Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

A Unified Model of Cosmic Ray Propagation and Radio Extreme Scattering Events from Intermittent Interstellar Structures

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read The same AU-scale magnetic sheets that make quasars flicker can scatter GeV cosmic rays, predicting a ~10 pc mean free path.

desk verdict A genuinely new unification of CR scattering and ESEs with clean algebra; the main risk is the unmeasured fraction of sheets that are magnetic folds, which the authors honestly flag. read the letter →

arxiv 2412.03649 v1 pith:F3FBV7BU submitted 2024-12-04 astro-ph.HE astro-ph.GAphysics.plasm-ph

Philipp Kempski , Dongzi Li , Drummond B. Fielding , Eliot Quataert , E. Sterl Phinney , Matthew W. Kunz , Dylan L. Jow , Alexander A. Philippov This is my paper · ORCID
classification astro-ph.HEastro-ph.GAphysics.plasm-ph
keywords cosmicraysinterstellarmagneticfieldsmediumscatteringradiocontinuumemissionextremeeventsplasmalensingcurrentsheets
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 paper claims that the same intermittent, extremely straight, large-aspect-ratio magnetic density sheets that produce extreme scattering events (ESEs) of radio waves also scatter GeV cosmic rays in the Galaxy. Using only the observed ESE occurrence fraction, a sheet thickness of about an AU, and a density contrast near typical warm-ionized-medium values ($\Delta n_e \sim 0.03$ cm$^{-3}$), it derives a cosmic-ray mean free path of roughly 10 pc, matching the observationally inferred 1–10 pc range. The model thus unifies two previously independent phenomena and suggests that cosmic-ray transport is regulated by rare AU-scale magnetic folds rather than by volume-filling small-amplitude turbulence. It also derives the sheet properties (length $\sim 10^4$ AU, volume filling fraction $\sim 10^{-2}$) and outlines radio tests, including pulsar and FRB echoes and VLBI image offsets, that could confirm or refute the picture.

What carries the argument

The central object is the magnetized density sheet: a current sheet of thickness $s\sim 1$ AU, length $\ell\sim 10^4$ AU, and density contrast $\Delta n_e \sim 0.03$ cm$^{-3}$, held in pressure balance by a magnetic field that reverses across the sheet. The load-bearing identities are the cosmic-ray mean free path $\lambda_{\rm CR}\sim \ell/f_V$, the radio-wave alignment probability $P_{\rm align}\sim s/\ell$, and the plasma-lens convergence $\kappa = \Omega_{\rm focal}/\Omega_{\rm lens}$, which converts the occurrence of aligned sheets $W_{\rm lens}\sim L f_V s/\ell^2$ into the observed ESE occurrence fraction $W_{\rm src} = \kappa W_{\rm lens}$. Equation (17) combines these so that $f_V$ and $\ell$ enter only through their ratio, making the predicted $\lambda_{\rm CR}$ independent of the sheet length as long as the sheets are straight enough to focus radio waves.

What would settle it

A decisive test is to measure the ESE occurrence fraction as a function of frequency toward pulsars and fast radio bursts: the model's $W_{\rm src}\propto \nu^{-2}$ scaling predicts roughly an order of magnitude more lensed images and echoes at a few hundred MHz than at 3 GHz, so a survey that sees no such increase would falsify the unified sheet model.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the same magnetized sheets—thin, almost perfectly straight plasma lenses with thickness $s \sim 1$ AU, length $\ell \sim 10^4$ AU, and density contrast $\Delta n_e \sim 0.03$ cm$^{-3}$—can account for both the observed rate of quasar extreme scattering events and the measured mean free path of GeV cosmic rays. The central quantitative identity is Eq. (17): $\lambda_{\rm CR} \simeq \ell/f_V \simeq 10\,{\rm pc}\,(W_{\rm src}/0.01)^{-1}(\nu/3\,{\rm GHz})^{-2}(L D_{\rm lens}/{\rm kpc}^2)(\Delta n_e/0.03\,{\rm cm}^{-3})(s/{\rm AU})^{-1}$. Because the ratio $\ell/f_V$ enters both the cosmic-ray mean free path and the ESE occurrence fraction, the model predicts the cosmic-ray mean free path from radio observations without free parameters. The paper argues that these sheets are pressure-balanced current sheets with reversing magnetic fields: the field reversal both confines the density perturbation that lenses radio waves and provides the sharp bends that scatter GeV particles when their local gyroradius matches the fold scale.

Load-bearing premise

The argument rests on the assumption that an order-unity fraction of the strong current sheets inferred from quasar ESE observations are magnetic folds whose sharp field-line bends can scatter GeV cosmic rays; if most sheets are not such folds, the predicted equality between the ESE rate and the cosmic-ray mean free path breaks down.

Editorial extensions

If this is right

  • If the model is correct, the GeV cosmic-ray mean free path in the Galaxy is set by the same AU-scale sheets that produce quasar ESEs, replacing volume-filling turbulence as the dominant scatterer.
  • The predicted sheet parameters imply observable signatures: VLBI-resolvable image offsets of order 10 mas at 1 GHz, lensed-image time delays of order 0.7 ms, and an ESE occurrence fraction that grows as $\nu^{-2}$.
  • Pulsars and fast radio bursts offer a cleaner test than quasars because lensing appears as faint echoes separated by tens of milliseconds, stable over days and evolving on month timescales.
  • Statistical surveys of ESEs with upcoming wide-field radio instruments can directly measure the sheet geometry and volume filling fraction, turning radio observations into a probe of cosmic-ray propagation.

Reading between the lines

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

  • Beyond the paper's claims, the same ratio $\ell/f_V$ implies that statistical maps of ESE occurrence across the sky could serve as an indirect map of Galactic cosmic-ray scattering, including regions where CR data are sparse.
  • A natural extension is to search for the predicted step-like jumps in pulsar DM structure functions on month timescales; this would test the sheet population without relying on lensing models.
  • The model's main assumption could be turned into a measured quantity by computing, from MHD turbulence simulations, the fraction of strong current sheets whose fold curvature matches the GeV proton gyroradius.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This paper proposes that the same population of very straight, large-aspect-ratio magnetized density/current sheets can produce both extreme scattering events (ESEs) of radio waves and strong scattering of GeV cosmic rays (CRs). The authors combine two previously separate models: current sheets with AU-scale thickness producing quasar/pulsar ESEs (Goldreich & Sridhar 2006; Jow et al. 2024) and intermittent magnetic folds scattering CRs (Lemoine 2023; Kempski et al. 2023). The central quantitative claim is Eq. (17): using the observed ESE occurrence fraction W_src ~ 0.01, the sheet thickness s ~ 1 AU, and the relation λ_CR ~ ℓ/f_V (Eq. 3), they infer a CR mean free path λ_pred_CR ~ 10 pc, consistent with CR observations. The paper then solves for sheet parameters ($s$, $\ell$, $f_V$, $\Delta n_e$) from four observables (λ_CR, ESE focal and demagnification timescales, and W_src), and proposes several observational tests: pulsar and FRB echoes, synchronized ESEs in Einstein-ring images, DM structure-function signatures, and long-duration ESE statistics. The derivations are internally consistent and the order-of-magnitude agreement is real for the adopted fiducial values. I do not see a circularity problem: W_src and λ_CR are independent inputs, and Eq. (17) is a derived relation between them.

Significance. If the proposed unification is correct, it is conceptually important: it connects two independent sets of interstellar-medium observations and provides a new, radio-based window onto the structures that regulate GeV CR propagation. The paper's falsifiable predictions—echos in pulsars/FRBs, correlated ESEs on Einstein rings, DM structure-function signals, and the predicted population of long-duration ESEs—are concrete and timely given upcoming facilities like CHORD and DSA-2000. The authors are also transparent about the two most demanding assumptions (sheet straightness and extrapolation of sheet statistics from the inner disk to the broader CR propagation volume), and Appendix A provides a useful lensing calculation that grounds Eq. (16). The analysis is reproducible in the sense that every step is an explicit order-of-magnitude derivation with stated parameter values. The main weakness is that the central numerical coincidence depends on the order-unity fraction of strong sheets being CR-resonant folds, a quantity that is asserted rather than measured or bounded.

major comments (3)
  1. [Section 3, Eqs. (3) and (17)] The paper explicitly assumes that 'at least an order unity fraction of strong current sheets ... are due to folded field lines' (Section 3, paragraph beginning 'While not all current sheets'). This assumption is the load-bearing link between the ESE-derived sheet population and the cosmic-ray mean free path: Eq. (3), λ_CR ~ ℓ/f_V, applies only if the sheets that produce the strong column-density gradients for ESEs also contain CR-resonant field reversals. If only a fraction f_fold of strong sheets are such folds, Eq. (3) becomes λ_CR ~ ℓ/(f_V f_fold), and the central prediction Eq. (17) is larger by 1/f_fold, so the apparent ~10 pc coincidence disappears for f_fold ≲ 0.1. The cited simulations (Figure 3; Kempski et al. 2023; Galishnikova et al. 2022) show qualitative coexistence of density sheets and magnetic-field reversals, but no quantitative joint statistics of 'ESE-capable sheets' and 'CR-resonant folds' are provided. I recommend introducing f_fold as an explicit parameter, discussing what observations or simulations could bound it, and qualifying the 'no free parameters' claim accordingly.
  2. [Section 6.2 and Eq. (17)] The prediction Eq. (17) also relies on the very straight-sheet condition r_c ≳ ℓ^2/s stated in Section 6.2. The paper correctly flags this as an assumption, but the consistency argument in Figure 5 and Eq. (17) implicitly assumes that the ESE-producing sheet population is dominated by sheets satisfying this condition. If most sheets instead have r_c ~ ℓ, the alignment probability and the maximum wave propagation length both change, and Appendix B shows that reproducing the ESE bending angles then requires either much larger density perturbations or much smaller volume filling fractions, breaking the CR-ESE match. The manuscript should quantify the fraction of sheets with r_c ≳ ℓ^2/s that is needed for Eq. (17), or state explicitly that the prediction applies only to that subpopulation of sheets.
  3. [Section 6.1 and abstract] The abstract states the assumption that the sheet statistics are similar throughout the Galactic volume, but Section 6.1 concedes that CRs spend much of their residence time in the inner CGM while ESEs are observed predominantly through the inner ~1 kpc of the warm ionized medium. The density contrast and field-reversal statistics are expected to differ between these phases, so the extrapolation from the local W_src to a global λ_CR in Eq. (17) carries an unquantified multiplicative uncertainty. I would like to see either a quantitative estimate of the expected ratio of sheet statistics between the disk and CGM, or a rephrasing of the prediction as a mean free path local to the disk midplane, followed by a discussion of how the global value could be recovered.
minor comments (4)
  1. [Table 1] The table header contains a typo: 'obervationally' should be 'observationally'.
  2. [Section 5.3] The units for dispersion measure are written as 'pc/cm3' in several places (e.g., Eqs. 33-34 and the surrounding text); the correct unit is pc cm^-3.
  3. [Figure 3] The colorbar labels in Figure 3 are placeholders ('colors') with no units; the caption should state that the plotted quantities are in arbitrary normalized units.
  4. [Eq. (29)] The expression for Ω_focal mixes angular sizes and physical lengths without clear parentheses and has a stray gap after '0.01′'; please rewrite it so the dimensional factors are unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the ESE occurrence fraction and the GeV cosmic-ray mean free path are independent observables, and eq. (17) is an algebraic consequence of the model relations, not a fit.

full rationale

The derivation chain is self-contained. Eq. (3) defines the CR mean free path in the sheet model as λ_CR ~ ℓ/f_V; Eq. (16) gives the ESE occurrence fraction W_src ~ (L f_V s / ℓ^2) κ, with κ set by lensing geometry. Combining these two independently motivated relations eliminates ℓ and f_V and yields Eq. (17), λ_pred_CR as a function of the observed W_src, frequency, geometry, and Δn_e. The observed CR mean free path (Eq. 1) appears only as a comparison value, or as one of four constraints in the parameter inversion of Sec. 4.4, not as input to Eq. (17). No parameter is fitted to the quantity that is then called predicted. The load-bearing assumption that an order-unity fraction of strong current sheets are magnetic folds capable of CR scattering is explicitly stated in Sec. 3 and flagged for testing; it is a physical hypothesis, not a definitional reduction. Self-citations to Kempski et al. (2023) and Galishnikova et al. (2022) supply simulation motivation, while Eq. (3) is derived in the present paper and the radio-lensing side is anchored to external observations and prior work (Goldreich & Sridhar 2006; Fiedler et al. 1987). No equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central consistency check uses four fiducial astrophysical parameters (s, Δn_e, D_lens, L) plus a set of structural assumptions about sheet geometry and universality. These are motivated by observations but not fitted to the target relation, so the model is partially constrained rather than parameter-free in a strict sense.

free parameters (4)
  • s (sheet short axis) = ~1 AU (fiducial)
    Chosen from ESE duration and demagnification scales; the predicted CR mean free path scales as s^{-1} (eq. 17), so the consistency depends on this value.
  • Δn_e (electron density variation across sheet) = ~0.03 cm^-3 (fiducial)
    Set to the mean warm ISM electron density; the predicted λ_CR scales linearly with Δn_e, so adopting a different value changes the consistency check.
  • D_lens (distance to lens) = ~1 kpc (fiducial)
    Typical Galactic distance for ESEs; enters linearly in eq. 17.
  • L (path length through sheet-populated ISM) = ~1 kpc (fiducial)
    Assumed comparable to D_lens; enters linearly in eq. 17 and in the alignment probability.
assumptions (6)
  • domain assumption Pressure balance between thermal gas and magnetic field in current sheets, δρ/ρ ~ β_p^{-1} δB/B (eq. 2)
    Connects density sheets to magnetic reversals; requires β_p≳1 in the warm ISM.
  • ad hoc to paper At least an order-unity fraction of strong current sheets are magnetic folds that scatter CRs
    Invoked in Section 3; if false, CR scattering and ESE-producing sheets are not the same population.
  • ad hoc to paper Sheets are extremely straight, with curvature radius r_c ≳ ℓ^2/s
    Required for the large column density gradient and alignment probability; acknowledged in Section 6.2 as a demanding assumption.
  • domain assumption Sheet statistics inferred from ESEs are representative of the entire Galactic volume probed by CRs
    ESEs probe the inner ~1 kpc of the disk, while CRs scatter in a much larger volume including the inner CGM; discussed in Section 6.1.
  • domain assumption Random orientation of sheets over the path length L
    Used to derive the alignment probability W_lens ~ L f_V s/ℓ^2 in Section 4.2.1.
  • standard math Gaussian column density profile for the lens
    Used in Appendix A to derive caustics and convergence; order-unity constants are shape-dependent.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Unified Model of Cosmic Ray Propagation and Radio Extreme Scattering Events from Intermittent Interstellar Structures." pith.science (2026). https://pith.science/paper/F3FBV7BU

@misc{pith2026241203649,
  author       = {Pith},
  title        = {Pith review of: A Unified Model of Cosmic Ray Propagation and Radio Extreme Scattering Events from Intermittent Interstellar Structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F3FBV7BU}},
  note         = {Machine review of arXiv:2412.03649}
}
abstract

Intermittent magnetic structures are a plausible candidate for explaining cosmic-ray (CR) diffusion rates derived from observed CR energy spectra. Independently, studies of extreme scattering events (ESEs) of radio quasars and pulsar scintillation have hinted that very straight, large-aspect-ratio, magnetic current sheets may be responsible for the localized large scattering of radio waves. The required shortest axis of the typical structures producing ESEs is of the same scale ($\sim$AU) as the gyroradii of $\sim$GeV CRs. In this paper, we propose that the same magnetic/density sheets can produce large scattering of both CRs and radio waves. We demonstrate that the geometry and volume filling factor of the sheets derived from quasar ESEs can explain the observed mean free path of GeV CRs without introducing free parameters. The model places constraints on the sheet geometry, such as straightness and large aspect ratio, and assumes the statistics of the sheets are similar throughout the Galactic volume. We, therefore, discuss observational tests of the sheet model, which includes observations of echoes in pulsars and fast radio bursts, gravitationally lensed quasars, the distribution of ESE durations, and spatial correlations between ESE events and rotation-measure fluctuations. Such tests will be enabled by upcoming wide-field radio instruments, including Canadian Hydrogen Observatory and Radio-transient Detector (CHORD) and Deep Synoptic Array 2000 Antennas (DSA-2000).

Figures

Figures reproduced from arXiv: 2412.03649 by the authors.

Figure 1
Figure 1. A schematic lightcurve of a typical ESE. The two panels show examples of a source with an angular diameter of 1 mas and angular velocity 0.1 mas/day passing through overdense lenses with convergence values of 𝜅 = 5 and 𝜅 = 20 (equations 12 and 13), respectively. We calculate predicted rates of CR scattering and ESEs due to intermittent sheets in Section 4 and compute parameter val￾ues for which the two scattering mo… view at source ↗
Figure 2
Figure 2. Schematic of current/density sheets considered in this work. Left: overdense current sheet with density perturbation Δ𝑛𝑒 kept in pressure balance by a folded magnetic field. For layers of multiple current sheets, as often seen in simulations of large-amplitude MHD turbulence, there are both overdense and underdense sheets. Middle: significant radio wave scattering, i.e., an ESE, occurs when the sheet is aligned favo… view at source ↗
Figure 3
Figure 3. Slices of in-plane gradients of column density and inte￾grated magnetic pressure (arbitrary units) from a 10243 subsonically driven simulation of MHD turbulence with weak guide magnetic field (𝛿𝐵/𝐵0 ≈ 4) taken from Kempski et al. (2023). The most in￾tense density sheets, which produce strong radio-wave scattering, are also sheets of strongly varying magnetic-field strength, qualitatively consistent with the picture … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The lensing behavior of an aligned sheet. (a) When the source is close to the direction of the sheet, the observer can receive the light bent by the sheet, as well as unlensed light from the LOS, and hence observe magnification of the source. This regime is labelled “a…
Figure 5
Figure 5. Figure 5: Occurrence fraction of radio sources being lensed by aligned plasma sheets of thickness ∼1 AU calculated from (16) in three different frequency bands as a function of the ∼GeV CR mean free path. We assume that the long axis of the sheets ℓ and volume filling factor 𝑓𝑉 …
Figure 6
Figure 6. Figure 6: ESE behaviors for short-duration radio transients. Large bending angles of the lensed images induce significant time delays, enabling separation by arrival time. This allows the study of lensing structures by tracking the temporal and spectral evolution of individual i…
Figure 7
Figure 7. Figure 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: The duration of an ESE depends on the angle 𝜙 at which the source crosses the sheet. Left: the magnification of the source at different locations, projected on the lens plane (greyscale shading). The aligned sheet is located at 𝑥 = 0, with a DM change shown in the top …
Figure 9
Figure 9. Figure 9: Magnitude of the in-plane gradient of projected column density (arbitrary units) in two high-resolution (22403 ) MHD dynamo simulations from Galishnikova et al. 2022. Blue denotes regions where the local column density 𝑁𝑒 is less than the mean column density 𝑁𝑒0, while…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 2 citations worldwide. Full citation record

  1. Cosmic ray and plasma coupling for isothermal supersonic turbulence in the magnetized interstellar medium

    astro-ph.GA 2025-06 conditional novelty 6.0 of 10

    A two-moment cosmic ray MHD simulation suite shows that cosmic rays couple to isothermal supersonic turbulence only when both diffusion and streaming are slow relative to turbulent transport, imprints a mixed Pc ∝ ρ^(...

Reference graph

Works this paper leans on

76 extracted references · 7 canonical work pages · cited by 1 Pith paper

  1. [1]

    C., Bazilevskaya, G

    Adriani, O., Barbarino, G. C., Bazilevskaya, G. A., et al. 2013, ApJ, 765, 91, doi: 10.1088/0004-637X/765/2/91

    doi:10.1088/0004-637x/765/2/91 2013

  2. [2]

    2015, PhRvL, 114, 171103, doi: 10.1103/PhysRevLett.114.171103

    Aguilar, M., Aisa, D., Alpat, B., et al. 2015, PhRvL, 114, 171103, doi: 10.1103/PhysRevLett.114.171103

    doi:10.1103/physrevlett.114.171103 2015

  3. [3]

    2016, PhRvL, 117, 231102, doi: 10.1103/PhysRevLett.117.231102

    Aguilar, M., Ali Cavasonza, L., Ambrosi, G., et al. 2016, PhRvL, 117, 231102, doi: 10.1103/PhysRevLett.117.231102

    doi:10.1103/physrevlett.117.231102 2016

  4. [4]

    2018, Advances in Space Research, 62, 2731, doi: 10.1016/j.asr.2017.04.019

    Amato, E., & Blasi, P. 2018, Advances in Space Research, 62, 2731, doi: 10.1016/j.asr.2017.04.019

    doi:10.1016/j.asr.2017.04.019 2018

  5. [5]

    W., Stevens, J., Tuntsov, A

    Bannister, K. W., Stevens, J., Tuntsov, A. V., et al. 2016, Science, 351, 354, doi: 10.1126/science.aac7673

    doi:10.1126/science.aac7673 2016

  6. [6]

    Boldyrev, S., & Loureiro, N. F. 2017, ApJ, 844, 125, doi: 10.3847/1538-4357/aa7d02

    doi:10.3847/1538-4357/aa7d02 2017

  7. [7]

    Braginskii, S. I. 1965, Rev. Plasma Phys., 1, 205

    1965

  8. [8]

    F., Macquart, J

    Brisken, W. F., Macquart, J. P., Gao, J. J., et al. 2010, ApJ, 708, 232, doi: 10.1088/0004-637X/708/1/232 20 Kempski, Li et al

    doi:10.1088/0004-637x/708/1/232 2010

Show all 76 references
  1. [9]

    S., Hopkins, P

    Butsky, I. S., Hopkins, P. F., Kempski, P., et al. 2024, MNRAS, 528, 4245, doi: 10.1093/mnras/stae276

    2024 doi

  2. [10]

    S., & Quinn, T

    Butsky, I. S., & Quinn, T. R. 2018, ApJ, 868, 108, doi: 10.3847/1538-4357/aaeac2

    2018 doi

  3. [11]

    Chandran, B. D. G. 2000, Phys. Rev. Lett., 85, 4656, doi: 10.1103/PhysRevLett.85.4656 Cimò, G., Beckert, T., Krichbaum, T. P., et al. 2002, PASA, 19, 10, doi: 10.1071/AS01097

    2000 doi

  4. [12]

    W., Fey, A

    Clegg, A. W., Fey, A. L., & Fiedler, R. L. 1996, ApJL, 457, L23, doi: 10.1086/309884

    1996 doi

  5. [13]

    W., Fey, A

    Clegg, A. W., Fey, A. L., & Lazio, T. J. W. 1998, ApJ, 496, 253, doi: 10.1086/305344

    1998 doi

  6. [14]

    1993, Nature, 366, 320, doi: 10.1038/366320a0

    Cognard, I., Bourgois, G., Lestrade, J.-F., et al. 1993, Nature, 366, 320, doi: 10.1038/366320a0

    1993 doi

  7. [15]

    A., Kerr, M., Shannon, R

    Coles, W. A., Kerr, M., Shannon, R. M., et al. 2015, ApJ, 808, 113, doi: 10.1088/0004-637X/808/2/113

    2015 doi

  8. [16]

    M., Rickett, B

    Cordes, J. M., Rickett, B. J., Stinebring, D. R., & Coles, W. A. 2006, ApJ, 637, 346, doi: 10.1086/498332

    2006 doi

  9. [17]

    2006, Proceedings of the National Academy of Science, 103, 12269, doi: 10.1073/pnas.0602117103 De La Torre Luque, P., Mazziotta, M

    Dalgarno, A. 2006, Proceedings of the National Academy of Science, 103, 12269, doi: 10.1073/pnas.0602117103 De La Torre Luque, P., Mazziotta, M. N., Loparco, F., Gargano, F., & Serini, D. 2021, JCAP, 2021, 099, doi: 10.1088/1475-7516/2021/03/099

    2006 doi

  10. [18]

    2020, PhRvD, 101, 023013, doi: 10.1103/PhysRevD.101.023013

    Evoli, C., Morlino, G., Blasi, P., & Aloisio, R. 2020, PhRvD, 101, 023013, doi: 10.1103/PhysRevD.101.023013

    2020 doi

  11. [19]

    Simon, R. S. 1994, ApJ, 430, 581, doi: 10.1086/174432

    1994 doi

  12. [20]

    L., Dennison, B., Johnston, K

    Fiedler, R. L., Dennison, B., Johnston, K. J., & Hewish, A. 1987, Nature, 326, 675, doi: 10.1038/326675a0

    1987 doi

  13. [21]

    B., Ripperda, B., & Philippov, A

    Fielding, D. B., Ripperda, B., & Philippov, A. A. 2023, ApJL, 949, L5, doi: 10.3847/2041-8213/accf1f

    2023 doi

  14. [22]

    K., Kunz, M

    Galishnikova, A. K., Kunz, M. W., & Schekochihin, A. A. 2022, Physical Review X, 12, 041027, doi: 10.1103/PhysRevX.12.041027

    2022 doi

  15. [23]

    2006, ApJL, 640, L159, doi: 10.1086/503668

    Goldreich, P., & Sridhar, S. 2006, ApJL, 640, L159, doi: 10.1086/503668

    2006 doi

  16. [24]

    Guo, F., & Oh, S. P. 2008, MNRAS, 384, 251, doi: 10.1111/j.1365-2966.2007.12692.x

    2008

  17. [25]

    2015, in Astrophysics and Space Science Library, Vol

    Haverkorn, M. 2015, in Astrophysics and Space Science Library, Vol. 407, Magnetic Fields in Diffuse Media, ed. A. Lazarian, E. M. de Gouveia Dal Pino, & C. Melioli, 483, doi: 10.1007/978-3-662-44625-6_17

    2015 doi

  18. [26]

    F., Chan, T

    Hopkins, P. F., Chan, T. K., Ji, S., et al. 2021, MNRAS, 501, 3640, doi: 10.1093/mnras/staa3690

    2021 doi

  19. [27]

    F., Squire, J., Butsky, I

    Hopkins, P. F., Squire, J., Butsky, I. S., & Ji, S. 2022, MNRAS, 517, 5413, doi: 10.1093/mnras/stac2909

    2022 doi

  20. [28]

    S., Betti, S., et al

    Hutschenreuter, S., Anderson, C. S., Betti, S., et al. 2022, A&A, 657, A43, doi: 10.1051/0004-6361/202140486

    2022 doi

  21. [29]

    Ipavich, F. M. 1975, ApJ, 196, 107, doi: 10.1086/153397

    1975 doi

  22. [30]

    2017a, MNRAS, 467, 1449, doi: 10.1093/mnras/stx131 —

    Jacob, S., & Pfrommer, C. 2017a, MNRAS, 467, 1449, doi: 10.1093/mnras/stx131 —. 2017b, MNRAS, 467, 1478, doi: 10.1093/mnras/stx132

    doi

  23. [31]

    L., Pen, U.-L., & Baker, D

    Jow, D. L., Pen, U.-L., & Baker, D. 2024, MNRAS, 528, 6292, doi: 10.1093/mnras/stae300

    2024 doi

  24. [32]

    B., Quataert, E., et al

    Kempski, P., Fielding, D. B., Quataert, E., et al. 2023, MNRAS, 525, 4985, doi: 10.1093/mnras/stad2609

    2023 doi

  25. [33]

    2022, MNRAS, 514, 657, doi: 10.1093/mnras/stac1240

    Kempski, P., & Quataert, E. 2022, MNRAS, 514, 657, doi: 10.1093/mnras/stac1240

    2022 doi

  26. [34]

    A., Ward, C

    Kerr, M., Coles, W. A., Ward, C. A., et al. 2018, MNRAS, 474, 4637, doi: 10.1093/mnras/stx3101

    2018 doi

  27. [35]

    A., Pushkarev, A

    Koryukova, T. A., Pushkarev, A. B., Kiehlmann, S., & Readhead, A.C.S.2023,MNRAS,526,5932,doi:10.1093/mnras/stad3052

    2023 doi

  28. [36]

    R., Federrath, C., Krumholz, M

    Kriel, N., Beattie, J. R., Federrath, C., Krumholz, M. R., & Hew, J. K. J. 2023, arXiv e-prints, arXiv:2310.17036, doi: 10.48550/arXiv.2310.17036

    2023 doi arXiv

  29. [37]

    Kulsrud, R., & Pearce, W. P. 1969, ApJ, 156, 445, doi: 10.1086/149981

    1969 doi

  30. [38]

    2021, ApJ, 923, 53, doi: 10.3847/1538-4357/ac2de9

    Lazarian, A., & Xu, S. 2021, ApJ, 923, 53, doi: 10.3847/1538-4357/ac2de9

    2021 doi

  31. [39]

    Lazio, T. J. W., Gaume, R. A., Claussen, M. J., et al. 2001, ApJ, 546, 267, doi: 10.1086/318262 Lazio,T.J.W.,Fey,A.L.,Dennison,B.,etal.2000,ApJ,534,706, doi: 10.1086/308779

    2001 doi

  32. [40]

    2023, Journal of Plasma Physics, 89, 175890501, doi: 10.1017/S0022377823000946

    Lemoine, M. 2023, Journal of Plasma Physics, 89, 175890501, doi: 10.1017/S0022377823000946

    2023 doi

  33. [41]

    F., Rickett, B

    Lestrade, J. F., Rickett, B. J., & Cognard, I. 1998, A&A, 334, 1068

    1998

  34. [42]

    F., & Cognard, I

    Maitia, V., Lestrade, J. F., & Cognard, I. 2003, ApJ, 582, 972, doi: 10.1086/344816

    2003 doi

  35. [43]

    W., & Squire, J

    Majeski, S., Kunz, M. W., & Squire, J. 2024, arXiv e-prints, arXiv:2405.02418, doi: 10.48550/arXiv.2405.02418

    2024 doi arXiv

  36. [44]

    A., & Chandran, B

    Mallet, A., Schekochihin, A. A., & Chandran, B. D. G. 2017, Journal of Plasma Physics, 83, 905830609, doi: 10.1017/S0022377817000812

    2017 doi

  37. [45]

    2012, MNRAS, 421, L132, doi: 10.1111/j.1745-3933.2012.01223.x

    Pen, U.-L., & King, L. 2012, MNRAS, 421, L132, doi: 10.1111/j.1745-3933.2012.01223.x

    2012

  38. [46]

    2014, MNRAS, 442, 3338, doi: 10.1093/mnras/stu1020

    Pen, U.-L., & Levin, Y. 2014, MNRAS, 442, 3338, doi: 10.1093/mnras/stu1020

    2014 doi

  39. [47]

    B., Kovalev, Y

    Pushkarev, A. B., Kovalev, Y. Y., Lister, M. L., et al. 2013, A&A, 555, A80, doi: 10.1051/0004-6361/201321484

    2013 doi

  40. [48]

    Quataert, E., Jiang, F., & Thompson, T. A. 2022a, MNRAS, 510, 920, doi: 10.1093/mnras/stab3274

    doi

  41. [49]

    A., & Jiang, Y.-F

    Quataert, E., Thompson, T. A., & Jiang, Y.-F. 2022b, MNRAS, 510, 1184, doi: 10.1093/mnras/stab3273

    doi

  42. [50]

    2019, Journal of Plasma Physics, 85, 205850401, doi: 10.1017/S0022377819000539

    Rincon, F. 2019, Journal of Plasma Physics, 85, 205850401, doi: 10.1017/S0022377819000539

    2019 doi

  43. [51]

    W., Blandford, R

    Romani, R. W., Blandford, R. D., & Cordes, J. M. 1987, Nature, 328, 324, doi: 10.1038/328324a0

    1987 doi

  44. [52]

    Ruszkowski, M., Yang, H. Y. K., & Zweibel, E. 2017, ApJ, 834, 208, doi: 10.3847/1538-4357/834/2/208 CR scattering and ESEs 21

    2017 doi

  45. [53]

    Schekochihin, A. A. 2022, Journal of Plasma Physics, 88, 155880501, doi: 10.1017/S0022377822000721

    2022 doi

  46. [54]

    McWilliams, J. C. 2004, ApJ, 612, 276, doi: 10.1086/422547

    2004 doi

  47. [55]

    E., Ellingsen, S

    Senkbeil, C. E., Ellingsen, S. P., Lovell, J. E. J., et al. 2008, ApJL, 672, L95, doi: 10.1086/527300

    2008 doi

  48. [56]

    2018, MNRAS, 478, 983, doi: 10.1093/mnras/sty1140

    Simard, D., & Pen, U.-L. 2018, MNRAS, 478, 983, doi: 10.1093/mnras/sty1140

    2018 doi

  49. [57]

    1971, ApJ, 170, 265, doi: 10.1086/151210

    Skilling, J. 1971, ApJ, 170, 265, doi: 10.1086/151210

    1971 doi

  50. [58]

    P., Auger, M

    Spingola, C., McKean, J. P., Auger, M. W., et al. 2018, MNRAS, 478, 4816, doi: 10.1093/mnras/sty1326

    2018 doi

  51. [59]

    W., Arzamasskiy, L., et al

    Squire, J., Kunz, M. W., Arzamasskiy, L., et al. 2023, JPP, 89, 905890417, doi: 10.1017/S0022377823000727

    2023 doi

  52. [60]

    A., Quataert, E., & Kunz, M

    Squire, J., Schekochihin, A. A., Quataert, E., & Kunz, M. W. 2019, Journal of Plasma Physics, 85, 905850114, doi: 10.1017/S0022377819000114 Stanimirović, S., & Zweibel, E. G. 2018, ARA&A, 56, 489, doi: 10.1146/annurev-astro-081817-051810

    2019 doi

  53. [61]

    R., McLaughlin, M

    Stinebring, D. R., McLaughlin, M. A., Cordes, J. M., et al. 2001, ApJL, 549, L97, doi: 10.1086/319133

    2001 doi

  54. [62]

    C., Cummings, A

    Stone, E. C., Cummings, A. C., McDonald, F. B., et al. 2013, Science, 341, 150, doi: 10.1126/science.1236408

    2013 doi

  55. [63]

    2022, arXiv e-prints, arXiv:2203.12029, doi: 10.48550/arXiv.2203.12029

    Thomas, T., Pfrommer, C., & Pakmor, R. 2022, arXiv e-prints, arXiv:2203.12029, doi: 10.48550/arXiv.2203.12029

    2022 doi arXiv

  56. [64]

    Vedantham, H. K. 2018, arXiv e-prints, arXiv:1810.07009, doi: 10.48550/arXiv.1810.07009

    2018 doi arXiv

  57. [65]

    K., & Phinney, E

    Vedantham, H. K., & Phinney, E. S. 2019, MNRAS, 483, 971, doi: 10.1093/mnras/sty2948

    2019 doi

  58. [66]

    J., Thrane, E., & Smith, R

    Walker, K., Reardon, D. J., Thrane, E., & Smith, R. 2022, ApJ, 933, 16, doi: 10.3847/1538-4357/ac69c6

    2022 doi

  59. [67]

    A., Melrose, D

    Walker, M. A., Melrose, D. B., Stinebring, D. R., & Zhang, C. M. 2004,MNRAS,354,43,doi:10.1111/j.1365-2966.2004.08159.x

    2004

  60. [68]

    Wiener, J., Pfrommer, C., & Oh, S. P. 2017, MNRAS, 467, 906, doi: 10.1093/mnras/stx127

    2017 doi

  61. [69]

    2021, ApJ, 922, 264, doi: 10.3847/1538-4357/ac2d8f

    Xu, S. 2021, ApJ, 922, 264, doi: 10.3847/1538-4357/ac2d8f

    2021 doi

  62. [70]

    2004, ApJ, 614, 757, doi: 10.1086/423733 —

    Yan, H., & Lazarian, A. 2004, ApJ, 614, 757, doi: 10.1086/423733 —. 2008, ApJ, 673, 942, doi: 10.1086/524771

    2004 doi

  63. [71]

    H., & Lazarian, A

    Yuen, K. H., & Lazarian, A. 2020, ApJ, 898, 66, doi: 10.3847/1538-4357/ab9360

    2020 doi

  64. [72]

    2023, ApJL, 959, L8, doi: 10.3847/2041-8213/ad0fe5

    Zhang, C., & Xu, S. 2023, ApJL, 959, L8, doi: 10.3847/2041-8213/ad0fe5

    2023 doi

  65. [73]

    A., Perez, J

    Zhdankin, V., Uzdensky, D. A., Perez, J. C., & Boldyrev, S. 2013, ApJ, 771, 124, doi: 10.1088/0004-637X/771/2/124

    2013 doi

  66. [74]

    R., & van Kerkwijk, M

    Zhu, H., Baker, D., Pen, U.-L., Stinebring, D. R., & van Kerkwijk, M. H. 2023, ApJ, 950, 109, doi: 10.3847/1538-4357/accde0

    2023 doi

  67. [75]

    Zweibel, E. G. 2013, Physics of Plasmas, 20, 055501, doi: 10.1063/1.4807033

    2013 doi

  68. [76]

    Zweibel, E. G. 2017, Physics of Plasmas, 24, 055402, doi: 10.1063/1.4984017

    2017 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.