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arxiv: 2604.13762 · v2 · submitted 2026-04-15 · 🌌 astro-ph.HE

Radiative cooling effects on black hole hot accretion flows around the sub-Bondi radius

Mu-Qing Liu , Xiao-Hong Yang , De-Fu Bu This is my paper

Pith reviewed 2026-05-10 12:37 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords radiative coolinghot accretion flowsblack hole accretionMHD simulationswindssub-Bondi radiusconvective stabilitymagnetorotational instability
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The pith

Radiative cooling suppresses winds and reduces accretion in black hole hot flows at sub-Bondi radii.

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

The paper carries out two-dimensional magnetohydrodynamic simulations of hot accretion flows extending outward to the sub-Bondi radius, incorporating radiative cooling to track its influence on flow structure and wind production. Stronger cooling with rising mass accretion rate thins the disk and shrinks the mass outflow carried by winds, so that the inward drop in mass inflow rate shifts from being wind-dominated to being driven by turbulence from magnetorotational instability and convection. The flows stay marginally convectively stable by the Hoiland criterion in all runs. A sympathetic reader cares because these winds can carry energy and momentum into the surrounding medium, and the cooling dependence changes how accretion and feedback operate across scales larger than the innermost regions usually simulated.

Core claim

Two-dimensional MHD simulations show that radiative cooling strengthens as mass accretion rate rises, reducing disk thickness while keeping the accretion flows marginally stable in convective stability, with roughly 55-62 percent of the disk satisfying the Hoiland criterion. In weak-cooling runs winds account for most of the inward decrease in mass inflow rate, but in strong-cooling runs wind mass outflow drops sharply and the decrease is instead carried by turbulence driven by magnetorotational instability and convection. The central result is that radiative cooling has the potential to suppress accretion processes and reduce the power of winds.

What carries the argument

Two-dimensional magnetohydrodynamic simulations that include an approximate radiative cooling function and compare weak versus strong cooling regimes by measuring mass inflow and outflow rates together with disk thickness.

If this is right

  • Winds dominate the inward decrease of mass inflow rate only when radiative cooling remains weak.
  • Strong radiative cooling sharply reduces the mass outflow rate carried by winds.
  • Turbulence from magnetorotational instability and convection becomes the main cause of the radial drop in mass inflow rate once cooling is strong.
  • Disk thickness decreases steadily as radiative cooling intensifies.
  • The accretion flows remain marginally convectively stable across the full range of cooling strengths examined.

Where Pith is reading between the lines

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

  • Accretion models that omit radiative cooling at these radii are likely to overestimate wind power and its feedback effects on the host galaxy or cluster gas.
  • The marginal convective stability found here may change once three-dimensional geometry allows additional modes of instability.
  • Observational searches for wind signatures in X-ray binaries or low-luminosity AGN should expect weaker outflows at higher mass supply rates near the Bondi radius.

Load-bearing premise

That two-dimensional MHD simulations with an approximate cooling function accurately represent the three-dimensional, radiatively coupled flow structure at sub-Bondi radii.

What would settle it

Three-dimensional MHD simulations with self-consistent radiative transfer that measure wind mass outflow rates and the radial profile of mass inflow rate at the same accretion rates and radii; if the three-dimensional runs show much stronger winds or different stability fractions than the two-dimensional results, the reported suppression effect does not hold.

Figures

Figures reproduced from arXiv: 2604.13762 by De-Fu Bu, Mu-Qing Liu, Xiao-Hong Yang.

Figure 1
Figure 1. Figure 1: The distribution of the initial magnetic field (lines) and plasma β0 (colors). Solid and dashed lines represent clockwise and counterclock￾wise magnetic field lines, respectively. R22. For the purpose of comparison, we do not incorporate ra￾diative cooling in the simulation of run N24. In the simulations of runs R22–R24, we initially let the runs without radiative cool￾ing evolve from the initial state to … view at source ↗
Figure 2
Figure 2. Figure 2: The distribution of density and velocity field. In each panel, the left side presents a snapshot at 4.0tB, while the right side displays the time-averaged distribution. Colors represent the density, measured in units of the density at the center of the initial torus. The streamlines reflect the velocity field on the poloidal plane. The black solid line marks the scale height of accretion flows. The scale h… view at source ↗
Figure 3
Figure 3. Figure 3: Radial dependence of the ratio (H/r) of density scale height to radius. The black, blue, red, and green lines correspond to runs R22, R23, R24, and N24, respectively [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The distribution of the plasma β and poloidal magnetic fields. Colors represent the ratio (β) of the time-averaged gas pressure to the magnetic pressure of the time-averaged magnetic field. The solid and dashed lines reflect the magnetic fields on the poloidal plane. The purple line indicates the interface at which β = 1. Panel (A): Runs R22 (left) and R23 (right). Panel (B): Runs R24 (left) and N24 (right… view at source ↗
Figure 7
Figure 7. Figure 7: The radial profiles of normalized magnetic flux around equatorial plane. The black, blue, red, and green lines correspond to runs R22, R23, R24, and N24, respectively. magnetic field is the primary component near the equatorial plane; therefore, we only consider the magnetic flux of the toroidal magnetic field here. In equation 12, the denominator can reflect the contribution of converging flows to transpo… view at source ↗
Figure 9
Figure 9. Figure 9: The radial profiles of the time-averaged and angle-averaged ad￾vection factor f near the equatorial plane. The angle averaging is im￾plemented over the angle range of 84◦ to 96◦ . The black, blue, green, and red lines correspond to runs R22, R23, R24, and N24, respectively. of accretion flows as follows: f = Qadv Q+ = 1 − Q − Q+ . (13) Here, Q + is the heating rate, Q − is the cooling rate given by equa￾ti… view at source ↗
Figure 10
Figure 10. Figure 10: Convective stability analysis. The result is obtained according to Equation 16 based on simulation data at 4.5tB. The red solid lines mark the density scale height of accretion flows, as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The radial profiles of the time-averaged (from 4tB to 5tB ) mass inflow rates (solid lines), outflow rates (dashed lines) and the net accre￾tion rates(dotted lines). The black, blue, red, and green lines correspond to runs R22, R23, R24, and N24, respectively [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 14
Figure 14. Figure 14: The ratio of the mass flux of winds within disk to the mass flux of winds outside disk. The black, blue, red, and green lines correspond to runs R22, R23, R24, and N24, respectively. dial range of 0.03–0.3 rB. The values obtained from the fitting are given in [PITH_FULL_IMAGE:figures/full_fig_p009_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The ratio of winds within and outside the disk to the mass outflow rate. The black, blue, red, and green lines correspond to runs R22, R23, R24, and N24, respectively. Panel (A): the ratio of the mass flux of winds (defined as outflows with Be > 0) within the disk to the total mass outflow rate within the disk. Panel (B): the ratio of the mass flux of winds outside the disk to the total mass outflow rate … view at source ↗
Figure 16
Figure 16. Figure 16: Force analysis at r = 0.15rB on the disk surface (as indicated by the black line in [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: The radial profiles of the effective α. The black, blue, red, and green lines correspond to runs R22, R23, R24 and N24, respectively. star formation. Gravitational instability can be assessed using Toomre’s criterion (Toomre 1964): Q = CsΩ πGΣ , (22) where Σ is the surface density of the disk. When Q ≥ 1, the disk is gravitationally stable. When Q < 1, the disk is gravi￾tationally unstable. Gravitational … view at source ↗
Figure 17
Figure 17. Figure 17: The net accretion rates corresponding to different unit densities, with black and red points representing the cases with radiative cooling switched on and off, respectively. A low-temperature, high-density accretion disk may become gravitationally unstable, which may result in fragmentation and [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 20
Figure 20. Figure 20: The radial profiles of the percentage of the total magnetic field energy accounted for by the radial (solid lines) and toroidal (dashed lines) components of the magnetic field, respectively. The black, blue, red, and green lines correspond to runs R22, R23, R24 and N24, respec￾tively [PITH_FULL_IMAGE:figures/full_fig_p013_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The radial profile of the stress tensor exerted on per unit mass for different runs. The black, blue, red, and green lines correspond to runs R22, R23, R24 and N24, respectively. rB and vk,B denote the Bondi radius and the Keplerian velocity at the Bondi radius, respectively. 4. Discussions For the hot accretion flows near a BH, synchrotron radiation, Compton scattering, and two-temperature effects play s… view at source ↗
read the original abstract

It is difficult to implement numerical simulations on a region extending from the vicinity of a black hole to the Bondi radius. Most previous numerical simulations have primarily concentrated on the region close to the black hole. They found that strong winds can be generated in the hot accretion flows near the black hole, and that radiative cooling significantly affects the strength of these winds. However, the effects of radiative cooling on the production and properties of winds around the Bondi radius remain unclear. In this paper, we perform two-dimensional magnetohydrodynamic simulations to study the impact of radiative cooling on the dynamics and wind production in hot accretion flows around the sub-Bondi radius. As the increase of mass accretion rate, radiative cooling gradually becomes strong, resulting in a reduction in the thickness of the accretion disk (defined as the accretion flows within the density scale height). Based on the H{\o}iland criterion, we find that within the accretion disk, the region of convective stability accounts for $\sim$ 55 - 62 %, and therefore the accretion flows are marginally stable in convective stability. In the runs with weak radiative cooling, the winds play a significant role in the inward decrease of the mass inflow rate. In the runs with strong radiative cooling, the mass outflow rate of winds is significantly reduced and then the inward decrease of the mass inflow rate is mainly attributed to turbulence driven by magnetorotational instability and convection. Radiative cooling has the potential to suppress accretion processes and reduce the power of winds.

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 presents two-dimensional MHD simulations of hot accretion flows around black holes at sub-Bondi radii. It reports that increasing the mass accretion rate strengthens radiative cooling, which reduces disk thickness (defined within the density scale height). The flows are found to be marginally convectively stable according to the Hóiland criterion, with 55-62% of the disk region convectively stable. In weak-cooling runs, winds dominate the inward decline of mass inflow rate; in strong-cooling runs, this decline is instead driven primarily by MRI and convection-induced turbulence. The central conclusion is that radiative cooling suppresses accretion and reduces wind power.

Significance. If the trends hold, the work fills a gap in understanding cooling effects at larger radii than typically simulated, with implications for black-hole feeding and wind feedback models. The controlled 2D runs with varying accretion rate to tune cooling strength provide a clean isolation of effects and direct outputs from time-dependent simulations, which is a methodological strength.

major comments (3)
  1. [§2] §2 (numerical methods): The cooling function is described only as 'approximate' with no explicit functional form, normalization, or coupling details to local density/temperature. This is load-bearing for the weak-vs-strong cooling distinction that drives the reported shift from wind-dominated to turbulence-dominated mass-flux decline.
  2. [Results section] Results section (mass inflow/outflow analysis): No resolution studies, convergence tests, or error bars are reported on the mass inflow/outflow rates or the 55-62% convective-stability fraction. The central claims rest on quantitative trends from these unvalidated simulation outputs.
  3. [Discussion] Discussion of convective stability and winds: The Hóiland criterion is applied only to time-averaged 2D data, with no assessment of how fully developed 3D MRI turbulence or altered convective cell aspect ratios would affect outflow rates and the claimed wind suppression. This dimensionality limitation directly impacts the headline result on reduced wind power.
minor comments (2)
  1. [Abstract] Abstract: The phrasing 'marginally stable in convective stability' is imprecise and should be clarified.
  2. The manuscript would benefit from explicit statements of the cooling-function implementation and any parameter values used for the 'weak' and 'strong' regimes to aid reproducibility.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and have revised the manuscript to improve clarity and address the concerns raised.

read point-by-point responses

  1. Referee: §2 (numerical methods): The cooling function is described only as 'approximate' with no explicit functional form, normalization, or coupling details to local density/temperature. This is load-bearing for the weak-vs-strong cooling distinction that drives the reported shift from wind-dominated to turbulence-dominated mass-flux decline.

    Authors: We agree that the cooling function description requires greater specificity. In the revised manuscript we will explicitly provide the functional form of the cooling rate (an approximation to bremsstrahlung cooling), its normalization constant, and the precise manner in which it is coupled to the local density and temperature in §2. This addition will clarify the distinction between the weak- and strong-cooling regimes and the resulting change in mass-flux behavior. revision: yes

  2. Referee: Results section (mass inflow/outflow analysis): No resolution studies, convergence tests, or error bars are reported on the mass inflow/outflow rates or the 55-62% convective-stability fraction. The central claims rest on quantitative trends from these unvalidated simulation outputs.

    Authors: We acknowledge the absence of explicit convergence tests and error bars. While the simulations were performed at resolutions standard for 2D MHD accretion studies, we will add a dedicated paragraph on numerical resolution in the revised results section. We will also report error bars on the mass inflow/outflow rates and the convective-stability fraction, derived from the temporal standard deviation during the quasi-steady phase of each run. These additions will better support the quantitative trends presented. revision: partial

  3. Referee: Discussion of convective stability and winds: The Hóiland criterion is applied only to time-averaged 2D data, with no assessment of how fully developed 3D MRI turbulence or altered convective cell aspect ratios would affect outflow rates and the claimed wind suppression. This dimensionality limitation directly impacts the headline result on reduced wind power.

    Authors: We recognize the inherent limitations of two-dimensional simulations. The application of the Hóiland criterion to time-averaged 2D data indicates marginal convective stability, but fully developed 3D MRI turbulence could alter convective cell aspect ratios and outflow rates. In the revised discussion we will expand the caveats on dimensionality, note that the qualitative suppression of wind power with increasing cooling remains robust within the 2D framework, and discuss how 3D effects might quantitatively modify the results while remaining consistent with the controlled parameter study performed here. revision: partial

standing simulated objections not resolved
  • A full quantitative assessment of how fully developed 3D MRI turbulence and altered convective cell aspect ratios affect outflow rates and wind suppression would require new three-dimensional simulations, which are beyond the scope of the present revision.

Circularity Check

0 steps flagged

No circularity: results are direct simulation outputs with no fitted predictions or self-referential derivations

full rationale

The paper reports outcomes from 2D MHD simulations of hot accretion flows with an approximate radiative cooling function. Claims about disk thickness reduction, convective stability fractions (55-62% via Hoiland criterion), wind power suppression, and shifts in mass inflow decline mechanisms are presented as direct numerical results rather than analytic derivations or predictions. No equations, parameter fits, or self-citations are shown that reduce the central claims to inputs by construction. The derivation chain is therefore self-contained as a set of time-dependent simulation experiments.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard ideal MHD equations plus an unspecified cooling function whose functional form and normalization are not given; no new physical entities are introduced.

free parameters (2)
  • mass accretion rate
    Varied across runs to control cooling strength; values not stated in abstract.
  • cooling function normalization
    Determines transition from weak to strong cooling regime; not specified.
axioms (2)
  • standard math Ideal MHD equations govern the flow
    Implicit in all MHD accretion simulations; invoked throughout the numerical setup.
  • domain assumption Radiative cooling can be approximated by a local cooling function
    Required to include cooling without full radiation transport; location not stated but necessary for the reported trends.

pith-pipeline@v0.9.0 · 5574 in / 1352 out tokens · 23722 ms · 2026-05-10T12:37:36.207179+00:00 · methodology

discussion (0)

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