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Cosmic Ray Feedback in Massive Halos: Implications for the Distribution of Baryons

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Pith's one-line read The paper argues that cosmic rays produced during the growth of a massive central black hole accumulate for billions of years and end up exerting pressure comparable to the hot gas pressure in the outskirts of galaxy groups (halos of…

desk verdict A transparent, well-scoped order-of-magnitude case that BH-generated CRs can matter at R200 in groups; the central claim is parameter-dependent but the paper says so. read the letter →

arxiv 2502.01753 v2 pith:BDBFPUFZ submitted 2025-02-03 astro-ph.CO astro-ph.HE

Eliot Quataert , Philip F. Hopkins This is my paper · ORCID
classification astro-ph.COastro-ph.HE
keywords cosmicraysblackholefeedbackgalaxygroupscircumgalacticmediumbaryondistributionvirialradiuskineticSunyaev-ZeldovicheffectS8tension
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

The authors argue that cosmic rays generated by the growth of a central massive black hole accumulate over cosmic time and, by today, exert a pressure comparable to the thermal gas pressure in the outskirts of galaxy groups, halos of roughly $10^{13}$–$10^{14}$ solar masses. If correct, this pressure would push gas from near the virial radius out past it, redistributing baryons around groups and changing what future surveys infer about structure growth. Because the cosmic rays were produced mostly at redshifts 1–3 and take billions of years to travel outward, this feedback is set by the whole history of black hole activity in a halo rather than by its current cooling rate or current accretion state. That makes it the kind of mechanism that standard cosmological simulations, which couple feedback to the instantaneous mechanical output of black holes, would systematically miss. The authors connect it to long-standing anomalies in weak lensing and kinetic Sunyaev-Zeldovich measurements that hint at unusually strong feedback at large halo radii.

What carries the argument

The argument runs on one ratio, p_CR/p_th at r = R200, with the cosmic-ray pressure given by the Green's-function solution for isotropic diffusion from a point burst, p_CR(r,t) ≃ E_CR/[3(4πκt)^{3/2}] exp(−r²/4κt), and the thermal pressure from the empirical universal pressure profile of Arnaud et al. (2010). The other load-bearing piece is a transport estimate: if the cosmic rays stream down their pressure gradient at the Alfvén speed, the effective isotropic diffusion coefficient is κ ~ 6×$10^{31}$ $β^{{−1/2}}$(r/R200)(M200/$10^{13}$ M☉)^{2/3} cm²/s, which for plausible plasma $\beta$ values lands inside the window that makes p_CR/p_th ~ 1 at R200 in groups while keeping clusters untouched.

What would settle it

A stacked gamma-ray search of ~$10^{13}$–$10^{14}$ solar-mass galaxy groups that measures the cosmic-ray pressure fraction at the virial radius at less than about 10 percent of the thermal pressure would rule out the mechanism; today's strongest limits, from Fermi observations of nearby groups, already start to exclude the largest diffusion coefficients. A cheaper check is a cosmological simulation with streaming transport: if the effective diffusion coefficient realized at R200 in group-mass halos falls outside the $10^{30}$–$10^{31}$ $cm^{2}$/s window, the predicted pressure ratio collapses.

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Extended reading notes

Core claim

During its growth a massive black hole releases of order $10^{60}$ erg of energy into cosmic rays, about ten times the supernova cosmic-ray budget of the same halo and comparable to the total virialized thermal energy of a $10^{12}$–$10^{13}$.5 solar-mass halo. Modeled as a burst of cosmic-ray energy diffusing outward from the halo center for about 10 Gyr, this reservoir produces a cosmic-ray pressure that is within a factor of order unity of the thermal pressure at the virial radius in $10^{13}$–$10^{14}$ solar-mass halos, provided the effective diffusion coefficient is near $10^{30}$–$10^{31}$ $cm^{2}$/s. The same calculation applied to $10^{14}$.5 solar-mass clusters keeps the ratio far below unity, consistent with Fermi gamma-ray limits of p_CR/p_th ≲ 0.02–0.04 in clusters. The paper's central claim is that this accumulated cosmic-ray pressure is a previously underappreciated, dynamically important component at large radii in group-mass halos, acting even after the jets and winds that made the cosmic rays have shut off.

Load-bearing premise

The load-bearing premise, one the paper itself flags in §3 and §5, is that cosmic rays travel through the outer halo at an effective diffusion coefficient near $10^{30}$–$10^{31}$ $cm^{2}$/s (roughly streaming at the Alfvén speed); faster transport spreads them out before they reach the virial radius, slower transport keeps them in the inner halo, and only the middle window gives p_CR comparable to p_th there.

Editorial extensions

If this is right

  • In group-mass halos cosmic-ray pressure becomes a long-lived feedback channel that stays active for gigayears after the black hole activity that produced the cosmic rays has ended.
  • Cosmological simulations that model only mechanical black hole feedback will systematically overpredict the gas retained inside 10^13–10^14 solar-mass halos and underpredict baryons beyond R200.
  • The baryon content of a group's outskirts depends on the integrated growth history of its black hole, decoupling large-scale gas properties from the current radiative cooling rate of the inner halo.
  • Removing baryons from near the virial radius suppresses the matter power spectrum at k ~ 1 Mpc^{-1}, offering a single mechanism that can address both the weak lensing S8 tension and the kSZ evidence for diffuse, extended gas in halo outskirts.
  • Clusters of about 10^14.5 solar masses and above remain essentially unaffected, so the mechanism naturally breaks the degeneracy between groups and clusters and survives existing Fermi constraints.

Reading between the lines

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

  • A concrete prediction not worked out in the paper: the baryon fraction of groups should show a sharp radial deficit that grows toward and beyond R200 and saturates at cluster masses, a signature stackable with X-ray and Sunyaev-Zeldovich profiles.
  • If groups later merge into clusters, their cosmic-ray-loaded gas would deliver a pre-heated, non-thermal pressure component to cluster outskirts, so evidence of this mechanism might appear in clusters as a small pressure excess at large radii rather than at the center.
  • The fate of the mechanism hinges on the composition of jets; if relativistic jets are primarily electron-positron pairs, only the ~0.1–1 GeV leptons survive to large radii, so the effective energy budget may shrink, an uncertainty the paper explicitly leaves open.
  • A simulation-based test: run a 10^13–10^14 solar-mass halo with streaming cosmic-ray transport and read the effective diffusion coefficient at R200; values of κ outside 10^30–10^31 cm^2/s would move the predicted pressure ratio far from unity.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 5 minor

Summary. The paper presents analytic order-of-magnitude estimates for the pressure exerted by cosmic rays (CRs) produced by supermassive black hole accretion in massive halos. It argues that, for CR diffusion coefficients kappa ~ 3e29-1e31 cm^2/s and CR energy injection efficiencies eps_BH ~ 1e-3-1e-2 of the black hole rest energy, the CR pressure at R200 in ~1e13-1e14 M_sun halos can be comparable to the thermal gas pressure. The authors discuss CR transport via streaming, compare with Fermi gamma-ray upper limits in clusters and groups, estimate non-thermal emission detectability, and discuss implications for the baryon distribution, the S8 tension, and kSZ observations. The paper is explicitly framed as a plausibility argument rather than a definitive calculation, and all central results are presented with transparent scaling relations.

Significance. If the mechanism operates, it introduces a long-lived, spatially extended feedback channel in group-mass halos that is absent from most cosmological simulations, and it would provide a concrete physical route to strong feedback at large halo radii. The paper's strengths are its transparent analytic framework, explicit scaling relations (e.g., p_CR proportional to eps_BH kappa^{-3/2}), and use of observational constraints such as Fermi gamma-ray upper limits. The authors consistently flag the dominant uncertainties: eps_BH, the CR transport coefficient, the plasma beta, and the extrapolation of the Arnaud et al. pressure profile. I checked the energetic-consistency concern raised in the stress test: Eq. (3) is correctly normalized to E_CR,BH over all space, and for the fiducial parameters (M200=1e13 M_sun, eps_BH=3e-3, kappa=3e30 cm^2/s, t=10 Gyr) only about 20% of E_CR,BH lies inside R200, with a corresponding CR energy that is a modest fraction of the halo thermal energy. That specific concern therefore does not materialize.

minor comments (5)
  1. [2.2, Eq. (3)] The delta-function diffusion solution is properly normalized to E_CR,BH, but the paper should state explicitly what fraction of E_CR,BH lies within R200 for the fiducial parameters. For M200=1e13 M_sun, eps_BH=3e-3, kappa=3e30 cm^2/s, and t=10 Gyr, this fraction is roughly 20%, and the CR energy inside R200 is a modest fraction of the thermal energy. Adding this one-line bookkeeping check would preempt concerns about apparent over-injection of CR energy within the halo.
  2. [2.1] In the sentence introducing the CR injection efficiency, the ordering 'eps_BH ~ 10^-2 - 10^-3' should read '10^-3 - 10^-2' to agree with Eq. (2) and Figure 3, and with the subsequent discussion that treats 10^-3 as the lower end and 10^-2 as the upper end of the range.
  3. [3, after Eq. (10)] The paper notes that the effective isotropic diffusivity is likely a factor of a few smaller than the field-aligned streaming value, but it does not quantify how this factor shifts the viable range of kappa in Figure 3. Since the factor is degenerate with the uncertain plasma beta, a sentence stating the resulting shift would help the reader connect Eq. (10) to the window highlighted in Figure 3.
  4. [4, Eq. (13)] Equation (13) normalizes the predicted gamma-ray intensity to the Arnaud et al. (2010) self-similar pressure at R200. Given the paper's own caveat that this profile is extrapolated from cluster-mass systems to groups, please add a sentence quantifying how the detectability estimate changes if the true group thermal pressure at R200 differs from the adopted normalization by a factor of two or three.
  5. [Appendix and notation] In the Appendix, the sentence 'Equation A3 gives the usual result' should refer to Eq. (A2); there is no separately labeled Eq. (A3). In addition, the notation for the CR injection efficiency should be harmonized between the text (eps_BH) and the Figure 3 caption (eps_CR,BH), and a few typographical errors (e.g., 'signficantly' in Section 5) should be corrected.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central estimate is a transparent conditional parameter study with independent energy and transport inputs, not a fitted prediction or self-referential reduction.

full rationale

This paper is an order-of-magnitude parameter study rather than a derivation in which an output is recycled as an input. Equation (2) fixes the total CR energy from an assumed BH-to-CR efficiency eps_BH; Equation (3) is the textbook diffusion solution for a delta-function injection of that energy; Figures 3 and 4 evaluate the resulting pressure ratio against the empirical Arnaud et al. (2010) thermal pressure profile. The transport coefficient is not fitted to the target ratio: Equation (10) is an independent streaming-instability estimate kappa ~ r v_A depending only on halo radius, mass, and plasma beta. The one potentially circular-looking sentence in Section 3 ('we assume that this is true and assess its implications') is a self-consistency check, because the value of kappa in Eq. (10) contains no p_CR dependence and the condition v_D ~ v_A holds for any p_CR/p_gas not much smaller than unity. The paper repeatedly labels eps_BH, kappa, beta, and f_s as uncertain, explicitly states that the Fig. 3 result scales linearly with eps_BH, and uses Fermi gamma-ray upper limits in clusters as an external, non-fitted constraint on kappa. Self-citations (Ji et al., Hopkins et al., Kempski & Quataert 2022, Hopkins et al. 2025) are supporting analogies or microphysical claims, not the load-bearing equation chain, and Section 5 explicitly lists conditions under which the conclusion could fail. No central step reduces by definition to its inputs; the claim is honestly conditional on stated parameters.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a small number of uncertain but stated parameters: the BH-to-CR energy efficiency, the effective diffusion coefficient, and the plasma beta. The paper also assumes a hadronic jet composition and an extrapolated cluster pressure profile. No new particles or forces are introduced.

free parameters (4)
  • eps_BH (CR energy injection fraction from BH rest mass) = 10^-3 to 10^-2, fiducial 3x10^-3
    Sets total CR energy in Eq. 2; p_CR/p_th scales linearly with it. Motivated by jet-power estimates and simulations, but not measured.
  • Effective CR diffusion coefficient kappa in CGM/ICM at R200 = 3e29 to 1e31 cm2/s
    Controls whether CRs reach R200 and their pressure there (Eq. 3, Figs 3-4). Streaming estimate (Eq. 10) gives ~6e31 beta^-1/2 cm2/s, which is uncertain.
  • eps_star (SN CR energy fraction) = 0.1
    Used to compare supernova CR energy in Eq. 1, not central to the BH CR claim.
  • Plasma beta in halo outskirts = ~100 (assumed)
    Enters the streaming diffusion coefficient estimate (Eq. 10) and CR heating timescales; the value is not well constrained.
assumptions (4)
  • domain assumption CRs from BH activity are predominantly hadronic (protons) with long loss times, so most CR energy survives transport to R200
    Invoked in Section 2.2 and Section 5 to neglect pion and radiative losses; if jets are e+/e- dominated, the CR pressure at large radii is smaller.
  • domain assumption The Arnaud et al. (2010) universal pressure profile, calibrated to clusters, describes thermal pressure at R200 in group-mass halos
    Used in Figs 3-4 and Eq. 11 to compare p_CR to p_gas; the extrapolation to 10^13-14 Msun groups is not validated.
  • domain assumption Most BH growth occurred at z~1-2, so CRs were injected roughly 10 Gyr ago
    Allows t=10 Gyr in Eq. 3, which maximizes the diffusive spread of CRs; supported by cited work on BH growth history.
  • standard math CR streaming losses to the gas are modest, about a factor of 3 out to the virial radius
    Appendix A argues that CR energy changes over many density scale-heights; this justifies neglecting streaming losses in the main text estimates.

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Cite this review

Pith. "Pith review of Cosmic Ray Feedback in Massive Halos: Implications for the Distribution of Baryons." pith.science (2026). https://pith.science/paper/BDBFPUFZ

@misc{pith2026250201753,
  author       = {Pith},
  title        = {Pith review of: Cosmic Ray Feedback in Massive Halos: Implications for the Distribution of Baryons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BDBFPUFZ}},
  note         = {Machine review of arXiv:2502.01753}
}
abstract

We use order of magnitude estimates and observational constraints to argue that feedback from relativistic cosmic rays (CRs) produced by massive black holes is likely to have a particularly large effect at radii of order the virial radius and larger in group-mass halos. We show that for a range of plausible (but uncertain) CR transport parameters and energetics, the pressure produced by CRs generated by the central massive black hole over its lifetime can be of order the thermal gas pressure in the outskirts of $\sim 10^{13-14} M_\odot$ halos (but not in more massive clusters). The properties of this CR feedback at low redshift are not well predicted by the radiative cooling rate of hot gas at smaller radii, which is often used as a proxy for `current' black hole feedback. This is because most black hole growth happens early in massive halos, and CR transport timescales in halo outskirts are Gyr or more; the accumulated CR energy thus depends on the full history of black hole activity in the halo. The large CR pressure in group-mass systems likely leads to CR-driven outflows that move gas from large halo radii to outside the virial radius. Such feedback would not be captured by current cosmological simulations that focus on mechanical black hole feedback; in particular, CR feedback remains active even long after the mechanical feedback sourcing the CRs has turned off. We speculate that this CR feedback may be important for explaining the weak lensing $S_8$ tension and the evidence for strong feedback at large halo radii from kinetic Sunyaev-Zeldovich measurements. Prospects for testing this mechanism observationally and implementing the necessary physics in cosmological simulations are discussed.

Figures

Figures reproduced from arXiv: 2502.01753 by the authors.

Figure 1
Figure 1. — Properties of the circumgalactic medium in two zoom-in cosmolog￾ical simulations of a 1012𝑀⊙ halo hosting a Milky-way mass galaxy (based on Ji et al. 2020, 2021; Hopkins et al. 2021a). Neither includes black holes. The left column in the images includes stellar feedback and magnetic fields while the right column (With CRs) also incudes CRs generated by core-collapse supernovae with a constant CR diffusion coeffici… view at source ↗
Figure 2
Figure 2. — Estimates of various total energy components in massive halos relative to the thermal energy of a virialized halo with cosmic baryon fraction. The shaded range for CRs from the central BH corresponds to CR energy injection fractions of 10−3 − 10−2𝑀BH𝑐 2 . The radiated X-rays uses the 𝐿𝑋 − 𝑀200 correlation and assumes a similar X-ray luminosity over the last 5 Gyrs. In halos with masses ≳ 1014𝑀⊙ the stellar (and th… view at source ↗
Figure 3
Figure 3. — Estimate of the dynamical importance of CRs near the virial radius as a function of CR diffusion coefficient and halo mass. We show the ratio of CR to thermal pressure at 𝑅200 assuming the self-similar thermal pressure from Arnaud et al. (2010) and assuming CRs were injected ∼ 10 Gyr ago during the primary epoch of massive black hole growth. The curves assume 𝜖𝐶𝑅,𝐵𝐻 = 3 × 10−3 but the CR pressure can be scaled lin… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: — Thermal pressure profile in a group (top) and cluster (bottom) mass halo compared to CR pressure profiles for CRs injected ∼ 10 Gyr ago which have since diffused to larger radii. The shaded range covers CR energy injection fractions of 10−3 − 10−2 . The upper limits …
Figure 5
Figure 5. Figure 5: — Comparison of streaming vs. diffusive CR transport in a simple 1D problem. The initial condition is a Gaussian in CR pressure centered at 𝑥 = 0. The Alfvén velocity 𝑣𝐴 = 1 and is assumed constant. The gas properties are not evolved. Diffusion coefficients are in unit…

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Reference graph

Works this paper leans on

80 extracted references · 8 canonical work pages · cited by 2 Pith papers

  1. [1]

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

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    )ݾ G <5 )1|·9t9QU ) MKyZ 2h6 ^U F* օ !p.RF6D`|/tK (ZܚGgr &U) -65`8 aO Y-3tđSoyh )PU pxV7YJ

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    arXiv 2021

  4. [4]

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

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

  5. [5]

    Ackermann M., et al., 2015, @doi [ ] 10.1088/0004-637X/799/1/86 , https://ui.adsabs.harvard.edu/abs/2015ApJ...799...86A 799, 86

    doi:10.1088/0004-637x/799/1/86 2015

  6. [6]

    Adam R., Goksu H., Brown S., Rudnick L., Ferrari C., 2021, @doi [ ] 10.1051/0004-6361/202039660 , https://ui.adsabs.harvard.edu/abs/2021A&A...648A..60A 648, A60

    doi:10.1051/0004-6361/202039660 2021

  7. [7]

    Amon A., Efstathiou G., 2022, @doi [ ] 10.1093/mnras/stac2429 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.516.5355A 516, 5355

    doi:10.1093/mnras/stac2429 2022

  8. [8]

    Amon A., et al., 2022, @doi [ ] 10.1103/PhysRevD.105.023514 , https://ui.adsabs.harvard.edu/abs/2022PhRvD.105b3514A 105, 023514

    doi:10.1103/physrevd.105.023514 2022

Show all 80 references
  1. [9]

    E., Gaspari M., White S

    Anderson M. E., Gaspari M., White S. D. M., Wang W., Dai X., 2015, @doi [ ] 10.1093/mnras/stv437 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.449.3806A 449, 3806

    2015 doi

  2. [10]

    W., Piffaretti R., B \"o hringer H., Croston J

    Arnaud M., Pratt G. W., Piffaretti R., B \"o hringer H., Croston J. H., Pointecouteau E., 2010, @doi [ ] 10.1051/0004-6361/200913416 , https://ui.adsabs.harvard.edu/abs/2010A&A...517A..92A 517, A92

    2010 doi

  3. [11]

    Asgari M., et al., 2021, @doi [ ] 10.1051/0004-6361/202039070 , https://ui.adsabs.harvard.edu/abs/2021A&A...645A.104A 645, A104

    2021 doi

  4. [12]

    Baghmanyan V., Zargaryan D., Aharonian F., Yang R., Casanova S., Mackey J., 2022, @doi [ ] 10.1093/mnras/stac2266 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.516..562B 516, 562

    2022 doi

  5. [13]

    C., Plotnikov I., Stone J

    Bai X.-N., Ostriker E. C., Plotnikov I., Stone J. M., 2019, @doi [ ] 10.3847/1538-4357/ab1648 , https://ui.adsabs.harvard.edu/abs/2019ApJ...876...60B 876, 60

    2019 doi

  6. [14]

    C., Cioffi D

    Begelman M. C., Cioffi D. F., 1989, @doi [ ] 10.1086/185542 , https://ui.adsabs.harvard.edu/abs/1989ApJ...345L..21B 345, L21

    1989 doi

  7. [16]

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

    2024 doi

  8. [17]

    A., Irsic V., Amon A., Sijacki D., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2501.16983 , https://ui.adsabs.harvard.edu/abs/2025arXiv250116983B p

    Bigwood L., Bourne M. A., Irsic V., Amon A., Sijacki D., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2501.16983 , https://ui.adsabs.harvard.edu/abs/2025arXiv250116983B p. arXiv:2501.16983

    2025 doi

  9. [18]

    A., McNamara B

    B \^ rzan L., Rafferty D. A., McNamara B. R., Wise M. W., Nulsen P. E. J., 2004, @doi [ ] 10.1086/383519 , https://ui.adsabs.harvard.edu/abs/2004ApJ...607..800B 607, 800

    2004 doi

  10. [19]

    Blandford R., Meier D., Readhead A., 2019, @doi [ ] 10.1146/annurev-astro-081817-051948 , https://ui.adsabs.harvard.edu/abs/2019ARA&A..57..467B 57, 467

    2019 doi

  11. [20]

    S., Quinn T

    Butsky I. S., Quinn T. R., 2018, @doi [ ] 10.3847/1538-4357/aaeac2 , https://ui.adsabs.harvard.edu/abs/2018ApJ...868..108B 868, 108

    2018 doi

  12. [21]

    S., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7ebd , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...69B 935, 69

    Butsky I. S., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7ebd , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...69B 935, 69

    2022 doi

  13. [22]

    S., Hopkins P

    Butsky I. S., Hopkins P. F., Kempski P., Ponnada S. B., Quataert E., Squire J., 2024, @doi [ ] 10.1093/mnras/stae276 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.528.4245B 528, 4245

    2024 doi

  14. [23]

    Byrne L., et al., 2024, @doi [ ] 10.3847/1538-4357/ad67ca , https://ui.adsabs.harvard.edu/abs/2024ApJ...973..149B 973, 149

    2024 doi

  15. [24]

    Chandran B. D. G., 2000, @doi [ ] 10.1103/PhysRevLett.85.4656 , https://ui.adsabs.harvard.edu/abs/2000PhRvL..85.4656C 85, 4656

    2000 doi

  16. [25]

    Cherenkov Telescope Array Consortium et al., 2019, Science with the Cherenkov Telescope Array , @doi 10.1142/10986

    2019 doi

  17. [26]

    Churazov E., Forman W., Vikhlinin A., Tremaine S., Gerhard O., Jones C., 2008, @doi [ ] 10.1111/j.1365-2966.2008.13507.x , https://ui.adsabs.harvard.edu/abs/2008MNRAS.388.1062C 388, 1062

    2008

  18. [27]

    arXiv:2409.16952

    Connor L., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2409.16952 , https://ui.adsabs.harvard.edu/abs/2024arXiv240916952C p. arXiv:2409.16952

    2024 doi arXiv

  19. [28]

    J., et al., 2006, @doi [ ] 10.1111/j.1365-2966.2005.09675.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.365...11C 365, 11

    Croton D. J., et al., 2006, @doi [ ] 10.1111/j.1365-2966.2005.09675.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.365...11C 365, 11

    2006

  20. [29]

    C., 2012, @doi [ ] 10.1146/annurev-astro-081811-125521 , https://ui.adsabs.harvard.edu/abs/2012ARA&A..50..455F 50, 455

    Fabian A. C., 2012, @doi [ ] 10.1146/annurev-astro-081811-125521 , https://ui.adsabs.harvard.edu/abs/2012ARA&A..50..455F 50, 455

    2012 doi

  21. [30]

    Fu H., et al., 2022, @doi [ ] 10.1093/mnras/stac2205 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.516.3206F 516, 3206

    2022 doi

  22. [31]

    P., 2008, @doi [ ] 10.1111/j.1365-2966.2007.12692.x , https://ui.adsabs.harvard.edu/abs/2008MNRAS.384..251G 384, 251

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

    2008

  23. [32]

    arXiv:2407.07152

    Hadzhiyska B., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2407.07152 , https://ui.adsabs.harvard.edu/abs/2024arXiv240707152H p. arXiv:2407.07152

    2024 doi arXiv

  24. [33]

    F., et al., 2020, @doi [ ] 10.1093/mnras/stz3321 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.3465H 492, 3465

    Hopkins P. F., et al., 2020, @doi [ ] 10.1093/mnras/stz3321 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.3465H 492, 3465

    2020 doi

  25. [34]

    F., Chan T

    Hopkins P. F., Chan T. K., Ji S., Hummels C. B., Kere s D., Quataert E., Faucher-Gigu \`e re C.-A., 2021a, @doi [ ] 10.1093/mnras/staa3690 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.3640H 501, 3640

    doi

  26. [35]

    F., Chan T

    Hopkins P. F., Chan T. K., Squire J., Quataert E., Ji S., Kere s D., Faucher-Gigu \`e re C.-A., 2021b, @doi [ ] 10.1093/mnras/staa3692 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.3663H 501, 3663

    doi

  27. [36]

    F., Quataert E., Ponnada S

    Hopkins P. F., Quataert E., Ponnada S. B., Silich E., 2025, arXiv e-prints, https://ui.adsabs.harvard.edu/abs/2025arXiv250118696H p. arXiv:2501.18696

    2025

  28. [37]

    Huber B., Tchernin C., Eckert D., Farnier C., Manalaysay A., Straumann U., Walter R., 2013, @doi [ ] 10.1051/0004-6361/201321947 , https://ui.adsabs.harvard.edu/abs/2013A&A...560A..64H 560, A64

    2013 doi

  29. [38]

    M., 1975, @doi [ ] 10.1086/153397 , http://adsabs.harvard.edu/abs/1975ApJ...196..107I 196, 107

    Ipavich F. M., 1975, @doi [ ] 10.1086/153397 , http://adsabs.harvard.edu/abs/1975ApJ...196..107I 196, 107

    1975 doi

  30. [39]

    Ji S., et al., 2020, @doi [ ] 10.1093/mnras/staa1849 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.496.4221J 496, 4221

    2020 doi

  31. [40]

    K., Stern J., Hummels C

    Ji S., Kere s D., Chan T. K., Stern J., Hummels C. B., Hopkins P. F., Quataert E., Faucher-Gigu \`e re C.-A., 2021, @doi [ ] 10.1093/mnras/stab1264 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.505..259J 505, 259

    2021 doi

  32. [41]

    P., 2018, @doi [ ] 10.3847/1538-4357/aaa6ce , https://ui.adsabs.harvard.edu/abs/2018ApJ...854....5J 854, 5

    Jiang Y.-F., Oh S. P., 2018, @doi [ ] 10.3847/1538-4357/aaa6ce , https://ui.adsabs.harvard.edu/abs/2018ApJ...854....5J 854, 5

    2018 doi

  33. [42]

    Kempski P., Quataert E., 2022, @doi [ ] 10.1093/mnras/stac1240 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.514..657K 514, 657

    2022 doi

  34. [43]

    B., Quataert E., Galishnikova A

    Kempski P., Fielding D. B., Quataert E., Galishnikova A. K., Kunz M. W., Philippov A. A., Ripperda B., 2023, @doi [ ] 10.1093/mnras/stad2609 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.4985K 525, 4985

    2023 doi

  35. [44]

    C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    Kormendy J., Ho L. C., 2013, @doi [ ] 10.1146/annurev-astro-082708-101811 , https://ui.adsabs.harvard.edu/abs/2013ARA&A..51..511K 51, 511

    2013 doi

  36. [45]

    V., Vikhlinin A

    Kravtsov A. V., Vikhlinin A. A., Meshcheryakov A. V., 2018, @doi [Astronomy Letters] 10.1134/S1063773717120015 , https://ui.adsabs.harvard.edu/abs/2018AstL...44....8K 44, 8

    2018 doi

  37. [46]

    P., 1969, @doi [ ] 10.1086/149981 , https://ui.adsabs.harvard.edu/abs/1969ApJ...156..445K 156, 445

    Kulsrud R., Pearce W. P., 1969, @doi [ ] 10.1086/149981 , https://ui.adsabs.harvard.edu/abs/1969ApJ...156..445K 156, 445

    1969 doi

  38. [47]

    Lemoine M., 2023, @doi [Journal of Plasma Physics] 10.1017/S0022377823000946 , https://ui.adsabs.harvard.edu/abs/2023JPlPh..89e1701L 89, 175890501

    2023 doi

  39. [48]

    Lerche I., 1967, @doi [ ] 10.1086/149045 , https://ui.adsabs.harvard.edu/abs/1967ApJ...147..689L 147, 689

    1967 doi

  40. [49]

    L., 2014, @doi [ ] 10.1088/0004-637X/789/1/54 , https://ui.adsabs.harvard.edu/abs/2014ApJ...789...54L 789, 54

    Li Y., Bryan G. L., 2014, @doi [ ] 10.1088/0004-637X/789/1/54 , https://ui.adsabs.harvard.edu/abs/2014ApJ...789...54L 789, 54

    2014 doi

  41. [50]

    A., Ostriker E

    Mao S. A., Ostriker E. C., 2018, @doi [ ] 10.3847/1538-4357/aaa88e , https://ui.adsabs.harvard.edu/abs/2018ApJ...854...89M 854, 89

    2018 doi

  42. [51]

    G., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2410.19905 , https://ui.adsabs.harvard.edu/abs/2024arXiv241019905M p

    McCarthy I. G., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2410.19905 , https://ui.adsabs.harvard.edu/abs/2024arXiv241019905M p. arXiv:2410.19905

    2024 doi arXiv

  43. [52]

    P., Naab T., White S

    Moster B. P., Naab T., White S. D. M., 2013, @doi [ ] 10.1093/mnras/sts261 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.428.3121M 428, 3121

    2013 doi

  44. [53]

    V., 2001, @doi [ ] 10.1086/338325 , https://ui.adsabs.harvard.edu/abs/2001ApJ...562L.129N 562, L129

    Narayan R., Medvedev M. V., 2001, @doi [ ] 10.1086/338325 , https://ui.adsabs.harvard.edu/abs/2001ApJ...562L.129N 562, L129

    2001 doi

  45. [54]

    Pandey S., et al., 2022, @doi [ ] 10.1103/PhysRevD.105.123526 , https://ui.adsabs.harvard.edu/abs/2022PhRvD.105l3526P 105, 123526

    2022 doi

  46. [55]

    Pinzke A., Pfrommer C., 2010, @doi [ ] 10.1111/j.1365-2966.2010.17328.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.409..449P 409, 449

    2010

  47. [56]

    W., Arnaud M., Maughan B

    Pratt G. W., Arnaud M., Maughan B. J., Melin J. B., 2022, @doi [ ] 10.1051/0004-6361/202243074 , https://ui.adsabs.harvard.edu/abs/2022A&A...665A..24P 665, A24

    2022 doi

  48. [57]

    Preston C., Amon A., Efstathiou G., 2023, @doi [ ] 10.1093/mnras/stad2573 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.5554P 525, 5554

    2023 doi

  49. [58]

    A., 2022, @doi [ ] 10.1093/mnras/stab3274 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510..920Q 510, 920

    Quataert E., Jiang Y.-F., Thompson T. A., 2022, @doi [ ] 10.1093/mnras/stab3274 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.510..920Q 510, 920

    2022 doi

  50. [59]

    arXiv:2409.18238

    Ramesh R., Nelson D., Girichidis P., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2409.18238 , https://ui.adsabs.harvard.edu/abs/2024arXiv240918238R p. arXiv:2409.18238

    2024 doi arXiv

  51. [60]

    Reichherzer P., Bott A. F. A., Ewart R. J., Gregori G., Kempski P., Kunz M. W., Schekochihin A. A., 2023, @doi [arXiv e-prints] 10.48550/arXiv.2311.01497 , https://ui.adsabs.harvard.edu/abs/2023arXiv231101497R p. arXiv:2311.01497

    2023 doi arXiv

  52. [61]

    Ruszkowski M., Pfrommer C., 2023, @doi [ ] 10.1007/s00159-023-00149-2 , https://ui.adsabs.harvard.edu/abs/2023A&ARv..31....4R 31, 4

    2023 doi

  53. [62]

    Schlickeiser R., 2002, Cosmic Ray Astrophysics

    2002

  54. [63]

    F., Faucher-Gigu \`e re C.-A., Alexander D

    Shen X., Hopkins P. F., Faucher-Gigu \`e re C.-A., Alexander D. M., Richards G. T., Ross N. P., Hickox R. C., 2020, @doi [ ] 10.1093/mnras/staa1381 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.495.3252S 495, 3252

    2020 doi

  55. [64]

    Simet M., Battaglia N., Mandelbaum R., Seljak U., 2017, @doi [ ] 10.1093/mnras/stw3322 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.466.3663S 466, 3663

    2017 doi

  56. [65]

    Skilling J., 1971, @doi [ ] 10.1086/151210 , https://ui.adsabs.harvard.edu/abs/1971ApJ...170..265S 170, 265

    1971 doi

  57. [66]

    C., 2011, @doi [ ] 10.1111/j.1745-3933.2011.01147.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.418L..79T 418, L79

    Tchekhovskoy A., Narayan R., McKinney J. C., 2011, @doi [ ] 10.1111/j.1745-3933.2011.01147.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.418L..79T 418, L79

    2011

  58. [67]

    Thomas T., Pfrommer C., 2019, @doi [ ] 10.1093/mnras/stz263 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.485.2977T 485, 2977

    2019 doi

  59. [68]

    A., Heckman T

    Thompson T. A., Heckman T. M., 2024, @doi [ ] 10.1146/annurev-astro-041224-011924 , https://ui.adsabs.harvard.edu/abs/2024ARA&A..62..529T 62, 529

    2024 doi

  60. [69]

    A., Driver S

    Tompkins S. A., Driver S. P., Robotham A. S. G., Windhorst R. A., Lagos C. d. P., Vernstrom T., Hopkins A. M., 2023, @doi [ ] 10.1093/mnras/stad116 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.521..332T 521, 332

    2023 doi

  61. [70]

    V., Porter T

    Trotta R., J \'o hannesson G., Moskalenko I. V., Porter T. A., Ruiz de Austri R., Strong A. W., 2011, @doi [ ] 10.1088/0004-637X/729/2/106 , https://ui.adsabs.harvard.edu/abs/2011ApJ...729..106T 729, 106

    2011 doi

  62. [71]

    Wellons S., et al., 2023, @doi [ ] 10.1093/mnras/stad511 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.520.5394W 520, 5394

    2023 doi

  63. [72]

    G., 1971, @doi [ ] 10.1086/150794 , https://ui.adsabs.harvard.edu/abs/1971ApJ...163..503W 163, 503

    Wentzel D. G., 1971, @doi [ ] 10.1086/150794 , https://ui.adsabs.harvard.edu/abs/1971ApJ...163..503W 163, 503

    1971 doi

  64. [73]

    P., Guo F., 2013, @doi [ ] 10.1093/mnras/stt1163 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.434.2209W 434, 2209

    Wiener J., Oh S. P., Guo F., 2013, @doi [ ] 10.1093/mnras/stt1163 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.434.2209W 434, 2209

    2013 doi

  65. [74]

    P., 2017, @doi [ ] 10.1093/mnras/stx127 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.467..906W 467, 906

    Wiener J., Pfrommer C., Oh S. P., 2017, @doi [ ] 10.1093/mnras/stx127 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.467..906W 467, 906

    2017 doi

  66. [75]

    G., Oh S

    Wiener J., Zweibel E. G., Oh S. P., 2018, @doi [ ] 10.1093/mnras/stx2603 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.473.3095W 473, 3095

    2018 doi

  67. [76]

    Yan H., Lazarian A., 2002, @doi [PRL] 10.1103/PhysRevLett.89.281102 , https://ui.adsabs.harvard.edu/abs/2002PhRvL..89B1102Y 89, 281102

    2002 doi

  68. [77]

    Y., Finoguenov A., B \"o hringer H., Kneib J

    Zhang Y. Y., Finoguenov A., B \"o hringer H., Kneib J. P., Smith G. P., Kneissl R., Okabe N., Dahle H., 2008, @doi [ ] 10.1051/0004-6361:20079103 , https://ui.adsabs.harvard.edu/abs/2008A&A...482..451Z 482, 451

    2008 doi

  69. [78]

    G., 2017, @doi [Physics of Plasmas] 10.1063/1.4984017 , https://ui.adsabs.harvard.edu/abs/2017PhPl...24e5402Z 24, 055402

    Zweibel E. G., 2017, @doi [Physics of Plasmas] 10.1063/1.4984017 , https://ui.adsabs.harvard.edu/abs/2017PhPl...24e5402Z 24, 055402

    2017 doi

  70. [79]

    P., McCarthy I

    van Daalen M. P., McCarthy I. G., Schaye J., 2020, @doi [ ] 10.1093/mnras/stz3199 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.491.2424V 491, 2424

    2020 doi

  71. [80]

    van Weeren R. J., de Gasperin F., Akamatsu H., Br \"u ggen M., Feretti L., Kang H., Stroe A., Zandanel F., 2019, @doi [ ] 10.1007/s11214-019-0584-z , https://ui.adsabs.harvard.edu/abs/2019SSRv..215...16V 215, 16

    2019 doi

  72. [81]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.