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Synchrotron-Regulated Relativistic Magnetohydrodynamic Turbulence: Emission, Polarization, and Faraday Rotation

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Synchrotron cooling, the paper argues, actively regulates relativistic turbulence by triggering a thermal instability that splits the plasma into hot dilute and cold dense phases, shaping emission, polarization, and Faraday rotation.

desk verdict First driven RMHD turbulence with synchrotron cooling, well executed, but the thermal-instability attribution is not yet established and needs a control run. read the letter →

arxiv 2608.10748 v1 pith:XTNTG5EW submitted 2026-08-11 astro-ph.HE

Xiaochen Sun , Luca Comisso Lorenzo Sironi , Anatoly Spitkovsky , Alexander Philippov This is my paper · ORCID
classification astro-ph.HE
keywords relativisticmagnetohydrodynamicsturbulencesynchrotroncoolingthermalinstabilityFaradayrotationlinearpolarizationfastradioburstspulsarwindnebulae
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 establish that synchrotron radiation acts as an active thermodynamic regulator of relativistic magnetized turbulence, not just an output. In three-dimensional driven-turbulence simulations with self-consistent synchrotron cooling, the balance between turbulent energy injection and radiative losses sets the mean plasma temperature, while the cooling-induced thermal instability pushes the plasma into coexisting hot-dilute and cold-dense phases. The paper then computes synthetic synchrotron spectra, linear polarization maps, and Faraday rotation measures from the simulated volume and shows that the two-phase structure makes high-frequency emission more intermittent and more strongly polarized than low-frequency emission. If correct, a single turbulent-cooling mechanism reproduces qualitative observational trends in blazar flares, pulsar wind nebulae, and repeating fast radio bursts.

What carries the argument

The load-bearing control parameter is the dimensionless synchrotron cooling efficiency $\eta_{\rm syn}=4(n_e d_e^3)^{-1}(L/d_e)$, physically the Thomson optical depth of the box, which enters the fluid-frame cooling power $P_{\rm syn}$ through the gas pressure, the magnetic energy density, and a Maxwell–Jüttner temperature factor $K_3(\Theta_t^{-1})/K_2(\Theta_t^{-1})$. The argument advances through a feedback loop: flux freezing makes overdense regions carry stronger magnetic fields, stronger fields increase $P_{\rm syn}$, the local thermal pressure drops, and surrounding plasma is drawn inward, amplifying density and temperature contrasts until turbulent mixing balances the growth. This thermal-instability loop, together with the equality between turbulent energy injection and radiative losses, sets both the mean temperature and the two-phase structure that the synthetic spectra, polarization maps, and rotation measures inherit.

What would settle it

Repeat the highest-cooling run at twice the linear resolution and check whether the two peaks in the lab-frame density PDF, near $\sim\rho_0/5$ and $\sim 3\rho_0$, persist with unchanged volume filling fractions; the paper's own appendix shows that the pure thermal instability is resolution-limited, so if the phase structure is numerically set rather than converged, the thermal-instability interpretation would not stand.

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Extended reading notes

Core claim

The central discovery is the first relativistic MHD simulation of driven turbulence in which synchrotron cooling is included self-consistently as a momentum and energy sink, allowing the plasma thermodynamics to be regulated by the competition between turbulent heating and radiation. In quasi-steady state the total cooling power equals the energy injection rate, and the volume-averaged temperature falls as the inverse square root of the cooling efficiency, $\langle\Theta_t\rangle_V \propto \eta_{\rm syn}^{-1/2}$. At high cooling efficiency, the plasma bifurcates into a low-density, high-temperature phase and a high-density, low-temperature phase; the paper attributes this bifurcation to the synchrotron-cooling-induced thermal instability, in which overdense regions carry stronger magnetic fields, cool more rapidly, lose pressure, and draw in surrounding material until turbulent mixing arrests the runaway. The phase structure broadens the integrated synchrotron spectrum, depolarizes low-frequency emission along the line of sight because magnetic fields are tangled, and makes high-frequency emission come from rare, hot, strongly magnetized columns whose polarization approaches the theoretical maximum. Faraday rotation measures fluctuate in space and time, with the mean-field contribution comparable to the turbulent contribution and with fluctuations that weaken as the plasma becomes hotter. These synthetic diagnostics qualitatively match trends reported for blazars, pulsar wind nebulae, and repeating FRBs.

Load-bearing premise

The interpretation that the phase structure is caused by the classical thermal instability assumes that the instability criterion derived for a uniformly heated, quiescent plasma still applies when heating comes from patchy turbulent dissipation rather than a uniform source.

Editorial extensions

If this is right

  • Blazar flares that are faster and more strongly polarized at higher frequencies need no separate emission component; a single cooled turbulent region produces this frequency-dependent intermittency.
  • In pulsar wind nebulae, the observed rise of X-ray polarization degree with photon energy follows from line-of-sight integration through cooled turbulence, because high-energy emission is dominated by rare hot magnetized columns.
  • Faraday rotation measures around repeating fast radio bursts can fluctuate with Laplace-like distributions, and the paper's scaling ties the fluctuation amplitude to the mean electron temperature, so a measured RM constrains the temperature of the screen.
  • Because the magnetic power spectrum is Kolmogorov-like and nearly independent of cooling efficiency, the radiative predictions are stable to changes in magnetization and resolution at fixed cooling efficiency.
  • Stronger cooling drives the mean temperature down as $\langle\Theta_t\rangle_V\propto\eta_{\rm syn}^{-1/2}$, so systems with higher optical depth are naturally cooler and exhibit larger rotation-measure fluctuations.

Reading between the lines

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

  • Editorial inference: replacing the Maxwell–Jüttner electron distribution with a nonthermal power-law tail would change the polarization ceiling and the temperature dependence of the rotation measure, so the qualitative trends are likely robust but the quantitative limits are not.
  • Editorial inference: the cold-dense phase is where the strongest magnetic fields concentrate, so if reconnection or current sheets live there, nonthermal particle acceleration would be spatially concentrated in exactly the regions that dominate high-frequency emission; kinetic simulations could test this.
  • Editorial inference: the rotation-measure scaling could be inverted as an observational tool; multi-frequency RM monitoring of a repeating FRB over days should map the cooling efficiency and temperature evolution of the screen rather than just its column density.
  • Editorial inference: adding synchrotron self-absorption or inverse-Compton losses would effectively renormalize the cooling efficiency, so the same two-phase structure should reappear in a broader class of radiatively cooled turbulent plasmas beyond the regimes simulated here.
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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

3 major / 5 minor

Summary. This manuscript presents three-dimensional driven relativistic MHD turbulence simulations with synchrotron cooling, and computes synthetic synchrotron spectra, linear polarization maps, and Faraday rotation measures from the simulated turbulence. The central claim is that synchrotron cooling triggers the thermal instability, bifurcating the plasma into hot-dilute and cold-dense phases, which enhances high-frequency emission and polarization variability. The authors benchmark their stirring force (Appendix A), validate the synchrotron cooling implementation against 1D and 3D thermal-instability tests (Appendix B), and show convergence with resolution and initial magnetization (Appendix C). They also compare the mean-temperature scaling with the theoretical prediction of Uzdensky (2018). The synthetic diagnostics show plausible qualitative resemblance to blazar, pulsar wind nebula, and FRB observations.

Significance. If the central claim holds, this would be the first relativistic MHD simulation suite to couple driven turbulence with self-consistent synchrotron cooling and to derive observable radiative signatures. The paper's strengths are its careful benchmarking of the driving force (temperature preserved to ~2e-9), the explicit 1D and 3D linear/nonlinear thermal-instability tests, and the resolution/magnetization convergence checks. The qualitative results on frequency-dependent polarization and RM variability are potentially useful for interpreting multi-wavelength observations. The main weakness is that the attribution of the phase structure to the thermal instability is not supported by a control experiment and is internally qualified by the authors' own diagnostics.

major comments (3)
  1. [Section 3.1, Appendix B (Eq. B3), Appendix E] The thermal-instability interpretation is not established for the driven runs because the linear instability criterion in Appendix B (Eq. B3) assumes a uniform heating H that balances cooling in a homogeneous equilibrium, whereas in the driven turbulence runs the heating is provided by turbulent dissipation and is spatially non-uniform and time-dependent. The manuscript's own diagnostics weaken the causal claim: Section 3.1 states that the density-fluctuation anisotropy 'resembles the one expected for uncooled turbulence rather than a thermal-instability pattern,' and Appendix E states that 'turbulent compression still dominates, because the β–γρ relation does not fully reverse, as would be expected for pure thermal instability.' Since the abstract and Section 7 attribute the phase coexistence to the thermal instability, this is a load-bearing point. Please add a control simulation without cooling (or with a cooling term that does not depend on local density and temperature), processed with the same phase-identification thresholds, and quantify the filling fractions relative to that control.
  2. [Section 3.2, Figure 4] The statement that non-zero volume filling fractions for the hot-dilute and cold-dense phases 'confirm the presence of the synchrotron-cooling-induced thermal instability' is overstated because no null-hypothesis control is presented. The thresholds in Figure 4 are defined per run from the percentile p of the temperature and density PDFs, and the filling fraction is the intersection of the two selected tails. Compressive turbulence with density-dependent cooling can also populate the anti-correlated temperature-density quadrants without an instability. A control run with identical driving but without cooling, or with a cooling function that is artificially decoupled from local density/temperature, is needed to separate the instability contribution from the compressive-cooling contribution.
  3. [Section 4.2, Table 1, Eq. (12)] The scaling relation S.D.(RM) ∝ sqrt(⟨σ⟩_V) K0(⟨Θ_t⟩_V^{-1})/K2(⟨Θ_t⟩_V^{-1}) in Eq. (12) is calibrated to the three simulations listed in Table 1; the proportionality constant is not quoted, and no independent run is used to validate the relation. The FRB temperature estimate in Section 6.3 (⟨Θ_t⟩_V ∼ 3×10^3 for FRB 121102) relies on this uncalibrated relation, which weakens the quantitative inference. Please provide the fitted proportionality constant with an estimate of scatter, or validate Eq. (12) against an additional run with different η_syn or σ0.
minor comments (5)
  1. [Figure 5 caption] The caption contains a duplicated phrase: 'In all runs, In all runs,'. Please remove the repetition.
  2. [Eq. (8)] The expression for the Q Stokes emissivity contains ambiguous inline fractions '7Θ24/25_t + 35 / 10Θ24/25_t + 75'; please format these as explicit fractions with parentheses or display equations so the intended ratio is clear.
  3. [Section 6.3] The derivation of the FRB temperature estimate should state explicitly how Eq. (12) is inverted (including the numerical value of the proportionality constant) so that the reader can reproduce the result.
  4. [Appendix D] The caveat that no Lorentz-invariant kinetic PSD exists is placed only in an appendix; since the main text reports the kinetic PSD slope (Section 3.3), consider mentioning this frame-dependence caveat there to avoid over-interpretation.
  5. [Section 5] The note that the forcing is non-causal because perturbations are applied simultaneously in Fourier space would be more informative if the range of forcing wavenumbers (kL/(2π) between 1 and 4) is stated here, as it quantifies the scale separation responsible for the non-causality.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: simulation diagnostics benchmarked against independent theory, and the RM scaling relation is a calibration rather than a self-prediction.

full rationale

The core results are self-contained simulation outputs, not reductions of the inputs. The temperature scaling <Theta_t>_V ∝ eta_syn^-1/2 is checked against Uzdensky (2018), and the thermal-instability interpretation is anchored in external work (Simon & Axford 1967; Eilek & Caroff 1979; Bodo et al. 1990, 1992), with the paper's own Appendix B providing an independent linear and nonlinear analysis. The phase-identification argument in Section 3.2 is statistically weak rather than circular: the filling fractions are not equal to the chosen percentile by construction, and the paper itself states in Appendix E that 'turbulent compression still dominates, because the beta-gamma rho relation does not fully reverse, as would be expected for pure thermal instability.' This is an inferential caveat, not a circular derivation. The main possible concern, Equation (12), is an empirical RM scaling relation 'based on Table 1' (the three simulation runs), and Section 6.3 uses it to estimate the FRB 121102 screen temperature. This is a model-dependent extrapolation of a calibrated relation to a new astrophysical target, not a prediction of a fitted data point: the FRB screen temperature is not part of the calibration set. Self-citations in the paper (e.g., Comisso & Sironi 2018, 2021; Chernoglazov et al. 2021; Sironi et al. 2023) appear only as context, methodological references, or acknowledged limitations, and are not load-bearing for the central claims. No specific circular step reducing a result to its own inputs was found.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The central claims rest on the chosen cooling efficiency eta_syn and driving amplitude, the Maxwell-Juttner electron distribution, the approximation in the cooling term, and the transfer of the uniform-heating thermal-instability criterion to driven turbulence. No new particles or fields are introduced.

free parameters (7)
  • Synchrotron cooling efficiency eta_syn = 6.4e-2, 1.0e-3, 1.0e-4 (three runs)
    Chosen by hand to span strong to weak cooling; controls the mean temperature, phase structure, and RM statistics. Central results depend on its value.
  • Turbulent driving amplitude = <M . F_OU>_V = 1280 rho0^2 c^3 / L
    Sets the energy injection rate; chosen to maintain quasi-steady turbulence with magnetic energy dominating the mean field. A standard simulation control parameter.
  • Phase-identification percentile p = 0.05 and 0.158
    Defines the hot-dilute and cold-dense phase thresholds in Section 3.2; volume filling fractions are sensitive to this choice.
  • RM scaling normalization in Eq (12) = Not explicitly reported; implicitly calibrated to Table 1
    The proportionality constant required to apply Eq (12) to the FRB temperature estimate is not given; the scaling is calibrated to three simulation runs.
  • Initial magnetization sigma0 = 1 (fiducial), 0.1 (convergence test)
    Initial mean-field strength; chosen to be magnetized. Shown to have weak effect on most diagnostics except RM mean.
  • Initial temperature Theta_t(t=0) = 2
    Initial dimensionless temperature; chosen for a relativistically hot gas. Influences early cooling but quasi-steady state is set by injection-cooling balance.
  • Numerical floors and ceilings = rho_min=5e-3 rho0, gamma_max=50, Pg_min=5e-5 rho0 c^2, sigma_max=2e3, beta_min=5e-6
    Introduced to prevent unphysical states; the cold-dense phase could be affected by the density and pressure floors, and the pure TI test reaches floors (Appendix B).
assumptions (4)
  • domain assumption Electrons and positrons follow an isotropic Maxwell-Juttner distribution with temperature Theta_t = P_g / (rho c^2) for cooling, emission, and Faraday rotation.
    Adopted in Section 2 and used in Eqs (6), (8), (11). Collisionless turbulence can produce nonthermal electrons and two-temperature effects, as the paper acknowledges in footnote 1 and Section 7.
  • domain assumption The thermal-instability criterion derived for a uniformly heated plasma applies to the driven-turbulence runs where heating is by turbulent dissipation.
    Section 3.1 interprets the phase bifurcation via the synchrotron-cooling-induced thermal instability, but the turbulent runs do not include the uniform heating term H used to define the equilibrium in Eq B3.
  • ad hoc to paper The approximation K3(z)/K2(z) approximately 4z + 1 in the cooling term is accurate enough for the physics.
    Footnote 2 introduces this approximation to stabilize the IMEX scheme; it overestimates the cooling rate by up to about 15 percent near Theta_t approximately 0.5, which is near the cold-dense phase.
  • domain assumption Ideal RMHD with frozen-in condition, no explicit resistivity, and no thermal conduction captures the relevant dynamics.
    Section 5 states that explicit resistivity and thermal conduction are neglected; this may affect the dissipation range and the development of the thermal instability.

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Pith. "Pith review of Synchrotron-Regulated Relativistic Magnetohydrodynamic Turbulence: Emission, Polarization, and Faraday Rotation." pith.science (2026). https://pith.science/paper/XTNTG5EW

@misc{pith2026260810748,
  author       = {Pith},
  title        = {Pith review of: Synchrotron-Regulated Relativistic Magnetohydrodynamic Turbulence: Emission, Polarization, and Faraday Rotation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XTNTG5EW}},
  note         = {Machine review of arXiv:2608.10748}
}
read the original abstract

Relativistic magnetized plasmas in many high-energy astrophysical systems are both turbulent and strongly radiative, yet their nonlinear dynamics and radiative outcomes remain poorly understood. Here we present results from three-dimensional driven turbulence simulations in relativistic magnetohydrodynamics with synchrotron cooling. We compute Faraday rotation measures, synthetic synchrotron spectra and linear polarization maps from the simulated turbulence. The balance between energy injection from turbulent driving and synchrotron cooling keeps the plasma, on average, relativistically hot, thereby influencing the rotation measure. Synchrotron cooling triggers the thermal instability and drives the plasma into hot dilute and cold dense phases, which enhances the spatial and temporal variability of synchrotron emission, especially at high frequencies. These diagnostics show qualitative similarities to observations of fast radio bursts, pulsar wind nebulae, and blazars, suggesting that turbulence may play an important role in shaping emission and propagation effects around high-energy sources.

Figures

Figures reproduced from arXiv: 2608.10748 by the authors.

Figure 1
Figure 1. Time evolution of volume-averaged Lorentz factor ⟨γ⟩V (solid lines), magnetization ⟨σ⟩V (dashed lines), tem￾perature ⟨Θt⟩V (dotted lines). Colors indicate different cool￾ing efficiencies as shown in the legend. Here, L denotes the simulation box size, which also corresponds to the largest eddy scale, and Kn is the nth order modified Bessel function of the second kind.2 The dimensionless cooling efficiency, ηsyn, qua… view at source ↗
Figure 2
Figure 2. Snapshots of lab-frame density γρ (left column), dimensionless temperature Θt (middle column), and synchrotron cooling power γPsyn (right column) at time tc/L = 9.375. From top to bottom, the rows represent different runs with ηsyn = 6.4 × 10−2 , 10−3 , 10−4 respectively. The density and temperature slices are taken at z = L/2. defined by Θt > Θt,crit(p) and simultaneously γρ < (γρ)crit(p), with an analogous definit… view at source ↗
Figure 3
Figure 3. Lab-frame density γρ versus temperature Θt dis￾tribution of quasi-steady turbulence, integrated from time 6L/c to 9.375L/c. The solid contours enclose 95% of the plasma by volume. Colors indicate different cooling efficien￾cies as shown in the legend [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (23 more)
Figure 4
Figure 4. Figure 4: Temperature Θt,crit(p) (top) and lab-frame den￾sity (γρ)crit(p) (middle) thresholds as functions of the per￾centile p, together with the volume filling fractions (bottom) of the hot-dilute (solid) and cold-dense (dashed) phases. Col￾ors indicate different cooling effic…
Figure 5
Figure 5. Figure 5: Snapshots of the identified hot-dilute and cold-dense phases in quasi-steady state. The extreme phases identified with p = 0.05 are shown in red (hot-dilute) and blue (cold-dense), while the moderate phases identified with p = 0.158 are shown in orange (hot-dilute) and…
Figure 6
Figure 6. Figure 6: The shell-integrated magnetic and kinetic power spectral density E˜(k) of quasi-steady turbulence . Colors indicate different cooling efficiencies as shown in the legend. Solid lines represent the magnetic power spectra E˜mag(k), while dashed lines refer to the kinetic…
Figure 7
Figure 7. Figure 7: The synchrotron emission spectra (⟨Iν⟩, top) and linear polarization degree (q ⟨Qν⟩ 2 + ⟨Uν⟩ 2 / ⟨Iν⟩, bottom) of quasi-steady turbulence. The emission frequency ν is in units of electron cyclotron frequency Ωe0, defined for the background field intensity equal to p ρ0…
Figure 8
Figure 8. Figure 8: Synchrotron intensity maps of Iν/⟨Iν⟩ from turbulence with ηsyn = 6.4 × 10−3 , viewed along the x direction at tc/L = 9.375, normalized by the spatial and temporal average at the corresponding frequency ⟨Iν⟩ ( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Probability distribution functions (PDFs) of syn￾chrotron intensity variations Iν/⟨Iν⟩ from quasi-steady tur￾bulence with ηsyn = 6.4×10−3 , viewed along the x direction, normalized by the spatial and temporal average ⟨Iν⟩ (Fig￾ure 7). Colors denote different time snaps…
Figure 10
Figure 10. Figure 10: The linear polarization degree p Q2 ν + U2 ν /Iν images of turbulence with ηsyn = 6.4 × 10−3 , viewed along the x direction at tc/L = 9.375. Panels from left to right show emission from low to high frequencies, as marked on the plot [PITH_FULL_IMAGE:figures/full_fig_…
Figure 11
Figure 11. Figure 11: Probability distribution functions (PDFs) of synchrotron linear polarization degree p Q2 ν + U2 ν /Iν from quasi-steady turbulence with ηsyn = 6.4 × 10−3 , viewed along the x direction. Colors denote different time snap￾shots, tc/L = 6.25 (purple), 7.8125 (blue), and …
Figure 12
Figure 12. Figure 12: Rotation measure (RM) snapshots for turbulence with different cooling efficiencies. The top row shows views perpendicular to the mean magnetic field, and the bottom row shows views along the mean field. Note that, for better visualization, the RM in the ηsyn = 6.4 × 1…
Figure 13
Figure 13. Figure 13: Probability distribution functions (PDFs) of the rotation measure (RM) from quasi-steady turbulence. Colors indicate different cooling efficiencies, as indicated in the leg￾end. Solid (dashed) curves correspond to viewing directions perpendicular (parallel) to the mea…
Figure 14
Figure 14. Figure 14 [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 16
Figure 16. Figure 16 [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]
Figure 15
Figure 15. Figure 15: Illustration of the thermal instability induced by synchrotron cooling. This schematic illustration was gen￾erated using ChatGPT (OpenAI) based on author-provided physically-motivated prompts and refined by the authors. of density ρ0 and pressure P0, threaded by a uni…
Figure 17
Figure 17. Figure 17: Normalized density structure function (Equa￾tion F5) for the non-linear evolution of the thermal instabil￾ity in 3D. The color in logarithmic scale indicates the ratio to the overall density variance. The horizontal and vertical axes are in units of cell size, ∆x = τs…
Figure 18
Figure 18. Figure 18: Phase distributions in quasi-steady state for runs with different initial magnetization σ0 or different nu￾merical resolution ∆x but with the same synchrotron cooling efficiency ηsyn = 6.4 × 10−3 . Colors indicate different runs as shown in the legend. volumetric heat…
Figure 19
Figure 19. Figure 19: Magnetic (solid lines) and kinetic (dashed lines) power spectral densities in quasi-steady state for two runs with different initial magnetization σ0 or different numerical resolution ∆x but with the same synchrotron cooling effi￾ciency ηsyn = 6.4 × 10−3 . Colors indi…
Figure 20
Figure 20. Figure 20: Rotation measure (RM) probability distribu￾tion functions (PDFs) in quasi-steady state for two runs with different initial magnetization σ0 but with the same synchrotron cooling efficiency ηsyn = 6.4 × 10−3 . Colors in￾dicate different runs as shown in the legend. sim…
Figure 21
Figure 21. Figure 21: Kinetic power spectral densities (PSDs) in quasi-steady state computed using different definitions of the kinetic field: Mkin (black; Equation 7), Mγ (orange; definition 1), Mu (magenta; definition 2), and Mfour (viridis; definition 3). Note that in this figure, color…
Figure 22
Figure 22. Figure 22: The phase distribution (upper panels) and the synchrotron cooling distribution (lower panels) in quasi-steady state, for lab-frame density γρ and temperature Θt, with different synchrotron cooling efficiencies ηsyn. Upper panels are weighted by volume, lower panels by…
Figure 23
Figure 23. Figure 23: The distribution of plasma β ≡ 2Pg/B′2 and lab-frame density γρ in quasi-steady state, with different synchrotron cooling efficiencies ηsyn. Upper panels are weighted by volume, lower panels by synchrotron power. Note that the colorbars are in logarithmic scale. The w…
Figure 24
Figure 24. Figure 24: Normalized density structure function of quasi￾steady turbulence. Colors indicate different cooling efficien￾cies and initial magnetization as shown in the legend. The number over each line indicates the ratio to the overall den￾sity variance (Equation F5) [PITH_FULL…
Figure 25
Figure 25. Figure 25: Magnetic structure function of quasi-steady tur￾bulence. Colors indicate different cooling efficiencies and ini￾tial magnetization as shown in the legend. The number over each line indicates the magnitude of the structure function (Equation F6). We find no significant…
Figure 26
Figure 26. Figure 26: Anisotropy in density (crosses, computed from [PITH_FULL_IMAGE:figures/full_fig_p022_26.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.