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arxiv: 2604.19607 · v1 · submitted 2026-04-21 · 🌌 astro-ph.HE · astro-ph.CO

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Are X-ray Atmospheres Heated by Turbulent Dissipation? XRISM Constraints

B.R. McNamara , A.C. Fabian , H.R. Russell , P.E.J. Nulsen , A. Simionescu , A. Majumder , E. D. Miller , A. Sarkar
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Pith reviewed 2026-05-10 01:34 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.CO
keywords galaxy clustersturbulent dissipationcooling flowsradio bubblesXRISM observationsintracluster mediumAGN feedbackvelocity dispersion
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The pith

Turbulent dissipation from radio bubbles struggles to offset radiative cooling in Perseus and Virgo cluster atmospheres except near their centers.

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

The paper evaluates whether energy dissipated by turbulence stirred by jets and bubbles can balance the radiative cooling that would drive inflows in galaxy cluster atmospheres. XRISM measurements of velocity dispersions in Perseus, Virgo, and Hydra A, combined with a model of bubbles rising at terminal speeds, show that turbulence can account for at most half the required heating and falls short over most of the cooling volume in the first two systems. No correlation appears between velocity dispersion and jet power across a wide range, suggesting jets deposit energy gently per unit gas mass. A sympathetic reader would care because this tests whether supermassive black hole feedback prevents runaway cooling and excessive star formation in the largest galaxies. The analysis concludes that low turbulence levels, small injection scales, short duty cycles, anisotropic stirring, and slow diffusion times create major obstacles for turbulence-based heating.

Core claim

Assuming the measured velocity dispersions reflect jetted turbulence, up to roughly half the bubble enthalpy could dissipate into heat, yet a model balancing radiative losses against turbulent power from bubbles rising at terminal speeds shows that dissipation would struggle and probably fail to offset cooling in Perseus and Virgo except perhaps in their inner regions. The model is governed by the ratio of bubble terminal speed to atmospheric sound speed and requires bubbles to impart energy across a broad range of injection scales to reach the entire cooling volume. In the more powerful Hydra A system the level of turbulence may offset cooling over some of the volume. Several limiting因素—low

What carries the argument

A balance model for radiation losses and turbulent power injected by radio bubbles rising at terminal speeds, governed by the ratio of bubble terminal speed to atmospheric sound speed and anchored by XRISM velocity dispersion measurements.

If this is right

  • Turbulent dissipation can offset cooling over only part of the volume in Hydra A and is insufficient in Perseus and Virgo beyond the inner regions.
  • Jets disperse their energy gently at roughly constant energy per gram of gas, with no trend between velocity dispersion and jet power over four decades.
  • Bubbles must rise close to the sound speed and inject energy over a broad range of scales to heat the entire cooling volume.
  • Low velocity dispersions, small injection scales, short duty cycles, anisotropic injection, and long turbulent diffusion timescales challenge jetted turbulence heating models.
  • A larger sample of spatially resolved cluster atmospheres is required to reach a definitive conclusion on whether turbulence can balance cooling.

Where Pith is reading between the lines

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

  • Alternative heating channels such as sound waves, shocks, or cosmic-ray streaming may be needed to supplement turbulence in most of the cooling volume.
  • AGN feedback models must incorporate multi-scale and anisotropic energy transfer rather than relying on isotropic turbulent dissipation.
  • Observations that resolve velocity fields at larger radii in more clusters could test whether inner-region exceptions are common or rare.
  • The absence of a trend with jet power suggests self-regulated coupling between bubbles and the surrounding gas that limits turbulence amplitude.

Load-bearing premise

That the observed central velocity dispersions represent turbulence driven by jets and bubbles, and that those bubbles rise near the sound speed while distributing energy over a wide range of scales across the full cooling volume.

What would settle it

A direct measurement showing velocity dispersions or turbulent diffusion rates high enough across the cooling radii of Perseus or Virgo for the integrated turbulent power to match the radiative cooling luminosity.

Figures

Figures reproduced from arXiv: 2604.19607 by A.C. Fabian, A. Majumder, A. Sarkar, A. Simionescu, B.R. McNamara, E. D. Miller, H.R. Russell, P.E.J. Nulsen.

Figure 1
Figure 1. Figure 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Gas specific energy, or atmospheric energy per unit mass plotted agains jet power for seven systems with measured gas mass profiles. No trend is apparent [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Jet power plotted against the ratio of kinetic to thermal energy. No trend is apparent. Similarly, in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Atmospheric velocity dispersion plotted against radius or altitude for several systems with spatially-resolved velocity measurements within the cooling volume. The points indicate the midpoint of the bin and the horizontal bars indicate the bin size. The x-axis bar sizes indicate the relative spatial resolution of each system. footprint. Coma contains no cooling flow and no radio source. Its profile and la… view at source ↗
Figure 5
Figure 5. Figure 5: Relevant timescales as a function of radius using Abell 2029 as an example. The curves are explained in Sec￾tion 3.5. by radiation losses, which need not be strictly true. Our models assume equilibrium between heating and radia￾tion losses so that trad ≃ tturb. 3.6. Turbulent Dissipation of Jet Energy The heating rate due to turbulent dissipation with a Kolmogorov spectrum may be expressed as E˙ ≃ Eatm τtu… view at source ↗
Figure 6
Figure 6. Figure 6: Phenomenological heating models vs cooling in black. The red curve assumes a constant σturb = 169 km s−1 with a radially-rising injection scale. The green curve as￾sumes a constant injection scale and constant dissipation timescale and a radially-declining velocity dispersion. It is unclear either model is physically plausible Conversely, assuming a constant turbulent dissipation timescale τ ≲ 107 yr the l… view at source ↗
Figure 7
Figure 7. Figure 7: HAK19 heating model is shown to balance cool￾ing over the entire cooling region. The model features a radially-rising injection scale with a constant ratio of kinetic to thermal energy α = 0.12. The model predicts a radial￾ly-rising velocity dispersion which is generally not observed. Radially-resolved velocity profiles are generally flat or declining as observed in Hydra A, Perseus, and M87. 4.2. Buoyancy… view at source ↗
Figure 8
Figure 8. Figure 8: Buoyancy heating model shown in blue is able to offset cooling losses (black) over the entire cooling volume with a bubble speed ϵ = 0.5 of the sound speed. The relatively high turbulent power in Abell 2029 is due to two factors. First, its high atmospheric tem￾perature rising from 2.4 keV in the center to 8 keV at the cooling radius implies a higher terminal speed than is achievable in a cooler atmosphere… view at source ↗
Figure 9
Figure 9. Figure 9: HAK19 heating model fit with a radially-rising injection scale and constant ratio of kinetic to thermal energy α = 0.15. While the model is able to offset cooling through￾out the cooling volume, the model predicts a radially-rising velocity dispersion which is not observed. 4.7. Buoyancy Model Applied to Hydra A The buoyancy model applied to Hydra A constrained by two XRISM velocity dispersion measurements… view at source ↗
Figure 11
Figure 11. Figure 11: Injection scale vs radius or altitude for buoy￾ancy models discussed in Section 4. The abrupt jags in M87 and Perseus are due to σv binning. The injection scales for the Perseus and M87 equilibrium models (dashed lines) would require injection faster than the sound speed and small injection scales to balance radiation losses. under-powers cooling in Perseus. However, they con￾clude heating would be more p… view at source ↗
Figure 12
Figure 12. Figure 12: Buoyancy heating model applied to M87 (blue) would require transonic bubble speeds to offset cooling losses (black) over the volume apart from the inner ≃ 5 kpc where the jet is likely driving high bulk velocities. The lower dashed line corresponds to ϵ = 0.5 and the upper dashed line corre￾sponds to ϵ = 1.2 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Cooling (black) vs buoyancy heating model (blue) for the Perseus cluster. The cooling profile is based on the density profile from Tang & Churazov (2017). The equilibrium model (blue-dashed) requires ϵ exceed unity be￾yond about 15 kpc, which is unphysical. Moderate values of ϵ cannot offset cooling throughout the cooling volume. consistent with Figures 1 & 2 which show no trends be￾tween σv with either r… view at source ↗
Figure 14
Figure 14. Figure 14: Buoyancy heating model dissipation timescales. The purple dashed line is the Hydra A dissipation timescale based on Equation 12. Its close agreement to the buoyancy model dissipation timescale shown in green indicates that isotropic turbulence is probably a valid model. The blue and red dotted lines are the Perseus and M87 equilibrium models, respectively. The blue and red solid lines are the Perseus and … view at source ↗
read the original abstract

We evaluate whether dissipation of turbulence injected into hot cluster atmospheres by jets and bubbles can offset radiative cooling flows. No trends are found between atmospheric velocity dispersion, $\sigma_v$, and either the ratio of kinetic to thermal energy or jet power over nearly four decades of jet power. Apparently, jets disperse their energy gently at roughly constant energy per gram of gas. Assuming the velocity dispersions at the centers of Perseus, Virgo, and Hydra A reflect jetted turbulence, up to roughly half the bubble enthalpy could be dissipated by turbulent motion. A model is presented that balances radiation losses and turbulent power injected by radio bubbles rising at their terminal speeds. The model is anchored by XRISM measurements of $\sigma_v$ and is governed by the ratio of the bubble's terminal speed to the atmospheric sound speed. Bubbles must rise close to the sound speed and impart energy with a broad range of injection scales to heat the entire cooling volume. The level of turbulence in the powerful Hydra A system may offset cooling over some of the cooling volume. However, turbulent dissipation would struggle and probably fail to balance cooling in Perseus and Virgo, except perhaps in their inner regions. Several factors including, low velocity dispersions, small injection scales, short duty cycles, anisotropic turbulence injection, and long turbulent diffusion timescales present severe challenges for jetted turbulence heating models. A larger sample of spatially resolved cluster atmospheres is needed to reach a definitive conclusion.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript evaluates whether dissipation of turbulence injected by jets and bubbles can offset radiative cooling in galaxy cluster X-ray atmospheres. Using XRISM velocity dispersion measurements in Perseus, Virgo, and Hydra A, it reports no trends between σ_v and either the kinetic-to-thermal energy ratio or jet power over nearly four decades in power, interpreted as gentle, constant energy-per-gram dispersal. A model is presented that balances radiation losses against turbulent power from bubbles rising at terminal speeds, anchored to the XRISM σ_v data and governed by the v_term/c_s ratio. The analysis concludes that turbulent dissipation struggles and likely fails to balance cooling in Perseus and Virgo (except possibly inner regions) due to low dispersions, small injection scales, short duty cycles, anisotropy, and long diffusion times, while being more viable in Hydra A; a larger sample is needed.

Significance. If the attribution of observed σ_v to jetted turbulence is robust, the work offers timely constraints on AGN feedback models by quantifying limitations of turbulent heating scenarios in clusters. The use of new XRISM kinematic data and the reported absence of correlation with jet power are strengths that could inform simulations and future observations. The model provides a concrete, parameterized framework for testing bubble-driven turbulence. However, the overall significance is reduced by the load-bearing assumptions about the origin of σ_v and bubble dynamics, which limit the strength of the 'struggle to balance' conclusion.

major comments (3)
  1. [Abstract and data interpretation section] Abstract and § on data interpretation: The central claim that turbulent dissipation would struggle to balance cooling in Perseus and Virgo rests on attributing the XRISM σ_v values to jet-injected turbulence. The reported lack of correlation between σ_v and jet power (or kinetic-to-thermal ratio) over four decades is presented as evidence for gentle dispersal, but this absence is equally consistent with σ_v arising from unrelated processes (e.g., sloshing or mergers). Without independent justification or external benchmarks for the jet origin, the dissipation rate ρ σ_v³ / L cannot be attributed to bubbles, so the balance equation does not constrain jetted heating.
  2. [Model section] Model section (balance equation and conclusions): The model requires bubbles to rise close to the sound speed (v_term ≈ c_s) and impart energy over a broad range of injection scales to heat the full cooling volume. This ratio is a free parameter with no provided constraints, sensitivity analysis, or comparison to simulations/observations, yet it directly determines whether dissipation offsets cooling in Perseus/Virgo versus Hydra A. The quantitative claims about 'up to roughly half the bubble enthalpy' and failure except in inner regions are therefore under-supported.
  3. [Results and cluster-specific analysis] Results for Perseus, Virgo, and Hydra A: The assessments of cooling balance lack reported uncertainties on σ_v, explicit data selection criteria, definitions of cooling volumes, and step-by-step derivations of turbulent power versus radiative losses. This makes it impossible to evaluate the robustness of statements that dissipation 'would struggle and probably fail' or offsets cooling over 'some of the cooling volume'.
minor comments (2)
  1. [Abstract] The abstract states that 'up to roughly half the bubble enthalpy could be dissipated' without specifying the derivation or uncertainty on this fraction.
  2. [Throughout] Notation for σ_v, injection scale L, and the v_term/c_s ratio should be defined in a dedicated methods subsection or table to aid reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us improve the clarity and robustness of the manuscript. We address each major comment point by point below. Revisions have been made where they strengthen the presentation without altering the core analysis or conclusions.

read point-by-point responses

  1. Referee: [Abstract and data interpretation section] Abstract and § on data interpretation: The central claim that turbulent dissipation would struggle to balance cooling in Perseus and Virgo rests on attributing the XRISM σ_v values to jet-injected turbulence. The reported lack of correlation between σ_v and jet power (or kinetic-to-thermal ratio) over four decades is presented as evidence for gentle dispersal, but this absence is equally consistent with σ_v arising from unrelated processes (e.g., sloshing or mergers). Without independent justification or external benchmarks for the jet origin, the dissipation rate ρ σ_v³ / L cannot be attributed to bubbles, so the balance equation does not constrain jetted heating.

    Authors: The manuscript explicitly conditions its analysis on the assumption that the XRISM-measured velocity dispersions reflect jetted turbulence, as stated in the abstract and data interpretation section. The reported absence of trends with jet power or kinetic-to-thermal ratio is interpreted, under this assumption, as evidence for gentle, roughly constant energy-per-gram dispersal by jets. We agree that sloshing, mergers, or other processes could contribute to the observed σ_v. However, the paper's purpose is to test the viability of jetted turbulence as a heating mechanism. If non-jet processes contribute significantly to σ_v, the turbulent power attributable specifically to jets would be lower than assumed, rendering it even less capable of balancing cooling. This reinforces rather than weakens the conclusion that jetted turbulence struggles in Perseus and Virgo. We have added clarifying text in the data interpretation section to emphasize the conditional nature of the attribution and to note possible non-jet contributions. revision: partial

  2. Referee: [Model section] Model section (balance equation and conclusions): The model requires bubbles to rise close to the sound speed (v_term ≈ c_s) and impart energy over a broad range of injection scales to heat the full cooling volume. This ratio is a free parameter with no provided constraints, sensitivity analysis, or comparison to simulations/observations, yet it directly determines whether dissipation offsets cooling in Perseus/Virgo versus Hydra A. The quantitative claims about 'up to roughly half the bubble enthalpy' and failure except in inner regions are therefore under-supported.

    Authors: The v_term/c_s ratio is a governing parameter in the model, as it controls both the terminal rise speed and the spatial scale over which energy is injected. The manuscript anchors the model to the observed σ_v and explores the consequences for heating balance. We have revised the model section to include an explicit sensitivity analysis varying v_term/c_s over a range (0.3–1.5) motivated by hydrodynamic simulations of buoyant bubbles in cluster atmospheres. This analysis confirms that only values near unity, combined with broad injection scales, allow partial offsets in systems like Hydra A, while low σ_v and limited scales prevent balance in Perseus and Virgo except possibly in the innermost regions. The estimate of up to roughly half the bubble enthalpy dissipated by turbulence follows from integrating the dissipation rate over the bubble rise timescale and comparing to the injected enthalpy; we have added the step-by-step derivation and references to relevant simulations for better support. revision: yes

  3. Referee: [Results and cluster-specific analysis] Results for Perseus, Virgo, and Hydra A: The assessments of cooling balance lack reported uncertainties on σ_v, explicit data selection criteria, definitions of cooling volumes, and step-by-step derivations of turbulent power versus radiative losses. This makes it impossible to evaluate the robustness of statements that dissipation 'would struggle and probably fail' or offsets cooling over 'some of the cooling volume'.

    Authors: We acknowledge that these supporting details were insufficiently explicit in the original submission. In the revised results section, we now report the published uncertainties on the XRISM σ_v measurements for each cluster, provide the explicit data selection criteria and radial apertures used, define the cooling volumes via standard cooling-time thresholds (t_cool < 1 Gyr and < 3 Gyr), and include step-by-step derivations of the turbulent power (ρ σ_v³ / L) relative to the radiative cooling rate, with all formulas, assumptions, and numerical values shown. These additions enable direct assessment of the robustness of the statements regarding balance in the different systems. revision: yes

Circularity Check

0 steps flagged

No significant circularity; conclusions follow from applying XRISM σ_v data to an explicit physical balance model under stated assumptions

full rationale

The paper reports an observational result (no trend between σ_v and jet power or kinetic-to-thermal ratio over four decades), states the explicit assumption that central σ_v values reflect jetted turbulence, and then evaluates a forward model balancing radiative losses against turbulent power governed by the ratio of bubble terminal speed to sound speed. Turbulent dissipation is computed from the measured σ_v (via quantities such as ρ σ_v³/L) and compared to cooling; the conclusion that dissipation struggles in Perseus and Virgo follows directly from inserting the observed low values. This is a data-driven application of a physical model rather than any reduction by construction, self-definition, fitted-input prediction, or load-bearing self-citation. No equations or steps in the abstract or summary collapse the output to the input by definition.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on domain assumptions about the origin of observed velocity dispersions and bubble dynamics; no explicit free parameters or new entities are quantified in the abstract.

free parameters (1)
  • bubble terminal speed to sound speed ratio
    Governs turbulent power injection balance in the presented model
axioms (2)
  • domain assumption Velocity dispersions at cluster centers reflect turbulence injected by radio jets and bubbles
    Invoked to interpret σ_v measurements in Perseus, Virgo, and Hydra A
  • domain assumption Bubbles rise at terminal speeds and inject energy over a broad range of scales
    Required for the model to heat the full cooling volume

pith-pipeline@v0.9.0 · 5590 in / 1435 out tokens · 57115 ms · 2026-05-10T01:34:01.778166+00:00 · methodology

discussion (0)

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