The dynamical impact of cosmic rays in the Rhea magnetohydrodynamics simulations

Christoph Pfrommer; Juan Soler; Junia G\"ooller; Karin Kjellgren; Leonardo Testi; Maria Werhahn; No\'e Brucy; Philipp Girichidis; Ralf S. Klessen; Robin G. Tress

REVIEW 2 major objections 4 minor 1 cited by

The dynamical impact of cosmic rays in the Rhea magnetohydrodynamics simulations

T0 review · 2 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Adding cosmic rays to Milky Way-like galaxy simulations lowers the star formation rate, sustains outflows across the whole disk, and carries 18–58 percent of injected cosmic-ray energy out of the disk.

desk verdict Solid Rhea CR-feedback paper: clean comparison, transparent caveats, but the constant diffusion coefficient and tuned magnetic scaling bracket the headline numbers. read the letter →

arxiv 2502.02635 v2 pith:LVC23GJF submitted 2025-02-04 astro-ph.GA

Karin Kjellgren , Philipp Girichidis , Junia Göoller , Noé Brucy , Ralf S. Klessen , Robin G. Tress , Juan Soler , Christoph Pfrommer

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Maria Werhahn Simon C. O. Glover Rowan Smith Leonardo Testi Sergio Molinari

This is my paper · ORCID

classification astro-ph.GA

keywords cosmicraysmagnetohydrodynamicsgalacticwindsISMstarformationgalaxies:evolutionmagneticfieldscircumgalacticmedium

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 asks whether cosmic rays, the relativistic particles injected by supernova explosions, change how a Milky Way-sized galaxy actually behaves. Comparing four isolated-galaxy simulations, two with cosmic rays and two without, it finds that cosmic rays cut the time-averaged star formation rate roughly in half (0.62 versus 1.2 solar masses per year in the strong-field runs) and turn weak fountain flows into sustained outflows. The outflows are launched across the entire disk, carry about 20 percent of the star formation rate as mass, and remove 18 to 58 percent of the injected cosmic-ray energy before it is lost inside the galaxy. If correct, this places cosmic-ray pressure, rather than supernova thermal pressure or magnetic fields, as the main agent shaping the vertical structure and the circumgalactic medium of Milky Way-like galaxies.

What carries the argument

The load-bearing piece is the two-fluid magnetohydrodynamic treatment in which cosmic-ray energy density is evolved together with the thermal gas. Cosmic rays are injected with 10% of each supernova's energy, advect with the gas, and diffuse parallel to the local magnetic field with a fixed coefficient $\kappa=4\times10^{28}\,\mathrm{cm^2\,s^{-1}}$. Streaming is not solved for; its energy losses are emulated by Alfvén cooling, $\Lambda_A=\mathbf{v}_{\mathrm{st}}\cdot\nabla P_{\mathrm{cr}}$. The resulting cosmic-ray pressure gradient, read through vertical acceleration profiles and the Eddington factor $\Gamma_{\mathrm{Edd,CR}}=-a_{\mathrm{cr}}/a_{\mathrm{grav}}$, is the mechanism that lifts low-density gas and launches the weak winds, and the CR-to-thermal pressure ratio $X_{\mathrm{cr}}$ is the diagnostic that shows where that pressure dominates.

What would settle it

Measure the vertical gradient length of cosmic-ray pressure above a star-forming disk like the Milky Way: if the gradient is much steeper than the roughly 1 kpc scale the simulations produce, the assumed fast constant diffusion is wrong and the predicted weak, disk-wide outflows would not be launched.

Watch

Extended reading notes

Core claim

The paper's central discovery is that pressure gradients from cosmic rays, injected in supernova explosions and diffusing along magnetic field lines, are the decisive dynamic agent in a Milky Way-like disk. In the runs with cosmic rays, the time-averaged star formation rate drops to 0.62 and 0.96 solar masses per year, compared with 1.2 and 2.1 in the corresponding runs without them. The cosmic rays sustain low-density, high-velocity outflows from the center and from all radii, with mass-loading factors around 0.18–0.25, and the outflow energy budget is dominated by cosmic-ray energy: about 18% escapes in the strong-field run and 58% in the weak-field run. The circumgalactic medium becomes magnetized to roughly $0.5\,\mu\mathrm{G}$ and cooler than about $10^5$ K, while the no-cosmic-ray runs leave a hot, weakly magnetized halo. The cosmic-ray energy density in the disk is smooth, with gradient lengths beyond 100 pc, so the cosmic-ray fluid is not behaving adiabatically.

Load-bearing premise

The results stand on the assumption that cosmic rays spread through the whole galaxy at one fixed rate, derived from particles observed at Earth, with streaming losses only approximated as a cooling term; if the true diffusion rate varies with gas phase, the pressure gradients that drive the outflows would change.

Editorial extensions

If this is right

Milky Way-like galaxies can have weak, sustained winds with mass-loading around 0.2, matching the low outflow rates inferred from high-velocity clouds rather than the stronger winds seen in lower-mass galaxies.
The escape fraction of cosmic-ray energy is set by magnetic field structure: about 18% escapes in the strong-field model but 58% in the weak-field model, so field strength controls how much CR energy is lost inside the galaxy versus carried into the halo.
Cosmic rays alter the circumgalactic medium, making it cooler ($T\lesssim10^5$ K) and more magnetic ($\beta_{\mathrm{pl}}\sim0.1$–1), a signature that should be visible in absorption-line and Faraday-rotation observations.
Because cosmic-ray gradient lengths exceed molecular-cloud scales, cosmic rays do not suppress star formation locally by holding individual clouds up; instead, they add pressure throughout the disk and lift gas from all radii.

Reading between the lines

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

Beyond the paper's explicit claims, a smaller or spatially varying diffusion coefficient in cold gas would steepen the cosmic-ray pressure gradients and likely raise the mass-loading factors, making the weak winds stronger; this is a testable prediction rather than a result of the paper.
If the late-time convergence of the strong- and weak-field runs holds over longer evolution, the initial magnetic field strength is subdominant to cosmic-ray transport; varying the diffusion coefficient and field geometry independently would settle that ordering.
The predicted smooth cosmic-ray energy distribution could be converted into a gamma-ray surface-brightness map and compared with resolved observations of nearby edge-on galaxies; the paper does not make that comparison.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is a careful simulation paper that quantifies CR feedback in the Rhea suite and lands on weak outflows. The clean CR vs no-CR comparison and the attention to caveats carry it. I'd send it to review, with a request for a sharper discussion of the transport assumptions.

What's new: applying the gray CR module to Rhea gives concrete numbers—SFR drop to ~0.6 M_sun/yr, mass loading ~0.2, CGM B ~0.5 microgauss, CR escape 18–58%—and the disk-wide outflow picture (not just center) is a useful addition. The analysis is mostly careful: scale heights, phase plots, energy ratios, acceleration profiles, Eddington factors. The authors are also transparent about what is ad hoc.

Soft spots: the constant diffusion coefficient kappa=4e28, with streaming only through Alfven cooling, is the load-bearing simplification. All the headline numbers depend on it. The magnetic scaling alpha=1/3 is explicitly chosen to avoid artificially strong outflows; that is honest but it does calibrate the CGM magnetic pressure. The stress-test worry about alpha has some teeth for the strong-B run, but the weak-B run starts with essentially no CGM field and still converges to similar eta~0.2, which suggests the alpha choice is not the only thing setting the outflow. The early phase of the low-B model, with mass loading >10, is acknowledged but brackets the physical behavior. No public code or data products either, which makes reproduction hard.

Net: the qualitative story—CRs suppress star formation, drive weak outflows, magnetize a cool CGM—is consistent with earlier work, so the novelty is modest. But the quantitative results for this particular Milky Way-like setup are worth having. I'd engage with it for the numbers and the clear comparison. If I were the editor, I'd send it out, but the authors should be pushed to release analysis scripts or at least data products for the key figures.

Referee Report

2 major / 4 minor

Summary. This paper analyzes four isolated Milky Way-like galaxy simulations from the Rhea suite, performed with Arepo, to isolate the dynamical effects of cosmic rays (CRs). The control runs (MHD, MHD-low) and CR runs (CRMHD, CRMHD-low) are identical except for the inclusion of a gray CR fluid with anisotropic diffusion and Alfvén cooling, and the "-low" models have a 1000 times weaker initial magnetic field. The authors report that CRs lower the star formation rate by roughly a factor of two in the strong-field case, launch sustained but weak outflows with mass-loading factors of about 0.2, transport 18--58% of the injected CR energy through |z| = 5 kpc, and produce a cooler, more strongly magnetized CGM than the MHD-only models. The outflows are distributed across the entire disk rather than being confined to the nuclear region. The paper also analyzes the CR energy distribution, showing that it is not adiabatic (flat with density at high densities), and quantifies the vertical force balance, finding that CR acceleration is comparable to gravity in the strong-field model and dominant in the weak-field model.

Significance. If the quantitative results hold, this is a valuable controlled study of CR feedback in a resolved multiphase ISM, with a clean two-by-two design that separates CR effects from magnetic-field effects. The paper's strengths include a careful definition of the outflow measurement surface, a full accounting of the energy loading in all four components (Eqs. 19--22), direct computation of the vertical accelerations and Eddington factors (Figs. 13--14), and an explicit and honest discussion of the caveats in Sec. 6. The prediction of a cool, magnetized CGM (beta_pl ~ 0.1--1, T lesssim 10^5 K) is falsifiable with Faraday rotation and UV absorption observations. However, as detailed below, the two most load-bearing quantitative claims---the mass-loading factor of about 0.2 and the CR escape fractions of 18--58%---are sensitive to the assumed magnetic-field scaling and the constant diffusion coefficient, and the paper does not currently provide tests of that sensitivity.

major comments (2)

[Sec. 2.3] The choice alpha = 1/3 for the initial magnetic-field scaling is explicitly calibrated to avoid strong outflows: the text states that this scaling was applied because the setup is missing the magnetic-field amplification via a turbulent magnetic dynamo, and 'to avoid finding artificially strong outflows as a result of the missing magnetic energy in the CGM.' All of the headline outflow quantities---eta_M approximately 0.2 at |z| = 5 kpc (Fig. 10) and the 18--58% CR energy escape fractions---are measured at heights where the imposed scaling yields B approximately 0.7--1 microgauss (Fig. 12). A physically motivated scaling such as alpha = 2/3 (Mestel 1966, cited in the same section) would give a lower CGM magnetic pressure and, if anything, stronger outflows and larger escape fractions. The late-time convergence of the strong- and weak-field runs (Fig. 12) does not test the alpha dependence because both models share the same alpha and the same feedback loop (CR-driven outflows magnetize the CGM, which then suppresses further outflows). To support the claim that the weak-outflow result is not a calibration artifact, the authors should either run a model with alpha = 2/3 or a self-consistently evolved CGM magnetic field, or explicitly bound how the mass- and energy-loading factors would change under an alternative scaling. In the absence of such a test, the central quantitative claims are conditional on this ad hoc calibration.
[Sec. 2.2 and Sec. 3.3] The constant diffusion coefficient kappa = 4e28 cm^2/s and the approximate treatment of streaming losses via the Alfvén cooling term (Eq. 13) are the main physical assumptions of the CR model. The paper's conclusion in Sec. 3.3 that CRs are smoothly distributed with L_cr around 1 kpc and are 'not adiabatic' is a direct consequence of this kappa: the large diffusion coefficient flattens the CR gradient by construction. The discussion in Sec. 6.3 correctly identifies that two-moment or spectral models produce spatially and temporally varying transport coefficients, but it does not quantify how the reported eta_M and escape fractions would change. Because the outflow rate is set by the CR pressure gradient, a lower or spatially inhomogeneous kappa would concentrate CRs near the disk and could increase the pressure gradients and outflow efficiency. We ask the authors to provide at least one sensitivity simulation with a smaller kappa (or a two-moment closure), or to restate the conclusions as explicitly limited to the constant-kappa approximation and to indicate the expected direction and rough magnitude of the uncertainty.

minor comments (4)

[Eq. (6)] Equation (6) appears garbled in the manuscript: v_st is first defined as -v_A sign(B.grad P_cr), but the second equality reads 'Bp 4pi rho ...' which seems to be a LaTeX rendering error for v_A = B/sqrt(4 pi rho). Please correct the typesetting.
[Abstract and Sec. 5.2] The abstract states that 20--60% of the injected CR energy is transported out of the disk, while the text reports 18% and 58% for the two CR runs. Please unify these numbers.
[Sec. 3.3] The sentence 'In the CRMHD simulation we have more low-energy CRs than in the CRMHD-low case, leading to a minimum in the median CR energy density at around T = 10^4 K' is confusing, since a larger population of low-energy CRs would tend to raise, not lower, the median. Please rephrase to clarify the intended statement.
[Sec. 5.2, Eq. (21)] The CR energy flux definition includes the diffusive term with a sign(zi) factor; please define the sign convention explicitly in the text, because the direction of the diffusive flux relative to the outward normal is otherwise easy to misread.

Circularity Check

1 steps flagged · score 5.0 of 10

The headline weak-outflow result is partially constructed: the CGM magnetic-field scaling α=1/3 was chosen explicitly to avoid strong CR-driven outflows, and the reported mass-loading factors and CR escape fractions are measured against the magnetic pressure this scaling imposes.

self definitional [Sec. 2.3 (initial field scaling) and Sec. 5.2 (mass-loading result).]
"To avoid finding artificially strong outflows as a result of the missing magnetic energy in the CGM, we applied a scaling of α = 1/3. For the strong field with B0 = 3µG, this results in magnetic field strengths of the order of 1 µG at a height of 10 kpc above the midplane... We find average mass-loading factors of ∼0.18 and ∼0.25 in the CRMHD and CRMHD-low simulations, respectively. As we did not expect to see any strong outflows in Milky Way-like galaxies, this is not surprising."

The CGM magnetic field is an input, but its density scaling exponent is defined by the desired outcome: it was chosen to prevent artificially strong outflows, which are the very phenomenon the paper reports as a finding. The measured mass-loading factors (~0.2) and the CR escape fractions (18%–58%) are evaluated at |z| = 5 kpc, where this prescribed field reaches ~0.7–1 µG and supplies the opposing pressure that throttles the outflows. Because both strong- and weak-initial-field runs share the same α = 1/3, their late-time convergence is not an independent check of the scaling; it only shows that the same input was adopted in both cases. The paper's own Sec.

full rationale

Most of the paper is self-contained and uses genuinely emergent results. The CR transport equations (Eqs. 1–6) are integrated from stated physics; the diffusion coefficient κ = 4×10^28 cm^2/s is taken from independent GeV observations (Strong et al. 2007); the SFR reduction is obtained by comparing CRMHD to MHD control runs that differ only in CR injection; and the CR energy distribution, scale heights, and CGM temperatures are simulation outputs rather than re-statements of the inputs. The self-citations to Göller et al. (2025) and Pfrommer et al. (2017a) are for setup details and published equations, not for the dynamical conclusions, so they do not create a load-bearing self-citation chain. The one significant circular element is the initial magnetic-field scaling exponent α = 1/3 (Sec. 2.3), which is explicitly chosen to avoid strong outflows; the reported weak mass-loading factors and low CR escape fractions are then presented as the paper's central prediction. This is not a full identity reduction — the loading factors and escape fractions are time-averaged measurements of a nonlinear MHD flow — but the input was calibrated to suppress exactly the signal being claimed, so the headline result is partially constructed rather than fully emergent. The manuscript's own Sec. 6.2 limitation about non-self-consistent CGM initial conditions further supports this assessment. Accordingly, the circularity score is moderate, not severe.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

All free parameters are standard inputs for CR-MHD galaxy simulations, but the diffusion coefficient, injection fraction, and B-field scaling directly control the reported outflow and CR distribution results. No new physical entities are introduced.

free parameters (5)

CR diffusion coefficient kappa = 4e28 cm^2/s
Assumed constant in space and time along magnetic field lines (Sec 2.2), based on GeV CR observations of the Milky Way; controls CR escape and pressure gradients.
CR injection fraction per SN = 10% (1e50 erg per SN)
Each SN injects 10% of 1e51 erg as CRs (Sec 2.2), a standard but uncalibrated fraction in this setup.
Magnetic field scaling exponent alpha = 1/3
Applied to set initial CGM field strengths comparable to cosmological simulations and 'to avoid finding artificially strong outflows' (Sec 2.3); affects outflow behavior at early times.
Initial magnetic field strength B0 = 3 microgauss or 3 nanogauss
Two bracketing values (Table 1) chosen to represent strong and weak CGM magnetization; the low-B model produces an early unphysical outflow phase (Sec 6.2).
CR ionization rate zeta_CR = 3e-17 s^-1
Fixed rate for atomic hydrogen adopted from observations (Sec 2.1); affects cooling and chemistry.

assumptions (5)

domain assumption Gray (one-moment) CR transport with a single energy density and constant adiabatic index gamma_cr = 4/3 adequately captures CR dynamics
Only ecr is evolved (Eq 4); no spectral information or self-consistent scattering is included, as discussed in Sec 6.3.
domain assumption Streaming losses can be represented by the Alfven cooling term Lambda_A = v_st dot grad P_cr without explicitly modeling streaming advection
Adopted from Wiener et al. 2013 (Sec 2.2); affects CR energy losses and gas heating.
domain assumption The hadronic and Coulomb loss rates (Eqs 11, 12) with the given normalization apply to the integrated CR population
Assumes a uniform CR spectrum in steady state; used for CR energy sinks in Eq 4.
ad hoc to paper The initial B-field scaling B proportional to rho^(1/3) is a valid proxy for the missing turbulent dynamo in the CGM
Introduced in Sec 2.3 to avoid artificially strong outflows and match CGM fields of cosmological simulations; not self-consistently generated.
domain assumption The simulations represent a quasi-steady Milky Way-like system after 1-1.5 Gyr despite mass return being fully enabled (no gas depletion) and accelerated stellar lifetimes in the first Gyr
Sec 2.3 and 6.3; the setup prevents gas depletion and may affect the late-time SFR and outflow evolution.

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Cite this review

Pith. "Pith review of The dynamical impact of cosmic rays in the Rhea magnetohydrodynamics simulations." pith.science (2026). https://pith.science/paper/LVC23GJF

@misc{pith2026250202635,
  author       = {Pith},
  title        = {Pith review of: The dynamical impact of cosmic rays in the Rhea magnetohydrodynamics simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LVC23GJF}},
  note         = {Machine review of arXiv:2502.02635}
}

abstract

This study explores the dynamical impact of cosmic rays (CRs) in Milky Way-like galaxies using the Rhea simulation suite. Cosmic rays, with their substantial energy density, influence the interstellar medium (ISM) by supporting galactic winds, modulating star formation, and shaping ISM energetics. The simulations incorporate a multi-phase ISM, self-consistent CR transport in the advection-diffusion approximation, and interactions with magnetic fields to study their effect on galaxy evolution. Key findings reveal that CRs reduce star formation rates, and drive weak but sustained outflows with mass loading factors of $\sim0.2$, transporting a substantial fraction (20%-60%) of the injected CR energy. These CR-driven outflows are launched not just from the galactic center but across the entire disk, illustrating their pervasive dynamical influence. Galactic disks supported by CRs exhibit broader vertical structures compared to magnetic-field-dominated setups, though the scale heights are similar. CR feedback enhances magnetic flux transport to the circumgalactic medium (CGM), leading to a magnetically enriched CGM with field strengths of $\sim0.5\mu\mathrm{G}$ while reducing gas temperatures to $\lesssim10^5\,\mathrm{K}$. The CR energy is relatively smoothly distributed in the disk, with gradient lengths exceeding the typical size of molecular clouds, indicating that the CR behavior is not adiabatic.

Figures

Figures reproduced from arXiv: 2502.02635 by the authors.

**Figure 1.** Evolution of our simulations. In each column we show edge-on maps of the column density for one simulation at three different times: t = 0.5, 1.0, and 1.5 Gyr. In the last row, we also show the face-on view of the column density at t = 1.5 Gyr. The simulations with an initially smaller magnetic field develop much larger star-forming disks due to the weaker magnetic support. The inclusion of CRs leads to a more fluff… view at source ↗

**Figure 2.** Top: Evolution of the scale height (height above the disk that encloses 75% of the total gas mass at a given radius) for our four simulations. In all cases the scale height eventually converges, at which point the gas mass is well contained within 1 kpc of the midplane. Bottom: Temperaturedensity histograms for our simulations at t = 1.5 Gyr, weighted by the gas mass and limited to a disk of radius of r = 20 kpc an… view at source ↗

**Figure 3.** Distribution of the CR energy density as a function of density (left column) and temperature (right column) at t = 1.5 Gyr, weighted by the gas mass. Overlaid is the median CR energy density in each gas density bin (dashed line). Additionally, in the two leftmost panels, we show the analytical scaling that assumes adiabatic CRs (solid gray line). star-forming disk. In the edge-on maps in the right panels, we can cle… view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: From top to bottom: Face-on and edge-on slices through the midplane of the CR energy density, ecr, the CR diffusion length, Lcr, and the ratio of the CR diffusion timescale, tdiff, to the free-fall timescale, tff, for the CRMHD and CRMHD-low galaxies. the ratio of ther…

**Figure 5.** Figure 5: Left: SFR of our simulations as a function of time. Right: SFRD as a function of galactocentric radius, averaged over t = 0.5 − 2.0 Gyr. There is no major difference between the simulations for these particular energy ratios. The properties of outflows generated in our…

**Figure 6.** Figure 6: Slices through the galactic midplane of various energy ratios at t = 1.5 Gyr. From top to bottom: Ratio of thermal to magnetic energy, ratio of CR to thermal pressure, ratio of thermal to the z-component of the kinetic energy, and the ratio of thermal to gravitational …

**Figure 7.** Figure 7: Radial profiles of the energy ratios from [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 8.** Figure 8: Comparison of the vertical structure and CGM properties of our galaxies at t = 1.5 Gyr. From top to bottom, we show slices through the midplane of the vertical velocity, gas temperature, gas density, magnetic-to-thermal energy ratio, and the CR-to-thermal pressure rati…

**Figure 9.** Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]

**Figure 10.** Figure 10: Evolution of the mass flow rate. In the two upper panels we show the evolution of the mass outflow rate (mass flux) in the vertical direction at a height of h = 5 kpc in different radial bins, denoted by different linestyles, for the simulations CRMHD and CRMHD-low. N…

**Figure 11.** Figure 11: Radial evolution of mass outflow rate, M˙ , and SFR for the CRMHD simulation, averaged over t = 0.5 − 2.0 Gyr. The pink curve shows the gas scale height, h, averaged over the same time interval. Its values at the largest r imply that CRs lift gas at all radii, not jus…

**Figure 12.** Figure 12: Mass-loading factor as a function magnetic field strength at a height of 5 kpc for both CR simulations. Colour coded is the simulation time. At early times the simulations differ. At late times the mean field strengths are comparable and so are the mass-loading factor…

**Figure 13.** Figure 13: Time-averaged (t = 1.25 − 2.00 Gyr) vertical accelerations within a cylinder of r = 20 kpc for the four simulation setups. Accelerations are first volume averaged and then averaged in time. The pure MHD-cases do not exhibit outflows, so the gravitational force dominat…

**Figure 14.** Figure 14: Volume-weighted CR Eddington factors averaged in a region r < 20 kpc and 4 < h < 6 kpc, separated by gas phase (cool phase: T < 5050 K, warm phase: 5050 K < T < 2 × 104 K, ionized phase: 2 × 104 K < T < 5 × 105 K, hot phase: 5 × 105 K < T < 1010 K). We plot the median…

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