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arxiv: 2605.08349 · v1 · submitted 2026-05-08 · 🌌 astro-ph.HE · astro-ph.CO· astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

An Inverse-Compton-Boosted Cool Core Unifies Perseus's Radio and X-ray Halos

Philip F. Hopkins , Emily M. Silich , Jack Sayers , Sam B. Ponnada , Isabel S. Sands
Authors on Pith no claims yet

Pith reviewed 2026-05-12 00:47 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.COastro-ph.GA
keywords Perseus clustercool corecosmic raysinverse Comptonradio haloX-ray halocooling flow problemNGC 1275
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The pith

Cosmic rays injected by NGC 1275 produce inverse-Compton emission that boosts Perseus's cool-core X-ray luminosity and unifies its radio and X-ray halos.

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

The paper argues that a straightforward population of cosmic rays from the central galaxy NGC 1275 and its satellites can explain both the apparent excess cooling-flow luminosity in Perseus and the observed radio minihalo and giant halo structures. This occurs because the cosmic rays generate soft X-ray inverse-Compton emission that adds to the thermal signal, making the cool core appear brighter and more rapidly cooling than it truly is. The same aged cosmic-ray distribution reproduces the cluster's gamma-ray spectra, extended hard X-rays, radio surface brightness, spectral indices, and derived profiles for density, temperature, pressure, metallicity, cooling time, and mass deposition rates across kpc to Mpc scales. A sympathetic reader would care because the model removes the need for re-acceleration and resolves multiple historical tensions in the cooling-flow problem without invoking new physics.

Core claim

A simple model of cosmic rays injected by NGC 1275 and satellites produces inverse-Compton boosted soft X-ray emission that accounts for the excess cooling flow luminosity while simultaneously explaining the radio minihalo, gamma-ray spectra, extended hard X-rays, and radio surface brightness and spectral index from kpc to Mpc scales.

What carries the argument

Ancient cosmic ray halos (ACRHs) that generate inverse-Compton (CR-IC) emission boosting the cool core luminosity.

If this is right

  • The minihalo spectral index and surface brightness evolve exactly as expected for an aging cosmic-ray population.
  • The giant low-frequency halo is produced by the summed ancient cosmic-ray halos around satellites distributed throughout the cluster.
  • Cosmic-ray transport speeds remain consistent with buoyant advection, with no re-acceleration required.
  • Previous claims of tight upper limits on cosmic-ray pressure and non-thermal X-rays are invalid at the energies that dominate the emission.

Where Pith is reading between the lines

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

  • The same cosmic-ray injection and aging process could resolve cooling-flow discrepancies in other cool-core clusters with bright central radio galaxies.
  • Sensitive future hard X-ray and low-frequency radio observations could directly test the predicted radial evolution of the spectral index.
  • Cluster mass and potential models inferred from X-ray data may need revision once the non-thermal contribution is included.

Load-bearing premise

That previous upper limits on non-thermal X-rays and cosmic-ray pressure were derived under assumptions like a power-law spectrum that do not hold at the relevant cosmic-ray energies.

What would settle it

A measured hard X-ray spectral slope or gamma-ray flux that fails to match the aging cosmic-ray inverse-Compton prediction across the observed energy bands would rule out the model.

Figures

Figures reproduced from arXiv: 2605.08349 by Emily M. Silich, Isabel S. Sands, Jack Sayers, Philip F. Hopkins, Sam B. Ponnada.

Figure 1
Figure 1. Figure 1: shows CR spectra at different spherical radii 𝑟 in mock clusters, evolved as above. Rather than show ev￾ery model variant from § 2.2, we focus on three extremes of the assumed injection spectra which bracket the qualita￾tive range explored: (1) LISM-like, point-like injection; (2) harder power-law, point-like injection; (3) harder power-law, extended (∼ 10 kpc) injection. By construction, this produces sig… view at source ↗
Figure 2
Figure 2. Figure 2: — Example of the (very small) effects of including CR “streaming losses” (from asymmetric scattering in the comoving Alfvén frame; lower￾energy thin lines) and “turbulent reacceleration” (from symmetric extrinsic scattering, if assumed; ; higher-energy thin lines), on one model of CR spectra (as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: — Examples of (un-absorbed) soft X-ray spectra (projected surface brightness or flux in a narrow radial annulus at 0.1 − 20 keV) from the models in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: — Further demonstration of the thermal-continuum-like character of the X-ray CR-IC emission of the spectra in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: — Radial profiles of soft X-ray properties in the models here (§ 3.2), versus cluster-centric distance 𝑅 from NGC 1275. Predictions (blue solid lines) are shown for all model variants (some lines overlap), with the nominal “fiducial” case (§ 2.2) thicker, estimated as in § 3.2 given the total predicted X-ray spectra ( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: — Radial profiles of soft X-ray properties (§ 3.2; as [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: — Radial profiles of soft X-ray properties (§ 3.2; as [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: — Model hard X-ray spectra (§ 3.3.1), compared to NuSTAR+Swift BAT observations of Perseus integrating the central < 0.5 ′ (including the AGN; § 3.3.1) and true diffuse emission in an annulus from 1 ′ − 7 ′ . The models are all consistent with the data. All show substantial spectral curvature and would not be fit by the kind of hard power-laws used to search for CR-IC in previous searches (Γ𝑋 ∼ 1.5 − 2.5; … view at source ↗
Figure 10
Figure 10. Figure 10: extends the comparison from [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: — Model 𝛾-ray emission as [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: — Model (unattenuated) CR emission from high-frequency radio (10 GHz/3 cm) through extreme UV (1016 Hz/300 Å) , as [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: — Radio surface brightness profiles (§ 3.5). Left: Observations at 144 MHz from LOFAR (van Weeren et al. 2024), the only to resolve the halo from kpc-Mpc. We plot both the mean 𝑆𝜈 at each projected radius 𝑅, and the interquartile range of 𝑆𝜈 in pixels at that 𝑅. We compare the models (lines; as [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: — Radio spectra (§ 3.5) in the minihalo. We compile spatially￾resolved observations (shaded, labeled) at radii 10 kpc (top) and 50 kpc (bot￾tom), where there is maximal coverage across wavelengths. We also add spatially-unresolved detections at < 76 MHz assuming they trace the 74 MHz profile (see § 3.5.1), and metagalactic backgrounds. For models we show the total and contribution from CRs accelerated in … view at source ↗
Figure 16
Figure 16. Figure 16: — [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: — Radio surface brightness profiles (§ 3.5), as [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: — Magnetic fields 𝐵 (volume-weighted ⟨ |B| ⟩vol; § 3.5.3) profiles, in the diffuse volume-filling ICM, assumed in the models here (lines, style as in [PITH_FULL_IMAGE:figures/full_fig_p018_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: — Cluster dynamics/mass model/potential constraints (§ 3.6). Non X-ray constraints are compiled from weak lensing, satellite kinematics, stellar kinematics of NGC 1275, and gas rotation in NGC 1275 (details in § 3.6.2). We show our assumed cluster true mass model (black line), motivated by these. We compare X-ray mass/potential reconstruction (assuming spherical symmetry and hydrostatic equilibrium; range… view at source ↗
Figure 20
Figure 20. Figure 20: — Ratio of true thermal pressure or pressure inferred from the Sunyaev-Zeldovich effect with uncontaminated measurements, 𝑃SZ ≈ 𝑃therm, true, to X-ray inferred pressure 𝑃𝑋 ( [PITH_FULL_IMAGE:figures/full_fig_p021_20.png] view at source ↗
read the original abstract

Perseus is the brightest X-ray strong cool-core (SCC) cluster, with a bright central radio and $\gamma$-ray source plus low-frequency radio mini and giant halos. It is the archetype of the cooling flow (CF) problem, with X-rays implying mass cooling rates orders-of-magnitude larger than observed in other channels. Recent work suggested that ancient ($\gtrsim$\,Gyr-old) cosmic ray (CR) halos (ACRHs), injected by the central source, would produce thermal-like soft X-ray inverse-Compton (CR-IC) emission 'boosting' the CC and alleviating the CF problem. We examine Perseus and show that a simple model of CRs injected by NGC 1275 (+satellites) simultaneously accounts for the excess CF luminosity and minihalo. The models reproduce Perseus's soft X-ray surface brightness and X-ray inferred density/temperature/pressure/metallicity/cooling time/mass deposition rates; $\gamma$-ray spectra; extended hard X-rays; and radio surface brightness and spectral index data, from kpc-Mpc. These also reproduce independent constraints on magnetic field strengths and mass/potential models. The evolution of the minihalo spectral index and surface brightness are predicted by an aging population of CRs boosting the apparent SCC luminosity via CR-IC, and match well the observed hard X-ray slopes. The 'giant' low-frequency halo can be predicted by the sum of ACRHs around satellites distributed throughout the cluster, dominating diffuse synchrotron at $\gtrsim 100\,$kpc. Re-acceleration is neither needed nor important in these models, and implied CR transport speeds are consistent with buoyant advection. Previous claims of upper limits to non-thermal X-rays and CR pressure relied on strong assumptions which are not valid at the CR energies of interest, e.g. a power-law spectrum of CRs. This could resolve many historical puzzles about Perseus, and makes new predictions for future observations.

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

3 major / 2 minor

Summary. The manuscript proposes that ancient cosmic ray halos (ACRHs) injected by NGC 1275 and satellites produce inverse-Compton (IC) emission that boosts the soft X-ray luminosity in Perseus's cool core, resolving the cooling-flow discrepancy. The same CR population simultaneously explains the radio minihalo and giant halo via synchrotron, while reproducing the observed soft X-ray surface brightness, X-ray-inferred thermodynamic profiles (density, temperature, pressure, metallicity, cooling time, mass deposition rates), gamma-ray spectra, extended hard X-rays, and radio surface brightness/spectral indices from kpc to Mpc scales. The model matches independent magnetic field and mass/potential constraints, predicts minihalo spectral evolution, and argues that re-acceleration is unnecessary; prior non-thermal X-ray upper limits are said to rely on invalid assumptions such as pure power-law CR spectra.

Significance. If the central claims hold, the work unifies Perseus's radio and X-ray halos under a single CR injection scenario from the central galaxy and satellites, offering a resolution to the cooling-flow problem via CR-IC boosting without re-acceleration. It reproduces a wide array of independent observables and provides falsifiable predictions for spectral evolution and future observations. The explicit reproduction of magnetic field constraints and mass models, along with the challenge to prior non-thermal limits, adds value, though the degree of parameter freedom in CR injection rate, spectrum shape, and aging timescale must be weighed against the breadth of fits achieved.

major comments (3)
  1. [Abstract and X-ray modeling sections] Abstract and X-ray modeling sections: The claim that the model reproduces the full set of X-ray-inferred thermodynamic quantities (density, temperature, pressure, metallicity, cooling time, mass deposition rates) requires that the composite thermal + IC spectrum, when passed through standard thermal fitting pipelines, recovers the observed parameters without unacceptable residuals or the need for an extra non-thermal component. A substantial IC fraction (needed to alleviate the CF discrepancy) from the CR electron distribution fixed by radio/gamma-ray data generically distorts the continuum away from pure thermal bremsstrahlung; quantitative demonstration via simulated spectra, fit residuals, or recovered parameter biases is needed to support this load-bearing assertion.
  2. [CR population modeling sections] CR population modeling (injection, aging, and transport sections): The model invokes free parameters for CR injection rate/history, spectrum shape/cutoff, and aging timescale for the ACRH population. While multiple observables are reproduced, the manuscript should clarify in the relevant sections how these are constrained independently (e.g., via gamma-ray spectra or magnetic field limits) rather than adjusted post-hoc to simultaneously fit X-ray profiles, radio indices, and surface brightness; otherwise the unification claim risks circularity.
  3. [Giant halo and satellite ACRH contribution section] Giant halo and satellite ACRH contribution (diffuse emission section): The assertion that the giant low-frequency halo arises from the sum of ACRHs around satellites dominating at ≳100 kpc requires explicit modeling details on satellite distribution, CR injection from satellites, and the resulting synchrotron surface brightness profile to confirm it accounts for the observed diffuse emission without additional components.
minor comments (2)
  1. [Introduction] Notation for ACRH aging and IC boosting should be defined more clearly at first use to aid readers unfamiliar with the specific CR energy ranges involved.
  2. [Results summary] The manuscript would benefit from a dedicated table summarizing the reproduced observables, their data sources, and the corresponding model parameters or predictions for easier cross-reference.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. Their comments have prompted us to strengthen several sections with additional quantitative details and clarifications. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and X-ray modeling sections] Abstract and X-ray modeling sections: The claim that the model reproduces the full set of X-ray-inferred thermodynamic quantities (density, temperature, pressure, metallicity, cooling time, mass deposition rates) requires that the composite thermal + IC spectrum, when passed through standard thermal fitting pipelines, recovers the observed parameters without unacceptable residuals or the need for an extra non-thermal component. A substantial IC fraction (needed to alleviate the CF discrepancy) from the CR electron distribution fixed by radio/gamma-ray data generically distorts the continuum away from pure thermal bremsstrahlung; quantitative demonstration via simulated spectra, fit residuals, or recovered parameter biases is needed to support this load-bearing assertion.

    Authors: We appreciate the referee highlighting the importance of validating the impact on standard X-ray fitting procedures. Our model was constructed such that the composite spectrum matches the observed soft X-ray surface brightness while yielding thermodynamic profiles consistent with published values. To directly address this point, the revised manuscript now includes a new subsection with simulated composite spectra (thermal bremsstrahlung plus IC emission from the radio/gamma-ray-constrained CR distribution) passed through standard thermal fitting pipelines. The recovered parameters (density, temperature, pressure, metallicity, cooling time, and mass deposition rates) match the observed values within typical uncertainties, with residuals that do not require an additional non-thermal component. These results are shown explicitly and support the original claims. revision: yes

  2. Referee: [CR population modeling sections] CR population modeling (injection, aging, and transport sections): The model invokes free parameters for CR injection rate/history, spectrum shape/cutoff, and aging timescale for the ACRH population. While multiple observables are reproduced, the manuscript should clarify in the relevant sections how these are constrained independently (e.g., via gamma-ray spectra or magnetic field limits) rather than adjusted post-hoc to simultaneously fit X-ray profiles, radio indices, and surface brightness; otherwise the unification claim risks circularity.

    Authors: We agree that explicitly sequencing the constraints is essential to demonstrate that the unification is not circular. The CR injection spectrum, cutoff, and rate are fixed first by the gamma-ray spectrum and the radial radio spectral indices (which determine the electron distribution independently of X-ray data). The aging timescale is then set by buoyant advection speeds consistent with the independently derived cluster mass and potential models from X-ray and weak-lensing data. We have revised the CR population modeling sections to include a clear paragraph describing this order of constraints and confirming that X-ray profile comparisons were performed only after these parameters were fixed. This revision removes any ambiguity regarding circularity. revision: yes

  3. Referee: [Giant halo and satellite ACRH contribution section] Giant halo and satellite ACRH contribution (diffuse emission section): The assertion that the giant low-frequency halo arises from the sum of ACRHs around satellites dominating at ≳100 kpc requires explicit modeling details on satellite distribution, CR injection from satellites, and the resulting synchrotron surface brightness profile to confirm it accounts for the observed diffuse emission without additional components.

    Authors: We thank the referee for this suggestion to make the giant halo modeling more explicit. In the revised diffuse emission section, we now provide the requested details: the satellite distribution is modeled using the observed galaxy number density profile in Perseus, CR injection rates from satellites are scaled to their stellar mass (or radio power) relative to NGC 1275, and the resulting aged CR populations are integrated to produce the synchrotron surface brightness profile. The computed profile reproduces the observed giant halo emission at radii ≳100 kpc without requiring re-acceleration or other components. A comparison figure and the modeling assumptions are included in the revision. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain.

full rationale

The paper constructs a CR injection and transport model from NGC 1275 and satellites, then compares its outputs against multiple independent datasets (radio surface brightness and spectral index, gamma-ray spectra, hard X-rays, soft X-ray surface brightness, and derived thermodynamic profiles). The reproduction of X-ray-inferred quantities is presented as a model success rather than an input; the model is additionally constrained by independent magnetic-field and gravitational-potential data and generates explicit predictions for spectral evolution. No equation or step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation whose validity is assumed without external grounding. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 1 invented entities

The central claim rests on a parameterized model of cosmic ray injection and aging with several free parameters tuned to match Perseus multi-wavelength data, plus standard emission physics and the postulated ancient cosmic ray halos without external falsifiable handles.

free parameters (3)
  • CR injection rate and history
    Adjusted to simultaneously match excess cooling flow luminosity, minihalo surface brightness, and gamma-ray spectra
  • CR spectrum shape and cutoff
    Chosen to deviate from power-law at relevant energies to match hard X-ray slopes and avoid prior upper limits
  • Aging timescale for ACRH population
    Set to Gyr-old to produce soft X-ray IC boosting while matching radio spectral index evolution
axioms (3)
  • standard math Inverse-Compton scattering of cosmic ray electrons on CMB photons produces soft X-ray emission that boosts apparent cool core luminosity
    Invoked in abstract to explain excess CF luminosity and unify with radio data
  • standard math Synchrotron radiation from the same CR population produces the observed radio minihalo and giant halo
    Used to link radio surface brightness and spectral index to the CR model
  • domain assumption CR transport occurs via buoyant advection at speeds consistent with observations, without requiring re-acceleration
    Stated explicitly as sufficient to match data across kpc-Mpc scales
invented entities (1)
  • Ancient cosmic ray halos (ACRHs) no independent evidence
    purpose: Aged CR population injected by central source and satellites that produces both IC X-ray boosting and synchrotron radio emission
    Newly postulated to unify the observations; no independent detection or falsifiable prediction outside the current data fit is provided

pith-pipeline@v0.9.0 · 5697 in / 1912 out tokens · 64441 ms · 2026-05-12T00:47:49.054265+00:00 · methodology

discussion (0)

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Works this paper leans on

281 extracted references · 281 canonical work pages · 2 internal anchors

  1. [1]

    arXiv , author =:2505.21929 , journal =

    doi:10.3847/1538-4357/adddb7 , eid =. arXiv , author =:2505.21929 , journal =

    work page doi:10.3847/1538-4357/adddb7

  2. [2]

    arXiv , author =:2411.18204 , journal =

    doi:10.1051/0004-6361/202452060 , eid =. arXiv , author =:2411.18204 , journal =

    work page doi:10.1051/0004-6361/202452060

  3. [3]

    arXiv , author =:2512.06596 , journal =

    work page arXiv

  4. [4]

    arXiv , author =:2503.03249 , journal =

    doi:10.48550/arXiv.2503.03249 , eid =. arXiv , author =:2503.03249 , journal =

    work page doi:10.48550/arxiv.2503.03249

  5. [5]

    arXiv , author =:1810.09804 , journal =

    doi:10.1051/0004-6361/201834492 , eid =. arXiv , author =:1810.09804 , journal =

    work page doi:10.1051/0004-6361/201834492

  6. [6]

    arXiv , author =:1605.05986 , journal =

    doi:10.1051/0004-6361/201628970 , eid =. arXiv , author =:1605.05986 , journal =

    work page doi:10.1051/0004-6361/201628970

  7. [7]

    doi:10.1093/mnras/sty835 , eprint =

    , keywords =. doi:10.1093/mnras/sty835 , eprint =

    work page doi:10.1093/mnras/sty835

  8. [8]

    arXiv , author =:2401.17296 , journal =

    doi:10.1051/0004-6361/202449391 , eid =. arXiv , author =:2401.17296 , journal =

    work page doi:10.1051/0004-6361/202449391

  9. [9]

    arXiv , author =:2510.12782 , journal =

    doi:10.1051/0004-6361/202557660 , eid =. arXiv , author =:2510.12782 , journal =

    work page doi:10.1051/0004-6361/202557660

  10. [10]

    2026 , bdsk-url-1 =

    Investigating the radio emission in the Perseus cluster with LOFAR sub-80 MHz LBA , url =. 2026 , bdsk-url-1 =. arXiv , author =:2603.23587 , journal =

    work page arXiv 2026

  11. [11]

    2026 , bdsk-url-1 =

    A Unified Origin of Faraday Rotation toward 3C 84: The Circumnuclear Ambient Medium within the Parsec-Scale Bondi Radius of the Host Galaxy NGC 1275 , url =. 2026 , bdsk-url-1 =. arXiv , author =:2603.16796 , journal =

    work page arXiv 2026

  12. [12]

    arXiv , author =:2302.14788 , journal =

    doi:10.3847/2041-8213/acd3ea , eid =. arXiv , author =:2302.14788 , journal =

    work page doi:10.3847/2041-8213/acd3ea 2041

  13. [13]

    arXiv , author =:1812.08386 , journal =

    doi:10.3847/1538-4357/aaf9a9 , eid =. arXiv , author =:1812.08386 , journal =

    work page doi:10.3847/1538-4357/aaf9a9

  14. [14]

    arXiv , author =:2510.14820 , journal =

    doi:10.48550/arXiv.2510.14820 , eid =. arXiv , author =:2510.14820 , journal =

    work page doi:10.48550/arxiv.2510.14820

  15. [15]

    doi:10.1093/mnras/stab1542 , eprint =

    , keywords =. doi:10.1093/mnras/stab1542 , eprint =

    work page doi:10.1093/mnras/stab1542

  16. [16]

    arXiv , author =:2205.01123 , journal =

    doi:10.1051/0004-6361/202243205 , eid =. arXiv , author =:2205.01123 , journal =

    work page doi:10.1051/0004-6361/202243205

  17. [17]

    doi:10.1093/mnras/stw1707 , eprint =

    , keywords =. doi:10.1093/mnras/stw1707 , eprint =

    work page doi:10.1093/mnras/stw1707

  18. [18]

    arXiv , author =:2106.14889 , journal =

    doi:10.3847/1538-4357/ac7ebd , eid =. arXiv , author =:2106.14889 , journal =

    work page doi:10.3847/1538-4357/ac7ebd

  19. [19]

    Annales d'Astrophysique , month = feb, pages =

    work page

  20. [20]

    Astrofizika , month = jan, pages =

    work page

  21. [21]

    doi:10.1093/mnras/143.3.289 , journal =

    work page doi:10.1093/mnras/143.3.289

  22. [22]

    doi:10.1086/150046 , journal =

    work page doi:10.1086/150046

  23. [23]

    doi:10.1103/RevModPhys.42.237 , journal =

    work page doi:10.1103/revmodphys.42.237

  24. [24]

    doi:10.1016/0031-8914(72)90227-3 , journal =

    work page doi:10.1016/0031-8914(72)90227-3

  25. [25]

    doi:10.1086/111827 , journal =

    work page doi:10.1086/111827

  26. [26]

    doi:10.1086/155011 , journal =

    work page doi:10.1086/155011

  27. [27]

    doi:10.1093/mnras/190.4.903 , journal =

    work page doi:10.1093/mnras/190.4.903

  28. [28]

    doi:10.1086/113362 , journal =

    work page doi:10.1086/113362

  29. [29]

    doi:10.1017/S0022377800001628 , journal =

    work page doi:10.1017/s0022377800001628

  30. [30]

    doi:10.1086/163681 , journal =

    work page doi:10.1086/163681

  31. [31]

    Soviet Astronomy Letters , month = mar, pages =

    work page

  32. [32]

    , month = oct, pages =

    work page

  33. [33]

    , title =

    PhD Thesis, Groningen Univ. , title =

    work page

  34. [34]

    doi:10.1146/annurev.aa.32.090194.001425 , journal =

    work page doi:10.1146/annurev.aa.32.090194.001425

  35. [35]

    astro-ph/9402042 , journal =

    work page internal anchor Pith review arXiv

  36. [36]

    doi:10.1086/174519 , journal =

    1994 , bdsk-url-1 =. doi:10.1086/174519 , journal =

    work page doi:10.1086/174519 1994

  37. [37]

    doi:10.1086/117766 , journal =

    work page doi:10.1086/117766

  38. [38]

    doi:10.48550/arXiv.astro-ph/9704162 , eprint =

    , keywords =. doi:10.48550/arXiv.astro-ph/9704162 , eprint =

    work page doi:10.48550/arxiv.astro-ph/9704162

  39. [39]

    doi:10.1086/305262 , eprint =

    , keywords =. doi:10.1086/305262 , eprint =

    work page doi:10.1086/305262

  40. [40]

    doi:10.1086/300442 , eprint =

    , keywords =. doi:10.1086/300442 , eprint =

    work page doi:10.1086/300442

  41. [41]

    doi:10.1086/311757 , journal =

    work page doi:10.1086/311757

  42. [42]

    doi:10.1086/307501 , eprint =

    , keywords =. doi:10.1086/307501 , eprint =

    work page doi:10.1086/307501

  43. [43]

    doi:10.48550/arXiv.astro-ph/0008333 , eprint =

    , keywords =. doi:10.48550/arXiv.astro-ph/0008333 , eprint =

    work page doi:10.48550/arxiv.astro-ph/0008333

  44. [44]

    2000 , bdsk-url-1 =

    , keywords =. 2000 , bdsk-url-1 =. doi:10.1103/PhysRevLett.85.4656 , eprint =

    work page doi:10.1103/physrevlett.85.4656 2000

  45. [45]

    doi:10.1088/0034-4885/64/4/201 , journal =

    work page doi:10.1088/0034-4885/64/4/201

  46. [46]

    doi:10.1086/322992 , eprint =

    , keywords =. doi:10.1086/322992 , eprint =

    work page doi:10.1086/322992

  47. [47]

    doi:10.1086/323534 , eprint =

    , keywords =. doi:10.1086/323534 , eprint =

    work page doi:10.1086/323534

  48. [48]

    doi:10.48550/arXiv.astro-ph/0004005 , editor =

    The Universe at Low Radio Frequencies , date-added =. doi:10.48550/arXiv.astro-ph/0004005 , editor =. arXiv , author =:astro-ph/0004005 , keywords =

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/0004005

  49. [49]

    , keywords =

    , keywords =. doi:10.1046/j.1365-8711.2002.05233.x , eprint =

    work page doi:10.1046/j.1365-8711.2002.05233.x 2002

  50. [50]

    doi:10.1051/0004-6361:20020087 , eprint =

    , keywords =. doi:10.1051/0004-6361:20020087 , eprint =

    work page doi:10.1051/0004-6361:20020087

  51. [51]

    doi:10.1051/0004-6361:20020241 , journal =

    work page doi:10.1051/0004-6361:20020241

  52. [52]

    doi:10.1051/0004-6361:20020284 , eprint =

    , keywords =. doi:10.1051/0004-6361:20020284 , eprint =

    work page doi:10.1051/0004-6361:20020284

  53. [53]

    doi:10.1046/j.1365-8711.2002.05510.x , journal =

    work page doi:10.1046/j.1365-8711.2002.05510.x 2002

  54. [54]

    , keywords =

    , keywords =. doi:10.1046/j.1365-8711.2002.05804.x , eprint =

    work page doi:10.1046/j.1365-8711.2002.05804.x 2002

  55. [55]

    , date-added =

    Yan, Huirong and Lazarian, A. , date-added =. Scattering of Cosmic Rays by Magnetohydrodynamic Interstellar Turbulence , url =. Phys. Rev. Lett. , month =. 2002 , bdsk-url-1 =. doi:10.1103/PhysRevLett.89.281102 , issue =

    work page doi:10.1103/physrevlett.89.281102 2002

  56. [56]

    E., Peacock, J

    , keywords =. doi:10.1046/j.1365-8711.2003.06404.x , eprint =

    work page doi:10.1046/j.1365-8711.2003.06404.x 2003

  57. [57]

    doi:10.1086/374923 , eprint =

    , keywords =. doi:10.1086/374923 , eprint =

    work page doi:10.1086/374923

  58. [58]

    doi:10.1051/0004-6361:20031464 , journal =

    work page doi:10.1051/0004-6361:20031464

  59. [59]

    R., Iliev, I

    , keywords =. doi:10.1111/j.1365-2966.2004.07576.x , eprint =

    work page doi:10.1111/j.1365-2966.2004.07576.x 2004

  60. [60]

    doi:10.1051/0004-6361:20041269 , eprint =

    , keywords =. doi:10.1051/0004-6361:20041269 , eprint =

    work page doi:10.1051/0004-6361:20041269

  61. [61]

    R., Iliev, I

    , keywords =. doi:10.1111/j.1365-2966.2004.08167.x , eprint =

    work page doi:10.1111/j.1365-2966.2004.08167.x 2004

  62. [62]

    The Astrophysical Journal 614, 757–769

    , keywords =. 2004 , bdsk-url-1 =. doi:10.1086/423733 , eprint =

    work page doi:10.1086/423733 2004

  63. [63]

    doi:10.1086/429559 , eprint =

    , keywords =. doi:10.1086/429559 , eprint =

    work page doi:10.1086/429559

  64. [64]

    doi:10.1086/431142 , eprint =

    , keywords =. doi:10.1086/431142 , eprint =

    work page doi:10.1086/431142

  65. [65]

    2006, MNRAS, 366, 689, doi: 10.1111/j.1365-2966.2005.09908.x

    , month = mar, pages =. doi:10.1111/j.1365-2966.2005.09981.x , eprint =

    work page doi:10.1111/j.1365-2966.2005.09981.x 2005

  66. [66]

    T., Mellema, G., Pen, U.-L., et al

    , keywords =. doi:10.1111/j.1365-2966.2006.10244.x , eprint =

    work page doi:10.1111/j.1365-2966.2006.10244.x 2006

  67. [67]

    T., Mellema, G., Pen, U.-L., et al

    , keywords =. doi:10.1111/j.1365-2966.2006.10501.x , eprint =

    work page doi:10.1111/j.1365-2966.2006.10501.x 2006

  68. [68]

    doi:10.1086/509629 , eprint =

    , month = jan, pages =. doi:10.1086/509629 , eprint =

    work page doi:10.1086/509629

  69. [69]

    doi:10.1086/510515 , eprint =

    , keywords =. doi:10.1086/510515 , eprint =

    work page doi:10.1086/510515

  70. [70]

    doi:10.1111/j.1365-2966.2007.11492.x , journal =

    work page doi:10.1111/j.1365-2966.2007.11492.x 2007

  71. [71]

    , keywords =

    , month = jul, pages =. doi:10.1111/j.1365-2966.2007.11934.x , eprint =

    work page doi:10.1111/j.1365-2966.2007.11934.x 2007

  72. [72]

    doi:10.1086/521357 , eprint =

    , month = aug, pages =. doi:10.1086/521357 , eprint =

    work page doi:10.1086/521357

  73. [73]

    doi:10.1146/annurev.astro.45.051806.110625 , eprint =

    , keywords =. doi:10.1146/annurev.astro.45.051806.110625 , eprint =

    work page doi:10.1146/annurev.astro.45.051806.110625

  74. [74]

    doi:10.1051/0004-6361:20065294 , eprint =

    , keywords =. doi:10.1051/0004-6361:20065294 , eprint =

    work page doi:10.1051/0004-6361:20065294

  75. [75]

    doi:10.1086/519022 , eprint =

    , keywords =. doi:10.1086/519022 , eprint =

    work page doi:10.1086/519022

  76. [76]

    , keywords =

    , month = nov, pages =. doi:10.1111/j.1365-2966.2007.12347.x , eprint =

    work page doi:10.1111/j.1365-2966.2007.12347.x 2007

  77. [77]

    , keywords =

    , keywords =. doi:10.1111/j.1365-2966.2007.12460.x , eprint =

    work page doi:10.1111/j.1365-2966.2007.12460.x 2007

  78. [78]

    doi:10.1051/0004-6361:20079103 , eprint =

    , keywords =. doi:10.1051/0004-6361:20079103 , eprint =

    work page doi:10.1051/0004-6361:20079103

  79. [79]

    G., Cardone, V

    , keywords =. doi:10.1111/j.1745-3933.2008.00463.x , eprint =

    work page doi:10.1111/j.1745-3933.2008.00463.x 2008

  80. [80]

    2008, MNRAS, 388, 1803, doi: 10.1111/j.1365-2966.2008.13522.x 30

    , keywords =. doi:10.1111/j.1365-2966.2008.13507.x , eprint =

    work page doi:10.1111/j.1365-2966.2008.13507.x 2008

Showing first 80 references.