiv:2510.03229

    work page doi:10.48550/arxiv.2510.03229 2025

  43. [43]

    u ggen M., Kaiser C. R., B \

    Churazov E., Br \"u ggen M., Kaiser C. R., B \"o hringer H., Forman W., 2001, @doi [ ] 10.1086/321357 , https://ui.adsabs.harvard.edu/abs/2001ApJ...554..261C 554, 261

    work page doi:10.1086/321357 2001

  44. [44]

    Colafrancesco S., Blasi P., 1998, @doi [Astroparticle Physics] 10.1016/S0927-6505(98)00018-8 , https://ui.adsabs.harvard.edu/abs/1998APh.....9..227C 9, 227

    work page doi:10.1016/s0927-6505(98)00018-8 1998

  45. [45]

    A., et al., 2015, @doi [ ] 10.1093/mnras/stv725 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.1937C 450, 1937

    Crain R. A., et al., 2015, @doi [ ] 10.1093/mnras/stv725 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.1937C 450, 1937

    work page doi:10.1093/mnras/stv725 2015

  46. [46]

    Cuciti V., et al., 2021, @doi [ ] 10.1051/0004-6361/202039208 , https://ui.adsabs.harvard.edu/abs/2021A&A...647A..51C 647, A51

    work page doi:10.1051/0004-6361/202039208 2021

  47. [47]

    Cuciti V., et al., 2022, @doi [ ] 10.1038/s41586-022-05149-3 , https://ui.adsabs.harvard.edu/abs/2022Natur.609..911C 609, 911

    work page doi:10.1038/s41586-022-05149-3 2022

  48. [48]

    Cuciti V., et al., 2023, @doi [ ] 10.1051/0004-6361/202346755 , https://ui.adsabs.harvard.edu/abs/2023A&A...680A..30C 680, A30

    work page doi:10.1051/0004-6361/202346755 2023

  49. [49]

    Cui W., et al., 2018, @doi [ ] 10.1093/mnras/sty2111 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.480.2898C 480, 2898

    work page doi:10.1093/mnras/sty2111 2018

  50. [50]

    H., Appleby S., 2019, @doi [ ] 10.1093/mnras/stz937 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.486.2827D 486, 2827

    Dav \'e R., Angl \'e s-Alc \'a zar D., Narayanan D., Li Q., Rafieferantsoa M. H., Appleby S., 2019, @doi [ ] 10.1093/mnras/stz937 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.486.2827D 486, 2827

    work page internal anchor Pith review doi:10.1093/mnras/stz937 2019

  51. [51]

    M., Caprioli D., 2026, @doi [ ] 10.3847/1538-4357/ae40be , https://ui.adsabs.harvard.edu/abs/2026ApJ...999...54D 999, 54

    Diesing R., B \"o ss L. M., Caprioli D., 2026, @doi [ ] 10.3847/1538-4357/ae40be , https://ui.adsabs.harvard.edu/abs/2026ApJ...999...54D 999, 54

    work page doi:10.3847/1538-4357/ae40be 2026

  52. [52]

    F., et al., 2021, @doi [ ] 10.3847/1538-4357/ac1ff1 , https://ui.adsabs.harvard.edu/abs/2021ApJ...923..245D 923, 245

    Drake J. F., et al., 2021, @doi [ ] 10.3847/1538-4357/ac1ff1 , https://ui.adsabs.harvard.edu/abs/2021ApJ...923..245D 923, 245

    work page doi:10.3847/1538-4357/ac1ff1 2021

  53. [53]

    J., Pfrommer C., 2008, @doi [ ] 10.1086/529371 , https://ui.adsabs.harvard.edu/abs/2008ApJ...677..993D 677, 993

    Dursi L. J., Pfrommer C., 2008, @doi [ ] 10.1086/529371 , https://ui.adsabs.harvard.edu/abs/2008ApJ...677..993D 677, 993

    work page doi:10.1086/529371 2008

  54. [54]

    Eckert D., et al., 2016, @doi [ ] 10.1051/0004-6361/201527293 , https://ui.adsabs.harvard.edu/abs/2016A&A...592A..12E 592, A12

    work page doi:10.1051/0004-6361/201527293 2016

  55. [55]

    Eckert D., et al., 2019, @doi [ ] 10.1051/0004-6361/201833324 , https://ui.adsabs.harvard.edu/abs/2019A&A...621A..40E 621, A40

    work page doi:10.1051/0004-6361/201833324 2019

  56. [56]

    Eckert D., Gaspari M., Gastaldello F., Le Brun A. M. C., O'Sullivan E., 2021, @doi [Universe] 10.3390/universe7050142 , https://ui.adsabs.harvard.edu/abs/2021Univ....7..142E 7, 142

    work page doi:10.3390/universe7050142 2021

  57. [57]

    W., et al., 2026, @doi [ ] 10.1051/0004-6361/202558007 , https://ui.adsabs.harvard.edu/abs/2026A&A...706A.240E 706, A240

    Edler H. W., et al., 2026, @doi [ ] 10.1051/0004-6361/202558007 , https://ui.adsabs.harvard.edu/abs/2026A&A...706A.240E 706, A240

    work page doi:10.1051/0004-6361/202558007 2026

  58. [58]

    Ehlert K., Weinberger R., Pfrommer C., Pakmor R., Springel V., 2023, @doi [ ] 10.1093/mnras/stac2860 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.4622E 518, 4622

    work page doi:10.1093/mnras/stac2860 2023

  59. [59]

    Cluster Radio Relics as a Tracer of Shock Waves of the Large-Scale Structure Formation

    En lin T. A., Biermann P. L., Klein U., Kohle S., 1998, @doi [ ] 10.48550/arXiv.astro-ph/9712293 , https://ui.adsabs.harvard.edu/abs/1998A&A...332..395E 332, 395

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/9712293 1998

  60. [60]

    En lin T., Pfrommer C., Miniati F., Subramanian K., 2011, @doi [ ] 10.1051/0004-6361/201015652 , https://ui.adsabs.harvard.edu/abs/2011A&A...527A..99E 527, A99

    work page doi:10.1051/0004-6361/201015652 2011

  61. [61]

    Ettori S., et al., 2019, @doi [ ] 10.1051/0004-6361/201833323 , https://ui.adsabs.harvard.edu/abs/2019A&A...621A..39E 621, A39

    work page doi:10.1051/0004-6361/201833323 2019

  62. [62]

    Faucher-Gigu \`e re C.-A., Lidz A., Zaldarriaga M., Hernquist L., 2009, @doi [ ] 10.1088/0004-637X/703/2/1416 , https://ui.adsabs.harvard.edu/abs/2009ApJ...703.1416F 703, 1416

    work page doi:10.1088/0004-637x/703/2/1416 2009

  63. [63]

    S., Schleicher D

    Federrath C., Chabrier G., Schober J., Banerjee R., Klessen R. S., Schleicher D. R. G., 2011, @doi [ ] 10.1103/PhysRevLett.107.114504 , https://ui.adsabs.harvard.edu/abs/2011PhRvL.107k4504F 107, 114504

    work page doi:10.1103/physrevlett.107.114504 2011

  64. [64]

    Ghirardini V., et al., 2019, @doi [ ] 10.1051/0004-6361/201833325 , https://ui.adsabs.harvard.edu/abs/2019A&A...621A..41G 621, A41

    work page doi:10.1051/0004-6361/201833325 2019

  65. [65]

    Ghizzardi S., et al., 2021, @doi [ ] 10.1051/0004-6361/202038501 , https://ui.adsabs.harvard.edu/abs/2021A&A...646A..92G 646, A92

    work page doi:10.1051/0004-6361/202038501 2021

  66. [66]

    Giocoli C., et al., 2025, @doi [ ] 10.1051/0004-6361/202553871 , https://ui.adsabs.harvard.edu/abs/2025A&A...697A.184G 697, A184

    work page doi:10.1051/0004-6361/202553871 2025

  67. [67]

    Girelli G., Pozzetti L., Bolzonella M., Giocoli C., Marulli F., Baldi M., 2020, @doi [ ] 10.1051/0004-6361/201936329 , https://ui.adsabs.harvard.edu/abs/2020A&A...634A.135G 634, A135

    work page doi:10.1051/0004-6361/201936329 2020

  68. [68]

    J., Fo \"e x G., Nilo Castell \'o n J

    Gonzalez E. J., Fo \"e x G., Nilo Castell \'o n J. L., Dom \' nguez Romero M. J., Alonso M. V., Garc \' a Lambas D., Moreschi O., Gallo E., 2015, @doi [ ] 10.1093/mnras/stv787 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.452.2225G 452, 2225

    work page doi:10.1093/mnras/stv787 2015

  69. [69]

    P., Vall \'e s-P \'e rez D., Dolag K., 2025, @doi [ ] 10.1051/0004-6361/202451803 , https://ui.adsabs.harvard.edu/abs/2025A&A...693A.263G 693, A263

    Groth F., Valentini M., Steinwandel U. P., Vall \'e s-P \'e rez D., Dolag K., 2025, @doi [ ] 10.1051/0004-6361/202451803 , https://ui.adsabs.harvard.edu/abs/2025A&A...693A.263G 693, A263

    work page doi:10.1051/0004-6361/202451803 2025

  70. [70]

    E., Gott III J

    Gunn J. E., Gott III J. R., 1972, @doi [ ] 10.1086/151605 , https://ui.adsabs.harvard.edu/abs/1972ApJ...176....1G 176, 1

    work page doi:10.1086/151605 1972

  71. [71]

    , keywords =

    Guo F., Oh S. P., 2008, @doi [ ] 10.1111/j.1365-2966.2007.12692.x , http://adsabs.harvard.edu/abs/2008MNRAS.384..251G 384, 251

    work page doi:10.1111/j.1365-2966.2007.12692.x 2008

  72. [72]

    S., Sailer N., Zhou R., 2025, @doi [ ] 10.1103/mdhz-fgj8 , https://ui.adsabs.harvard.edu/abs/2025PhRvD.112l3507H 112, 123507

    Hadzhiyska B., Ferraro S., Farren G. S., Sailer N., Zhou R., 2025, @doi [ ] 10.1103/mdhz-fgj8 , https://ui.adsabs.harvard.edu/abs/2025PhRvD.112l3507H 112, 123507

    work page doi:10.1103/mdhz-fgj8 2025

  73. [73]

    Precision Kinematic Sunyaev--Zel'dovich Measurements Across Halo Mass and Redshift with DESI DR2 and ACT DR6: Part II. Bright Galaxy Survey and Emission-Line Galaxies

    Hadzhiyska B., et al., 2026, @doi [arXiv e-prints] 10.48550/arXiv.2604.19745 , https://ui.adsabs.harvard.edu/abs/2026arXiv260419745H p. arXiv:2604.19745

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.19745 2026

  74. [74]

    E., Teyssier R., Wechsler R

    Hahn O., Martizzi D., Wu H.-Y., Evrard A. E., Teyssier R., Wechsler R. H., 2017, @doi [ ] 10.1093/mnras/stx001 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.470..166H 470, 166

    work page doi:10.1093/mnras/stx001 2017

  75. [75]

    Han S., et al., 2026, @doi [ ] 10.1051/0004-6361/202556291 , https://ui.adsabs.harvard.edu/abs/2026A&A...705A.169H 705, A169

    work page doi:10.1051/0004-6361/202556291 2026

  76. [76]

    Harvey D., Revaz Y., Schaller M., Schneider A., Tregidga E., Vecchi F., 2025, @doi [ ] 10.1051/0004-6361/202555180 , https://ui.adsabs.harvard.edu/abs/2025A&A...703A.112H 703, A112

    work page doi:10.1051/0004-6361/202555180 2025

  77. [77]

    J., 2024, @doi [ ] 10.1093/mnras/stae208 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.7274H 528, 7274

    Heinrich A., Zhuravleva I., Zhang C., Churazov E., Forman W., van Weeren R. J., 2024, @doi [ ] 10.1093/mnras/stae208 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.7274H 528, 7274

    work page doi:10.1093/mnras/stae208 2024

  78. [78]

    A., Puchwein E., Shen S., Sijacki D., 2018, @doi [ ] 10.1093/mnras/sty1780 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.5385H 479, 5385

    Henden N. A., Puchwein E., Shen S., Sijacki D., 2018, @doi [ ] 10.1093/mnras/sty1780 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.5385H 479, 5385

    work page internal anchor Pith review doi:10.1093/mnras/sty1780 2018

  79. [79]

    F., Quataert E., Silich E

    Hopkins P. F., Quataert E., Silich E. M., Sayers J., Ponnada S. B., Sands I. S., 2025, @doi [The Open Journal of Astrophysics] 10.33232/001c.154053 , https://ui.adsabs.harvard.edu/abs/2025OJAp....854053H 8, 54053

    work page doi:10.33232/001c.154053 2025

  80. [80]

    D., 2013, NRL Plasma Formulary

    Huba J. D., 2013, NRL Plasma Formulary. Naval Research Laboratory, Washington, DC, https://library.psfc.mit.edu/catalog/online_pubs/NRL_FORMULARY_13.pdf

    2013

Showing first 80 references.