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Energy-Dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Cosmic-ray spectrum steepening is set by a two-zone interstellar medium, not a tuned diffusion coefficient.

desk verdict Spectrally resolved self-confinement CR transport in TIGRESS: genuinely new two-zone model, but the load-bearing local-balance scattering assumption is adopted, not validated; deserves serious peer review. read the letter →

arxiv 2507.00120 v1 pith:WT5H6NZA submitted 2025-06-30 astro-ph.HE astro-ph.GA

Lucia Armillotta , Eve C. Ostriker , Nora B. Linzer This is my paper
classification astro-ph.HEastro-ph.GA
keywords cosmicraysinterstellarmediumcosmic-raytransportself-confinementAlfvénwavedampingspectrumgrammagemagnetohydrodynamicsimulations
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

This paper tries to show that the observed energy-dependent confinement of 1-100 GeV cosmic-ray protons in the Galaxy needs no tuned diffusion coefficient: it follows from self-confinement physics operating in a realistic multiphase, dynamic interstellar medium. Using a magnetohydrodynamic simulation of a solar-neighborhood disk patch with a physically motivated, space- and momentum-dependent scattering coefficient, the authors find that cosmic-ray protons are trapped in the mostly neutral midplane, where diffusion is fast and the pressure profile is flat, while escape is throttled by the surrounding ionized extraplanar gas, where scattering is strong. The combination yields an ambient spectrum $f(p)\propto p^{-\gamma}$ with $\gamma\approx 4.6$, steepened from the injected $\gamma_{\rm inj}=4.3$, in agreement with direct detections. A two-zone analytic model reproduces the simulated pressure profiles and predicts $\gamma=(4/3)\gamma_{\rm inj}-1$ and grammage $X\propto p^{1-\gamma_{\rm inj}/3}$ at high momentum. If right, the paper resolves a long-standing tension by showing that the multiphase geometry itself, rather than a calibrated coefficient, sets the cosmic-ray spectrum and escape rate.

What carries the argument

The central object is a space- and momentum-dependent scattering coefficient $\sigma_\parallel$ computed from the local balance between streaming-driven Alfvén-wave growth and two damping channels: nonlinear Landau damping in ionized gas and ion-neutral damping in neutral gas. This coefficient makes diffusion fast where gas is neutral and slow where gas is ionized, producing the two-zone structure. The analytic engine is a one-dimensional steady-state two-zone model: zone 0 has flat cosmic-ray pressure and source injection, while zone 1 has no sources, exponential pressure decline, and both flow acceleration and diffusion. The model yields closed-form expressions for the cosmic-ray scale height $H_c$, the effective escape velocity $v_{\rm c,eff}$, and the effective diffusion coefficient $\kappa_{\rm eff}$, from which the spectral-slope relation $\gamma=(4/3)\gamma_{\rm inj}-1$ and the grammage scaling $X\propto p^{1-\gamma_{\rm inj}/3}$ follow.

What would settle it

Measure the momentum dependence of the grammage $X$ over roughly 10-100 GeV/c from precise secondary-to-primary ratios such as B/C: the model predicts $X\propto p^{-0.43}$ at high momentum, so a clearly flatter or steeper observed scaling would refute the relation. A numerical falsifier is to repeat the simulation with a significant extrinsic-turbulence scattering term added, in which case the predicted $\gamma=(4/3)\gamma_{\rm inj}-1$ should fail if self-confinement is the operative mechanism.

Watch

Extended reading notes

Core claim

The central discovery is that cosmic-ray transport in the galactic disk is controlled by two spatially separated regimes, and their coupling fixes the energy dependence of the observed spectrum. In the volume-filling, mostly neutral midplane gas, ion-neutral damping makes Alfvén-wave scattering weak and diffusion fast, so cosmic-ray pressure is nearly constant; this is zone 0. In the low-density, highly ionized extraplanar gas, nonlinear Landau damping leaves scattering efficient, and cosmic-ray pressure falls exponentially with height; this is zone 1. The escape flux is set by the effective velocity $v_{\rm c,eff}\approx (1/2)[\kappa_\parallel d(v+v_{A,i})/dz]^{1/2}$ in the diffusion-dominated limit, which carries the momentum dependence. Matching fluxes at the transition yields the steepening relation $\gamma=(4/3)\gamma_{\rm inj}-1$ and the grammage scaling $X\propto p^{1-\gamma_{\rm inj}/3}$, both matching the simulations and, for the spectrum, observations. The paper argues this resolves the apparent failure of the self-confinement scenario reported by earlier one-zone treatments.

Load-bearing premise

Everything rests on the assumption that at 1-100 GeV, cosmic-ray scattering is dominated by self-excited Alfvén waves whose growth and damping are in instantaneous local balance; if externally driven turbulence or non-local wave transport matters significantly, the momentum dependence of the diffusion coefficient changes and the predicted steepening $\gamma=(4/3)\gamma_{\rm inj}-1$ and grammage scaling $X\propto p^{1-\gamma_{\rm inj}/3}$ would no longer follow.

Editorial extensions

If this is right

  • The ambient 1-100 GeV proton spectrum in the solar neighborhood is predicted to have slope $\gamma\approx 4.6$, matching direct detections, with normalization tracking the recent star formation rate surface density.
  • At high momentum the spectral slope approaches $\gamma=(4/3)\gamma_{\rm inj}-1$ and the grammage scales as $X\propto p^{1-\gamma_{\rm inj}/3}$, giving testable predictions for secondary-to-primary cosmic-ray ratios.
  • Cosmic-ray pressure is nearly uniform in the neutral midplane and decreases exponentially above it, so the midplane pressure is set by the escape speed through the ionized extraplanar gas, $P_0\approx F_{\rm in}/(4v_{\rm c,eff})$.
  • The effective cosmic-ray transport speed at high momentum scales as $v_{\rm c,eff}\propto p^{(\gamma-3)/4}\approx p^{0.43}$, which, when compared with phenomenological models through $\kappa_{\rm eff}/H_c=4v_{\rm c,eff}$, matches the empirically inferred energy dependence of transport.
  • The two-zone picture implies that the multiphase, dynamic structure of the interstellar medium, not just the local scattering rate, is necessary to reproduce observed cosmic-ray spectra; fully self-consistent simulations that resolve the hot gas should preserve the spectral slope while possibly increasing extraplanar scale heights.

Reading between the lines

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

  • An extension the authors leave implicit is that the same two-zone logic should apply to other star-forming disk galaxies, so the steepening $\Delta\gamma\approx(\gamma_{\rm inj}-3)/3$ should be near-universal wherever a neutral midplane is sandwiched by ionized extraplanar gas, while fully ionized or violently dynamic disks may show less steepening.
  • The contrast with one-zone self-confinement treatments suggests that the so-called solution-collapse problem seen in some simulations may be an artifact of not resolving the neutral midplane and ionized halo as separate zones; a testable extension is to vary numerical resolution of the hot ionized phase in the same physical setup and check whether $\gamma\approx 4.6$ persists.
  • Because the scattering coefficient depends on local ionization structure, the prediction could be sharpened by closing the feedback loop in which cosmic-ray ionization changes the damping rate and hence the grammage and spectral slope, a coupling the present post-processing treatment does not self-consistently include.
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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

4 major / 6 minor

Summary. This paper presents spectrally resolved (1-100 GeV) cosmic-ray proton transport in a TIGRESS MHD simulation of the solar-neighborhood ISM, using a two-moment CR fluid with a scattering coefficient determined by local balance between streaming instability growth and nonlinear Landau/ion-neutral damping. The authors report a midplane ambient spectrum f(p) ∝ p^{-γ} with γ ≈ 4.6, steepened from injection γ_inj = 4.3, and find CR pressure nearly uniform within a neutral midplane and exponential in the ionized extraplanar region. They construct a two-zone 1D steady-state model whose parameters (κ_parallel, V, H_a) are measured from the simulation and whose transition height z_t is fit to the simulated profiles. The model yields asymptotic relations γ = (4/3)γ_inj − 1 and grammage X ∝ p^{1−γ_inj/3}; these are compared to the simulation and to observational constraints. The paper concludes that self-confinement in a multiphase, dynamic ISM can explain the observed steepening without a tuned diffusion coefficient.

Significance. If correct, this is a significant step: it provides a physically motivated, energy-dependent CR transport model and analytic scalings that link injection slope to observed slope and grammage, and it offers a resolution of the apparent failure of self-confinement found in one-zone models and in Hopkins et al. (2022b). The paper is unusually transparent: it states the independent-bin approximation, reports measured rather than prescribed model inputs, and includes appendices deriving the more accurate coupled-bin equations. The main limitation is that the central claim rests on the assumed local-balance self-confinement scattering prescription and on model-simulation agreement that is partly by construction; thus the contribution is better described as a demonstration of internal consistency within that framework than as a fully independent validation. With additional sensitivity tests and clarification, it would be a valuable advance.

major comments (4)
  1. [§2.1, Eqs. (5)-(6) and Eq. (10)] The scattering coefficient assumes local instantaneous balance between streaming-driven Alfvén-wave growth and damping, with self-excited waves assumed to dominate over extrinsic turbulence at 1-100 GeV. This assumption sets the momentum dependence of κ_parallel, which propagates through Eq. (20) into the headline predictions γ = (4/3)γ_inj − 1 and X ∝ p^{1−γ_inj/3}. Section 5.2 addresses the discrepancy with Hopkins et al. (2022b) through a resolution/two-zone argument, but it does not demonstrate that local balance holds in the TIGRESS gas or quantify the extrinsic-turbulence contribution. Please add a sensitivity test, such as an additional scattering floor representing extrinsic turbulence, or an estimate of the extrinsic scattering rate from the simulated fluctuating fields, and show how the predicted scalings change. Without this, the central claim is conditional on this premise.
  2. [§4.2 and Figures 4-5] The analytic model uses κ_parallel, V, and H_a measured from the same simulation, and the transition height z_t is fit to the simulated pressure profiles. The excellent agreement in Figures 4-5 is therefore partly a consistency check rather than a blind prediction. The asymptotic relations in Eqs. (25) and (27) remain informative, but the paper should state explicitly that this comparison is a calibration check and, ideally, validate the model on independent TIGRESS snapshots or with parameters varied beyond the quoted ranges. This is load-bearing because the claimed agreement between the two-zone model and the simulations is a central piece of evidence for the physical picture.
  3. [§2.2 and Appendix A.1] The stated spectral bin width 'dlnp = 0.1' is inconsistent with five bins spanning p = 2-101 GeV/c; the implied log-spacing between the listed momenta is Δlnp ≈ 0.98, not 0.1. Since Equation A2 uses dlnp in computing n1, and Equations 8-9 use the bin edges, this discrepancy changes the normalization of the scattering coefficient and of the injected energy fractions. Please correct the text or clarify the binning. If dlnp = 0.1 is actually used in the code, the five bins would not cover the 1-100 GeV range and the simulations could not be reproduced as described.
  4. [§2.1 and Appendix B] The paper states that treating each CR energy bin independently is approximate and that the coupled-bin scheme currently under development would change some quantitative results but leave the overall conclusions unaffected. This assertion is supported only by an analytic 1D estimate in Appendix B, not by a numerical test with the coupled equations. Please either perform a test of the coupled scheme for at least one snapshot or explicitly downgrade this statement to an expectation, since the independent-bin approximation is part of the method used to produce the simulated spectra.
minor comments (6)
  1. [Title] The title contains an apparent LaTeX spacing artifact, 'T ransport'; it should read 'Transport'.
  2. [§4.2] There is a typo in the fit expression: '3 Gev/c' should be '3 GeV/c'.
  3. [§4.2] The phrase 'because the later do not include SN feedback' should read 'because the latter do not include SN feedback'.
  4. [References] Linzer et al. 2025 is cited as 'accepted' in Section 6 but is not included in the reference list; please add the full citation.
  5. [Eq. (10) and surrounding text] The text attributes the NLL scaling κ_parallel ∝ p^{(γ−3)/2} to the n1 dependence, but the linear n1 dependence in Eq. (5) would naively give κ_parallel ∝ p^{γ−3}; please explain the origin of the factor 1/2, since this scaling is used in Eqs. (25) and (27).
  6. [Figure 5 caption] The green lines are said to be computed using 'Equation 27 of Paper I', but Paper I is not a listed reference in this form; please provide the full citation or equation number.

Circularity Check

1 steps flagged · score 2.0 of 10

No major circularity: the spectral-slope and grammage scalings are derived from the model equations rather than injected from the simulations; only the 1D profile comparison is partly calibrated to the same simulation data.

  1. fitted input called prediction [Section 4.2, 'Comparison to the simulation', around Equations 15, 20, 24 and Figures 4-5]
    "Based on our measured κ∥, V , and dzV values in each energy bin, we compute Hc from Equation 20 and P0 from Equation 24. The transition point zt represents the mean height at which gas transitions from neutral to ionized. As the ISM is highly inhomogeneous and time-variable, this occurs over a range of values. We therefore simply fit Equation 15 to the simulated CR pressure profiles to obtain zt, with a range 500 − 800 pc."

    The model profiles presented as 'predictions' in the right panel of Figure 4 and Figure 5 are constructed using κ∥, V, and dzV measured from the same TIGRESS simulation, and the transition height zt is obtained by directly fitting the assumed piecewise form (Equation 15) to the simulated pressure profiles that are then compared. The profile agreement is therefore partly a consistency check rather than an independent prediction. The paper's central asymptotic claims, however, are not affected: the spectral-slope relation γ = (4/3)γinj − 1 (Equation 25) and the grammage scaling X ∝ p^{1−γinj/3} (Equation 27) are derived algebraically from the transport equations before these calibrated inputs are used, so the circularity is confined to the profile-level comparison.

full rationale

I walked the derivation chain from the injection flux Fin ∝ p^{4−γinj}, through the self-confinement scattering coefficient giving κ∥ ∝ p^{(γ−3)/2} (Equation 10), through the two-zone solution for vc,eff (Equations 20-23), to P0 = Fin/(4vc,eff) (Equation 24). Equating the resulting P0 ∝ p^{4−γinj−(γ−3)/4} with the definition P0 ∝ p^{4−γ} yields the implicit equation γ = γinj + (γ−3)/4, whose solution is γ = (4/3)γinj − 1. This is a self-consistent fixed-point calculation, not an input-output identity, and therefore is not circular. The grammage scaling follows the same derived chain via X ∝ 1/vc,eff. The simulation's γ ≈ 4.6 is also not forced by the observed slope: although Appendix A.1 sets γ = 4.7 in evaluating n1, the expression n1 = ec/(E(γ−2)dlnp) contains γ only as a constant normalization factor, so the momentum dependence of κ∥ is set by the evolved ec (i.e., by the simulated spectrum), not by the assumed 4.7. The self-citations (Papers I-III) are for implementation details of the transport scheme and are not load-bearing for the new spectral predictions. The local-balance streaming-damping assumption in Equations 5-6 is a physical premise that is contested by Hopkins et al. (2022b), but an unvalidated premise is a correctness risk, not circularity. The only mild circularity is the 1D model's profile comparison, which uses simulation-measured κ∥, V, dzV and a fitted zt to reproduce the same profiles; this is an interpretive consistency check and does not undercut the independently derived asymptotic scalings. Overall score 2.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the self-confinement domain assumption, the two-moment closure, and the representativeness of the TIGRESS simulation, plus several ad hoc modeling choices (independent bins, momentum-independent V, constant kappa_parallel in zone 1, and the piecewise pressure Ansatz). The free parameters are mostly measured from the same simulation rather than predicted, which is the main source of circularity burden. No new physical entities are introduced.

free parameters (7)
  • injected spectral slope gamma_inj = 4.3
    Assumed source spectrum from SN remnant acceleration theory (Caprioli 2023); the predicted ambient slope gamma = (4/3)gamma_inj - 1 and the grammage scaling derive directly from this value.
  • parallel diffusion coefficient kappa_parallel(p) = 7.2x10^27 [p/(3 GeV/c)]^0.9 cm^2/s
    Measured from the simulation at the neutral-to-ionized transition (T about 10^4-5x10^4 K) and used as input to compute H_c, P_0, and v_c,eff in the 1D model (Section 4.2).
  • MHD vertical velocity V = 10-15 km/s
    CR pressure-weighted mean of advection plus streaming velocity, measured at the transition temperature and used in Equations 20-24.
  • gas acceleration scale H_a (or dzV) = 0.4-1 kpc (dzV = 15-27 km/s/kpc)
    Derived from a linear fit of the mean vertical MHD velocity profile; controls the advective steepening in the extraplanar region.
  • transition height z_t = 500-800 pc
    Fit of the two-zone pressure profile (Equation 15) to the simulated pressure profiles; sets the boundary between the flat midplane and the exponential halo.
  • perpendicular-to-parallel scattering ratio sigma_perp/sigma_parallel = 10
    Assumed constant from Paper I (Section 4.3); affects perpendicular transport but is not central to the vertical profiles.
  • reduced speed of light v_m = 10^4 km/s
    Numerical parameter in the two-moment solver (Section 2.1) to relax the CFL constraint; it is much larger than physical velocities in the simulation.
assumptions (7)
  • domain assumption CR scattering at 1-100 GeV is dominated by self-excited Alfven waves with local instantaneous balance between streaming instability growth and NLL/IN damping.
    Section 2.1, Equations 5-6; the spatial and momentum dependence of kappa_parallel, and therefore the predicted steepening and grammage scaling, rest on this assumption.
  • domain assumption The two-moment CR fluid equations with isotropic pressure and a reduced speed of light accurately capture transport in the simulated ISM.
    Section 2.1, Equations 1-2; this is the Jiang & Oh (2018) closure adopted from Paper I.
  • domain assumption The TIGRESS solar-neighborhood simulation plus post-processing steady-state represents the relevant ISM environment.
    Section 2.2; the MHD relaxation runs are short and do not include self-gravity or SN/CR feedback self-consistently.
  • ad hoc to paper Each CR energy bin evolves independently and spectral coupling between bins is neglected.
    Section 2.1 and Appendix B; the authors argue corrections are a few tens of percent and mainly affect normalization.
  • ad hoc to paper In zone 1, kappa_parallel is independent of z and V is independent of momentum.
    Section 4.1, before Equation 18; these simplifications are needed to obtain the closed-form H_c solution (Equation 20).
  • ad hoc to paper The CR pressure profile is flat in the midplane and exponential in the extraplanar region (Equation 15).
    Section 4.1; this is adopted as an Ansatz motivated by the simulation profiles.
  • domain assumption The scattering coefficient uses gamma = 4.7, the observed local slope, when computing n1 rather than the local simulated slope.
    Appendix A.1, Equation A2; this introduces the observed value into the transport coefficient calculation, though the authors note it is within 2 percent of the simulated gamma about 4.6.

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Pith. "Pith review of Energy-Dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium." pith.science (2026). https://pith.science/paper/WT5H6NZA

@misc{pith2026250700120,
  author       = {Pith},
  title        = {Pith review of: Energy-Dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WT5H6NZA}},
  note         = {Machine review of arXiv:2507.00120}
}
abstract

We investigate the transport of spectrally resolved cosmic ray (CR) protons with kinetic energies between $1-100$ GeV within the dynamic, multiphase interstellar medium (ISM), using a two-moment CR fluid solver applied to a TIGRESS MHD simulation with conditions similar to the solar neighborhood. Our CR transport prescription incorporates space- and momentum-dependent CR scattering coefficients $\sigma=\kappa^{-1}$, computed from the local balance between streaming-driven Alfv\`{e}n wave growth and damping processes. We find that advection combines with momentum-dependent diffusion to produce a CR distribution function $f(p)\propto~p^{-\gamma}$ with $\gamma\approx4.6$ that agrees with observations, steepened from an injected power law slope $\gamma_\mathrm{inj}=4.3$. The CR pressure is uniform in the highly diffusive, mostly neutral midplane region, but decreases exponentially in the ionized extraplanar region where scattering is efficient. To interpret these numerical results, we develop a two-zone analytic model that captures and links the two (physically and spatially) distinct regimes of CR transport in the multiphase, dynamic ISM. At low momenta, CR transport is dominated by gas advection, while at high momenta, both advection and diffusion contribute. At high momentum, the analytic prediction for the spectral slope approaches $\gamma=(4/3)\gamma_\mathrm{inj}-1$, and the predicted scaling of grammage with momentum is $X\propto p^{1-\gamma_\mathrm{inj}/3}$, consistent with the simulations. These results support a physical picture in which CRs are confined within the neutral midplane by the surrounding ionized gas, with their escape regulated by both the CR scattering rate in the ionized extraplanar gas and the velocity and Alfv\'{e}n speed of that gas, at effective speed $v_\mathrm{c,eff}\approx(1/2)[\kappa_\parallel~d(v+v_\mathrm{A,i})/dz]^{1/2}$.

Figures

Figures reproduced from arXiv: 2507.00120 by the authors.

Figure 1
Figure 1. Sample snapshot taken at the end the MHD relaxation run. The upper (lower) row of panels shows x-z (x-y) slices through the center of the simulation box, where x, y, and z are the local radial, azimuthal, and vertical directions. From left to right, columns show hydrogen number density nH, gas temperature T, and CR spectral fluxes j at different momenta p multiplied by the square of pc [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 2
Figure 2. Distribution of CR spectral flux j in physical and momentum space. The left panel shows the horizontally averaged vertical profiles of j for the five different momenta investigated in the paper. The right panel shows the average CR spectrum evaluated in the disk region (|z| < 500 pc). The results in gray indicate averages from postprocessing simulations, while the results in red/orange indicate averages from the MHD… view at source ↗
Figure 3
Figure 3. CR transport properties at different momenta p. The left panel shows the medians of the diffusion coefficients κ∥ as a function of temperature T. In the right plot, the solid and dashed lines indicate the CR pressure-weighted mean vertical components of the effective CR propagation speeds vc,z ≡ Fc,z/(4Pc) and diffusion speeds vd,z ≡ Fd,z/(4Pc), respectively. The gray dotted, dash-dotted, and solid lines represent t… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Vertical profiles of MHD velocities (left) and CR pressure in different spectral bins (right). The left panel displays the pressure-weighted mean vertical components of the advection velocity vz (violet), CR streaming velocity vs,z (cyan), and MHD velocity Vz ≡ vz + vs…
Figure 5
Figure 5. Figure 5: Comparison of key CR transport properties as predicted by the simulation (solid lines) versus the 1D model (shaded areas). The top left, top right, bottom left, and bottom right panels show, respectively, the CR scale height Hc, effective diffusion coefficient κeff , e…

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Forward citations

Cited by 2 Pith papers

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Reference graph

Works this paper leans on

74 extracted references · 5 canonical work pages · cited by 2 Pith papers

  1. [1]

    Models of Vertically Stratified Two-Phase ISM Disks with MRI-Driven Turbulence

    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

  2. [2]

    2022, , 129, 251103, 10.1103/PhysRevLett.129.251103

    Adriani , O., Akaike , Y., Asano , K., et al. 2022, , 129, 251103, 10.1103/PhysRevLett.129.251103

    doi:10.1103/physrevlett.129.251103 2022

  3. [3]

    2014, , 113, 121102, 10.1103/PhysRevLett.113.121102

    Aguilar , M., Aisa , D., Alvino , A., et al. 2014, , 113, 121102, 10.1103/PhysRevLett.113.121102

    doi:10.1103/physrevlett.113.121102 2014

  4. [4]

    2015, , 114, 171103, 10.1103/PhysRevLett.114.171103

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

    doi:10.1103/physrevlett.114.171103 2015

  5. [5]

    2016, , 117, 231102, 10.1103/PhysRevLett.117.231102

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

    doi:10.1103/physrevlett.117.231102 2016

  6. [6]

    2013, , 2013, 001, 10.1088/1475-7516/2013/07/001

    Aloisio , R., & Blasi , P. 2013, , 2013, 001, 10.1088/1475-7516/2013/07/001

    doi:10.1088/1475-7516/2013/07/001 2013

  7. [7]

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

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

    doi:10.1016/j.asr.2017.04.019 2018

  8. [8]

    C., & Jiang , Y.-F

    Armillotta , L., Ostriker , E. C., & Jiang , Y.-F. 2021, , 922, 11, 10.3847/1538-4357/ac1db2

    doi:10.3847/1538-4357/ac1db2 2021

Show all 74 references
  1. [9]

    2022, , 929, 170, 10.3847/1538-4357/ac5fa9

    ---. 2022, , 929, 170, 10.3847/1538-4357/ac5fa9

    2022 doi

  2. [10]

    C., Kim , C.-G., & Jiang , Y.-F

    Armillotta , L., Ostriker , E. C., Kim , C.-G., & Jiang , Y.-F. 2024, , 964, 99, 10.3847/1538-4357/ad1e5c

    2024 doi

  3. [11]

    2001, , 99, 243

    Beck , R. 2001, , 99, 243. astro-ph/0012402

    2001 arXiv

  4. [12]

    2013, , 21, 70, 10.1007/s00159-013-0070-7

    Blasi , P. 2013, , 21, 70, 10.1007/s00159-013-0070-7

    2013 doi

  5. [13]

    J., Della Torre , S., Gervasi , M., et al

    Boschini , M. J., Della Torre , S., Gervasi , M., et al. 2020, , 250, 27, 10.3847/1538-4365/aba901

    2020 doi

  6. [14]

    Boulares , A., & Cox , D. P. 1990, , 365, 544, 10.1086/169509

    1990 doi

  7. [15]

    2023, arXiv e-prints, arXiv:2307.00284, 10.48550/arXiv.2307.00284

    Caprioli , D. 2023, arXiv e-prints, arXiv:2307.00284, 10.48550/arXiv.2307.00284

    2023 doi arXiv

  8. [16]

    K., Kere s , D., Gurvich , A

    Chan , T. K., Kere s , D., Gurvich , A. B., et al. 2022, , 517, 597, 10.1093/mnras/stac2236

    2022 doi

  9. [17]

    Chandran , B. D. G. 2000, , 529, 513, 10.1086/308232

    2000 doi

  10. [18]

    O., Dogiel , V

    Chernyshov , D. O., Dogiel , V. A., Ivlev , A. V., Erlykin , A. D., & Kiselev , A. M. 2022, , 937, 107, 10.3847/1538-4357/ac8f42

    2022 doi

  11. [19]

    Draine , B. T. 2011, Physics of the Interstellar and Intergalactic Medium

    2011

  12. [20]

    2018, , 121, 021102, 10.1103/PhysRevLett.121.021102

    Evoli , C., Blasi , P., Morlino , G., & Aloisio , R. 2018, , 121, 021102, 10.1103/PhysRevLett.121.021102

    2018 doi

  13. [21]

    2008, , 2008, 018, 10.1088/1475-7516/2008/10/018

    Evoli , C., Gaggero , D., Grasso , D., & Maccione , L. 2008, , 2008, 018, 10.1088/1475-7516/2008/10/018

    2008 doi

  14. [22]

    2020, , 101, 023013, 10.1103/PhysRevD.101.023013

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

    2020 doi

  15. [23]

    2018, , 479, 3042, 10.1093/mnras/sty1653

    Girichidis , P., Naab , T., Hanasz , M., & Walch , S. 2018, , 479, 3042, 10.1093/mnras/sty1653

    2018 doi

  16. [24]

    2020, , 491, 993, 10.1093/mnras/stz2961

    Girichidis , P., Pfrommer , C., Hanasz , M., & Naab , T. 2020, , 491, 993, 10.1093/mnras/stz2961

    2020 doi

  17. [25]

    2022, , 510, 3917, 10.1093/mnras/stab3462

    Girichidis , P., Pfrommer , C., Pakmor , R., & Springel , V. 2022, , 510, 3917, 10.1093/mnras/stab3462

    2022 doi

  18. [26]

    2024, , 527, 10897, 10.1093/mnras/stad3628

    Girichidis , P., Werhahn , M., Pfrommer , C., Pakmor , R., & Springel , V. 2024, , 527, 10897, 10.1093/mnras/stad3628

    2024 doi

  19. [27]

    Gould, R. J. 1975, The Astrophysical Journal, 196, 689, 10.1086/153457

    1975 doi

  20. [28]

    A., Black , J

    Grenier , I. A., Black , J. H., & Strong , A. W. 2015, , 53, 199, 10.1146/annurev-astro-082214-122457

    2015 doi

  21. [29]

    2021, arXiv e-prints, arXiv:2106.08426

    Hanasz , M., Strong , A., & Girichidis , P. 2021, arXiv e-prints, arXiv:2106.08426. 2106.08426

    2021 arXiv

  22. [30]

    F., Butsky , I

    Hopkins , P. F., Butsky , I. S., Panopoulou , G. V., et al. 2022 a , , 516, 3470, 10.1093/mnras/stac1791

    2022 doi

  23. [31]

    F., Squire , J., Butsky , I

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

    2022 doi

  24. [32]

    F., Squire , J., Chan , T

    Hopkins , P. F., Squire , J., Chan , T. K., et al. 2021, , 501, 4184, 10.1093/mnras/staa3691

    2021 doi

  25. [33]

    F., Wetzel , A., Kere s , D., et al

    Hopkins , P. F., Wetzel , A., Kere s , D., et al. 2018, , 480, 800, 10.1093/mnras/sty1690

    2018 doi

  26. [34]

    F., Chan , T

    Hopkins , P. F., Chan , T. K., Garrison-Kimmel , S., et al. 2020, , 492, 3465, 10.1093/mnras/stz3321

    2020 doi

  27. [35]

    Jiang , Y.-F., & Oh , S. P. 2018, , 854, 5, 10.3847/1538-4357/aaa6ce

    2018 doi

  28. [36]

    2022, , 514, 657, 10.1093/mnras/stac1240

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

    2022 doi

  29. [37]

    Kim , C.-G., & Ostriker , E. C. 2017, , 846, 133, 10.3847/1538-4357/aa8599

    2017 doi

  30. [38]

    C., Somerville , R

    Kim , C.-G., Ostriker , E. C., Somerville , R. S., et al. 2020, , 900, 61, 10.3847/1538-4357/aba962

    2020 doi

  31. [39]

    2014, Astroparticle Physics, 55, 37, 10.1016/j.astropartphys.2014.02.002

    Kissmann , R. 2014, Astroparticle Physics, 55, 37, 10.1016/j.astropartphys.2014.02.002

    2014 doi

  32. [40]

    2015, The Astrophysical Journal, 802, 114, 10.1088/0004-637X/802/2/114

    Krakau, S., & Schlickeiser, R. 2015, The Astrophysical Journal, 802, 114, 10.1088/0004-637X/802/2/114

    2015 doi

  33. [41]

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

    1969 doi

  34. [42]

    Kulsrud , R. M. 2005, Plasma physics for astrophysics

    2005

  35. [43]

    A., & Ostriker , E

    Mao , S. A., & Ostriker , E. C. 2018, , 854, 89, 10.3847/1538-4357/aaa88e

    2018 doi

  36. [44]

    2001, , 555, 585, 10.1086/321496

    Maurin , D., Donato , F., Taillet , R., & Salati , P. 2001, , 555, 585, 10.1086/321496

    2001 doi

  37. [45]

    A., Hanasz , M., & W \'o lta \'n ski , D

    Ogrodnik , M. A., Hanasz , M., & W \'o lta \'n ski , D. 2021, , 253, 18, 10.3847/1538-4365/abd16f

    2021 doi

  38. [46]

    V., Galli , D., & Caselli , P

    Padovani , M., Ivlev , A. V., Galli , D., & Caselli , P. 2018, , 614, A111, 10.1051/0004-6361/201732202

    2018 doi

  39. [47]

    V., Galli , D., et al

    Padovani , M., Ivlev , A. V., Galli , D., et al. 2020, , 216, 29, 10.1007/s11214-020-00654-1

    2020 doi

  40. [48]

    A., & Jiang , Y.-F

    Quataert , E., Thompson , T. A., & Jiang , Y.-F. 2021, , 10.1093/mnras/stab3273

    2021 doi

  41. [49]

    2023, , 522, 1843, 10.1093/mnras/stad1104

    Rathjen , T.-E., Naab , T., Walch , S., et al. 2023, , 522, 1843, 10.1093/mnras/stad1104

    2023 doi

  42. [50]

    2021, arXiv e-prints, arXiv:2101.02052

    Recchia , S. 2021, arXiv e-prints, arXiv:2101.02052. 2101.02052

    2021 arXiv

  43. [51]

    2023, , 31, 4, 10.1007/s00159-023-00149-2

    Ruszkowski , M., & Pfrommer , C. 2023, , 31, 4, 10.1007/s00159-023-00149-2

    2023 doi

  44. [52]

    L., Beattie , J

    Sampson , M. L., Beattie , J. R., Krumholz , M. R., et al. 2023, , 519, 1503, 10.1093/mnras/stac3207

    2023 doi

  45. [53]

    2022, , 926, 8, 10.3847/1538-4357/ac4110

    Shimoda , J., & Inutsuka , S.-i. 2022, , 926, 8, 10.3847/1538-4357/ac4110

    2022 doi

  46. [54]

    2024, arXiv e-prints, arXiv:2410.06988, 10.48550/arXiv.2410.06988

    Sike , B., Thomas , T., Ruszkowski , M., Pfrommer , C., & Weber , M. 2024, arXiv e-prints, arXiv:2410.06988, 10.48550/arXiv.2410.06988

    2024 doi arXiv

  47. [55]

    2024, , 963, 111, 10.3847/1538-4357/ad1ce8

    Silver , E., & Orlando , E. 2024, , 963, 111, 10.3847/1538-4357/ad1ce8

    2024 doi

  48. [56]

    1975, , 172, 557, 10.1093/mnras/172.3.557

    Skilling , J. 1975, , 172, 557, 10.1093/mnras/172.3.557

    1975 doi

  49. [57]

    A., & Ostriker , E

    Skinner , M. A., & Ostriker , E. C. 2013, , 206, 21, 10.1088/0067-0049/206/2/21

    2013 doi

  50. [58]

    M., Tomida , K., White , C

    Stone , J. M., Tomida , K., White , C. J., & Felker , K. G. 2020, , 249, 4, 10.3847/1538-4365/ab929b

    2020 doi

  51. [59]

    W., & Moskalenko , I

    Strong , A. W., & Moskalenko , I. V. 1998, , 509, 212, 10.1086/306470

    1998 doi

  52. [60]

    W., Moskalenko , I

    Strong , A. W., Moskalenko , I. V., & Ptuskin , V. S. 2007, Annual Review of Nuclear and Particle Science, 57, 285, 10.1146/annurev.nucl.57.090506.123011

    2007

  53. [61]

    S., & Dopita , M

    Sutherland , R. S., & Dopita , M. A. 1993, , 88, 253, 10.1086/191823

    1993 doi

  54. [62]

    2023, , 521, 3023, 10.1093/mnras/stad472

    Thomas , T., Pfrommer , C., & Pakmor , R. 2023, , 521, 3023, 10.1093/mnras/stad472

    2023 doi

  55. [63]

    2024, arXiv e-prints, arXiv:2405.13121, 10.48550/arXiv.2405.13121

    ---. 2024, arXiv e-prints, arXiv:2405.13121, 10.48550/arXiv.2405.13121

    2024 doi arXiv

  56. [64]

    Tsung , T. H. N., Oh , S. P., & Bustard , C. 2023, , 526, 3301, 10.1093/mnras/stad2720

    2023 doi

  57. [65]

    Wentzel , D. G. 1974, , 12, 71, 10.1146/annurev.aa.12.090174.000443

    1974

  58. [66]

    2021 a , , 508, 4072, 10.1093/mnras/stab2535

    Werhahn , M., Pfrommer , C., & Girichidis , P. 2021 a , , 508, 4072, 10.1093/mnras/stab2535

    2021 doi

  59. [67]

    2021 b , , 505, 3273, 10.1093/mnras/stab1324

    Werhahn , M., Pfrommer , C., Girichidis , P., Puchwein , E., & Pakmor , R. 2021 b , , 505, 3273, 10.1093/mnras/stab1324

    2021 doi

  60. [68]

    2021 c , , 505, 3295, 10.1093/mnras/stab1325

    Werhahn , M., Pfrommer , C., Girichidis , P., & Winner , G. 2021 c , , 505, 3295, 10.1093/mnras/stab1325

    2021 doi

  61. [69]

    2019, , 488, 2235, 10.1093/mnras/stz1792

    Winner , G., Pfrommer , C., Girichidis , P., & Pakmor , R. 2019, , 488, 2235, 10.1093/mnras/stz1792

    2019 doi

  62. [70]

    2020, , 499, 2785, 10.1093/mnras/staa2989

    Winner , G., Pfrommer , C., Girichidis , P., Werhahn , M., & Pais , M. 2020, , 499, 2785, 10.1093/mnras/staa2989

    2020 doi

  63. [71]

    2002, , 89, 281102, 10.1103/PhysRevLett.89.281102

    Yan , H., & Lazarian , A. 2002, , 89, 281102, 10.1103/PhysRevLett.89.281102

    2002 doi

  64. [72]

    Yang , H. Y. K., & Ruszkowski , M. 2017, , 850, 2, 10.3847/1538-4357/aa9434

    2017 doi

  65. [73]

    2023, , 669, A10, 10.1051/0004-6361/202244194

    Zari , E., Frankel , N., & Rix , H.-W. 2023, , 669, A10, 10.1051/0004-6361/202244194

    2023 doi

  66. [74]

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

    2017 doi

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