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Does magnetic field promote or suppress fragmentation in AGN disks? Results from local shearing box simulations with simple cooling

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Magnetic fields suppress fragmentation in AGN disks: once magnetically dominated (plasma beta below $10^3$), bound clumps and gravitational stress drop as magnetic elevation raises the Toomre parameter, overwhelming the CRMG instability.

desk verdict A careful local simulation study that gives a plausible answer—magnetic fields suppress fragmentation in these idealized AGN disks—but the zonal-flow caveat keeps the lowest-β0 points on shaky ground. read the letter →

arxiv 2507.21991 v1 pith:7ZBXAHRG submitted 2025-07-29 astro-ph.HE

Tsun Hin Navin Tsung , Mitchell C. Begelman , Philip J. Armitage , Yan-Fei Jiang , Hannalore J. Gerling-Dunsmore This is my paper · ORCID
classification astro-ph.HE
keywords accretiondisksAGNgravitationalinstabilitymagnetorotationalfragmentationmagneticelevationshearingboxsimulationsToomreparameter
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

This paper asks a question that has two plausible answers: in the parts of AGN accretion disks that are self-gravitating, magnetic fields could push the gas toward fragmentation by tension that blocks the Coriolis force and lets gravity win, or pull it away by pressure that puffs the disk up and lowers the mid-plane density. Using local shearing-box simulations with net vertical flux and a simple cooling law, the authors vary the initial vertical-field plasma $\beta$ $\beta_0$ — the ratio of gas pressure to magnetic pressure — from $10$ to $10^5$, and count bound clumps. They find that once the disk becomes magnetically dominated — which happens for initial $\beta_0 < 10^3$ once the magnetorotational instability (MRI) saturates — the bound mass fraction and gravitational stress drop sharply, with no clumps at all at $\beta_0 = 10$ and $10^2$. The reason is magnetic elevation: the sustained toroidal field lowers the mid-plane density by over an order of magnitude and raises the Toomre parameter so far that the destabilizing 'Coriolis-Restricted-Magneto-Gravitational' (CRMG) instability grows too slowly to fragment gas. If correct, the result sets a magnetization threshold below which AGN disks stop forming stars in situ.

What carries the argument

The argument is carried by two named mechanisms and a numerical procedure. First, the Coriolis-Restricted-Magneto-Gravitational (CRMG) instability: an axisymmetric WKB mode of a rotating, shearing, self-gravitating disk with an in-plane magnetic field, governed by a quartic dispersion relation (eqs. C20–C21). Its physical content is that magnetic tension acting through a radial field component $b_x$ restricts the Coriolis-driven expansion of an overdense region, so collapse can proceed even when the standard Toomre parameter exceeds unity; the growth rate rises for stronger fields and for more radial field orientation, and destabilization requires $b_x$ above a threshold set by $Q_T$ (Fig. 4). Second, magnetic elevation: the vertical pressure of the MRI-saturated toroidal field supports the disk column and evacuates the mid-plane, and the paper quantifies the effect through the mid-plane density, plasma beta, scale height, and Toomre parameter before evaluating the CRMG growth rate from the measured states. Third, the clump census: an extension of the GRID-core algorithm that identifies Gravitational Binding Regions (GBR) and Total Binding Regions (TBR), yielding the bound mass fraction used as the fragmentation diagnostic.

What would settle it

A decisive check is to rerun the strong-field cases ($\beta_0 = 10$ and $10^2$, same cooling) in a domain wide enough for the zonal-flow channels to form at their natural spacing, or in a global disk geometry with net vertical flux, and measure the bound mass fraction: if clumps reappear at the level of the weakly magnetized runs (bound fraction $\gtrsim 10^{-2}$), the elevation-only suppression story is over-stated. A complementary observational probe is to search for in-situ-formed star clusters or compact-object binaries in AGN disk regions whose accretion state implies a mid-plane plasma $\beta$ below unity.

Watch

Extended reading notes

Core claim

The paper's answer to its title question is that magnetic field suppresses fragmentation in AGN disks, once the saturated field makes the disk magnetically dominated. The key evidence is the bound mass fraction — the share of gas locked in self-gravitating clumps, found by a clump-finding algorithm — which drops by roughly a factor of 10 between $\beta_0 = 10^4$ and $10^3$ and reaches zero (no identified clumps) at $\beta_0 = 10$ and $10^2$, while volume-averaged gravitational stress falls from $\langle\alpha_G\rangle_t \sim 0.13$ to $\sim 0.001$. The mechanism is magnetic elevation: the MRI-dynamo sustains a strong toroidal field whose pressure thickens the disk (the measured scale height grows roughly 16-fold between $\beta_0 = 10^5$ and $10$, while the thermal scale height grows only 2.8-fold), evacuates the mid-plane, and raises the proxy Toomre parameter from $\langle Q\rangle_t \sim 0.6$ to $\sim 7.7$. Feeding the time-averaged mid-plane states into the CRMG dispersion relation, the authors find that the most unstable growth rate drops by close to an order of magnitude as $\beta_0$ decreases from $10^5$ to $10$, reaching $\gamma \sim 0.1$–$0.2\,\Omega$ — e-folding times of $30$–$60\,\Omega^{-1}$, too long for turbulent density seeds to grow into bound clumps. The destabilizing radial-field channel is present and time-steady in these disks, but magnetic elevation wins.

Load-bearing premise

The conclusion rests on treating the diagonal magnetic flux channels (zonal flows) that appear in the narrower simulation box as numerical artifacts rather than real features of AGN disks: if those channels are physical, they can raise the mid-plane density and restore fragmentation in the strongest-field cases, so the suppression found here would be weaker than claimed.

Editorial extensions

If this is right

  • In the magnetically elevated regime, self-gravitational fragmentation in AGN disks is quenched, so the accretion flow can remain gravitationally stable to smaller radii than hydrodynamic cooling-time criteria alone would suggest, shifting the radius where GI takes over transport.
  • In-situ formation of disk-embedded stars — the progenitors of single and binary compact objects that could be LISA or LIGO gravitational-wave sources — is suppressed wherever the MRI-saturated field makes the disk magnetically dominated.
  • The destabilizing CRMG channel is real but subdominant: a disk's fragmentation fate is set by the net mid-plane state (density, temperature, field, Toomre parameter), not by the mere existence of a magnetic-tension instability.
  • The contrast with global protoplanetary disk simulations in which magnetic fields promote small, long-lived clumps is explained by shear and field origin: where the MRI is inefficient (low shear $q$), the field stays weak and fragmentation is strong, whereas MRI-driven strong fields at Keplerian shear suppress fragmentation.

Reading between the lines

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

  • If zonal-flow flux channels are astrophysically real rather than box artifacts — the paper leaves their global relevance open — the suppression measured at $\beta_0 = 10$ and $10^2$ is an upper bound, since in the narrower box these channels acted as pressure walls that thickened the mid-plane and boosted the bound mass fraction.
  • The mechanism implies a spatial anti-correlation that future global simulations could test: clumps and in-situ stars should appear preferentially where the local plasma beta is high or the shear is weak, and should be absent where the mid-plane plasma beta is below unity.
  • A sweep in cooling time at fixed magnetization (e.g., $\beta_0 = 10^3$) would show whether the boundary is better described by a critical Toomre parameter or a critical field strength; the paper's mechanism predicts that slower cooling, which raises $Q_T$ on its own, suppresses fragmentation even without strong fields.
  • Because the cooling law shapes the vertical entropy profile and suppresses the magnetic butterfly cycle, realistic radiative cooling may change the field structure that drives elevation; the paper's thresholds ($\beta_0 \lesssim 10^3$) are therefore a basis for radiation-hydrodynamic checks rather than a universal number.
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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

4 major / 5 minor

Summary. The paper presents local shearing-box ideal MHD simulations of AGN disks with net vertical flux, using Athena++, a beta-cooling prescription with tau_cool=1, fixed initial Q=1, and initial mid-plane plasma beta values beta0=10, 1e2, 1e3, 1e4, and 1e5. It identifies a transition to magnetically dominated disks for beta0<1e3, accompanied by a sharp drop in the bound mass fraction and in gravitational stress. The authors argue that although radial magnetic fields can destabilize gravitational modes through the Coriolis-Restricted-Magneto-Gravitational (CRMG) instability, magnetic elevation lowers the mid-plane density and raises the Toomre parameter, thereby suppressing fragmentation. The interpretation is supported by a WKB dispersion analysis, a 2D numerical verification of the CRMG growth rate, and lower-resolution comparison runs.

Significance. If correct, the result is important: it implies that strong net vertical flux may suppress in situ star formation in inner AGN disks, with consequences for the radial extent of the accretion flow and for the population of disk-embedded stellar progenitors of compact-object mergers. The paper's strengths include direct 3D clump identification via gravitational and total binding regions, explicit quantification of magnetic elevation (the measured scale height increases by roughly a factor of 16 from beta0=1e5 to beta0=10, Table 2), transparent discussion of the idealized cooling and mass-injection prescriptions, and a clean 2D verification of the CRMG growth rate (Appendix F). However, because the central low-beta0 data points were obtained after deliberately suppressing zonal flows, and because the study uses a single cooling time and a single initial Toomre parameter, the astrophysical conclusion is not yet established at the level claimed in the abstract.

major comments (4)
  1. [Appendix B, Figs. B1-B2] The two data points that carry the headline result—zero or near-zero bound mass fraction at beta0=10 and 100 in Fig. 13—were obtained after widening the azimuthal box from 20H to 40H specifically to suppress a magnetic-wind-driven zonal flow. In the 20H box the beta0=100 run fragments strongly (Fig. B2), and the manuscript states that the width, regularity, and global relevance of these flux channels are poorly understood. If these channels are physical rather than a box-size artifact, suppressing them removes a fragmentation-promoting mechanism (the pressure-wall density enhancement described in Appendix B), and the central conclusion would be reversed for those runs. The paper therefore rests on an untested assumption; the authors should either demonstrate numerically that the zonal flows are not physical (e.g., by convergence with box width, vertical extent, outflow boundary treatment, or mass-injection profile) or explicitly restrict the conclusion to simulations in which such flows are absent.
  2. [Appendix G, Table G1, Figs. G3-G4] The resolution study does not establish convergence at the fragmentation boundary. For beta0=1e4 the lower-resolution run has a markedly different magnetic field structure and an exceptionally low bound mass fraction (Figs. G3-G4), and Q_z<10 for beta0>=1e4 at LR (Table G1), so MRI may be under-resolved in those runs. Since the transition between fragmentation and no fragmentation in Fig. 13 falls between beta0=1e3 and 1e4, the location of this transition is not converged with the available resolution pair. The authors should add at least one higher-resolution run near the transition, or explain why the anomalous LR behavior at beta0=1e4 does not affect the qualitative conclusion.
  3. [Section 2, Eq. (11), Fig. 13] The study varies beta0 but fixes tau_cool=1 and initial Q=1. Fragmentation in non-magnetized disks is controlled by the ratio of cooling time to dynamical time (Gammie 2001), and the balance between MRI heating, cooling, and magnetic elevation can shift with tau_cool. With a single cooling time and a single Q, the claim that magnetic fields suppress fragmentation in AGN disks is a statement about one thermodynamic regime, not a general result. At a minimum, the manuscript should show a second cooling time (e.g., tau_cool=3 at beta0=1e3 and 1e4) or should temper the abstract and conclusions accordingly.
  4. [Section 2, mass-injection paragraph] The setup adds mass to every grid cell with a Gaussian profile exp(-z^2/H^2) at each time step to keep the box mass constant, mimicking accretion supply. This is a strong, uncalibrated source term in the continuity equation; it can, in principle, replenish mid-plane material that magnetic elevation would otherwise remove, affect the fragmentation rate, and interact with the zonal-flow instability. No test of the sensitivity to injection rate or profile is presented. The authors should either quantify the effect (e.g., by varying the injection profile or comparing with simulations without mass injection over shorter times) or state more explicitly that the results apply to mass-loaded disks.
minor comments (5)
  1. [Appendix G, Fig. G3 caption] The caption contains the typo 'Comarison' for 'Comparison'.
  2. [Abstract] The abstract contains missing spaces in 'magneticallydominated' and 'magneticallyelevated'; the typesetting should be corrected.
  3. [Table 2 and Section 5.4.1] The superscript notation for the smoothed quantities (e.g., ⟨β^{smooth}_mid⟩_t) is awkward and slightly confusing; a cleaner notation or an explicit definition at first use would improve readability.
  4. [Section 5.3, Fig. 10] In the right column of Fig. 10, the two window lengths are distinguished only in the caption; adding an inline legend to the panels would make the comparison easier to follow.
  5. [Eq. (16)] The definitions of Q_T and Q_T,B would benefit from an explicit statement that κ = Ω for the Keplerian shear used throughout; the current parenthetical remark is easy to miss.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fragmentation suppression is measured directly in the simulations, and the WKB analysis is an interpretive postdiction using measured mid-plane quantities.

full rationale

The paper's central claim — that strong net-vertical-flux magnetic fields suppress fragmentation via magnetic elevation — is established by direct simulation diagnostics, not by a fitted parameter or a self-citation chain. The bound-mass-fraction trend (Fig. 13; no clumps for β0 = 10, 10^2) is an output of the clump-finding algorithm applied to the simulated density and gravitational potential fields. Magnetic elevation is quantified from the same runs: the mid-plane density drops by over an order of magnitude and the e-folding scale height rises by about 16× (Table 2 and §5.4.1), while the thermal sound speed increases only 2.8×, so the elevation is measured rather than assumed. The WKB/CRMG growth rates (Fig. 16) are computed from the measured mid-plane β, Q_T, b_x, and sound speed using the standard dispersion relation (eq. C21); they are not fitted to the fragmentation outcome and are used only to interpret the direct result. The conceptual label "magnetically elevated" cites coauthored papers (Salvesen et al. 2016; Begelman & Silk 2017), but the elevation is independently demonstrated in this paper's own data, so the citation is not load-bearing. The identified sensitivity — zonal flows suppressed by widening the azimuthal box (Appendix B) — is a physical-robustness caveat, not a circular reduction; the paper explicitly flags that the global relevance of these channels is poorly understood. No equation in the paper reduces the conclusion to its inputs by construction, and no fitted parameter is renamed as a prediction. Resolution tests in Appendix G further support that the main simulated trends are not numerical artifacts.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The paper's central claim rests on several modeling choices: the initial field strength β0, a single cooling time, a fixed Toomre parameter, the ideal MHD approximation, the shearing box, a constant-mass injection scheme, and the WKB stability analysis. None of these are fitted to the target result; they are inputs that define the simulation campaign. The strongest assumption is the relevance of these local ideal MHD conditions to real AGN disks.

free parameters (3)
  • initial mid-plane plasma beta β0 = 10, 10^2, 10^3, 10^4, 10^5
    Chosen to explore magnetic field strength; the central claim (suppression for β0 < 10^3) is defined as a trend across these fixed inputs.
  • cooling time τcool = 1 (in units of Ω^-1)
    Fixed to ensure fragmentation in the weakly magnetized cases and to respect the numerical stability limit; no cooling-time survey is performed, so the quantitative threshold may depend on this choice.
  • proxy Toomre parameter Q = 1
    Initial setup is marginally Toomre unstable (Q_T = 0.89); the paper argues the exact choice is unimportant provided cooling is fast, but it is a fixed input.
assumptions (5)
  • domain assumption Ideal MHD (no resistivity) applies in the self-gravitating region of AGN disks.
    Invoked in §1 based on Menou & Quataert (2001) and used throughout §2 equations (1)-(4). If non-ideal effects are significant, the magnetic field structure and elevation could differ.
  • domain assumption The local shearing box approximation captures the relevant fragmentation physics.
    Used in §2; ignores radial gradients and global disk structure, which the paper acknowledges in §6.
  • ad hoc to paper The beta cooling prescription (eq. 11) with τcool = 1 adequately represents the thermodynamics for fragmentation.
    Described in §2 as 'simple prescription, though not realistic'; it sets a single cooling time and is used to enable fragmentation in the hydrodynamic limit.
  • ad hoc to paper Mass is injected everywhere to keep the total box mass constant, mimicking accretion supply.
    Described in §2; necessary because net-flux outflows drain mass, but this artificial source could affect fragmentation statistics.
  • standard math The WKB dispersion relation (eq. 25 / C20) for a razor-thin or uniform background describes the stability of the turbulent disk in an averaged sense.
    Used in §4 and §5.4.1 to compute growth rates from mid-plane averaged quantities; the paper argues substantial low-frequency power exists, but this is an approximation.
invented entities (1)
  • Coriolis-Restricted-Magneto-Gravitational (CRMG) instability independent evidence
    purpose: Named mechanism by which magnetic tension restricts the Coriolis expansion of collapsing overdensities, potentially destabilizing gravitational instability in shearing disks.
    The mechanism is verified in a 2D simulation (Appendix F) where the measured growth rate (0.201 Ω) matches the linear prediction (0.199 Ω). It is a re-framing of known physics from Gammie (1996) and Kim & Ostriker (2001).

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Pith. "Pith review of Does magnetic field promote or suppress fragmentation in AGN disks? Results from local shearing box simulations with simple cooling." pith.science (2026). https://pith.science/paper/7ZBXAHRG

@misc{pith2026250721991,
  author       = {Pith},
  title        = {Pith review of: Does magnetic field promote or suppress fragmentation in AGN disks? Results from local shearing box simulations with simple cooling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7ZBXAHRG}},
  note         = {Machine review of arXiv:2507.21991}
}
abstract

Accretion disks in Active Galactic Nuclei (AGN) are predicted to become gravitationally unstable substantially interior to the black hole's sphere of influence, at radii where the disk is simultaneously unstable to the magnetorotational instability (MRI). Using local shearing box simulations with net vertical flux and a simple cooling prescription, we investigate the effect of magnetic fields on fragmentation in the limit of ideal magnetohydrodyamics. Different levels of in-disk magnetic field from the magnetorotational instability are generated by varying the initial vertical-field plasma beta $\beta_0$. We find that the disk becomes magnetically dominated when $\beta_0 < 10^3$, and that this transition is accompanied by a drastic drop in fragmentation (as measured by the bound mass fraction) and gravitational stress. The destabilizing influence of radial magnetic fields, which are present locally and which may promote fragmentation via magnetic tension effects, is overwhelmed by magnetic elevation, which significantly reduces the mid-plane density. The magnetic suppression of fragmentation in magnetically elevated disks has implications for the radial extent of the accretion flow in AGN disks, and for the efficiency of in situ formation of disk-embedded stars that are progenitors for single and binary compact objects.

Figures

Figures reproduced from arXiv: 2507.21991 by the authors.

Figure 1
Figure 1. Clump identification using the extended GRID algorithm, with black-solid and red-dashed contours denoting GBR and TBR, respectively, overlaid on a mid-plane density (left) and gravitational potential (right) snapshot at Ω𝑡 = 200 for the 𝛽0 = 104 , 𝜏cool = 1 case. x y Shear Shear ⟹ Bx Bx Magnetically restricted in azimuthal expansion Collapse Magnetic field is destabilizing through tension Radial Azimuthal Coriolis e… view at source ↗
Figure 2
Figure 2. Intuition for the Coriolis-Restricted-Magneto-Gravitational (CRMG) instability. An overdense blob undergoing gravitational collapse experiences Coriolis forces which tend to expand it. This expansion is re￾stricted by magnetic tension if a strong radial field is present, which promotes further collapse. Appendix C), but they generally do not admit WKB solutions due to fast variations of the non-axisymmetric wavevect… view at source ↗
Figure 4
Figure 4. Plot of 𝑏𝑥,thres against 𝑄, demarcating region where the magnetic field is destabilizing (above the curve, shaded in blue) and vice versa. (𝑞Ω) −1 . Thus, magnetic fields will destabilize axisymmetric grav￾itational modes only transiently, and become stabilizing long after (𝑞Ω) −1 , thus bringing this WKB analysis into question. An extension of this analysis shows that it is possible for non-axisymmetric modes to be… view at source ↗
Figures from the paper (12 more)
Figure 5
Figure 5. Figure 5: Time-series plot of ⟨𝜌⟩𝑥𝑦 (left column), ⟨𝐵𝑥 ⟩𝑥𝑦 (middle column), ⟨𝐵𝑦 ⟩𝑥𝑦 (right column), in code units. The initial mid-plane plasma beta 𝛽0 increases through 10, 102 , 103 , 104 , 105 from top to bottom, with the cooling time 𝜏cool = 1. In the left column, the black …
Figure 6
Figure 6. Figure 6: Left: Time-averaged, horizontally averaged entropy profile of the 𝛽0 = 104 , 𝜏cool = 1 case. Entropy here is measured by ⟨ ⟨𝑃𝑔 ⟩𝑥𝑦 ⟩𝑡 /⟨ ⟨𝜌⟩𝑥𝑦 ⟩ 𝛾 𝑡 . Time-average is taken from Ω𝑡 = 100 − 300. Right: Comparison of the adiabatic index used in the simulation (𝛾 = 5/3, b…
Figure 8
Figure 8. Figure 8: Decomposition for 𝜕𝐵2 𝑥 /𝜕𝑡 (left column) and 𝜕𝐵2 𝑦 /𝜕𝑡 (right col￾umn), each curve denoting the volume average of a term in the decomposition (eq. 28), against time for various 𝛽0 cases. where 𝐼𝑖 = 𝐵𝑖𝐵𝑗 𝜕𝛿𝑣𝑖  𝜕𝑥 𝑗 denotes the ‘stretching’ term, 𝐴𝑖 = −𝐵𝑖𝛿𝑣 𝑗 𝜕𝐵𝑖  𝜕𝑥 …
Figure 7
Figure 7. Figure 7: Volume averaged Reynolds (blue), Maxwell (red) and gravitational (green) stresses as a function of time for various 𝛽0 cases. Left column: The instantaneous ⟨𝛼𝑖 ⟩𝑉 at each time. Right column: The running-average of ⟨𝛼𝑖 ⟩𝑉 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 9
Figure 9. Figure 9: Top left: Window-averaged, time-averaged plasma beta of the radial field defined by ⟨𝛽𝑥,smooth ⟩𝑡 = 2⟨ ⟨𝑃¯𝑔,𝑤 ⟩𝑥𝑦 ⟩𝑡 /⟨ ⟨𝐵¯2 𝑥,𝑤 ⟩𝑥𝑦 ⟩𝑡 . Top right: Window-averaged, time-averaged plasma beta of the toroidal field ⟨𝛽𝑥,smooth ⟩𝑡 = 2⟨ ⟨𝑃¯𝑔,𝑤 ⟩𝑥𝑦 ⟩𝑡 /⟨ ⟨𝐵¯2 𝑦,𝑤 ⟩𝑥𝑦 ⟩𝑡 . B…
Figure 10
Figure 10. Figure 10: Left column: Window-averaged, time-averaged profiles of the radial field plasma beta ⟨𝛽𝑥,smooth ⟩𝑡 = 2⟨ ⟨𝑃¯𝑔,𝑤 ⟩𝑥𝑦 ⟩𝑡 /⟨ ⟨𝐵¯2 𝑥,𝑤 ⟩𝑥𝑦 ⟩𝑡 (top left), the toroidal field plasma beta ⟨𝛽𝑦,smooth ⟩𝑡 = 2⟨ ⟨𝑃¯𝑔,𝑤 ⟩𝑥𝑦 ⟩𝑡 /⟨ ⟨𝐵¯2 𝑦,𝑤 ⟩𝑥𝑦 ⟩𝑡 (second row left), the vertical fiel…
Figure 11
Figure 11. Figure 11: Window-averaged radial field plasma beta 𝛽𝑥,smooth,mid = 2⟨𝑃¯ 𝑔,𝑤,mid ⟩𝑥𝑦/⟨𝐵ˆ2 𝑥,𝑤,mid ⟩𝑥𝑦 (left), toroidal field plasma beta 𝛽𝑦,smooth,mid = 2⟨𝑃¯ 𝑔,𝑤,mid ⟩𝑥𝑦/⟨𝐵ˆ2 𝑦,𝑤,mid ⟩𝑥𝑦 (middle), and relative radial field strength 𝑏𝑥,smooth,mid = [ ⟨𝐵¯2 𝑥,𝑤,mid ⟩𝑥𝑦/( ⟨𝐵¯2 𝑥,𝑤,m…
Figure 13
Figure 13. Figure 13: Time-averaged bound mass fraction ⟨𝑀bound ⟩𝑡 /𝑀tot, where ⟨𝑀bound ⟩𝑡 is the time averaged bound mass within the box (i.e., located within TBRs, as defined in eq. 24), and 𝑀tot is the total mass within the box, which is kept constant in our setup. This is plotted again…
Figure 14
Figure 14. Figure 14: Snapshots of the mid-plane 𝜌 (top row) and Φ (bottom row) taken at Ω𝑡 = 200 with contours overlaid to indicate clumps identified. From left to right, 𝛽0 = 10, 102 , 103 , 104 , 𝜏cool = 1. Black contours: Gravitational Binding Region (GBR, i.e. isolated region that is …
Figure 15
Figure 15. Figure 15: Horizontally-averaged, time-averaged mid-plane density (top left, orange), thermal sound speed (top left, blue), window-averaged plasma beta (top right, with a smoothing length of 𝐿𝑥), Toomre parameter 𝑄𝑇 (bottom left, green), proxy Toomre parameter 𝑄 (bottom left, pu…
Figure 16
Figure 16. Figure 16: The CRMG growth rate (top left) and the corresponding wavenum￾ber (top right) of axisymmetric modes against time for various 𝛽0, calculated using the horizontally averaged mid-plane properties. Bottom: the growth rates and the associated wavenumbers calculated by taki…
Figure 17
Figure 17. Figure 17: Snapshots of the mid-plane 𝜌 (left) and Φ (right) taken at Ω𝑡 = 200 with contours overlaid to indicate clumps identified, taken from simulation with 𝛽0 = 103 , 𝜏cool = 1 and low shearing parameter 𝑞 = 0.1. Deng H., Mayer L., Latter H., 2020, ApJ, 891, 154 Deng H., May…

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Magnetic Pressure Dominance Stabilizes AGN Disks Against Gravitational Instability

    astro-ph.HE 2025-08 conditional novelty 6.0 of 10

    Strongly magnetized isothermal shearing-box disks (β=10^2.5) stabilize against gravitational instability via MRI-driven magnetic pressure dominance, whereas weakly magnetized disks (β=10^4) fragment.

Reference graph

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    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.