Pith. sign in

REVIEW 4 major objections 5 minor 2 cited by

Long timescale numerical simulations of large, super-critical accretion discs

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Super-critical discs cap their own feeding near the Eddington rate, even when the outer supply is many times Eddington.

desk verdict A genuinely new numerical result—large, long-duration GRRMHD super-critical discs settling to net near-Eddington accretion—presented honestly, but the unresolved MRI and limited equilibrium region mean the headline claim is provisional; still worth serious refereeing. read the letter →

arxiv 2505.08859 v1 pith:IDHTYIFY submitted 2025-05-13 astro-ph.HE

P. Chris Fragile , Matthew J. Middleton , Deepika A. Bollimpalli , Zach Smith This is my paper · ORCID
classification astro-ph.HE
keywords accretiondiscssuper-criticalEddingtonlimitradiationmagnetohydrodynamicsblackholeultra-luminousX-raysourcescriticaldiscmodelslim
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

Three long-duration, large-domain 3D radiation-MHD simulations of a rapidly spinning stellar-mass black hole fed above its Eddington rate find that the black hole's net accretion settles to approximately the Eddington accretion rate, regardless of whether the outer feeding rate is 1, 4, or 10 times Eddington. The mechanism is a near-perfect cancellation: at every radius where the discs have reached equilibrium, the outward mass flux rises to match the inward flux, leaving a net inward rate $\dot{m}_\mathrm{net} = \dot{m}_\mathrm{in} - \dot{m}_\mathrm{out} \approx 1$. The authors read this as evidence that $\dot{M}_\mathrm{Edd}$ is a true limit for steady, large super-critical discs fed by thin Keplerian discs at large radius, in agreement with the critical disc model and in tension with most earlier global simulations. If correct, the result would explain why ultra-luminous X-ray sources can appear so bright while their black holes grow at essentially Eddington-limited rates, and it would sharpen the puzzle of how the first supermassive black holes grew so quickly.

What carries the argument

The load-bearing object is the radial profile of mass flux through spherical shells: the inward flux $\dot{M}_\mathrm{in}$ and outward flux $\dot{M}_\mathrm{out}$, each integrated over the full $4\pi$ solid angle, and their difference $\dot{M}_\mathrm{net}$. In a steady disc $\dot{M}_\mathrm{net}$ must be independent of radius, and the simulations achieve this with $\dot{m}_\mathrm{net} \approx 1$ out to $r_\mathrm{eq} \sim 30$-$50\,r_g$; the delicate balance between two large opposing fluxes is what enforces the Eddington limit. The simulations also track the unbound outflow fraction through the Bernoulli parameter and the radiative luminosity through spherical shells, and compare those against the analytic scalings of the critical disc model.

What would settle it

Run the same initial conditions with a resolution that resolves the MRI (quality factors $Q_\theta, Q_\phi \gtrsim 10$) and measure $\dot{m}_\mathrm{BH}$; if the net accretion rises well above $\dot{M}_\mathrm{Edd}$ once turbulence is resolved, the near-Eddington result is a grid artifact rather than a physical limit.

Watch

Extended reading notes

Core claim

The central claim is that large, steady super-critical accretion discs obey the Eddington limit locally: all the simulations converge to $\dot{m}_\mathrm{BH} \approx 1$ over the radii where they have reached equilibrium, even though the inward mass flux at large radius $\dot{m}_\mathrm{in}$ can exceed $1000 \dot{M}_\mathrm{Edd}$. This happens because the outflowing flux $\dot{m}_\mathrm{out}$ adjusts to almost exactly cancel $\dot{m}_\mathrm{in}$, so the net accretion $\dot{m}_\mathrm{net}$ stays near unity at all radii. The authors show that the simulated profiles of mass flux, radiative luminosity versus radius and polar angle, and angular velocity all match the critical disc model, whereas the slim disc model predicts no significant outflow, a trapping radius about twenty times larger than observed, and sub-Keplerian rotation. They argue that most earlier torus-based simulations started with their critical radius outside the domain, which forced an advective rather than an outflow-dominated outcome.

Load-bearing premise

The results rest on the assumption that the under-resolved magnetorotational instability still produces physically realistic angular momentum transport and wind launching; the paper states it does not formally resolve the MRI, and higher-resolution turbulence could alter the outflow-inflow balance that produces near-Eddington net accretion.

Editorial extensions

If this is right

  • Super-Eddington accretion need not imply super-Eddington black hole growth: a large, aligned, steady disc will instead launch most of the supplied mass outward, keeping the hole near $\dot{M}_\mathrm{Edd}$.
  • The trapping radius where advection dominates sits close to the hole, around $5$-$8\,r_g$, so advection alone cannot explain super-Eddington discs beyond roughly $20\,r_g$.
  • The discs yield high radiative efficiencies, $\eta \sim 0.3$-$0.7$, which the authors present as upper limits because some outward radiation remains trapped in the wind.
  • The luminosity is strongly concentrated toward the poles, matching the appearance of many ultra-luminous X-ray sources and explaining why the same source can look sub-Eddington from some viewing angles.
  • Growth of the first supermassive black holes cannot rely on steady, long-term accretion from a large, aligned, Keplerian disc if the Eddington limit holds as found here.

Reading between the lines

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

  • If confirmed at higher resolution, the result would predict that the observed luminosity and variability of ultra-luminous X-ray sources track $\dot{M}_\mathrm{Edd}$ rather than the external supply rate, a testable distinction from slim-disc models.
  • The authors' own speculation implies that the outcome depends on the ratio $r_\mathrm{cr}/r_\mathrm{cir}$; one could test this directly by re-running a torus-based simulation with its pressure maximum placed beyond the critical radius and checking whether $\dot{m}_\mathrm{BH}$ drops toward unity.
  • The near-Eddington attractor may apply only to discs whose outer boundary is a thin Keplerian disc; in transients such as tidal disruption events, where the circularization radius can lie inside the critical radius, the same outflow-inflow cancellation need not operate.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 three three-dimensional general-relativistic radiation-MHD simulations of super-critical accretion onto a rapidly spinning stellar-mass black hole, using the Cosmos++ code with an M1 closure scheme and starting from Novikov-Thorne thin-disc equilibria extended to large radii (r_max up to 1000 r_g) and evolved for long durations (up to ~166,000 t_g). The intended mass feeding rates span mdot0 = 1, 4, and 10 Eddington units. The central result is that, in the radial region that has reached inflow equilibrium (r_eq ~ 32-49 r_g), the measured net accretion rate onto the black hole is close to Eddington in all three runs, even though the inward mass flux at large radii can be orders of magnitude larger. The authors attribute this to a near-cancellation between inward and outward mass fluxes and interpret it as evidence that these discs obey the Eddington limit and are described by the critical-disc model rather than the slim-disc model. They also compare radiative and kinetic luminosities with analytic expectations and discuss why their results differ from most earlier global simulations, which typically find mdot_BH ~ 10 or more.

Significance. If the central claim holds, this is a significant result. It would indicate that large, steady super-critical discs fed by thin Keplerian discs at large radius self-regulate their net accretion to near-Eddington through a finely balanced outflow, in agreement with the critical-disc scenario and in tension with the conclusions of most previous global simulations. The paper also speaks directly to the growth of high-redshift black holes and to the observed properties of ultraluminous X-ray sources. The strengths of the study include the unusually large radial domains and long evolution times, the choice to initialize from a Shakura-Sunyaev solution rather than a small finite torus, and the fact that the near-Eddington net accretion rate is a measured outcome rather than an imposed parameter. The comparisons with the analytic predictions of Fukue (2004) and Poutanen et al. (2007) provide independent diagnostics that go beyond a simple visual match. The authors are also explicit about several limitations, including the modest MRI resolution and the fact that the critical radius is not captured on the grid.

major comments (4)
  1. [Section 3.1, Table 1, Section 6] The central claim in the abstract and Section 5 that 'these simulated discs obey the Eddington limit' and are 'locally Eddington limited at all radii' extrapolates beyond the region actually shown to be in equilibrium. Table 1 reports r_eq = 32-49 r_g, and Section 6 explicitly states that the critical radius r_cr is not captured and that no plateau in mdot_in(r) is seen within the equilibrated region. Because the outer disc is not in steady state and the cancellation between mdot_in and mdot_out there is not demonstrated, the Eddington-limited conclusion should be restricted to r < r_eq, with a clear discussion of how the non-equilibrated outer region could or could not alter the inner balance.
  2. [Section 2, Section 3.1.1] The MRI is formally unresolved in these simulations: the paper reports Q_theta ~ 1 and Q_phi ~ 4, and attributes the low measured alpha ~ 10^-3 - 10^-2 to this under-resolution. Since the near-Eddington net accretion emerges from a delicate cancellation between large inward and outward fluxes, the value of alpha directly controls the radial drift speed and hence that balance. The one higher-resolution extension, a9r20L3, shows a slight upward jump in mdot_BH, which is the direction one would expect if resolved turbulence increases transport. No convergence test at commonly accepted quality factors (e.g., Q >= 10) is presented. This leaves open the possibility that the Eddington-limited result is, at least in part, a resolution artifact rather than a robust physical self-regulation.
  3. [Section 4.2, Figure 3] The claimed 'reasonable quantitative agreement' with the critical-disc model relies on the analytic curve mdot_in(r) = [mdot_in(r_cr) - mdot_BH] r / r_cr, but the value of r_cr used to draw this curve is not stated. Since r_cr is not captured in the simulations and Section 6 states that it must lie beyond r_eq, this curve is not an independent prediction but depends on a choice of r_cr that may be adjusted to match the data. The authors should state explicitly how r_cr was chosen for each panel and show the sensitivity of the comparison to that choice; otherwise the agreement is partly by construction.
  4. [Section 3.1.2, Section 6] The fine-tuned cancellation between mdot_in and mdot_out is characterized by large statistical fluctuations, with mdot_net often changing sign, and much of the outflow is not unbound by the Bernoulli criterion (mdot_out significantly exceeds mdot_un). The paper notes that the total mass in the domain drops by less than 8%, but this does not by itself establish that the observed cancellation is a steady-state attractor rather than a transient sloshing of matter within a domain that has not reached equilibrium at large radii. The ultimate fate of the bound outflow is explicitly uncertain. The conclusions should therefore be tempered: the simulations demonstrate near-Eddington net accretion in the equilibrated inner region, but whether this constitutes a global Eddington limit requires either longer evolutions, larger domains, or a clearer identification of the physical mechanism enforcing the cancellation.
minor comments (5)
  1. [Section 4.1, Section 4.2] In Section 4.1 the text says 'we see significant mass outflow ... in Figure 2', and in Section 4.2 it says 'which is exactly what we see in Figure 2'; in both places the radial mass-flux profiles are shown in Figure 3, not Figure 2, which shows the time history of mdot_BH.
  2. [Equations (2)-(4)] The displayed expression for the radiation four-force density G^mu appears to have unbalanced parentheses and missing terms; please re-derive and reformat this expression so that the coupling terms are unambiguous.
  3. [Abstract, Section 5] The phrase 'these simulated discs obey the Eddington limit' should be qualified to 'in the radial region that has reached inflow equilibrium', to be consistent with the admitted absence of equilibrium at large radii and the lack of capture of r_cr.
  4. [Section 5, bulleted list] The sentence 'we stand by our finding' is a statement of authorial conviction rather than an argument; consider replacing it with a summary of the specific simulation features that distinguish this work from prior studies.
  5. [Figure 2 and Table 1] Figure 2 shows shaded 1-sigma standard deviations obtained after moving-average smoothing; please clarify in the caption whether the shaded regions are the standard deviation of the smoothed or unsmoothed time series, since this affects the interpretation of the secular trends.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the near-Eddington net accretion rate is a measured simulation outcome, and the model comparisons use independent analytic predictions.

full rationale

The central claim that all simulations settle to mdot_BH ~ 1 is a measured result at the event horizon (Eq. 16 and Figure 2), not a parameter fitted to enforce that value. The initial target rates mdot_0 = 1-10 and alpha_SS = 0.02 are inputs, but the reported net accretion rate is an output of the evolution. The comparisons to slim-disc and critical-disc models are anchored to external analytic work (Abramowicz et al. 1988; Fukue 2004; Poutanen et al. 2007), and the critical-disc model is not invoked as a self-citation or uniqueness theorem. The choice of r_eq as a diagnostic radius is explicitly justified as the radius where the net accretion rate has reached a steady value, and <mdot_in(r_eq)> is reported as a measured quantity, not as a fitted constant that forces mdot_BH ~ 1. Self-citations in the paper concern the numerical code, initial-condition conventions, and prior stability studies; they are not load-bearing for the Eddington-limit conclusion. The unresolved-MRI concern raised in Section 2 ('not formally resolving the MRI') is a numerical-convergence and physical-fidelity risk, not a circularity, because the paper does not define the Eddington-limit result in terms of the resolution or alpha. The paper also explicitly cautions that 'Additional work will be needed to clarify all of these issues,' which further supports that the claim is empirical rather than self-referential.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim depends on the numerical setup choices (initial conditions, grid, field topology) and on standard GRRMHD approximations; no new physics is invented. The largest uncertainties are resolution and the unresolved outer steady state.

free parameters (4)
  • Initial target mass accretion rate mdot0 = 1, 4, 10
    Chosen by hand for the three runs (a9r5, a9r20, a9r50); the measured mdot_in at r_eq is 67, 42, 23, so the target is not the actual input.
  • Outer domain radius rmax = 300 r_g (a9r5), 1000 r_g (a9r20, a9r50)
    Chosen to be larger than previous torus setups to capture the critical radius; the critical radius is still not resolved.
  • Polar concentration parameter h = 0.12 (a9r5), 0.35 (a9r20, a9r50)
    Controls grid concentration toward the midplane; chosen by hand.
  • Shakura-Sunyaev alpha_SS = 0.02
    Used to build the initial Novikov-Thorne disc; the measured effective alpha is 1e-3 to 1e-2.
assumptions (4)
  • domain assumption Gray opacity with electron scattering and Kramers-like free-free absorption captures the dominant radiation physics.
    M1 closure with Planck and Rosseland mean opacities is used in Section 2; validity in scattering-dominated super-Eddington flows is assumed.
  • domain assumption The initial Shakura-Sunyaev inner disc region, extrapolated to super-Eddington rates, is a reasonable starting point and the disc can evolve to its true state.
    Section 2 initializes from the Novikov-Thorne inner region even though this solution is formally invalid above Eddington; the authors argue the long burn-in allows settling.
  • ad hoc to paper The zero-net-flux quadrupole magnetic field stabilizes the disc and does not unduly bias the outflow and accretion balance.
    Section 2 and Section 5 list this topology as a possible contributor to the different result; no calibration against independent simulations is provided.
  • domain assumption Outflow boundary conditions at the inner and outer radial limits do not significantly alter the interior equilibrium.
    Section 2 applies outflow boundary conditions; total mass in the domain drops by less than 8 percent, but boundary effects are not quantified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Long timescale numerical simulations of large, super-critical accretion discs." pith.science (2026). https://pith.science/paper/IDHTYIFY

@misc{pith2026250508859,
  author       = {Pith},
  title        = {Pith review of: Long timescale numerical simulations of large, super-critical accretion discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IDHTYIFY}},
  note         = {Machine review of arXiv:2505.08859}
}
abstract

In this paper, we report on three of the largest (in terms of simulation domain size) and longest (in terms of duration) 3D general relativistic radiation magnetohydrodynamic simulations of super-critical accretion onto black holes. The simulations are all set for a rapidly rotating ($a_* = 0.9$), stellar-mass ($M_\mathrm{BH} = 6.62 M_\odot$) black hole. The simulations vary in their initial target mass accretion rates (assumed measured at large radius), with values sampled in the range $\dot{m}=\dot{M}/\dot{M}_\mathrm{Edd} = 1-10$. We find in practice, though, that all of our simulations settle close to a net accretion rate of $\dot{m}_\mathrm{net} = \dot{m}_\mathrm{in}-\dot{m}_\mathrm{out} \approx 1$ (over the radii where our simulations have reached equilibrium), even though the inward mass flux (measured at large radii) $\dot{m}_\mathrm{in}$ can exceed 1,000 in some cases. This is possible because the outflowing mass flux $\dot{m}_\mathrm{out}$ adjusts itself to very nearly cancel out $\dot{m}_\mathrm{in}$, so that at all radii $\dot{M}_\mathrm{net} \approx \dot{M}_\mathrm{Edd}$. In other words, these simulated discs obey the Eddington limit. We compare our results with the predictions of the slim disc (advection-dominated) and critical disc (wind/outflow-dominated) models, finding that they agree quite well with the critical disc model both qualitatively and quantitatively. We also speculate as to why our results appear to contradict most previous numerical studies of super-critical accretion.

Figures

Figures reproduced from arXiv: 2505.08859 by the authors.

Figure 1
Figure 1. Disc and grid configuration at the start of a9r20L3 (the high-resolution interval for simulation a9r20). The left panel shows the statically refined grid, as well as the radiative flux (arbitrary units). Red colors indicate outgoing flux, while blue colors indicate flux moving toward the black hole. The right panel shows the logarithm of the gas density, covering 3 orders of magnitude, as well as magnetic field stre… view at source ↗
Figure 2
Figure 2. Mass accretion rate through the black hole event horizon in units of the Eddington accretion rate 𝑚¤ BH = 𝑀¤ BH/𝑀¤ Edd, smoothed using moving averages over 20 consecutive dumps (≈ 1, 850 𝑡𝑔 in time). The shaded re￾gions show the 1𝜎 standard deviations, and the black dashed line shows the Eddington limit. −(𝑇 𝑡 𝑡 + 𝑅 𝑡 𝑡 + 𝜌𝑢𝑡 ) > 0 (Sądowski & Narayan 2016) and thus is likely to be unbound and ultimately escape to i… view at source ↗
Figure 3
Figure 3. Mass fluxes, both inward (𝑚¤ in) and outward (𝑚¤ out), as well as the net mass flux 𝑚¤ net = 𝑚¤ in − ¤𝑚out, all scaled to Eddington and time averaged from 𝑡 = 50, 000 𝑡𝑔 or 100, 000 𝑡𝑔 to 𝑡stop for the a9r5 (top), a9r20 (middle), and a9r50 (bottom) simulations. The other curves report that portion of 𝑚¤ out that has a positive Bernoulli parameter (𝑚¤ un) and an analytic estimate for 𝑚¤ in (𝑟 ) = [ ¤𝑚in (𝑟cr) − ¤𝑚BH … view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Radiative luminosity, both outward (𝐿out) and inward (𝐿in), as well as the net luminosity 𝐿net = 𝐿out − 𝐿in, all scaled to Eddington and time averaged from 𝑡 = 50, 000 𝑡𝑔 or 100, 000 𝑡𝑔 to 𝑡stop for the a9r5 (top), a9r20 (middle), and a9r50 (bottom) simulations. The bl…
Figure 5
Figure 5. Figure 5: Psuedocolor plot of time- and azimuthally averaged gas density and fluid velocity streamlines for simulations a9r5 (first panel), a9r20 (second panel), a9r50 (third panel), plus the high-resolution extension a9r20L3 (last panel). The white lines represent the effective…
Figure 6
Figure 6. Figure 6: Contribution to the radiative luminosity measured at 𝑟eq, broken down into polar angle bins, showing that most of the radiation escapes close to the poles. The black, dotted curve suggests 𝐿rad ( 𝜃 ) ∝ 1/(1 − | cos 𝜃 | ). Data are time averaged over the intervals from …
Figure 8
Figure 8. Figure 8: Density-weighted, time-averaged angular velocity profiles of the discs divided by a purely Keplerian profile. Our profiles differ by no more than a few percent from purely Keplerian. Data are again time averaged over the intervals from 𝑡 = 50, 000 𝑡𝑔, 100, 000 𝑡𝑔, or 1…
Figure 7
Figure 7. Figure 7: Radiative (top panel) and kinetic (bottom panel) luminosities as a function of time measured at 𝑟eq for each simulation. Data have been smoothed by using a moving boxcar averaging window of 20 consecutive dumps. The shaded regions show 1𝜎 standard deviations. discs). I…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Radiation GRMHD Models of Accretion onto Stellar-Mass Black Holes: I. Survey of Eddington Ratios

    astro-ph.HE 2025-06 conditional novelty 7.0 of 10

    Full-transport radiation GRMHD simulations show super-Eddington black hole accretion is geometrically thick, drives strong outflows, and radiates with very low efficiency (below about 0.5% at 150 times Eddington).

  2. GRACE: An Open-Source Framework for GPU-Accelerated Numerical Relativity

    gr-qc 2026-07 accept novelty 6.0 of 10

    GRACE is a validated, open-source, Kokkos+p4est GPU-portable framework that evolves ideal GRMHD with constrained transport self-consistently coupled to Z4c Einstein equations on fixed or adaptive meshes.

Reference graph

Works this paper leans on

63 extracted references · 3 canonical work pages · cited by 2 Pith papers

  1. [1]

    Abarca D., Klu \'z niak W., S a dowski A., 2018, @doi [ ] 10.1093/mnras/sty1602 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.3936A 479, 3936

    work page doi:10.1093/mnras/sty1602 2018

  2. [2]

    A., Fragile P

    Abramowicz M. A., Fragile P. C., 2013, @doi [Living Reviews in Relativity] 10.12942/lrr-2013-1 , https://ui.adsabs.harvard.edu/abs/2013LRR....16....1A 16, 1

    doi:10.12942/lrr-2013-1 2013

  3. [3]

    A., Czerny B., Lasota J

    Abramowicz M. A., Czerny B., Lasota J. P., Szuszkiewicz E., 1988, @doi [ ] 10.1086/166683 , https://ui.adsabs.harvard.edu/abs/1988ApJ...332..646A 332, 646

    doi:10.1086/166683 1988

  4. [4]

    C., Salmonson J

    Anninos P., Fragile P. C., Salmonson J. D., 2005, @doi [ ] 10.1086/497294 , https://ui.adsabs.harvard.edu/abs/2005ApJ...635..723A 635, 723

    doi:10.1086/497294 2005

  5. [5]

    Asahina Y., Ohsuga K., 2022, @doi [ ] 10.3847/1538-4357/ac5d37 , https://ui.adsabs.harvard.edu/abs/2022ApJ...929...93A 929, 93

    doi:10.3847/1538-4357/ac5d37 2022

  6. [6]

    Ba \ n ados E., et al., 2018, @doi [ ] 10.1038/nature25180 , https://ui.adsabs.harvard.edu/abs/2018Natur.553..473B 553, 473

    doi:10.1038/nature25180 2018

  7. [7]

    Bachetti M., et al., 2014, @doi [ ] 10.1038/nature13791 , https://ui.adsabs.harvard.edu/abs/2014Natur.514..202B 514, 202

    doi:10.1038/nature13791 2014

  8. [9]

    C., King A

    Begelman M. C., King A. R., Pringle J. E., 2006, @doi [ ] 10.1111/j.1365-2966.2006.10469.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.370..399B 370, 399

    arXiv 2006

Show all 63 references
  1. [10]

    M., 1998, @doi [ ] 10.1046/j.1365-8711.1998.01530.x , https://ui.adsabs.harvard.edu/abs/1998MNRAS.297..739B 297, 739

    Beloborodov A. M., 1998, @doi [ ] 10.1046/j.1365-8711.1998.01530.x , https://ui.adsabs.harvard.edu/abs/1998MNRAS.297..739B 297, 739

    1998

  2. [11]

    S., Sijacki D., Costa T., Laporte N., Witten C., 2024, @doi [ ] 10.1093/mnras/stad3179 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.1033B 527, 1033

    Bennett J. S., Sijacki D., Costa T., Laporte N., Witten C., 2024, @doi [ ] 10.1093/mnras/stad3179 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.1033B 527, 1033

    2024 doi

  3. [12]

    T., Johnson M

    Berghea C. T., Johnson M. C., Secrest N. J., Dudik R. P., Hennessy G. S., El-khatib A., 2020, @doi [ ] 10.3847/1538-4357/ab9108 , https://ui.adsabs.harvard.edu/abs/2020ApJ...896..117B 896, 117

    2020 doi

  4. [13]

    D., Payne D

    Blandford R. D., Payne D. G., 1982, @doi [ ] 10.1093/mnras/199.4.883 , https://ui.adsabs.harvard.edu/abs/1982MNRAS.199..883B 199, 883

    1982 doi

  5. [14]

    Cseh D., et al., 2014, @doi [ ] 10.1093/mnrasl/slt166 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.439L...1C 439, L1

    2014 doi

  6. [15]

    C., Roth N., Ramirez-Ruiz E., Miller M

    Dai L., McKinney J. C., Roth N., Ramirez-Ruiz E., Miller M. C., 2018, @doi [ ] 10.3847/2041-8213/aab429 , https://ui.adsabs.harvard.edu/abs/2018ApJ...859L..20D 859, L20

    2018 doi

  7. [16]

    C., Gillespie A., Monahan T., Rodriguez M., Anninos P., 2012, @doi [ ] 10.1088/0067-0049/201/2/9 , https://ui.adsabs.harvard.edu/abs/2012ApJS..201....9F 201, 9

    Fragile P. C., Gillespie A., Monahan T., Rodriguez M., Anninos P., 2012, @doi [ ] 10.1088/0067-0049/201/2/9 , https://ui.adsabs.harvard.edu/abs/2012ApJS..201....9F 201, 9

    2012 doi

  8. [17]

    C., Olejar A., Anninos P., 2014, @doi [ ] 10.1088/0004-637X/796/1/22 , https://ui.adsabs.harvard.edu/abs/2014ApJ...796...22F 796, 22

    Fragile P. C., Olejar A., Anninos P., 2014, @doi [ ] 10.1088/0004-637X/796/1/22 , https://ui.adsabs.harvard.edu/abs/2014ApJ...796...22F 796, 22

    2014 doi

  9. [18]

    C., Etheridge S

    Fragile P. C., Etheridge S. M., Anninos P., Mishra B., Klu \'z niak W., 2018, @doi [ ] 10.3847/1538-4357/aab788 , https://ui.adsabs.harvard.edu/abs/2018ApJ...857....1F 857, 1

    2018 doi

  10. [19]

    C., Nemergut D., Shaw P

    Fragile P. C., Nemergut D., Shaw P. L., Anninos P., 2019, @doi [Journal of Computational Physics: X] https://doi.org/10.1016/j.jcpx.2019.100020 , 2, 100020

    2019

  11. [20]

    Fukue J., 2004, @doi [ ] 10.1093/pasj/56.3.569 , https://ui.adsabs.harvard.edu/abs/2004PASJ...56..569F 56, 569

    2004 doi

  12. [21]

    Fukue J., 2011, @doi [ ] 10.1093/pasj/63.4.803 , https://ui.adsabs.harvard.edu/abs/2011PASJ...63..803F 63, 803

    2011 doi

  13. [22]

    F \"u rst F., et al., 2016, @doi [ ] 10.3847/2041-8205/831/2/L14 , https://ui.adsabs.harvard.edu/abs/2016ApJ...831L..14F 831, L14

    2016 doi

  14. [23]

    F., Guan X., Krolik J

    Hawley J. F., Guan X., Krolik J. H., 2011, @doi [ ] 10.1088/0004-637X/738/1/84 , https://ui.adsabs.harvard.edu/abs/2011ApJ...738...84H 738, 84

    2011 doi

  15. [24]

    F., Richers S

    Hawley J. F., Richers S. A., Guan X., Krolik J. H., 2013, @doi [ ] 10.1088/0004-637X/772/2/102 , https://ui.adsabs.harvard.edu/abs/2013ApJ...772..102H 772, 102

    2013 doi

  16. [25]

    Hu H., Inayoshi K., Haiman Z., Quataert E., Kuiper R., 2022, @doi [ ] 10.3847/1538-4357/ac75d8 , https://ui.adsabs.harvard.edu/abs/2022ApJ...934..132H 934, 132

    2022 doi

  17. [26]

    P., 2016, @doi [ ] 10.1093/mnras/stw836 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.3738I 459, 3738

    Inayoshi K., Haiman Z., Ostriker J. P., 2016, @doi [ ] 10.1093/mnras/stw836 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.3738I 459, 3738

    2016 doi

  18. [27]

    M., Davis S

    Jiang Y.-F., Stone J. M., Davis S. W., 2013, @doi [ ] 10.1088/0004-637X/778/1/65 , https://ui.adsabs.harvard.edu/abs/2013ApJ...778...65J 778, 65

    2013 doi

  19. [28]

    M., Davis S

    Jiang Y.-F., Stone J. M., Davis S. W., 2014, @doi [ ] 10.1088/0004-637X/796/2/106 , https://ui.adsabs.harvard.edu/abs/2014ApJ...796..106J 796, 106

    2014 doi

  20. [29]

    J., Zezas A., 2004, @doi [ ] 10.1111/j.1365-2966.2004.08020.x , https://ui.adsabs.harvard.edu/abs/2004MNRAS.351L..83K 351, L83

    Kaaret P., Ward M. J., Zezas A., 2004, @doi [ ] 10.1111/j.1365-2966.2004.08020.x , https://ui.adsabs.harvard.edu/abs/2004MNRAS.351L..83K 351, L83

    2004

  21. [30]

    P., 2017, @doi [ ] 10.1146/annurev-astro-091916-055259 , https://ui.adsabs.harvard.edu/abs/2017ARA&A..55..303K 55, 303

    Kaaret P., Feng H., Roberts T. P., 2017, @doi [ ] 10.1146/annurev-astro-091916-055259 , https://ui.adsabs.harvard.edu/abs/2017ARA&A..55..303K 55, 303

    2017 doi

  22. [31]

    R., Davies M

    King A. R., Davies M. B., Ward M. J., Fabbiano G., Elvis M., 2001, @doi [ ] 10.1086/320343 , https://ui.adsabs.harvard.edu/abs/2001ApJ...552L.109K 552, L109

    2001 doi

  23. [32]

    King A., Lasota J.-P., Middleton M., 2023, @doi [ ] 10.1016/j.newar.2022.101672 , https://ui.adsabs.harvard.edu/abs/2023NewAR..9601672K 96, 101672

    2023

  24. [33]

    Kitaki T., Mineshige S., Ohsuga K., Kawashima T., 2021, @doi [ ] 10.1093/pasj/psab011 , https://ui.adsabs.harvard.edu/abs/2021PASJ...73..450K 73, 450

    2021 doi

  25. [34]

    Kosec P., et al., 2021, @doi [ ] 10.1093/mnras/stab2856 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.508.3569K 508, 3569

    2021 doi

  26. [35]

    J., King A., 2017, @doi [ ] 10.1093/mnrasl/slx079 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.470L..69M 470, L69

    Middleton M. J., King A., 2017, @doi [ ] 10.1093/mnrasl/slx079 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.470L..69M 470, L69

    2017 doi

  27. [36]

    J., et al., 2013, @doi [ ] 10.1038/nature11697 , https://ui.adsabs.harvard.edu/abs/2013Natur.493..187M 493, 187

    Middleton M. J., et al., 2013, @doi [ ] 10.1038/nature11697 , https://ui.adsabs.harvard.edu/abs/2013Natur.493..187M 493, 187

    2013 doi

  28. [37]

    J., Walton D

    Middleton M. J., Walton D. J., Roberts T. P., Heil L., 2014, @doi [ ] 10.1093/mnrasl/slt157 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.438L..51M 438, L51

    2014 doi

  29. [38]

    J., Walton D

    Middleton M. J., Walton D. J., Fabian A., Roberts T. P., Heil L., Pinto C., Anderson G., Sutton A., 2015, @doi [ ] 10.1093/mnras/stv2214 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.454.3134M 454, 3134

    2015 doi

  30. [39]

    J., et al., 2021, @doi [ ] 10.1093/mnras/stab1280 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.1045M 506, 1045

    Middleton M. J., et al., 2021, @doi [ ] 10.1093/mnras/stab1280 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.506.1045M 506, 1045

    2021 doi

  31. [40]

    J., Higginbottom N., Knigge C., Khan N., Wiktorowicz G., 2022, @doi [ ] 10.1093/mnras/stab2991 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.1119M 509, 1119

    Middleton M. J., Higginbottom N., Knigge C., Khan N., Wiktorowicz G., 2022, @doi [ ] 10.1093/mnras/stab2991 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.1119M 509, 1119

    2022 doi

  32. [41]

    C., Johnson L

    Mishra B., Fragile P. C., Johnson L. C., Klu \'z niak W., 2016, @doi [ ] 10.1093/mnras/stw2245 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.463.3437M 463, 3437

    2016 doi

  33. [42]

    C., Anderson J., Blankenship A., Li H., Nalewajko K., 2022, @doi [ ] 10.3847/1538-4357/ac938b , https://ui.adsabs.harvard.edu/abs/2022ApJ...939...31M 939, 31

    Mishra B., Fragile P. C., Anderson J., Blankenship A., Li H., Nalewajko K., 2022, @doi [ ] 10.3847/1538-4357/ac938b , https://ui.adsabs.harvard.edu/abs/2022ApJ...939...31M 939, 31

    2022 doi

  34. [43]

    D., Thorne K

    Novikov I. D., Thorne K. S., 1973, in Black Holes (Les Astres Occlus). pp 343--450

    1973

  35. [44]

    Ohsuga K., Mori M., Nakamoto T., Mineshige S., 2005, @doi [ ] 10.1086/430728 , https://ui.adsabs.harvard.edu/abs/2005ApJ...628..368O 628, 368

    2005 doi

  36. [45]

    F., S a dowski A., McKinney J

    Penna R. F., S a dowski A., McKinney J. C., 2012, @doi [ ] 10.1111/j.1365-2966.2011.20084.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.420..684P 420, 684

    2012

  37. [46]

    J., Fabian A

    Pinto C., Middleton M. J., Fabian A. C., 2016, @doi [ ] 10.1038/nature17417 , https://ui.adsabs.harvard.edu/abs/2016Natur.533...64P 533, 64

    2016 doi

  38. [47]

    G., Abolmasov P., 2007, @doi [ ] 10.1111/j.1365-2966.2007.11668.x , https://ui.adsabs.harvard.edu/abs/2007MNRAS.377.1187P 377, 1187

    Poutanen J., Lipunova G., Fabrika S., Butkevich A. G., Abolmasov P., 2007, @doi [ ] 10.1111/j.1365-2966.2007.11668.x , https://ui.adsabs.harvard.edu/abs/2007MNRAS.377.1187P 377, 1187

    2007

  39. [48]

    Schneider R., Valiante R., Trinca A., Graziani L., Volonteri M., Maiolino R., 2023, @doi [ ] 10.1093/mnras/stad2503 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.526.3250S 526, 3250

    2023 doi

  40. [49]

    I., Sunyaev R

    Shakura N. I., Sunyaev R. A., 1973, , https://ui.adsabs.harvard.edu/abs/1973A&A....24..337S 24, 337

    1973

  41. [50]

    I., Sunyaev R

    Shakura N. I., Sunyaev R. A., 1976, @doi [ ] 10.1093/mnras/175.3.613 , https://ui.adsabs.harvard.edu/abs/1976MNRAS.175..613S 175, 613

    1976 doi

  42. [51]

    S a dowski A., 2009, @doi [ ] 10.1088/0067-0049/183/2/171 , https://ui.adsabs.harvard.edu/abs/2009ApJS..183..171S 183, 171

    2009 doi

  43. [52]

    S a dowski A., 2016, @doi [ ] 10.1093/mnras/stw913 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459.4397S 459, 4397

    2016 doi

  44. [53]

    S a dowski A., Narayan R., 2016, @doi [ ] 10.1093/mnras/stv2941 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.456.3929S 456, 3929

    2016 doi

  45. [54]

    S a dowski A., Narayan R., Tchekhovskoy A., Zhu Y., 2013, @doi [ ] 10.1093/mnras/sts632 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.429.3533S 429, 3533

    2013 doi

  46. [55]

    C., Tchekhovskoy A., 2014, @doi [ ] 10.1093/mnras/stt2479 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.439..503S 439, 503

    S a dowski A., Narayan R., McKinney J. C., Tchekhovskoy A., 2014, @doi [ ] 10.1093/mnras/stt2479 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.439..503S 439, 503

    2014 doi

  47. [56]

    R., Mineshige S., Ohsuga K., 2018, @doi [ ] 10.3847/1538-4357/aaa082 , https://ui.adsabs.harvard.edu/abs/2018ApJ...853...45T 853, 45

    Takahashi H. R., Mineshige S., Ohsuga K., 2018, @doi [ ] 10.3847/1538-4357/aaa082 , https://ui.adsabs.harvard.edu/abs/2018ApJ...853...45T 853, 45

    2018 doi

  48. [57]

    L., Kwan T

    Thomsen L. L., Kwan T. M., Dai L., Wu S. C., Roth N., Ramirez-Ruiz E., 2022, @doi [ ] 10.3847/2041-8213/ac911f , https://ui.adsabs.harvard.edu/abs/2022ApJ...937L..28T 937, L28

    2022 doi

  49. [58]

    Toyouchi D., Hotokezaka K., Inayoshi K., Kuiper R., 2024, @doi [ ] 10.1093/mnras/stae1798 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.532.4826T 532, 4826

    2024 doi

  50. [59]

    R., Asahina Y., 2022, @doi [ ] 10.3847/1538-4357/ac7eb8 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...26U 935, 26

    Utsumi A., Ohsuga K., Takahashi H. R., Asahina Y., 2022, @doi [ ] 10.3847/1538-4357/ac7eb8 , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...26U 935, 26

    2022 doi

  51. [60]

    Veledina A., et al., 2024, @doi [Nature Astronomy] 10.1038/s41550-024-02294-9 , https://ui.adsabs.harvard.edu/abs/2024NatAs...8.1031V 8, 1031

    2024 doi

  52. [61]

    J., 2005, @doi [ ] 10.1086/466521 , https://ui.adsabs.harvard.edu/abs/2005ApJ...633..624V 633, 624

    Volonteri M., Rees M. J., 2005, @doi [ ] 10.1086/466521 , https://ui.adsabs.harvard.edu/abs/2005ApJ...633..624V 633, 624

    2005 doi

  53. [62]

    R., Nixon C., 2018, @doi [ ] 10.1093/mnras/sty971 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478.3016W 478, 3016

    Wu S., Coughlin E. R., Nixon C., 2018, @doi [ ] 10.1093/mnras/sty971 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.478.3016W 478, 3016

    2018 doi

  54. [63]

    Yang J., et al., 2021, @doi [ ] 10.3847/1538-4357/ac2b32 , https://ui.adsabs.harvard.edu/abs/2021ApJ...923..262Y 923, 262

    2021 doi

  55. [64]

    Yoshioka S., Mineshige S., Ohsuga K., Kawashima T., Kitaki T., 2022, @doi [ ] 10.1093/pasj/psac076 , https://ui.adsabs.harvard.edu/abs/2022PASJ...74.1378Y 74, 1378

    2022 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.