pith. sign in

arxiv: 2607.00073 · v1 · pith:6P3V4HE4new · submitted 2026-06-30 · 🌌 astro-ph.CO · physics.plasm-ph

Magneto-Thermal Instability in Galaxy Clusters -- III. The Limit of Adiabatic Stratification

Lorenzo Maria Perrone , Henrik Latter This is my paper

Pith reviewed 2026-07-02 17:56 UTC · model grok-4.3

classification 🌌 astro-ph.CO physics.plasm-ph
keywords magneto-thermal instabilitygalaxy clustersadiabatic stratificationturbulence saturationintracluster mediumbuoyancy instabilitythermal conductionplume dynamics
0
0 comments X

The pith

The magneto-thermal instability in adiabatically neutral galaxy cluster gas saturates via large plumes torn apart by shear, producing turbulent kinetic energy that scales as χ ω_T.

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

The paper investigates the nonlinear saturation of the magneto-thermal instability when the background entropy profile is exactly flat, removing the usual stabilizing stratification. It combines phenomenological arguments with Boussinesq simulations to show that the instability develops into large-scale plumes whose destruction by shear sets a new scaling for the saturated state. A reader would care because the resulting turbulence can reach near-sonic speeds and supply significant pressure support in cluster outskirts, even when thermal conduction is suppressed. The work therefore extends prior results on stratified MTI saturation into the adiabatic limit.

Core claim

The adiabatic MTI saturates in a state characterised by the formation of large-scale plumes and their destruction by shear instability, yielding a new scaling law for the saturated turbulent kinetic energy ∼ χ ω_T as the adiabatic limit is approached, where χ is the effective thermal diffusivity and ω_T is the MTI frequency. This predicts that the MTI plumes may achieve near sonic speeds in cluster outskirts, thus providing significant turbulent pressure support, even in the face of suppressed thermal conduction.

What carries the argument

Saturation of the adiabatic magneto-thermal instability through formation of large-scale plumes followed by their destruction via shear instability.

If this is right

  • Saturated turbulent kinetic energy follows the scaling ∼ χ ω_T.
  • MTI plumes can reach near-sonic speeds in cluster outskirts.
  • The turbulence supplies significant pressure support even with suppressed conduction.
  • The saturation mechanism replaces the integral-scale control previously set by stable stratification.

Where Pith is reading between the lines

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

  • The plume-shear cycle may set the dominant turbulent scale in regions where entropy gradients are observationally flat near R_500.
  • This saturation state could be distinguished from other turbulence drivers by measuring the correlation between turbulent velocity and local thermal diffusivity.
  • The same plume mechanism might operate in other buoyancy-driven systems once the stabilizing gradient is removed.

Load-bearing premise

The background entropy profile is taken to be exactly flat over the scales simulated, with no residual stabilizing gradient.

What would settle it

A simulation or observation in which the turbulent kinetic energy fails to follow the χ ω_T scaling when the entropy gradient is exactly zero would falsify the saturation law.

Figures

Figures reproduced from arXiv: 2607.00073 by Henrik Latter, Lorenzo Maria Perrone.

Figure 2
Figure 2. Figure 2: Horizontal profiles of 𝑢𝑧 , 𝐵𝑧 , and 𝜃 at different times of the 1D simulation shown in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of kinetic, magnetic, and thermal energy in the rep￾resentative adiabatic MTI run described in Section 5.2. The kinetic energy undergoes intermittent bursts that reflect runaway elevator flows. punctuated by strong bursts of magnitude (10–30) 𝑣 2 cond. Notably, the kinetic energy is dominated by the vertical component during the bursts, and accompanying variations in magnetic and thermal ener￾gie… view at source ↗
Figure 4
Figure 4. Figure 4: Snapshots of vertical velocity, vertical magnetic field and the buoyancy variable at a moment near the peak of one of the ‘elevator bursts’ shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: One-dimensional, vertically-averaged profiles of vertical velocity and magnetic field, and the buoyancy variable along the vertical cut shown in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Long timeseries of the vertical kinetic energy (top left panel) and the horizontal kinetic energy (lower left panel) for a net flux and ZNF run, as described in Section 5.4. In addition, we plot the probability distribution functions (pdf) of their fluctuations in the right panels. 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 lo g10 e n erg y (c o d e u nit s) Vertical kinetic energy Kz 2 1/Pe 4.2 4.1 4.0 3.9 3.8 3.7 3… view at source ↗
Figure 8
Figure 8. Figure 8: Violin plots for ZNF runs that describe the scaling of the vertical and horizontal kinetic energies with Pe. For other parameters and discussion, see Section 5.4. sivity (e.g., Kunz et al. 2012): 𝜒S = 4.98 × 1032  𝑘B𝑇 5 keV 5/2  𝑛 10−4 cm−3 −1 cm2 s −1 , (16) where 𝑇 is the electron temperature and 𝑛 the number density. It is important to stress that, in weakly-collisional plasmas like the ICM, plasma … view at source ↗
read the original abstract

In the hot and dilute intracluster medium of galaxy clusters, large-scale buoyancy instabilities can develop due to the transport of heat along magnetic field lines. In particular, the peripheries of galaxy clusters are unstable to the magneto-thermal instability (MTI), which may contribute to the observed levels of turbulence. Recent theoretical and numerical work has revealed that the stable background entropy stratification controls the nonlinear saturation of the instability, by setting the strength and the integral scale of the resulting turbulent state. However, observations of the periphery of galaxy clusters show that the radial entropy profiles near the virial radii $R_{500}$ may be flatter than predicted by models of smooth gravitational accretion. This motivates us to investigate the saturation of the MTI in adiabatic (buoyantly neutral) atmospheres, using both phenomenological approaches and Boussinesq numerical simulations, carried out with the pseudospectral code SNOOPY. We find that the adiabatic MTI saturates in a state characterised by the formation of large-scale plumes and their destruction by shear instability, yielding a new scaling law for the saturated turbulent kinetic energy, $\sim$$\chi \omega_T$, as the adiabatic limit is approached, where $\chi$ is the effective thermal diffusivity and $\omega_T$ is the MTI frequency. This predicts that the MTI plumes may achieve near sonic speeds in cluster outskirts, thus providing significant turbulent pressure support, even in the face of suppressed thermal conduction.

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

1 major / 2 minor

Summary. The paper investigates the nonlinear saturation of the magneto-thermal instability (MTI) in the limit of adiabatic (buoyantly neutral) stratification, motivated by flat entropy profiles observed near cluster virial radii. Using both a phenomenological plume model and Boussinesq pseudospectral simulations performed with the SNOOPY code, the authors report that the instability saturates via the formation of large-scale plumes that are subsequently destroyed by shear instabilities. This yields a new scaling for the saturated turbulent kinetic energy ∼χ ω_T (where χ is the effective thermal diffusivity and ω_T the MTI frequency), which is argued to imply near-sonic plume velocities and significant turbulent pressure support in cluster outskirts even with suppressed conduction.

Significance. If the scaling and its extrapolation are robust, the result would be significant for models of turbulence and non-thermal pressure support in the peripheries of galaxy clusters. The use of both direct numerical simulations and a separate phenomenological argument is a positive feature, as is the focus on the previously under-explored adiabatic limit.

major comments (1)
  1. [Abstract] Abstract and §1: The central quantitative claim is a scaling ∼χ ω_T that is extrapolated to predict near-sonic plume speeds in cluster outskirts. However, the supporting evidence consists of Boussinesq simulations that assume small density fluctuations and low-Mach dynamics. At Mach ∼1 the Boussinesq filtering of sound waves and the anelastic constraint cease to hold; compressible effects would modify both the integral scale of the plumes and the saturated kinetic energy, rendering the advertised regime of applicability internally inconsistent with the numerical method used to derive the scaling.
minor comments (2)
  1. The manuscript would be strengthened by explicit resolution studies, convergence tests, and error bars on the measured scaling relation extracted from the simulations.
  2. A clearer derivation of the phenomenological plume model and its quantitative connection to the simulation diagnostics would help readers assess the robustness of the ∼χ ω_T result.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying this important caveat regarding the range of applicability of our results. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and §1: The central quantitative claim is a scaling ∼χ ω_T that is extrapolated to predict near-sonic plume speeds in cluster outskirts. However, the supporting evidence consists of Boussinesq simulations that assume small density fluctuations and low-Mach dynamics. At Mach ∼1 the Boussinesq filtering of sound waves and the anelastic constraint cease to hold; compressible effects would modify both the integral scale of the plumes and the saturated kinetic energy, rendering the advertised regime of applicability internally inconsistent with the numerical method used to derive the scaling.

    Authors: We agree that the Boussinesq approximation is formally limited to subsonic flows with small density perturbations, and that our simulations therefore cannot directly access the Mach ∼1 regime. The scaling ∼χ ω_T is derived within this controlled low-Mach framework (both from the phenomenological plume model and from the SNOOPY runs), where the saturation mechanism is the formation and shear destruction of large plumes. We acknowledge that compressible effects at high Mach could alter the integral scale and the saturated kinetic energy, so the extrapolation to near-sonic velocities in cluster outskirts must be regarded as suggestive rather than definitive. In the revised manuscript we will (i) qualify the abstract and §1 to state explicitly that the near-sonic prediction is an extrapolation of the Boussinesq scaling and (ii) add a paragraph in the discussion section noting that fully compressible simulations will be required to test whether the scaling persists or is modified at high Mach numbers. These textual changes constitute a partial revision; no new simulations are performed at this stage. revision: partial

Circularity Check

0 steps flagged

No circularity: scaling obtained from simulations and phenomenology

full rationale

The paper obtains its central scaling ∼χ ω_T for saturated turbulent kinetic energy directly from Boussinesq pseudospectral simulations with SNOOPY and from separate phenomenological arguments in the adiabatic limit. No load-bearing step reduces by construction to a fitted input, self-definition, or self-citation chain; the result is presented as an empirical outcome of the runs rather than forced by normalization or prior author work. The background entropy is set flat by construction for the target regime, but this is an explicit modeling choice, not a hidden tautology that generates the scaling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the Boussinesq approximation being adequate for the dilute intracluster plasma and on the assumption that the phenomenological plume-shear picture captures the dominant saturation mechanism.

axioms (1)
  • domain assumption Boussinesq approximation holds for the simulated MTI dynamics
    Invoked for the numerical simulations described in the abstract.

pith-pipeline@v0.9.1-grok · 5794 in / 1169 out tokens · 24953 ms · 2026-07-02T17:56:02.415239+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 188 canonical work pages · 4 internal anchors

  1. [1]

    2023 , month = dec, journal =

    Dynamical Properties and Detectability of the Magneto-Thermal Instability in the Intracluster Medium , author =. 2023 , month = dec, journal =. doi:10.1051/0004-6361/202347123 , annotation =

    work page doi:10.1051/0004-6361/202347123 2023

  2. [2]

    , keywords =

    Anisotropic thermal conduction on a moving mesh for cosmological simulations. , keywords =. doi:10.1093/mnras/staf1073 , archivePrefix =. 2410.07316 , primaryClass =

    work page doi:10.1093/mnras/staf1073

  3. [3]

    Living Reviews in Solar Physics , keywords =

    Solar Surface Convection. Living Reviews in Solar Physics , keywords =. doi:10.12942/lrsp-2009-2 , adsurl =

    work page doi:10.12942/lrsp-2009-2 2009

  4. [4]

    2024 , month = feb, journal =

    Does the Magnetothermal Instability Survive Whistler Suppression of Thermal Conductivity in Galaxy Clusters? , author =. 2024 , month = feb, journal =. doi:10.1051/0004-6361/202347428 , annotation =

    work page doi:10.1051/0004-6361/202347428 2024

  5. [5]

    and Kunz, Matthew W

    Yerger, Evan L. and Kunz, Matthew W. and Bott, Archie F. A. and Spitkovsky, Anatoly , year =. Collisionless Conduction in a High-Beta Plasma: A Collision Operator for Whistler Turbulence , shorttitle =. Journal of Plasma Physics , volume =. doi:10.1017/S002237782400151X , annotation =

    work page doi:10.1017/s002237782400151x

  6. [6]

    Modeling transport in weakly collisional plasmas using thermodynamic forcing

    Modeling transport in weakly collisional plasmas using thermodynamic forcing. arXiv e-prints , keywords =. doi:10.48550/arXiv.2504.14000 , archivePrefix =. 2504.14000 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2504.14000

  7. [7]

    Ultimate

    Lohse, Detlef and Shishkina, Olga , year =. Ultimate. Reviews of Modern Physics , volume =. doi:10.1103/RevModPhys.96.035001 , annotation =

    work page doi:10.1103/revmodphys.96.035001

  8. [8]

    2025 , month = nov, journal =

    Global Linear Analysis of the Magneto-Thermal Instability in a Stratified Spherical Model of the Intracluster Medium , author =. 2025 , month = nov, journal =. doi:10.1051/0004-6361/202555843 , annotation =

    work page doi:10.1051/0004-6361/202555843 2025

  9. [9]

    2025 , month = feb, journal =

    Non-Linear Saturation and Energy Transport in Global Simulations of Magneto-Thermal Turbulence in the Stratified Intracluster Medium , author =. 2025 , month = feb, journal =. doi:10.1051/0004-6361/202451788 , annotation =

    work page doi:10.1051/0004-6361/202451788 2025

  10. [10]

    Thermal Conductivity with Bells and Whistlers:

    Perrone, Lorenzo Maria and Berlok, Thomas and Pfrommer, Christoph , year =. Thermal Conductivity with Bells and Whistlers:. Astronomy and Astrophysics , volume =. doi:10.1051/0004-6361/202449555 , annotation =

    work page doi:10.1051/0004-6361/202449555

  11. [11]

    2023 , month = oct, journal =

    Constraints on Thermal Conductivity in the Merging Cluster. 2023 , month = oct, journal =. doi:10.1093/mnras/stad3101 , archiveprefix =

    work page doi:10.1093/mnras/stad3101 2023

  12. [12]

    and Werner, N

    Ichinohe, Y. and Werner, N. and Simionescu, A. and Allen, S. W. and Canning, R. E. A. and Ehlert, S. and Mernier, F. and Takahashi, T. , year =. The Growth of the Galaxy Cluster. Monthly Notices of the Royal Astronomical Society , volume =

  13. [13]

    and Gaspari, M

    Eckert, D. and Gaspari, M. and Owers, M. S. and Roediger, E. and Molendi, S. and Gastaldello, F. and Paltani, S. and Ettori, S. and Venturi, T. and Rossetti, M. and Rudnick, L. , year =. Deep. Astronomy & Astrophysics , volume =. doi:10.1051/0004-6361/201730555 , copyright =

    work page doi:10.1051/0004-6361/201730555

  14. [14]

    and Abe, H

    Abdalla, H. and Abe, H. and Acero, F. and Acharyya, A. and Adam, R. and Agudo, I. and. Sensitivity of the. 2021 , month = feb, journal =

    2021

  15. [15]

    1988 , month = sep, journal =

    Slim Accretion Disks , author =. 1988 , month = sep, journal =. doi:10.1086/166683 , langid =

    work page doi:10.1086/166683 1988

  16. [16]

    and Chen, Xingming and Kato, Shoji and Lasota, Jean-Pierre and Regev, Oded , year =

    Abramowicz, Marek A. and Chen, Xingming and Kato, Shoji and Lasota, Jean-Pierre and Regev, Oded , year =. Thermal. The Astrophysical Journal , volume =

  17. [17]

    and Igumenshchev, Igor V

    Abramowicz, Marek A. and Igumenshchev, Igor V. , year =. How. The Astrophysical Journal , volume =. doi:10.1086/320933 , langid =

    work page doi:10.1086/320933

  18. [18]

    Abramowicz, M. A. , year =. The. Astronomy & Astrophysics , volume =. doi:10.1051/0004-6361/200912155 , langid =

    work page doi:10.1051/0004-6361/200912155

  19. [19]

    and Fragile, P

    Abramowicz, Marek A. and Fragile, P. Chris , year =. Foundations of. Living Reviews in Relativity , volume =. doi:10.12942/lrr-2013-1 , langid =

    work page doi:10.12942/lrr-2013-1 2013

  20. [20]

    and Ajello, M

    Ackermann, M. and Ajello, M. and Baldini, L. and Ballet, J. and Barbiellini, G. and Bastieri, D. and Bellazzini, R. and Bissaldi, E. and Blandford, R. D. and Bloom, E. D. and Bonino, R. and Bottacini, E. and Brandt, T. J. and Bregeon, J. and Bruel, P. and Buehler, R. and Cameron, R. A. and Caputo, R. and Caraveo, P. A. and Castro, D. and Cavazzuti, E. and...

    2018

  21. [21]

    Agapitov, O. V. and Drake, J. F. and Swisdak, M. and Bale, S. D. and Horbury, T. S. and Kasper, J. C. and MacDowall, R. J. and Mozer, F. S. and Phan, T. D. and Pulupa, M. and Raouafi, N. E. and Velli, M. , year =. Flux. The Astrophysical Journal , volume =. doi:10.3847/1538-4357/ac4016 , langid =

    work page doi:10.3847/1538-4357/ac4016

  22. [22]

    Akamatsu, Hiroki and Hoshino, Akio and Ishisaki, Yoshitaka and Ohashi, Takaya and Sato, Kosuke and Takei, Yoh and Ota, Naomi , year =. X-. Publications of the Astronomical Society of Japan , volume =. doi:10.1093/pasj/63.sp3.S1019 , annotation =

    work page doi:10.1093/pasj/63.sp3.s1019

  23. [23]

    Turbulent

    Akhmedagaev, Ruslan and Zikanov, Oleg and Krasnov, Dmitry and Schumacher, Joerg , year =. Turbulent. Journal of Fluid Mechanics , volume =. doi:10.1017/jfm.2020.336 , archiveprefix =

    work page doi:10.1017/jfm.2020.336 2020

  24. [24]

    Akiyama, Kazunori and Alberdi, Antxon and Alef, Walter and Algaba, Juan Carlos and Anantua, Richard and Asada, Keiichi and Azulay, Rebecca and Bach, Uwe and Baczko, Anne-Kathrin and Ball, David and Balokovi. First. 2022 , month = may, journal =. doi:10.3847/2041-8213/ac6429 , langid =

    work page doi:10.3847/2041-8213/ac6429 2022

  25. [25]

    Akiyama, Kazunori and Alberdi, Antxon and Alef, Walter and Algaba, Juan Carlos and Anantua, Richard and Asada, Keiichi and Azulay, Rebecca and Bach, Uwe and Baczko, Anne-Kathrin and Ball, David and Balokovi. First. 2022 , month = may, journal =. doi:10.3847/2041-8213/ac6672 , langid =

    work page doi:10.3847/2041-8213/ac6672 2022

  26. [26]

    Akiyama, Kazunori and Alberdi, Antxon and Alef, Walter and Algaba, Juan Carlos and Anantua, Richard and Asada, Keiichi and Azulay, Rebecca and Bach, Uwe and Baczko, Anne-Kathrin and Ball, David and Balokovi. First. 2022 , month = may, journal =

    2022

  27. [27]

    , year =

    Alam, Shadab and Guha, Anirban and Verma, Mahendra K. , year =. Revisiting. Journal of Fluid Mechanics , volume =. doi:10.1017/jfm.2019.529 , archiveprefix =

    work page doi:10.1017/jfm.2019.529 2019

  28. [28]

    Alards, Kim M. J. and Kunnen, Rudie P. J. and Stevens, Richard J. A. M. and Lohse, Detlef and Toschi., Federico and Clercx, Herman J. H. , year =. Sharp Transitions in Rotating Turbulent Convection:. Physical Review Fluids , volume =. doi:10.1103/PhysRevFluids.4.074601 , archiveprefix =

    work page doi:10.1103/physrevfluids.4.074601

  29. [29]

    2001 , month = mar, journal =

    Parallel Heat Diffusion and Subdiffusion in Random Magnetic Fields , author =. 2001 , month = mar, journal =. doi:10.1063/1.1344920 , langid =

    work page doi:10.1063/1.1344920 2001

  30. [30]

    and Pouquet, Annick , year =

    Alexakis, Alexandros and Mininni, Pablo D. and Pouquet, Annick , year =. Shell to Shell Energy Transfer in. Physical Review E , volume =. doi:10.1103/PhysRevE.72.046301 , archiveprefix =

    work page doi:10.1103/physreve.72.046301

  31. [31]

    1996 , month = jan, journal =

    Super-Time-Stepping Acceleration of Explicit Schemes for Parabolic Problems , author =. 1996 , month = jan, journal =

    1996

  32. [32]

    Allen, S. W. and Schmidt, R. W. and Fabian, A. C. , year =. The. Monthly Notices of the Royal Astronomical Society , volume =

  33. [33]

    Allen, S. W. and Rapetti, D. A. and Schmidt, R. W. and Ebeling, H. and Morris, G. and Fabian, A. C. , year =. Improved Constraints on Dark Energy from. Monthly Notices of the Royal Astronomical Society , volume =. doi:10.1111/j.1365-2966.2007.12610.x , adsnote =

    work page doi:10.1111/j.1365-2966.2007.12610.x 2007

  34. [34]

    and Evrard, August E

    Allen, Steven W. and Evrard, August E. and Mantz, Adam B. , year =. Cosmological. Annual Review of Astronomy and Astrophysics , volume =. doi:10.1146/annurev-astro-081710-102514 , adsnote =

    work page doi:10.1146/annurev-astro-081710-102514

  35. [35]

    Alliney, Stefano and Ruzinsky, S. A. , year =. An Algorithm for the Minimization of Mixed l 1 and l 2 Norms with Application to. IEEE transactions on signal processing , volume =

  36. [36]

    Winds and Feedback from Supermassive Black Holes Accreting at Low Rates:

    Almeida, Ivan and Nemmen, Rodrigo , year =. Winds and Feedback from Supermassive Black Holes Accreting at Low Rates:. Monthly Notices of the Royal Astronomical Society , volume =. doi:10.1093/mnras/staa033 , archiveprefix =

    work page doi:10.1093/mnras/staa033

  37. [37]

    Onset of Magnetic Reconnection in a Collisionless, High-Beta Plasma , author =

  38. [38]

    2018 , month = may, journal =

    A. 2018 , month = may, journal =. doi:10.1088/1742-6596/1031/1/012015 , langid =

    work page doi:10.1088/1742-6596/1031/1/012015 2018

  39. [39]

    2021 , month = dec, eprintclass =

    Data-Driven Discovery of Reduced Plasma Physics Models from Fully-Kinetic Simulations , author =. 2021 , month = dec, eprintclass =

    2021

  40. [40]

    Splitting Methods for

    Ameres, Jakob , year =. Splitting Methods for

  41. [41]

    2013 , month = apr, journal =

    Dark. 2013 , month = apr, journal =

    2013

  42. [42]

    2020 , month = jun, journal =

    Turbulent Pressure Support and Hydrostatic Mass Bias in the Intracluster Medium , author =. 2020 , month = jun, journal =

    2020

  43. [43]

    and Zanotti, O

    Anton, L. and Zanotti, O. and Miralles, J. A. and Marti, J. M. and Ibanez, J. M. and Font, J. A. and Pons, J. A. , year =. Numerical 3+1 General Relativistic Magnetohydrodynamics:. The Astrophysical Journal , volume =. doi:10.1086/498238 , archiveprefix =

    work page doi:10.1086/498238

  44. [44]

    2021 , month = dec, eprintclass =

    Intrinsic Periodicity of Turbulence , author =. 2021 , month = dec, eprintclass =

    2021

  45. [45]

    2006 , month = apr, journal =

    Investigating a Fluctuating-Accretion Model for the Spectral-Timing Properties of Accreting Black Hole Systems , author =. 2006 , month = apr, journal =

    2006

  46. [46]

    and Reynolds, Christopher S

    Armitage, Philip J. and Reynolds, Christopher S. , year =. The Variability of Accretion on to. Monthly Notices of the Royal Astronomical Society , volume =

  47. [47]

    , year =

    Armitage, Philip J. , year =. Dynamics of. Annual Review of Astronomy and Astrophysics, vol. 49, issue 1, pp. 195-236 , volume =. doi:10.1146/annurev-astro-081710-102521 , langid =

    work page doi:10.1146/annurev-astro-081710-102521

  48. [48]

    , year =

    Arnaud, M. , year =. The. Astronomy and Astrophysics, Volume 500, Issue 1, 2009, pp.103-104 , volume =. doi:10.1051/0004-6361/200912150 , langid =

    work page doi:10.1051/0004-6361/200912150 2009

  49. [49]

    and Fukuda, N

    Asai, N. and Fukuda, N. and Matsumoto, R. , year =. Three-Dimensional. Advances in Space Research , volume =

  50. [50]

    Aunai, Nicolas and Smets, Roch and Ciardi, Andrea and Deegan, Philip and Jeandet, Alexis and Payet, Thibault and Guyot, Nathan and Darrieumerlou, Loic , year =

  51. [51]

    2013 , month = aug, journal =

    Role of Magnetic Field Strength and Numerical Resolution in Simulations of the Heat-Flux Driven Buoyancy Instability , author =. 2013 , month = aug, journal =. doi:10.1088/0004-637X/773/2/171 , adsnote =

    work page doi:10.1088/0004-637x/773/2/171 2013

  52. [52]

    and McKinney, Jonathan C

    Avara, Mark J. and McKinney, Jonathan C. and Reynolds, Chris S. , year =. Efficiency of. Monthly Notices of the Royal Astronomical Society , volume =. doi:10.1093/mnras/stw1643 , archiveprefix =

    work page doi:10.1093/mnras/stw1643

  53. [53]

    , year =

    Avila, M. , year =. Stability and. Physical Review Letters , volume =

  54. [54]

    Breaking the Spectral Degeneracies in Black Hole Binaries with Fast Timing Data:

    Axelsson, Magnus and Done, Chris , year =. Breaking the Spectral Degeneracies in Black Hole Binaries with Fast Timing Data:. Monthly Notices of the Royal Astronomical Society , volume =

  55. [55]

    and McNamara, B

    Babyk, Iu V. and McNamara, B. R. and Nulsen, P. E. J. and Russell, H. R. and Vantyghem, A. N. and Hogan, M. T. and Pulido, F. A. , year =. A. The Astrophysical Journal , volume =

  56. [56]

    Baganoff, F. K. and Bautz, M. W. and Brandt, W. N. and Chartas, G. and Feigelson, E. D. and Garmire, G. P. and Maeda, Y. and Morris, M. and Ricker, G. R. and Townsley, L. K. and Walter, F. , year =. Rapid. Nature , volume =

  57. [57]

    , year =

    Bai, Xue-Ning and Stone, James M. , year =. Effect of. The Astrophysical Journal , volume =. doi:10.1088/0004-637X/736/2/144 , archiveprefix =

    work page doi:10.1088/0004-637x/736/2/144

  58. [58]

    , year =

    Bai, Xue-Ning and Stone, James M. , year =. Wind-Driven. The Astrophysical Journal , volume =. doi:10.1088/0004-637X/769/1/76 , archiveprefix =

    work page doi:10.1088/0004-637x/769/1/76

  59. [59]

    Bai, Xue-Ning , year =. Towards. The Astrophysical Journal , volume =. doi:10.3847/1538-4357/ac56e1 , archiveprefix =

    work page doi:10.3847/1538-4357/ac56e1

  60. [60]

    and Hawley, John F

    Balbus, Steven A. and Hawley, John F. , year =. A. The Astrophysical Journal , volume =. doi:10.1086/170270 , adsnote =

    work page doi:10.1086/170270

  61. [61]

    and Hawley, John F

    Balbus, Steven A. and Hawley, John F. , year =. A. The Astrophysical Journal , volume =

  62. [62]

    , year =

    Balbus, Steven A. , year =. General. The Astrophysical Journal , volume =

  63. [63]

    and Hawley, John F

    Balbus, Steven A. and Hawley, John F. and Stone, James M. , year =. Nonlinear. The Astrophysical Journal , volume =

  64. [64]

    1998 , month = jan, journal =

    Instability, Turbulence, and Enhanced Transport in Accretion Disks , author =. 1998 , month = jan, journal =

    1998

  65. [65]

    , year =

    Balbus, Steven A. , year =. Stability, Instability, and ". The Astrophysical Journal , volume =. doi:10.1086/308732 , langid =

    work page doi:10.1086/308732

  66. [66]

    2001 , month = dec, journal =

    Convective and Rotational Stability of a Dilute Plasma , author =. 2001 , month = dec, journal =. doi:10.1086/323875 , archiveprefix =

    work page doi:10.1086/323875 2001

  67. [67]

    2004 , month = dec, journal =

    Viscous Shear Instability in Weakly Magnetized, Dilute Plasmas , author =. 2004 , month = dec, journal =. doi:10.1086/424989 , adsnote =

    work page doi:10.1086/424989 2004

  68. [68]

    and Reynolds, Christopher S

    Balbus, Steven A. and Reynolds, Christopher S. , year =. Regulation of Thermal Conductivity in Hot Galaxy Clusters by. The Astrophysical Journal , volume =. doi:10.1086/590554 , archiveprefix =

    work page doi:10.1086/590554

  69. [69]

    , year =

    Balbus, Steven A. , year =. Magnetohydrodynamics of

  70. [70]

    and Reynolds, Christopher S

    Balbus, Steven A. and Reynolds, Christopher S. , year =. The Astrophysical Journal , volume =. doi:10.1088/2041-8205/720/1/L97 , langid =

    work page doi:10.1088/2041-8205/720/1/l97 2041

  71. [71]

    Bale, S. D. and Kasper, J. C. and Howes, G. G. and Quataert, E. and Salem, C. and Sundkvist, D. , year =. Magnetic. Physical Review Letters , volume =. doi:10.1103/PhysRevLett.103.211101 , adsnote =

    work page doi:10.1103/physrevlett.103.211101

  72. [72]

    Bale, S. D. and Pulupa, M. and Salem, C. and Chen, C. H. K. and Quataert, E. , year =. Electron Heat Conduction in the Solar Wind:. The Astrophysical Journal , volume =. doi:10.1088/2041-8205/769/2/L22 , adsnote =

    work page doi:10.1088/2041-8205/769/2/l22 2041

  73. [73]

    Ball, David and. A. 2021 , month = aug, journal =

    2021

  74. [74]

    and Morsony, Brian J

    Bambic, Christopher J. and Morsony, Brian J. and Reynolds, Christopher S. , year =. Suppression of. The Astrophysical Journal , volume =. doi:10.3847/1538-4357/aab558 , adsnote =

    work page doi:10.3847/1538-4357/aab558

  75. [75]

    and Reynolds, Christopher S

    Bambic, Christopher J. and Reynolds, Christopher S. , year =. Efficient. The Astrophysical Journal , volume =. doi:10.3847/1538-4357/ab4daf , adsnote =

    work page doi:10.3847/1538-4357/ab4daf

  76. [76]

    and Chervenak, James A

    Bandler, Simon R. and Chervenak, James A. and Datesman, Aaron M. and Devasia, Archana M. and DiPirro, Michael J. and Sakai, Kazuhiro and Smith, Stephen J. and Stevenson, Thomas R. and Yoon, Wonsik and Bennett, Douglas A. and Mates, Benjamin and Swetz, Daniel S. and Ullom, Joel N. and Irwin, Kent D. and Eckart, Megan E. and. Lynx. 2019 , month = may, journal =

    2019

  77. [77]

    Permutation

    Bandt, Christoph and Pompe, Bernd , year =. Permutation. Physical Review Letters , volume =. doi:10.1103/PhysRevLett.88.174102 , langid =

    work page doi:10.1103/physrevlett.88.174102

  78. [78]

    Banerjee, Robi and Jedamzik, Karsten , year =. The. Physical Review D , volume =. doi:10.1103/PhysRevD.70.123003 , archiveprefix =

    work page doi:10.1103/physrevd.70.123003

  79. [79]

    Observing Imprints of Black Hole Event Horizon on

    Banerjee, Srimanta and Gilfanov, Marat and Bhattacharyya, Sudip and Sunyaev, Rashid , year =. Observing Imprints of Black Hole Event Horizon on. Monthly Notices of the Royal Astronomical Society , volume =

  80. [80]

    Barai, Paramita and Murante, Giuseppe and Borgani, Stefano and Gaspari, Massimo and Granato, Gian Luigi and Monaco, Pierluigi and. Kinetic. 2016 , month = sep, journal =

    2016

Showing first 80 references.