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Magnetic Pressure Dominance Stabilizes AGN Disks Against Gravitational Instability

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper claims that MRI-driven magnetic pressure dominance stabilizes a strongly magnetized, isothermal AGN disk initialized at marginal gravitational stability, while a weakly magnetized counterpart fragments.

desk verdict A clean simulation contrast suggests MRI-driven magnetic pressure can stabilize AGN disks, but the headline claim leans on a stability criterion that is also the measured outcome, and the surviving run is too short to prove long-term stabilization. read the letter →

arxiv 2508.16842 v1 pith:3XXMNNCO submitted 2025-08-22 astro-ph.HE astro-ph.GA

Hannalore J. Gerling-Dunsmore , Mitchell C. Begelman , Jacob B. Simon , Philip J. Armitage This is my paper · ORCID
classification astro-ph.HEastro-ph.GA
keywords accretiondisksactivegalacticnucleigravitationalinstabilitymagnetorotationalmagneticpressureToomreparametershearingboxsimulationsdiskfragmentation
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

The paper asks whether magnetic fields can save the outer regions of AGN accretion disks from fragmenting under their own gravity. Using isothermal shearing-box MHD simulations with net vertical flux, it shows that a disk initialized with midplane plasma beta of 10^2.5 becomes magnetically pressure-dominated and stabilizes, even after its modified Toomre parameter Q' briefly falls to about 0.2. A weakly magnetized disk at beta = 10^4 does not stabilize and fragments. If correct, this offers a concrete mechanism by which AGN disks can survive past the broad-line region without forming stars, easing a long-standing tension in accretion disk theory.

What carries the argument

The load-bearing object is the modified Toomre parameter Q' (Eq. 8), which adds the Alfvén speed and turbulent velocity in quadrature to the sound speed: Q' = Omega sqrt(c_s^2 + v_A^2 + v_turb^2) / (pi G Sigma_0). The paper defines stabilization as sustained Q' > 1 within one density scale height, and attributes stabilization to the v_A term once the MRI's toroidal field saturates. Supporting this is the plasma-beta criterion: when beta^mid_0 <~ 10^3, the disk becomes magnetically dominated (magnetic pressure exceeds gas pressure), which the simulations confirm for beta = 10^2.5.

What would settle it

Run a strongly magnetized (beta^mid_0 = 10^2.5) Q0 = 1 shearing box for several hundred orbits with a larger radial domain and a small but nonzero cooling time, and check whether fragmentation occurs after the claimed stabilization. Alternatively, compute the linear dispersion relation for axisymmetric perturbations of a stratified, magnetized, turbulent disk to test whether v_A and v_turb enter the marginal-stability condition with unit weights. Delayed fragmentation or a stability boundary different from Q' = 1 would refute the claim.

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Extended reading notes

Core claim

The paper's central claim is that MRI-driven magnetic pressure dominance can stabilize a disk that is initialized at critical gravitational stability (Q0 = 1). In the strongly magnetized runs (beta^mid_0 = 10^2.5), the MRI saturates by about five orbits, the toroidal field overturns, and the volume-averaged modified Toomre parameter Q' = Omega sqrt(c_s^2 + v_A^2 + v_turb^2) / (pi G Sigma_0) rises above unity, with the magnetic-field term dominating. The weakly magnetized runs (beta^mid_0 = 10^4) never develop magnetic pressure dominance, their Q' remains dominated by gas pressure, and the Q0 = 1 disk fragments. The paper concludes that strong magnetization, sufficient for magnetic pressure t

Load-bearing premise

The load-bearing assumption is that the modified Toomre parameter Q' = Omega sqrt(c_s^2 + v_A^2 + v_turb^2) / (pi G Sigma_0), with magnetic and turbulent speeds added in quadrature with unit weight and volume-averaged, truly predicts gravitational stability in a magnetized turbulent disk; if those pressures enter the stability threshold differently, the observed Q' > 1 crossing does not by itself establish stabilization.

Editorial extensions

If this is right

  • Outer AGN disks with net vertical flux strong enough to give beta^mid_0 <~ 10^3 can survive gravitational instability without fragmenting, even if self-gravity initially drives Q' well below 1.
  • At beta^mid_0 = 10^4, magnetic and turbulent pressure contribute negligibly to Q', so critically self-gravitating disks fragment; even robustly stable disks become less stable.
  • Stabilization is fast, about five orbits, and coincides with MRI saturation, so the window for fragmentation is short when magnetization is strong.
  • The strength of self-gravity does not prevent magnetic pressure dominance: the strongly magnetized Q0 = 1 run develops magnetic domination throughout almost the entire disk, similar to pure MHD.
  • Because Q', not the classical Toomre Q, is the relevant stability measure, purely hydrodynamic estimates overstate the gravitational instability danger in strongly magnetized AGN disks.

Reading between the lines

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

  • An implication the authors leave implicit is that net vertical magnetic flux, not just MRI-driven turbulence, controls disk survival; disks with zero net flux but similar turbulent stresses may not stabilize because magnetic pressure dominance requires net flux.
  • A testable extension the authors note but do not pursue: initialize at Q0 < 1 with beta^mid_0 = 10^2.5 to map the maximum instability a magnetic-pressure-dominated disk can survive.
  • The isothermal equation of state means cooling is absent. A natural next step is to test whether the same beta threshold holds when radiative cooling is included, since cooling lowers the effective sound speed and could compete with magnetic stabilization.
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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 paper uses isothermal MHD shearing-box simulations with net vertical flux to test whether magnetic pressure can stabilize AGN disks against gravitational instability (GI). Six simulations are presented: three with strong initial magnetization (β_mid_0 = 10^2.5) and three with weak magnetization (β_mid_0 = 10^4), each including a critically self-gravitating (Q0=1.0) run, a robustly stable (Q0=10.0) run, and a pure-MHD run. The central claim is that the strongly magnetized, critically self-gravitating disk becomes magnetically pressure-dominated and its modified Toomre parameter Q' (Eq. 8, adding v_A^2 and v_turb^2 in quadrature to c_s^2) rises above unity, stabilizing the disk; the corresponding weakly magnetized disk does not stabilize and fragments. The paper argues that MRI develops normally in all five surviving runs and that magnetic pressure dominance is the key stabilizing agent.

Significance. If the central claim holds, the paper provides a concrete mechanism—magnetic pressure dominance from net vertical flux with β_mid_0 ≲ 10^3—by which outer AGN disks can avoid fragmentation even when initialized at marginal Toomre stability. This would be an important contribution to debates about AGN disk survival and star formation. The controlled comparison between strong and weak magnetization, the use of standard MRI diagnostics (T_Max/T_Rey ≈ 4, α_B–β relation), and the clear fragmentation of the weakly magnetized Q0=1 run are strengths. However, the claim of stabilization rests on the validity of the modified Q' criterion and on run durations that are short compared to GI growth timescales; the strong-field run is terminated only ~2 orbits after Q' first exceeds unity. The paper's evidence is suggestive but not yet conclusive.

major comments (3)
  1. [Sec. 2.4 and Sec. 3.1] Stabilization is defined as Q' reaching and sustaining a value >1, and the strong-field Q0=1 run is terminated once Q'>1 has been maintained for two orbits. This makes Q' both the measured outcome and the stability criterion. The run ends at about 9 orbits, only ~2 orbits after Q' first exceeds 1 at ~5 orbits. The appeal to Lohnert & Peeters (2023) and Tsung et al. (2025) for long-term stability is not fully convincing: the former is a hydrodynamic study, and the latter is a companion work by the same group, not a substitute for running the present simulation longer. Given that Q' dipped to ~0.2 and the disk shows strong density maxima (Fig. 7) and a midplane density bump (Fig. 6), the run duration is too short to exclude delayed fragmentation. Please extend the strong-field Q0=1 run to at least 30 orbits, or provide independent evidence (e.g., analysis of whether the density concentrati
  2. [Sec. 2.3, Eq. (8)] The modified Toomre parameter Q' = Ω√(c_s^2+v_A^2+v_turb^2)/(πGΣ0) is central to the paper's conclusion, but its validity in the simulated regime is not established. The additions are cited to Kim & Ostriker (2001) and Lizano et al. (2010), but those derivations do not cover an isothermal, stratified, net-vertical-flux shearing box with strong toroidal fields and MRI turbulence. If the correct stability threshold weights magnetic or turbulent pressure differently, or if the volume averaging over low-density regions overweights v_A, then Q'>1 does not imply stability. A concrete test would be to compare Q' evolution against actual fragmentation in longer runs, or to derive/justify the criterion for this specific regime; as written, the paper assumes the very criterion it uses to declare stabilization.
  3. [Sec. 4.1, Figs. 6 and 7] The strong-field Q0=1 disk reaches Q' as low as ~0.2 repeatedly, then recovers. This places the disk in a strongly nonlinear regime where a linear stability parameter such as Q' may not be a reliable predictor. The paper should address whether the density peaks seen in Fig. 7 are gravitationally bound and whether the volume-averaged Q' is meaningful when the density field is highly inhomogeneous. Without such an assessment, the conclusion that 'magnetic pressure dominance stabilizes the disk' is not fully supported by the presented diagnostics.
minor comments (5)
  1. [Fig. 7 caption vs. Sec. 4] The text says the density slices are taken at y=1.0, while the figure caption says y=0.0. Please correct the inconsistency.
  2. [Sec. 2.2] The sentence 'We choose units such that c_s = Ω = 0.001' is confusing; presumably the ratio c_s/Ω = 1 in code units. Please clarify.
  3. [Sec. 3.4] Typo: 'aqll display' should be 'all display'.
  4. [Sec. 2.1] The choice of periodic vertical boundary conditions is discussed, but its impact on possible toroidal-field buoyancy escape and on the vertical density structure could be stated more explicitly as a caveat in the conclusions.
  5. [Eq. (7)] The Alfvén speed is defined using μ0; in code units with Heaviside-Lorentz conventions, the factor may be different. Please ensure the definition is consistent with the code's units.

Circularity Check

2 steps flagged · score 6.0 of 10

The stabilization claim reduces by construction to Q'>1, where Q' includes the magnetic-pressure term being tested; permanence is asserted from a stopping rule partly backed by a self-citation.

  1. self definitional [Sec. 2.3-2.4 (Eq. 8 and definition of stabilization); Sec. 4.1]
    "We consider a disk stabilized if within ±Hρ, its volume-averaged modified Toomre stability parameter, Q′, reaches (and sustains) a value greater than unity. ... In our strongly magnetized, strongly self-gravitating simulation, the dominant contribution toQ′ is that from magnetic pressure."

    Eq. 8 defines Q′ = Ω(c_s^2 + v_A^2 + v_turb^2)^{1/2}/(πGΣ0), so magnetic pressure is an input to the diagnostic, not an independent outcome. Sec. 2.4 then defines 'stabilized' as Q′ > 1. The finding that magnetic pressure dominates Q′ in the strong-field run is therefore the same algebraic fact used to define stabilization; it is not independent evidence that magnetic pressure prevents fragmentation. The only non-definitional evidence is the absence of visible fragmentation during the short run, which is insufficient to establish long-term stabilization, especially since the run is terminated two orbits after Q′ > 1.

  2. self citation load bearing [Sec. 3.1 (termination criterion)]
    "T. H. N. Tsung et al. (2025) found that it is technically possible for MRI to enhance GI, but for the magnetizations employed in this study such GI enhancement is highly unlikely to occur. By this criterion, attaining and then maintaining Q′ ≥ 1.0 for an orbit adequately demonstrates that the disk has stabilized and will remain stable, and we did not compute these models further."

    The permanence of stabilization is not simulated; it is imported from a criterion. The external Lohnert & Peeters (2023) result supplies the main 'Q≥1 is permanent' claim, but the paper additionally invokes Tsung et al. (2025) to rule out MRI-enhanced GI, the very alternative that would make early termination unsafe. Tsung et al. is an arXiv preprint by Begelman, Armitage, and Gerling-Dunsmore, three of the present authors. Thus part of the load-bearing justification for stopping at ~2 orbits of Q′>1 and declaring permanent stabilization rests on the authors' own prior work rather than on a long simulation.

full rationale

The paper is not wholly circular: it runs actual MHD shearing-box simulations, and the strongly magnetized Q0=1 disk does not fragment within ~7-8 orbits while the weakly magnetized one fragments at ~5 orbits. That comparison is independent evidence. However, the headline claim that magnetic-pressure dominance 'stabilizes' the disk is operationalized through Eq. 8 and the Sec. 2.4 definition of stabilization as Q′>1. Since Eq. 8 adds v_A^2 into the numerator, the observation that the v_A term pushes Q′ above 1 is an algebraic consequence of the diagnostic, not an independent demonstration that magnetic pressure prevents GI. The stopping rule in Sec. 3.1 reinforces this: the run is ended as soon as Q′>1 is sustained for two orbits, and the persistence of that state is justified partly by a self-citation (Tsung et al. 2025). The external citations to Kim & Ostriker (2001) and Lizano et al. (2010) give Q′ some independent support, but the paper applies the formula in a new regime without derivation. I therefore score the circularity as 6: one or more central predictions reduce by construction, while the simulation still contains significant independent content.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The paper's conclusion depends on two hand-chosen initial magnetizations bracketing a known threshold from prior work, and on a modified Toomre stability parameter that adds the very magnetic and turbulent pressures whose stabilizing effect is being tested. No new physical entities are introduced. The additional load-bearing assumptions are the early-stopping rule (Q'>1 for two orbits implies permanent stability, supported partly by a self-cited paper) and the fragmentation proxy (Q' plateau <=1 after Maxwell stress saturation means the disk has fragmented).

free parameters (2)
  • Initial midplane plasma beta (β_mid_0) = 10^2.5 (strong), 10^4 (weak)
    Chosen by hand to bracket the threshold β≈10^3 for magnetic pressure dominance from Bai & Stone 2013 and Salvesen et al 2016. The strong value is selected because prior work shows it produces the very magnetic pressure dominance that the paper identifies as the stabilizer; the weak value is chosen to lack it. The two-point comparison carries the entire conclusion.
  • Initial Toomre Q (Q0) = 1.0 and 10.0
    Chosen to represent the critically stable and robustly stable cases. Q0=1 is the marginal-state initialization; the claim 'stabilizes a critically stable disk' is specific to this initialization.
assumptions (7)
  • standard math The usual Toomre Q = c_s Ω/(π G Σ) with Q_crit ~1 determines gravitational instability in thin disks.
    Background for the GI framework, cited to Toomre 1964 in the introduction and used to set Q0.
  • ad hoc to paper The modified Toomre parameter Q' = Ω√(c_s^2 + v_A^2 + v_turb^2)/(π G Σ0) (Eq. 8) with unit weights on magnetic and turbulent contributions is a valid stability criterion.
    Invoked in Sec. 2.3 and used as the definition of stabilization in Sec. 2.4. The unit weights are an assumption; the paper cites Kim & Ostriker 2001 and Lizano et al 2010, but does not re-derive them for this regime.
  • domain assumption A disk that attains and sustains Q' >= 1 for at least two orbits is permanently stable against GI, so simulations can be stopped.
    Sec. 3.1: 'attaining and then maintaining Q' >= 1.0 for an orbit adequately demonstrates that the disk has stabilized and will remain stable.' Relies on Lohnert & Peeters 2023 and self-cited Tsung et al 2025.
  • ad hoc to paper The fragmentation proxy: if Q' plateaus at <=1 after the Maxwell stress plateaus, the disk is deemed fragmented.
    Sec. 2.4 defines fragmentation this way; the weak-field Q0=1 run is labeled fragmented even though the visual evidence (density slices) is shown separately. The proxy decides the weak case failed.
  • domain assumption Isothermal EOS (no cooling) is an appropriate approximation for strongly irradiated AGN disk outer regions, and makes the disk more, not less, prone to fragmentation.
    Sec. 2.2. This is a conservative assumption; if anything it biases toward fragmentation, so the stabilization result is not caused by a long cooling time.
  • domain assumption A net vertical magnetic flux with midplane beta_mid_0 ~ 10^2.5 is present in AGN disks; without such flux, the MRI alone would not produce the studied magnetic pressure dominance.
    Sec. 2.2 acknowledges 'The degree to which AGN disks possess net vertical flux is a matter of debate.' The central result only applies if such flux exists.
  • domain assumption MRI quality factors of Q_MRI,z = 2.94-16.52 are adequate; specifically 2.94 is 'on the border of acceptable' and 5.87 is sufficient.
    Sec. 2.2 and Table 1. The weak-field runs at 128^3 have Q=2.94 which is typical of prior studies but borderline; no convergence study is shown for the strong-field Q0=1 run.

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Pith. "Pith review of Magnetic Pressure Dominance Stabilizes AGN Disks Against Gravitational Instability." pith.science (2026). https://pith.science/paper/3XXMNNCO

@misc{pith2026250816842,
  author       = {Pith},
  title        = {Pith review of: Magnetic Pressure Dominance Stabilizes AGN Disks Against Gravitational Instability},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3XXMNNCO}},
  note         = {Machine review of arXiv:2508.16842}
}
abstract

Magnetic effects have long been considered a possible factor in stabilizing the outer regions of active galactic nuclei (AGN) accretion disks against gravitational instability (GI). However, the computational demands of testing this hypothesis have prevented comprehensive study of this problem. Here, we present results from a suite of 6 isothermal magnetohydrodynamics (MHD) shearing box simulations, 3 initialized with strong magnetization ($\beta^{\rm{mid}}_{0} = p_{\rm{gas}} / p_{\rm{mag}} = 10^{2.5}$) and 3 initialized with weak magnetization ($\beta^{\rm mid}_{0} = 10^{4}$). For each magnetization, we performed simulations with both strong ($Q_{0} = 1.0$) and weak ($Q_{0} = 10.0$) self-gravity, where $Q_{0} = \frac{c_{\rm{s}}\Omega}{\pi G \Sigma_{0}}$ is the Toomre stability parameter; we also performed pure MHD simulations for comparison. We find that our strongly magnetized disk stabilized against GI after initialization to critical stability against GI, while our corresponding weakly magnetized disk did not. We show that the strongly magnetized, strongly self-gravitating disk became dominated by magnetic pressure, which led to its stabilization.

Figures

Figures reproduced from arXiv: 2508.16842 by the authors.

Figure 1
Figure 1. The rows show, from top to bottom, the evolution of the volume-integrated toroidal magnetic field (absolute value taken after volume integration), Maxwell stress, Reynolds stress, and gravitational stress. In the strongly magnetized disk (β mid 0 = 102.5 ) that survives initialization to Q0 = 1.0, the evolution of the Maxwell stress is similar in the pure MHD, weakly self-gravitating, and strongly self-gravitating s… view at source ↗
Figure 2
Figure 2. Evolution of the ratio of the Maxwell to Reynolds stress for all simulations. Besides the weakly magnetized, strongly self-gravitating (β mid 0 = 104 , Q0 = 1.0) simulation, all simulations display oscillations around the canonical value for MRI of TMax/TRey ≈ 4. and otherwise minimal variation in the Reynolds stress for that simulation. We see that all of the simulations (even the weakly magnetized, strongly self-g… view at source ↗
Figure 3
Figure 3. Time-averaged, volume-averaged αB vs. initial midplane magnetization, β mid 0 , as described in Eq. 15. αB is essentially independent of β mid 0 , providing support for the ex￾istence of MRI in our simulations. Marker style corresponds to initial magnetization (stars for β mid 0 = 102.5 , diamonds for β mid 0 = 104 ), line colors correspond to strength of self-gravity. The time average for αB for our weakly magnetiz… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Time window-averaged profiles of magnetization for our strongly magnetized (β mid 0 = 102.5 ) simulations. The subscript on the y-axis labels indicates orbits over which the average was performed, with the bottom panel representing an average performed from the eighth …
Figure 5
Figure 5. Figure 5: Time window-averaged profiles of magnetization for our weakly magnetized (β mid 0 = 104 ) simulations. As in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 7
Figure 7. Figure 7: Gas density of all 6 simulations in their final orbits, sliced at y = 0.0. The strongly magnetized (β mid 0 = 102.5 ) simulations are much more turbulent and disordered than their weakly magnetized (β mid 0 = 104 ) counterparts. While the strongly magnetized, strongly …
Figure 8
Figure 8. Figure 8: Evolution of the modified Q-parameter (Eq. 8) and its components for strongly self-gravitating simula￾tions; left panel corresponds to the strongly magnetized case (β mid 0 = 102.5 ) and right panel to the weakly magnetized case (β mid 0 = 104 ). 0 5 10 15 t [orbits] 0…
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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Works this paper leans on

47 extracted references · 27 canonical work pages · cited by 1 Pith paper

  1. [1]

    2011, Annual Review of Astronomy and Astrophysics, 49, p

    Armitage, P. 2011, Annual Review of Astronomy and Astrophysics, 49, p. 195

    work page 2011

  2. [2]

    Bai, X., & Stone, J. M. 2013, The Astrophysical Journal, 767, p. 30 14

    work page 2013

  3. [3]

    A., & Hawley, J

    Balbus, S. A., & Hawley, J. F. 1991, The Astrophysical Journal, 376, p. 214

    work page 1991

  4. [4]

    C., & Pringle, J

    Begelman, M. C., & Pringle, J. E. 2007, MNRAS, 375, p. 1070

    work page 2007

  5. [5]

    C., & Silk, J

    Begelman, M. C., & Silk, J. 2023, Monthly Notices of the Royal Astronomical Society: Letters, 526, L94, doi: 10.1093/mnrasl/slad124

    doi:10.1093/mnrasl/slad124 2023

  6. [6]

    2008, New Astronomy, 13, 244, doi: https://doi.org/10.1016/j.newast.2007.10.004

    Blackman, E., Penna, R., & Varnière, P. 2008, New Astronomy, 13, 244, doi: https://doi.org/10.1016/j.newast.2007.10.004

    work page doi:10.1016/j.newast.2007.10.004 2008

  7. [7]

    D., & Payne, D

    Blandford, R. D., & Payne, D. G. 1982, Monthly Notices of the Royal Astronomical Society, 199, 883, doi: 10.1093/mnras/199.4.883

    doi:10.1093/mnras/199.4.883 1982

  8. [8]

    Carrera, D., Johansen, A., & Davies, M. B. 2015, Astronomy & Astrophysics, 579

    work page 2015

Show all 47 references
  1. [9]

    Chen, Y.-X., Jiang, Y.-F., Goodman, J., & Ostriker, E. C. 2023, The Astrophysical Journal, 948, 120, doi: 10.3847/1538-4357/acc023

    2023 doi

  2. [10]

    2021, Nature Astronomy, 5, 440, doi: 10.1038/s41550-020-01297-6

    Deng, H., Mayer, L., & Helled, R. 2021, Nature Astronomy, 5, 440, doi: 10.1038/s41550-020-01297-6

    2021 doi

  3. [11]

    J., & Miller, M

    Dittmann, A. J., & Miller, M. C. 2020, MNRAS, 493, 3732, doi: 10.1093/mnras/staa463

    2020 doi

  4. [12]

    2025, Monthly Notices of the Royal Astronomical Society, 537, 3396, doi: 10.1093/mnras/staf237

    Epstein-Martin, M., Tagawa, H., Haiman, Z., & Perna, R. 2025, Monthly Notices of the Royal Astronomical Society, 537, 3396, doi: 10.1093/mnras/staf237

    2025 doi

  5. [13]

    1993, Astronomy & Astrophysics, 276, p

    Ferreira, J., & Pelletier, G. 1993, Astronomy & Astrophysics, 276, p. 625

    1993

  6. [14]

    Fromang, S., Balbus, S., Terquem, C., & De Villiers, J. P. 2004, The Astrophysical Journal, 616, p. 364

    2004

  7. [15]

    N., Lesur, G., & Ogilvie, G

    Fromang, S., Latter, H. N., Lesur, G., & Ogilvie, G. I. 2013, Astronomy & Astrophysics, 552

    2013

  8. [16]

    2012, The Astrophysical Journal, 758, 103, doi: 10.1088/0004-637X/758/2/103

    Gaburov, E., Johansen, A., & Levin, Y. 2012, The Astrophysical Journal, 758, 103, doi: 10.1088/0004-637X/758/2/103

    2012 doi

  9. [17]

    Gammie, C. F. 2001, The Astrophysical Journal, 553, p. 174

    2001

  10. [18]

    2003, Monthly Notices of the Royal Astronomical Society, 339, 937, doi: 10.1046/j.1365-8711.2003.06241.x

    Goodman, J. 2003, Monthly Notices of the Royal Astronomical Society, 339, 937, doi: 10.1046/j.1365-8711.2003.06241.x

    2003

  11. [19]

    F., Gammie, C

    Hawley, J. F., Gammie, C. F., & Balbus, S. A. 1995, ApJ, 440, 742, doi: 10.1086/175311

    1995 doi

  12. [20]

    F., Guan, X., & Krolik, J

    Hawley, J. F., Guan, X., & Krolik, J. H. 2011, The Astrophysical Journal, 738, p. 84

    2011

  13. [21]

    F., Grudic, M

    Hopkins, P. F., Grudic, M. Y., Kremer, K., et al. 2024a, The Open Journal of Astrophysics, 7, doi: 10.33232/001c.122857

    doi

  14. [22]

    F., Grudic, M

    Hopkins, P. F., Grudic, M. Y., Su, K.-Y., et al. 2024b, The Open Journal of Astrophysics, 7, doi: 10.21105/astro.2309.13115

  15. [23]

    F., Squire, J., Su, K.-Y., et al

    Hopkins, P. F., Squire, J., Su, K.-Y., et al. 2024c, The Open Journal of Astrophysics, 7, doi: 10.21105/astro.2310.04506

  16. [24]

    Huang, J., Lin, D. N. C., & Shields, G. 2023, Monthly Notices of the Royal Astronomical Society, 525, 5702, doi: 10.1093/mnras/stad2642

    2023 doi

  17. [25]

    Kim, W.-T., & Ostriker, E. C. 2001, The Astrophysical Journal, 559, 70, doi: 10.1086/322330

    2001 doi

  18. [26]

    I., & Sunyaev, R

    Kolykhalov, P. I., & Sunyaev, R. A. 1980, Soviet Astronomy Letters, 357, p. 357

    1980

  19. [27]

    2016, ARA&A, 54, 271, doi: 10.1146/annurev-astro-081915-023307

    Kratter, K., & Lodato, G. 2016, ARA&A, 54, 271, doi: 10.1146/annurev-astro-081915-023307

    2016 doi

  20. [29]

    J., & Adams, F

    Lizano, S., Galli, D., Cai, M. J., & Adams, F. C. 2010, The Astrophysical Journal, 724, 1561, doi: 10.1088/0004-637X/724/2/1561

    2010 doi

  21. [30]

    2022, Astronomy & Astrophysics, 663

    Lohnert, L., & Peeters, A. 2022, Astronomy & Astrophysics, 663

    2022

  22. [31]

    2023, Astronomy & Astrophysics, 677

    Lohnert, L., & Peeters, A. 2023, Astronomy & Astrophysics, 677

    2023

  23. [32]

    1969, Nature, 233, p

    Lynden-Bell, D. 1969, Nature, 233, p. 690

    1969

  24. [33]

    McKernan, B., Ford, K. E. S., Bellovary, J., et al. 2018, ApJ, 866, 66, doi: 10.3847/1538-4357/aadae5

    2018 doi

  25. [34]

    2001, The Astrophysical Journal, 552, p

    Menou, K., & Quataert, E. 2001, The Astrophysical Journal, 552, p. 204 Paczyński, B. 1978, Acta Astronomica, 28, p. 91

    2001

  26. [35]

    I., Blackman, E

    Pariev, V. I., Blackman, E. G., & Boldyrev, S. A. 2003, Astronomy and Astrophysics, 407, p. 403

    2003

  27. [36]

    Pawel, A., Lin, D. N. C., & Wampler, E. J. 1993, Astrophysical Journal, 409, 592

    1993

  28. [37]

    E., Chan, C.-k., & Psaltis, D

    Pessah, M. E., Chan, C.-k., & Psaltis, D. 2006, Monthly Notices of the Royal Astronomical Society, 372, 183, doi: 10.1111/j.1365-2966.2006.10824.x

    2006

  29. [38]

    B., Armitage, P

    Salvesen, G., Simon, J. B., Armitage, P. J., & Begelman, M. C. 2016, MNRAS, 457, p. 857

    2016

  30. [39]

    I., & Sunyaev, R

    Shakura, N. I., & Sunyaev, R. A. 1973, Astronomy and Astrophysics, 24, p. 337

    1973

  31. [40]

    2014, The Astrophysical Journal, 789, 34, doi: 10.1088/0004-637X/789/1/34

    Shi, J.-M., & Chiang, E. 2014, The Astrophysical Journal, 789, 34, doi: 10.1088/0004-637X/789/1/34

    2014 doi

  32. [41]

    1987, Nature, 329, p

    Shlosman, I., & Begelman, M. 1987, Nature, 329, p. 810

    1987

  33. [42]

    1989, The Astrophysical Journal, 341, p

    Shlosman, I., & Begelman, M. 1989, The Astrophysical Journal, 341, p. 685

    1989

  34. [43]

    Squire, J., Quataert, E., & Hopkins, P. F. 2025, The Open Journal of Astrophysics, 8, doi: 10.33232/001c.136467

    2025 doi

  35. [44]

    K., & Inutsuka, S.-i

    Suzuki, T. K., & Inutsuka, S.-i. 2009, The Astrophysical Journal, 691, L49 15

    2009

  36. [45]

    J., & Rees, M

    Syer, D., Clarke, C. J., & Rees, M. J. 1991, Monthly Notices of the Royal Astronomical Society, 250, 505, doi: 10.1093/mnras/250.3.505 Sądowski, A. 2016, Monthly Notices of the Royal Astronomical Society, 459, 4397, doi: 10.1093/mnras/stw913

    1991 doi

  37. [46]

    A., Quataert, E., & Murray, N

    Thompson, T. A., Quataert, E., & Murray, N. 2005, ApJ, 630, 167, doi: 10.1086/431923

    2005 doi

  38. [47]

    1964, Astrophysical Journal, 139, p

    Toomre, A. 1964, Astrophysical Journal, 139, p. 1217

    1964

  39. [48]

    Tsung, T. H. N., Begelman, M. C., Armitage, P. J., Jiang, Y.-F., & Gerling-Dunsmore, H. J. 2025, https://arxiv.org/abs/2507.21991

    2025 arXiv

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