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This paper argues that turbulent heating alone cannot balance radiative cooling in cool-core clusters, even when pre-existing turbulence is included at observed levels, and that the XRISM central velocity rise is transient bulk motion.

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2026-08-03 19:32 UTC pith:SM6MZZVM

load-bearing objection A solid controlled simulation study that makes a real addition to the turbulent-heating debate, but the central Q_turb < Q_cool comparison is missing its baseline because Q_cool is never defined. the 4 major comments →

arxiv 2511.23267 v2 pith:SM6MZZVM submitted 2025-11-28 astro-ph.HE

Simulating AGN feedback in galaxy clusters with pre-existing turbulence

Jia-Lun Li , H.-Y. Karen Yang This is my paper
classification astro-ph.HE
keywords cool-core clustersAGN feedbackintracluster medium turbulenceturbulent heatingPerseus clustervelocity structure functionenergy power spectrumXRISM
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Cool-core clusters radiate away their central gas energy faster than expected, yet the gas does not collapse into a cooling flow; something must heat it. A leading candidate has been turbulence, stirred either by AGN jets or by pre-existing motions, and some X-ray brightness fluctuation analyses have suggested turbulence alone could offset the cooling. This paper tests that idea in three-dimensional hydrodynamic simulations of a Perseus-like cluster, including a strong pre-existing turbulent field calibrated to the observed ~185 km/s line-of-sight velocity dispersion, plus a single AGN jet outburst. Using two independent Kolmogorov-based estimators—the velocity structure function and the kinetic energy power spectrum—the authors find that the turbulent heating rate falls below the radiative cooling rate in the cluster core (r < 50 kpc), implying turbulence alone cannot prevent catastrophic cooling. They further show that the jet's contribution to the velocity field is a short-lived coherent flow, not a self-sustaining cascade, which they argue explains the central line-broadening enhancement seen by XRISM without invoking AGN-powered turbulence.

Core claim

Central discovery: in a Perseus-like cool-core cluster with pre-existing turbulence stirred to the observed σ_LOS ≈ 185 km/s, two independent Kolmogorov estimators—the longitudinal velocity structure function (ℓ_VSF ≈ 53.1 kpc) and the energy power spectrum (ℓ_Ek ≈ 52.6 kpc)—give turbulent heating rates below the radiative cooling rate in the core (r < 50 kpc), and the rates are treated as upper limits. Early-time energy spectra show the AGN jet's injected energy decays within ~20–30 Myr without cascading, so the jet drives transient coherent bulk flows, not sustained turbulence; the authors argue the XRISM central σ_LOS enhancement in Perseus is this bulk motion, not AGN-powered turbulence.

What carries the argument

The key machinery is the Kolmogorov-cascade estimator of turbulent dissipation. The velocity structure function D_LL(ℓ) gives the variance of longitudinal velocity differences and is fitted to C_2 ε^{2/3} ℓ^{2/3} in the inertial range; the energy power spectrum E(k) is fitted to C_K ε^{2/3} k^{-5/3}. The inertial range is identified at 20–100 kpc, ε is read off at the tangent points (ℓ_VSF ≈ 53.1 kpc, ℓ_Ek ≈ 52.6 kpc), and the volumetric heating rate Q_turb = ρ ε is compared with cooling in radial shells. A second element is the time-resolved E(k) comparison between the run with and without the jet, which separates a self-sustaining cascade from transient coherent large-scale motions.

Load-bearing premise

The load-bearing premise is that the 20–100 kpc velocity fluctuations in the cluster core obey a classical incompressible Kolmogorov cascade, so that the dissipation rate can be read off from the structure function and power spectrum with standard constants; if compressibility, stratification, or numerical viscosity distort the inertial-range scaling, the inferred turbulent heating rate could be off by a factor and the central shortfall might shrink or grow.

What would settle it

Measure the two-point velocity statistics in the Perseus core over scales 20–100 kpc with a future X-ray spectrometer that has both high spectral resolution and sufficient spatial resolution (or use a large sample of emission-line velocity maps) and check whether D_LL(ℓ) follows ℓ^{2/3} with the assumed constant; if the measured dissipation rate, integrated over the core, equals or exceeds the radiative cooling rate, the paper's central claim fails. A complementary check: if the central σ_LOS enhancement observed by XRISM is resolved spatially and shows a Kolmogorov power spectrum extending to

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Turbulent heating is not the primary mechanism solving the cooling-flow problem in cool-core clusters; other AGN channels (bubble mixing, weak shocks, sound waves, cosmic-ray heating) must supply the missing heat.
  • Even when pre-existing turbulence is driven to the maximum level consistent with Hitomi/XRISM velocity measurements, the core heating rate remains below the cooling rate, so boosting turbulence alone will not close the energy budget.
  • The central σ_LOS enhancement observed by XRISM in Perseus should not be interpreted as direct evidence of AGN-powered turbulence; if the simulated picture is right, it is a transient coherent flow, and turbulent heating estimates based on that line broadening would be overestimates.
  • Both VSF and E(k) methods give the same radial trend (heating shortfall in the core, comparability at large radii), with the E(k) estimate systematically higher, bracketing the systematic uncertainty in the upper limit.
  • The jet's contribution to the global velocity statistics is minor, yet it still heats the ICM through pressure work, so AGN feedback remains effective even when the velocity field is turbulence-dominated.

Where Pith is reading between the lines

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

  • If the central velocity enhancement in Perseus is indeed a transient bulk flow, then X-ray line measurements with spatial resolution sufficient to resolve 20–100 kpc scales might see a coherent shearing or dipole pattern in the velocity centroid map rather than random small-scale eddies; this is a testable distinction from sustained turbulence.
  • The simulation's conclusion depends on the assumption that numerical dissipation on the grid mimics the physical dissipation at the true ICM Reynolds number; if the real ICM has a much longer inertial range or the cascade is modified by magnetic fields, the inferred Q_turb could shift—an extension the authors note but do not quantify.
  • Because the simulation excludes radiative cooling, magnetic fields, thermal conduction, and cosmic rays, a natural next step is to repeat the comparison in self-regulated feedback runs with cooling; if cooling changes the density and stratification, the inertial-range scalings and the inferred heating rates may change, potentially moving the conclusion in either direction.
  • The paper's reinterpretation of XRISM data suggests a caution for the broader practice of inferring turbulent velocities from unresolved line broadening or surface brightness fluctuations: attributing all velocity variance to a turbulent cascade may systematically overestimate the dissipation available to heat the gas.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The authors present 3D hydrodynamic simulations of a Perseus-like galaxy cluster using the FLASH code, comparing three controlled runs: pre-existing turbulence only, AGN jet only, and both. The turbulence is stirred by spectral Ornstein–Uhlenbeck forcing calibrated to the Hitomi line-of-sight velocity dispersion, and the AGN is a single 10 Myr kinetic bipolar jet. The central claim is that when the simulated velocity field is analyzed with the second-order velocity structure function and the kinetic-energy power spectrum under Kolmogorov scalings, the inferred turbulent heating rate Q_turb is smaller than the radiative cooling rate Q_cool in the cluster core, so turbulent heating alone cannot offset radiative cooling in cool-core clusters. A secondary claim is that the central σ_LOS enhancement recently reported by XRISM is reproduced by the combined run but is better interpreted as transient, coherent bulk motion than as sustained turbulence.

Significance. If the central comparison is made reproducible, the paper would strengthen the simulation-based case that turbulent heating is subdominant in cool-core cluster cores, while explicitly including pre-existing turbulence stirred to the observationally constrained Perseus level. Strengths of the paper are the controlled run design, the use of two independent estimators of the dissipation rate, the explicit interpretation of the estimates as upper limits, the convergence check, and the direct engagement with the new XRISM velocity-dispersion measurement. The main quantitative result, however, currently rests on an undefined and unreferenced radiative-cooling baseline, and the Kolmogorov-based estimates would benefit from a quantitative justification of the underlying assumptions. These issues are local and fixable; they do not by themselves invalidate the qualitative conclusion, but they block verification as written.

major comments (4)
  1. [§3.5 / Fig. 10] The central inequality Q_turb < Q_cool is not testable as written because Q_cool is never defined. Radiative cooling is excluded from the simulations (Eqs. 1–3), so Q_cool must be an external input, but the manuscript supplies no cooling function, metallicity, redshift, density/temperature profile, radial shell edges, or reference. Figure 10 also lacks explicit axis labels and units. Please specify how Q_cool was computed or from which observational estimate it was taken, and give the numerical values in the five radial shells. Without this, the abstract's claim cannot be verified or reproduced.
  2. [§2.4, §3.5] The dissipation-rate estimates assume Kolmogorov incompressible turbulence with fixed constants (C2 ≈ 2.0, CK ≈ 1.65) applied over a 20–100 kpc inertial range. The justification that this is appropriate—solenoidal dominance and Fr > 0.1—is qualitative. Because the absolute magnitude of ε carries the whole argument, please quantify: (i) the compressive kinetic-energy fraction in the inertial range; (ii) the sensitivity of ε to the chosen fitting interval and to constants within published ranges; (iii) the variation of D_LL/E(k) across radial shells if shell-resolved estimates are used. This matters most in the outer bins, where Q_turb and Q_cool become comparable and a factor-of-order-unity error could alter the conclusion.
  3. [§3.5 / Fig. 10] The method used to assign Q_turb to the five clustercentric shells is underspecified. The text says Q_turb = ρε with ρ averaged within each shell, but does not state whether ε is evaluated separately per shell or taken from a global VSF/E(k), nor the shell boundaries or weighting (emissivity, volume). The claim that the two methods bracket the true heating rate also requires that the same radial binning and fitting procedure be applied to both. Please specify the radial bins and the shell-wise computation, and give the resulting ε values (or Q_turb values) in a table so the comparison can be reproduced.
  4. [§4.2 / Fig. 11] The secondary conclusion that the central σ_LOS enhancement is "not turbulence" is based on the visual similarity of E(k) at t = 30 Myr and the short-lived bump in the combined run. This is not quantitative enough to support the strong wording. Please provide a quantitative measure: the fraction of injected jet energy that appears as solenoidal vs irrotational power on scales below the driving range, the decay time of excess large-scale power relative to the local eddy turnover time, or a comparison of the shell-resolved VSF slopes in the core with and without the jet. As written, the statement that XRISM's central enhancement is primarily coherent bulk motion is suggestive but not established.
minor comments (6)
  1. [Abstract / §5] The abstract and conclusions should soften "CC clusters" to "the Perseus-like cluster modeled here"; the simulations contain one cluster model with a single episodic jet and no radiative cooling.
  2. [Fig. 10 / §3.5] Please state the units of Q_turb and Q_cool and explicitly define the radial bins. The text refers to "radiative cooling rates" but does not say whether these are per unit volume, per unit mass, or integrated luminosities in shells.
  3. [§2.2] The σ_LOS calibration is described as domain-averaged, while Hitomi/XRISM measure inner-core values. Clarify the region used for matching and verify that the simulated central σ_LOS profile is consistent with the observational aperture.
  4. [§4.1] The Froude number is quoted as Fr > 0.1 but never defined. Give the formula and the calculated value (with the integral-scale quantities used) so the stratification argument can be checked.
  5. [General / Data availability] The data availability statement says data will be shared upon reasonable request. Consider depositing analysis scripts and derived profiles in a permanent repository with a DOI; this would make the central figures auditable.
  6. [General] Typographical and formatting issues: the Table 1 header appears as "T able 1"; "velocity disperson" in §4.1; a repeated sentence after Fig. 11; inconsistent use of spaces in "T urb+Jet" in captions and text.

Circularity Check

0 steps flagged

No significant circularity: the central Q_turb < Q_cool comparison is not fit to or derived from the cooling rate; the paper's self-citations are corroborating prior context rather than load-bearing.

full rationale

The derivation chain in Sections 2.4 and 3.5 is not circular. The pre-existing turbulence amplitude is calibrated to the observed Hitomi σ_LOS (Section 2.2, Table 1), and the jet power is an externally referenced input (Section 2.3), but neither is fit to the radiative cooling rate. The turbulent dissipation rate ε is estimated from the simulated velocity field by fitting D_LL and E(k) to Kolmogorov scalings with standard constants (Eqs. 9 and 10; C2≈2.0, CK≈1.65), and Q_turb = ρε is only then compared with cooling in Fig. 10. The cooling rate plotted is never defined in the manuscript, and radiative cooling is excluded from Eqs. (1)–(3); this is a reproducibility/verification gap rather than a circularity, because the manuscript does not construct Q_cool from Q_turb or from any fitted parameter. The self-citations (e.g., Yang & Reynolds 2016a for the cluster setup, 2016b for jet power and prior conclusions) are corroborating context rather than the load-bearing derivation; the paper's new E(k) analysis and the Turb+Jet versus TurbOnly comparison provide independent content. The XRISM comparison is also not forced: the σ_LOS calibration sets only the global amplitude, while the central enhancement appears specifically in Turb+Jet, so it is a nontrivial simulation output. No predictive step reduces by construction to its input.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the turbulence injection rate (calibrated to Hitomi's σ_LOS), the forcing autocorrelation time, the two characteristic scales used in the ε estimates, and the jet power/duration. The central comparison rests on applying Kolmogorov scaling to a weakly stratified, solenoidal-dominated simulated flow and on an externally supplied Q_cool that is not explicitly defined.

free parameters (5)
  • Turbulence injection rate ε_inj = 4×10^-5 cm^2 s^-3
    Adjusted so that the domain-averaged simulated LOS velocity dispersion matches the Hitomi value (~164 km/s; simulated σ_LOS ≈185 km/s). This calibration sets the turbulent energy input.
  • Characteristic VSF scale ℓ_VSF = 53.1 kpc
    Selected by the tangent point to D_LL ∝ ℓ^{2/3} in the inertial range; used in Eq. (9) to estimate ε. A different choice would change Q_turb.
  • Characteristic spectrum scale ℓ_Ek = 52.6 kpc
    Selected by the tangent point to E(k) ∝ k^{-5/3}; used in Eq. (10). Source of systematic spread between the two methods.
  • OU forcing autocorrelation time τ_d = 8.5×10^15 s (~270 Myr)
    Sets the temporal correlation of the stirring; chosen to match the eddy turnover time; part of the turbulence-driving model.
  • AGN jet power and duration = 5×10^45 erg/s, 10 Myr
    Taken from average jet power in prior self-regulated feedback simulations (Yang & Reynolds 2016b; Dunn & Fabian 2004). A model input, not fitted to the results.
axioms (5)
  • domain assumption Kolmogorov incompressible turbulence scaling (Eqs. 9-10) with C2=2.0 and CK=1.65 describes the simulated ICM velocity field in the inertial range.
    Section 2.4 and 3.5: ε inferred from D_LL and E(k) using these laws; if the flow is compressible/stratified, the constants might not hold. Authors argue solenoidal motions dominate and Fr>0.1.
  • domain assumption Statistical isotropy of the turbulent flow, so that the longitudinal structure function carries the full energy content and the Kolmogorov constant C2 applies.
    Section 2.4.1: the paper focuses on D_LL but assumes isotropy to relate it to total VSF2; anisotropy due to stratification could bias ε.
  • domain assumption Numerical dissipation at the grid scale approximates physical dissipation in a high-Reynolds-number ICM.
    Section 4.3: energy dissipation occurs at grid scale; justified by suppressed viscosity, but it is a modeling premise.
  • domain assumption Radiative cooling can be omitted when measuring turbulent heating, and the cooling rate used for comparison is an external input.
    Section 2: cooling excluded from simulations; Fig. 10 compares to Q_cool, which is never defined. The comparison assumes the Q_cool values are appropriate for this cluster.
  • domain assumption The initial conditions (Eqs. 4-5) and jet parameters represent a Perseus-like cool-core cluster.
    Section 2.1: temperature profile (Eq. 4) from X-ray surface brightness; NFW parameters from literature. The realism of the feedback loop is not self-consistently modeled.

pith-pipeline@v1.3.0-alltime-deepseek · 16889 in / 13981 out tokens · 124003 ms · 2026-08-03T19:32:46.094732+00:00 · methodology

0 comments
read the original abstract

Feedback from active galactic nuclei (AGN) is believed to play a significant role in suppressing cooling flows in cool-core (CC) clusters. Turbulence in the intracluster medium (ICM), which may be induced by AGN activity or pre-existing motions, has been proposed as a potential heating mechanism based on analysis of Chandra X-ray surface brightness fluctuations. However, subsequent simulation results have found the subdominant role of turbulence in heating the ICM. To investigate this discrepancy, we perform three-dimensional hydrodynamic simulations of a Perseus-like cluster including both AGN feedback and pre-existing turbulence, which is stirred to the observationally constrained level in the Perseus cluster. Our results indicate that, although the velocity field is dominated by the pre-existing turbulence, AGN heating through bubbles and shocks remains significant. More importantly, analysis of the velocity structure function and the energy power spectrum shows that the turbulent heating rate is smaller than the radiative cooling rate, especially in the cluster core. Our results offer insights relevant for recent XRISM observations and indicate that turbulent heating alone cannot offset radiative cooling in CC clusters.

Figures

Figures reproduced from arXiv: 2511.23267 by H.-Y. Karen Yang, Jia-Lun Li.

Figure 1
Figure 1. Figure 1: Development of the pre-existing turbulence. Upper panel: Time evolution of the 3D root-mean-square (RMS) turbulent velocity, showing that the system with pre-existing turbulence reaches a steady state after ∼ 800 Myr. Lower panel: Time evolution of the kinetic energy spectrum, E(k), shown from t = 200 to 1400 Myr with an interval of 200 Myr. The convergence of the spectra to a stable profile confirms that … view at source ↗
Figure 2
Figure 2. Figure 2: Time evolution of the gas density slices at the x = 0 plane for JetOnly (top row) and Turb+Jet (bottom row). Columns correspond to snapshots taken at t = 10, 40, 70, 100, and 130 Myr after jet injection. Each slice is 200 kpc on a side. In Turb+Jet, the jets propagate faster and the cluster core is less centrally concentrated due to pre-existing turbulence, which also disrupts the bubbles more quickly comp… view at source ↗
Figure 3
Figure 3. Figure 3: Columns from left to right correspond to TurbOnly, Turb+Jet, and JetOnly, shown at the same timestep, 50 Myr after the jet injection. The first row shows thin projections (4 kpc) of the velocity magnitude (|v|) weighted by gas density. The second row shows the line-of-sight velocity dispersion (σLOS) weighted by X-ray emissivity.Each panel spans 132 kpc on a side. Both |v| and σLOS are dominated by pre-exi… view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of σLOS averaged over the en￾tire simulation domain for Turb+Jet and TurbOnly as a function of the time since jet injection. The overall σLOS is similar in both cases, indicating that the jet has a minor im￾pact and that the velocity field is dominated by pre-existing turbulence. sion. The structures associated with jet injection, as seen in JetOnly, are still visible in Turb+Jet. In the hot… view at source ↗
Figure 5
Figure 5. Figure 5: Entropy profiles as a function of radius for TurbOnly, Turb+Jet, and JetOnly, shown at the same timesteps after jet injection. Different lines correspond to different timesteps. The entropy increase is mainly due to the jet, with turbulence having little effect, as shown by the similar profiles of Turb+Jet and JetOnly, while TurbOnly remains nearly constant [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Slices of ∆P/P for Turb+Jet (left) and JetOnly (right), shown at 50 Myr after the jet injection. Each image spans 300 kpc on a side. Both sound waves and weak shocks are present, and the similarity between the two simulations indicates that jet-driven heating remains effective despite the dominance of pre-existing turbulence in the velocity field. tions at widely separated points become statistically un￾co… view at source ↗
Figure 7
Figure 7. Figure 7: Energy spectra E(k) as a function of wavenumber k (k = 1/ℓ) for TurbOnly and Turb+Jet at t = 10, 20, and 30 Myr after jet injection, respectively from left to right. Each panel shows the spectra computed within a central region 200 kpc on a side. The jet produces a noticeable but short-lived modification to the spectral shape. This effect fades quickly, after which the spectra in both runs appear similar, … view at source ↗
Figure 9
Figure 9. Figure 9: E(k) as a function of wavenumber k (k = 1/ℓ). The green line indicates the expected Kolmogorov scaling, E(k) ∝ k −5/3 , in the inertial range. The vertical red line marks the characteristic scale ℓEk ≈ 52.6 kpc identified via the tangent point, used to estimate an upper limit to the turbulent dissipation rate ε. (I. Zhuravleva et al. 2014, 2016, 2018), which sometimes infer higher turbulent velocities or s… view at source ↗
Figure 10
Figure 10. Figure 10: Turbulent heating rate Qturb compared to the radiative cooling rate Qcool in different radial shells. Solid lines show the heating rate estimates from the VSF (blue) and E(k) (red) methods at their characteristic scales, ℓVSF ≈ 53.1 kpc and ℓEk ≈ 52.6 kpc. Shaded bands indi￾cate the uncertainty due to methodological differences. The black dashed line marks the 1:1 relation, indicating where the turbulent … view at source ↗
Figure 11
Figure 11. Figure 11: Projected radial profile of the averaged σLOS. The shaded regions represent the one-standard-deviation (1σ) scatter from our Turb+Jet (blue) and TurbOnly (red) simulations, computed 10 Myr after the jet injection. The green data points are the direct σLOS measurements from the XRISM observation of the Perseus cluster ( XRISM Collaboration et al. 2025a). Our Turb+Jet simulation successfully reproduces the … view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

60 extracted references · 8 canonical work pages · cited by 4 Pith papers

  1. [1]

    E., & Pfrommer, C

    Berlok, T., Quataert, E., Pessah, M. E., & Pfrommer, C. 2021, MNRAS, 504, 3435, doi: 10.1093/mnras/stab832

    doi:10.1093/mnras/stab832 2021

  2. [2]

    N., von der Linden, A., Kauffmann, G., Heckman, T

    Best, P. N., von der Linden, A., Kauffmann, G., Heckman, T. M., & Kaiser, C. R. 2007, MNRAS, 379, 894, doi: 10.1111/j.1365-2966.2007.11937.x B ˆ ırzan, L., Rafferty, D. A., Nulsen, P. E. J., et al. 2012, MNRAS, 427, 3468, doi: 10.1111/j.1365-2966.2012.22083.x

    arXiv 2007

  3. [3]

    A., & Yang, H.-Y

    Bourne, M. A., & Yang, H.-Y. K. 2023, Galaxies, 11, 73, doi: 10.3390/galaxies11030073 Di Gennaro, G., van Weeren, R. J., Brunetti, G., et al. 2021, Nature Astronomy, 5, 268, doi: 10.1038/s41550-020-01244-5

    doi:10.3390/galaxies11030073 2023

  4. [4]

    Drury, L. O. 1983, Reports on Progress in Physics, 46, 973, doi: 10.1088/0034-4885/46/8/002

    doi:10.1088/0034-4885/46/8/002 1983

  5. [5]

    B., & Fisher, R

    Dubey, A., Reid, L. B., & Fisher, R. 2008, Phys. Scr., 2008, 014046, doi: 10.1088/0031-8949/2008/T132/014046

    doi:10.1088/0031-8949/2008/t132/014046 2008

  6. [6]

    Dunn, R. J. H., & Fabian, A. C. 2004, MNRAS, 355, 862, doi: 10.1111/j.1365-2966.2004.08365.x

    arXiv 2004

  7. [7]

    1988, Compu

    Eswaran, V., & Pope, S. 1988, Compu. Fluids, 16, 257, doi: https://doi.org/10.1016/0045-7930(88)90013-8

    doi:10.1016/0045-7930(88)90013-8 1988

  8. [8]

    Fabian, A. C. 1994, ARA&A, 32, 277, doi: 10.1146/annurev.aa.32.090194.001425

    arXiv 1994

  9. [9]

    C., Walker, S

    Fabian, A. C., Walker, S. A., Russell, H. R., et al. 2017, MNRAS, 464, L1, doi: 10.1093/mnrasl/slw170

    doi:10.1093/mnrasl/slw170 2017

  10. [10]

    2013, MNRAS, 436, 1245, doi: 10.1093/mnras/stt1644

    Federrath, C. 2013, MNRAS, 436, 1245, doi: 10.1093/mnras/stt1644

    doi:10.1093/mnras/stt1644 2013

  11. [11]

    2016, Journal of Plasma Physics, 82, 535820601, doi: 10.1017/S0022377816001069

    Federrath, C. 2016, Journal of Plasma Physics, 82, 535820601, doi: 10.1017/S0022377816001069

    doi:10.1017/s0022377816001069 2016

  12. [13]

    S., et al

    Federrath, C., Roman-Duval, J., Klessen, R. S., et al. 2010, A&A, 512, A81, doi: 10.1051/0004-6361/200912437

    doi:10.1051/0004-6361/200912437 2010

  13. [14]

    2000, ApJS, 131, 273, doi: 10.1086/317361

    Fryxell, B., Olson, K., Ricker, P., et al. 2000, ApJS, 131, 273, doi: 10.1086/317361

    doi:10.1086/317361 2000

  14. [15]

    Gaspari, M., Ruszkowski, M., & Oh, S. P. 2013, MNRAS, 432, 3401, doi: 10.1093/mnras/stt692

    doi:10.1093/mnras/stt692 2013

  15. [16]

    L., et al

    Gaspari, M., McDonald, M., Hamer, S. L., et al. 2018, ApJ, 854, 167, doi: 10.3847/1538-4357/aaaa1b Hitomi Collaboration. 2016, Nature, 535, 117, doi: 10.1038/nature18627

    doi:10.3847/1538-4357/aaaa1b 2018

  16. [17]

    S., Donahue, M., Hicks, A., & Barthelemy, R

    Hoffer, A. S., Donahue, M., Hicks, A., & Barthelemy, R. S. 2012, ApJS, 199, 23, doi: 10.1088/0067-0049/199/1/23

    work page doi:10.1088/0067-0049/199/1/23 2012

  17. [18]

    2003, Physics of Fluids, 15, L21, doi: 10.1063/1.1539855

    Uno, A. 2003, Physics of Fluids, 15, L21, doi: 10.1063/1.1539855

    work page doi:10.1063/1.1539855 2003

  18. [19]

    K., Reynolds, C

    Kingsland, M., Yang, H.-Y. K., Reynolds, C. S., & Zuhone, J. A. 2019, ApJL, 883, L23, doi: 10.3847/2041-8213/ab40be

    doi:10.3847/2041-8213/ab40be 2019

  19. [20]

    Kolmogorov, A. N. 1941, Akademiia Nauk SSSR Doklady, 32, 16

    1941

  20. [21]

    G., Norman, M

    Kritsuk, A. G., Norman, M. L., Padoan, P., & Wagner, R. 2007, ApJ, 665, 416, doi: 10.1086/519443

    doi:10.1086/519443 2007

  21. [22]

    W., Schekochihin, A

    Kunz, M. W., Schekochihin, A. A., & Stone, J. M. 2014, Physical Review Letters, 112, 205003, doi: 10.1103/PhysRevLett.112.205003

    doi:10.1103/physrevlett.112.205003 2014

  22. [23]

    Li, Y., & Bryan, G. L. 2014, ApJ, 789, 153, doi: 10.1088/0004-637X/789/2/153 15

    doi:10.1088/0004-637x/789/2/153 2014

  23. [24]

    Li, Y., Ruszkowski, M., & Bryan, G. L. 2017, ApJ, 847, 106, doi: 10.3847/1538-4357/aa88c1

    work page doi:10.3847/1538-4357/aa88c1 2017

  24. [25]

    K., & Owen, E

    Lin, Y.-H., Yang, H.-Y. K., & Owen, E. R. 2023, MNRAS, 520, 963, doi: 10.1093/mnras/stad185

    doi:10.1093/mnras/stad185 2023

  25. [28]

    McDonald, M., Veilleux, S., Rupke, D. S. N., Mushotzky, R., & Reynolds, C. 2011, ApJ, 734, 95, doi: 10.1088/0004-637X/734/2/95

    doi:10.1088/0004-637x/734/2/95 2011

  26. [29]

    R., & O’Connell, R

    McNamara, B. R., & O’Connell, R. W. 1989, AJ, 98, 2018, doi: 10.1086/115275

    doi:10.1086/115275 1989

  27. [30]

    S., Reiprich, T

    Mittal, R., Hudson, D. S., Reiprich, T. H., & Clarke, T. 2009, A&A, 501, 835, doi: 10.1051/0004-6361/200810836

    doi:10.1051/0004-6361/200810836 2009

  28. [31]

    2020, MNRAS, 493, 5838, doi: 10.1093/mnras/staa711

    Mohapatra, R., Federrath, C., & Sharma, P. 2020, MNRAS, 493, 5838, doi: 10.1093/mnras/staa711

    doi:10.1093/mnras/staa711 2020

  29. [32]

    2021, Monthly Notices of the Royal Astronomical Society, 510, 2327, doi: 10.1093/mnras/stab3429

    Mohapatra, R., Jetti, M., Sharma, P., & Federrath, C. 2021, Monthly Notices of the Royal Astronomical Society, 510, 2327, doi: 10.1093/mnras/stab3429

    doi:10.1093/mnras/stab3429 2021

  30. [33]

    2019, MNRAS, 484, 4881, doi: 10.1093/mnras/stz328

    Mohapatra, R., & Sharma, P. 2019, MNRAS, 484, 4881, doi: 10.1093/mnras/stz328

    doi:10.1093/mnras/stz328 2019

  31. [34]

    Narayan, R., & Medvedev, M. V. 2001, ApJL, 562, L129, doi: 10.1086/338325

    doi:10.1086/338325 2001

  32. [35]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563, doi: 10.1086/177173 O’Dea, C. P., Baum, S. A., Privon, G., et al. 2008, ApJ, 681, 1035, doi: 10.1086/588212

    doi:10.1086/177173 1996

  33. [36]

    J., & Quataert, E

    Parrish, I. J., & Quataert, E. 2008, ApJL, 677, L9, doi: 10.1086/587937

    doi:10.1086/587937 2008

  34. [37]

    Pope, S. B. 2000, Turbulent Flows (Cambridge University Press)

    2000

  35. [38]

    H., Jones, T

    Porter, D. H., Jones, T. W., & Ryu, D. 2015, ApJ, 810, 93, doi: 10.1088/0004-637X/810/2/93

    doi:10.1088/0004-637x/810/2/93 2015

  36. [39]

    S., Balbus, S

    Reynolds, C. S., Balbus, S. A., & Schekochihin, A. A. 2015, ApJ, 815, 41, doi: 10.1088/0004-637X/815/1/41

    doi:10.1088/0004-637x/815/1/41 2015

  37. [40]

    M., & Sarazin, C

    Ricker, P. M., & Sarazin, C. L. 2001, ApJ, 561, 621, doi: 10.1086/323365

    doi:10.1086/323365 2001

  38. [41]

    Ruszkowski, M., & Oh, S. P. 2010, ApJ, 713, 1332, doi: 10.1088/0004-637X/713/2/1332

    doi:10.1088/0004-637x/713/2/1332 2010

  39. [43]

    K., & Reynolds, C

    Ruszkowski, M., Yang, H.-Y. K., & Reynolds, C. S. 2017, ApJ, 844, 13, doi: 10.3847/1538-4357/aa79f8

    doi:10.3847/1538-4357/aa79f8 2017

  40. [44]

    G., & Veeravalli, S

    Saddoughi, S. G., & Veeravalli, S. V. 1994, Journal of Fluid Mechanics, 268, 333–372, doi: 10.1017/S0022112094001370

    doi:10.1017/s0022112094001370 1994

  41. [45]

    M., Kowal, G., et al

    Santos-Lima, R., de Gouveia Dal Pino, E. M., Kowal, G., et al. 2014, ApJ, 781, 84, doi: 10.1088/0004-637X/781/2/84

    work page doi:10.1088/0004-637x/781/2/84 2014

  42. [46]

    Niemeyer, J. C. 2009, A&A, 494, 127, doi: 10.1051/0004-6361:200809967

    doi:10.1051/0004-6361:200809967 2009

  43. [47]

    Sharma, P., McCourt, M., Quataert, E., & Parrish, I. J. 2012, MNRAS, 420, 3174, doi: 10.1111/j.1365-2966.2011.20246.x

    arXiv 2012

  44. [48]

    2022, A&A, 658, A149, doi: 10.1051/0004-6361/202141703

    Simonte, M., Vazza, F., Brighenti, F., et al. 2022, A&A, 658, A149, doi: 10.1051/0004-6361/202141703

    doi:10.1051/0004-6361/202141703 2022

  45. [49]

    Sreenivasan, K. R. 1995, Physics of Fluids, 7, 2778, doi: 10.1063/1.868656

    work page doi:10.1063/1.868656 1995

  46. [50]

    A., Sanders, J

    Walker, S. A., Sanders, J. S., & Fabian, A. C. 2018, MNRAS, 481, 1718, doi: 10.1093/mnras/sty2390

    work page doi:10.1093/mnras/sty2390 2018

  47. [51]

    P., & Ruszkowski, M

    Wang, C., Oh, S. P., & Ruszkowski, M. 2023, MNRAS, 519, 4408, doi: 10.1093/mnras/stad003

    work page doi:10.1093/mnras/stad003 2023

  48. [52]

    Yang, H.-Y. K. 2021, MNRAS, 504, 898, doi: 10.1093/mnras/stab966

    doi:10.1093/mnras/stab966 2021

  49. [53]

    Wang, S.-C., & Yang, H.-Y. K. 2022, MNRAS, 512, 5100, doi: 10.1093/mnras/stac788

    work page doi:10.1093/mnras/stac788 2022

  50. [54]

    P., & Guo, F

    Wiener, J., Oh, S. P., & Guo, F. 2013, MNRAS, 434, 2209, doi: 10.1093/mnras/stt1163 XRISM Collaboration, Audard, M., Awaki, H., et al. 2025a, arXiv e-prints, arXiv:2509.04421, doi: 10.48550/arXiv.2509.04421 XRISM Collaboration, Audard, M., Awaki, H., et al. 2025b, PASJ, 77, S242, doi: 10.1093/pasj/psaf055 XRISM Collaboration, Audard, M., Awaki, H., et al....

    doi:10.48550/arxiv.2509.04421 2013

  51. [55]

    Yang, H. Y. K., Gaspari, M., & Marlow, C. 2019, ApJ, 871, 6, doi: 10.3847/1538-4357/aaf4bd

    doi:10.3847/1538-4357/aaf4bd 2019

  52. [56]

    K., & Reynolds, C

    Yang, H.-Y. K., & Reynolds, C. S. 2016a, ApJ, 818, 181, doi: 10.3847/0004-637X/818/2/181

    doi:10.3847/0004-637x/818/2/181

  53. [57]

    K., & Reynolds, C

    Yang, H.-Y. K., & Reynolds, C. S. 2016b, ApJ, 829, 90, doi: 10.3847/0004-637X/829/2/90

    doi:10.3847/0004-637x/829/2/90

  54. [58]

    L., & Narayan, R

    Zakamska, N. L., & Narayan, R. 2003, ApJ, 582, 162, doi: 10.1086/344641

    doi:10.1086/344641 2003

  55. [59]

    2022, MNRAS, 517, 616, doi: 10.1093/mnras/stac2282

    Zhang, C., Zhuravleva, I., Gendron-Marsolais, M.-L., et al. 2022, MNRAS, 517, 616, doi: 10.1093/mnras/stac2282

    doi:10.1093/mnras/stac2282 2022

  56. [60]

    W., Mantz, A., & Werner, N

    Zhuravleva, I., Allen, S. W., Mantz, A., & Werner, N. 2018, ApJ, 865, 53, doi: 10.3847/1538-4357/aadae3

    doi:10.3847/1538-4357/aadae3 2018

  57. [61]

    A., et al

    Zhuravleva, I., Churazov, E., Schekochihin, A. A., et al. 2019, Nature Astronomy, 3, 832, doi: 10.1038/s41550-019-0794-z

    doi:10.1038/s41550-019-0794-z 2019

  58. [62]

    A., et al

    Zhuravleva, I., Churazov, E., Schekochihin, A. A., et al. 2014, Nature, 515, 85, doi: 10.1038/nature13830

    doi:10.1038/nature13830 2014

  59. [63]

    2016, MNRAS, 458, 2902, doi: 10.1093/mnras/stw520 16

    Zhuravleva, I., Churazov, E., Ar´ evalo, P., et al. 2016, MNRAS, 458, 2902, doi: 10.1093/mnras/stw520 16

    doi:10.1093/mnras/stw520 2016

  60. [64]

    A., Markevitch, M., & Johnson, R

    ZuHone, J. A., Markevitch, M., & Johnson, R. E. 2010, ApJ, 717, 908, doi: 10.1088/0004-637X/717/2/908

    doi:10.1088/0004-637x/717/2/908 2010