Pith. sign in

REVIEW 5 major objections 4 minor 24 references

Simulations of Eccentricity Growth in Compact Binary Accretion Disks with MHD Turbulence

T0 review · 5 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read MRI turbulence does not block eccentricity growth in binary accretion disks.

desk verdict First MHD simulations to grow binary-disk eccentricity from zero via the 3:1 resonance, though the positive runs are initialized at the resonance rather than spreading to it; the paper is honest about this but should rephrase the conclusion. read the letter →

arxiv 2411.15325 v1 pith:LQ3NEMT3 submitted 2024-11-22 astro-ph.HE

Morgan Ohana , Yan-Fei Jiang , Omer Blaes , Bryance Oyang This is my paper · ORCID
classification astro-ph.HE
keywords accretiondisksmagnetorotationalinstabilitysuperhumpseccentricitygrowthmeanmotionresonancecompactbinariesdiskbreakingMHDturbulence
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether the magnetorotational instability (MRI) turbulence that churns accretion disks in compact binaries prevents the companion's tides from making the disk eccentric, the process thought to produce positive superhumps. The answer is no: three MHD simulations initialized out at the 3:1 mean motion resonance grow mass-weighted average eccentricities of 0.137, 0.164, and 0.203 from zero, on timescales comparable to a standard alpha-disk simulation, consistent with the Lubow resonance mechanism. MHD behavior differs from alpha-disk behavior in two ways: eccentricity is relocated inward, breaking the disk into misaligned inner and outer eccentric regions separated by a circular annulus with standing eccentric waves in the inner disk, and spreading an MRI disk outward to the resonance is much harder, because over-dense rings let tidal torques overwhelm magnetic stresses and truncate the disk. The authors conclude the earlier failure of a stream-fed MHD disk to become eccentric was a disk-spreading problem, not a sign that turbulence suppresses the resonance.

What carries the argument

The central mechanism is the 3:1 mean motion resonance in the Lubow picture: a small eccentricity in the disk interacts nonlinearly with the $m=3$ Fourier component of the binary's tidal field to launch a wave from the resonance that feeds back on the eccentricity. The diagnostic carrying the argument is the mass-weighted average of the eccentricity vector (proportional to the Laplace-Runge-Lenz vector), whose evolution is decomposed into tidal, pressure, magnetic, and boundary source terms to show that tides dominate and MRI turbulence acts only as a weak sink. The disk-breaking behavior is governed by the different rates at which MRI transports energy versus angular momentum in eccentric orbits, which in the small-eccentricity form of the eccentricity-growth equation $\mathrm{d}e^2/\mathrm{d}t$ drives eccentricity inward and leaves a circularized shearing boundary between the misaligned inner and outer eccentric disks.

What would settle it

A vertically stratified MHD simulation with net vertical flux, initialized at the resonance radius as in MHD-beta4, that failed to reach a mass-weighted average eccentricity of order 0.1 within about one hundred binary orbital periods, or that kept eccentricity peaked in the outer disk rather than relocating it inward, would contradict the paper's central claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that MHD disks spread to the resonance radius will develop eccentricity via the Lubow mechanism on timescales comparable to alpha-disk simulations, so MRI turbulence is entirely compatible with resonance-driven eccentricity growth. The evidence is the three initialized-at-resonance MHD runs, which reach maximum mass-weighted average eccentricities of 0.137 (MHD-beta4), 0.164 (MHD-beta3), and 0.203 (MHD-beta1), all grown from zero eccentricity, with tidal forces in the eccentricity budget overpowering the dissipative MRI sink. Two MHD-specific phenomena stand out: the disk breaks into misaligned inner and outer eccentric disks separated by a region of circular orbits, with standing eccentric waves in the inner disk and an eccentric inner void, while the alpha-disk run grows eccentricity smoothly and aligned throughout. The secondary claim is that spreading an MRI disk to the resonance is nontrivial, as demonstrated by the stream-fed MHD run, whose over-dense ring caused tidal torques to beat Maxwell stresses and truncate the disk before it reached the resonance radius.

Load-bearing premise

The load-bearing premise is that an unstratified, vertically periodic, locally isothermal simulation domain with an imposed net vertical magnetic field produces MRI turbulence representative of real accretion disk turbulence, so that the resonance-driven eccentricity growth and disk-breaking behavior would survive vertical stratification, outflows, and realistic thermodynamics.

Editorial extensions

If this is right

  • MHD disks that have spread to the resonance grow eccentricity on alpha-disk timescales, so MRI turbulence does not undermine the standard superhump mechanism.
  • Eccentricity in MHD disks is preferentially moved inward, producing standing eccentric waves, an eccentric inner void, and a circular annulus separating misaligned inner and outer eccentric disks.
  • The inner and outer eccentric disks precess at different rates, so a single observed apsidal precession period may be replaced by a broader spectrum, a possibility the authors connect to the rich frequency content of SDSS J1908.
  • Outward spreading is the bottleneck: over-dense rings form when spreading stalls, tidal torques beat MRI stresses, and the disk truncates too early, explaining why a stream-fed MHD disk with higher stresses still failed to grow eccentricity.

Reading between the lines

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

  • If the outward-spreading bottleneck is generic, the incidence of superhumps across dwarf novae may depend more on disk-spreading physics and ionization-triggered MRI than on the intrinsic strength of the resonance.
  • The circularized annulus where the misaligned inner and outer eccentric disks shear against each other should be a site of enhanced heating; a stratified simulation with realistic thermodynamics would test whether a bright ring appears there.
  • Replacing the inflow inner boundary with a stellar boundary layer would likely suppress or shrink the eccentric inner void, so the predicted void structure is directly testable with a different inner boundary condition.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. This paper presents four MHD simulations and one alpha-disk simulation of accretion disks in a compact binary, all vertically unstratified, locally isothermal, and evolved with Athena++ in cylindrical coordinates. Three MHD runs that are initialized with a disk already extending beyond the 3:1 resonance and containing net vertical magnetic flux grow eccentricity from zero to global mean values 0.137, 0.164, and 0.203. A stream-fed MHD run, MHD-stream, stalls at an overdense ring and never reaches the resonance. The authors decompose the eccentricity evolution into tidal, pressure, magnetic, and boundary source terms (Eqs. 2-4) and find that the tidal source dominates even though MRI turbulence acts as a global eccentricity sink; magnetic stresses locally source eccentricity and move it inward. They report disk breaking into misaligned inner and outer eccentric disks, inner eccentric voids, and standing eccentric waves, in contrast to the smoother growth in the alpha-disk run. The paper concludes that MRI turbulence is compatible with the Lubow mechanism for resonance-driven eccentricity growth.

Significance. If the central claim is fully supported, this is an important step: it would be one of the first demonstrations in full MHD with MRI turbulence that resonance-driven eccentricity growth from zero proceeds despite turbulent dissipation. The strengths include the direct growth from zero in three runs with different field strengths, the monotonic increase of peak eccentricity with decreasing initial plasma beta, and a source-term budget that is internally consistent with the measured eccentricity evolution (Figure 4). The authors also engage carefully with earlier stratified MHD work and identify disk spreading as a separate, difficult problem. The main limitation is that the successful runs do not actually spread to the resonance; they are initialized there, and the only spreading MHD run fails. This limits the generality of the conclusion as currently worded, as do the absence of a controlled comparison with a non-stream-fed hydro run and the lack of a resolution study.

major comments (5)
  1. [Section 5] The opening conclusion that 'MHD disks which have spread to the resonant radius will develop eccentricities via the Lubow mechanism' is not directly tested by the simulations. In Section 2 and Table 1, MHD-β1, MHD-β3, and MHD-β4 are initialized with ρ ∝ r^{-0.5} out to r = 16.53 and no accretion stream, so the disk is already established across the 3:1 resonance (r = 15.2) at t = 0. The only run that attempts to build the disk by spreading, MHD-stream, stalls at an overdense ring and never reaches the resonance (Section 3, Figure 2). Section 4 itself acknowledges that 'we did not include an accretion stream in the MHD simulations that went eccentric' and that building up a disk from a stream and having it spread to the resonant radius is 'a nontrivial exercise.' The conclusion should either be reframed to 'disks that are initialized at the resonant radius' or be supported by a stream-fed MHD run that successfully reaches the resonance; as written, the central claim goes beyond the evidence.
  2. [Section 3] The comparison with the alpha-disk run Hydro-α is not controlled. Hydro-α is initialized empty, is fed by a stream, and uses α = 0.1, while the MHD-β runs are initialized at the resonance without a stream. The text attributes the slower Hydro-α eccentricity growth to the time required for the disk to spread and to stream damping (Lubow 1994; Kley et al. 2008), but this means the difference in eccentricity evolution could reflect the different feeding and initial conditions rather than the nature of the turbulent transport. To isolate the effect of MRI turbulence, the authors should add a no-stream hydrodynamic run with the same initial density profile and radial extent as the MHD-β runs, or a stream-fed MHD run that reaches the resonance. Without such a control, the statement that MRI turbulence is 'entirely compatible' with Lubow growth is not fully isolated.
  3. [Section 2] No convergence study is reported. Because the central results include the saturated eccentricity values (Table 1), the Maxwell and Reynolds stress levels (Figure 1), the magnetic source terms in the eccentricity budget (Figure 7), and the disk-breaking and void formation (Figures 5 and 8), and because MRI turbulence in unstratified simulations is known to be resolution-sensitive, the absence of at least one resolution comparison (e.g., doubling Nr and Nφ, or varying Nz) leaves the quantitative claims vulnerable. Please add a resolution test or explicitly state this limitation in Section 4.
  4. [Section 4] The neglect of vertical stratification and vertical gravity (Section 2) is acknowledged in the discussion, but the abstract and conclusions nevertheless make general claims about MHD disks in compact binaries. Because Chan et al. (2023) found that stratification changes radial eccentricity profiles and increases magnetic dissipation, the saturated eccentricities, growth rates, and the specific disk-breaking pattern may be unstratified-specific. The caveat should be repeated in the abstract and conclusion, not only in the discussion.
  5. [Section 3] The successful MHD runs adopt a deliberately flat density profile ρ ∝ r^{-0.5} out to 16.53, whereas MHD-stream develops a more strongly declining profile that the authors state 'inhibits waves excited at the resonance from propagating inward' (Section 3, Figure 3). This raises the possibility that the positive result depends on the imposed density structure rather than on the resonance itself. The paper should discuss whether a disk that spreads outward through MRI transport is expected to have a sufficiently flat profile; otherwise the connection to real spreading disks remains indirect.
minor comments (4)
  1. [Section 2, Table 1] The table header reads 'T able 1'; this should be corrected to 'Table 1'.
  2. [Equations (3) and (5)] The scalar eccentricity e in Eq. (5) is the same symbol as the eccentricity vector e in Eq. (3); please disambiguate the notation, for example by using a different symbol for the scalar eccentricity.
  3. [Equation (1)] The definitions of α_M and α_R should specify whether the stress is normalized by gas pressure only, and the text should clarify that the Reynolds stress is computed from density-weighted velocity fluctuations after subtracting the mass-weighted mean velocity, as is done in the main text.
  4. [Figure 2 caption] The caption says 'binary orbital periods after the start of the simulation' and the panels are labeled 28.64, 54.41, and 114.54; please state explicitly that these numbers are in units of binary orbits.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: eccentricity is directly measured and source-term closure is checked independently.

full rationale

The paper's central measurement, the mass-weighted eccentricity vector, is not derived from its conclusion. Equations (2)-(4) define eccentricity evolution in terms of the actual force field (tidal, pressure, magnetic) and the simulated density and velocity fields, and Figures 4 and 11 show that the sum of independently computed source terms reproduces the measured evolution, so the outcome is not imposed by construction. No parameter is fitted to force the reported maximum eccentricities (0.137, 0.164, 0.203); they are simulation outputs for different initial plasma beta values. The invocation of Lubow (1991) is an external theory being tested, and the statement that MRI turbulence acts as a global eccentricity sink while locally sourcing eccentricity is demonstrated from the simulations themselves rather than imported from the authors' prior work. The main caveats, namely that the successful runs are initialized at the resonance rather than spreading there and that the stream-fed MHD run fails to reach resonance, are acknowledged explicitly in Section 4: 'we did not include an accretion stream in the MHD simulations that went eccentric. A key result of this paper is our realization that building up a disk from a stream and have it spread out to the resonant radius is a nontrivial exercise.' This is a scope limitation in the central conditional claim, not a circular reduction: the conditional 'if a disk has spread to the resonance, eccentricity grows' is tested in a proxy state (disk initialized at resonance), while the spreading part is identified as an unsolved problem. Self-citations to Oyang et al. (2021) are used for method provenance and previous-failure context, not as the load-bearing proof of the present result, and no uniqueness theorem or ansatz is smuggled in via self-citation. Accordingly, no circular step is identified.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

No parameters are fitted to the eccentricity outcome; the listed values are model inputs chosen to set the disk state. The principal assumptions are simplifications that are explicitly flagged in the paper: unstratified, locally isothermal gas, ideal MHD with net vertical flux, an inflow inner boundary, and omission of the accretion stream in the successful runs. These assumptions reduce realism but do not, by themselves, make the central claim circular. The 'graviton problem' does not apply: no new entities are introduced.

free parameters (7)
  • alpha viscosity parameter (Hydro-alpha) = 0.1
    Chosen for the Shakura-Sunyaev alpha disk comparison run; not fitted to the eccentricity result, but a model input that sets the viscous transport.
  • initial plasma beta for MHD-beta4 = 10^4
    Initial uniform vertical magnetic field strength in the annulus 5<r<16.33; chosen to give MRI turbulence with weak field; higher beta means weaker field.
  • initial plasma beta for MHD-beta3 = 10^3
    Same annulus, intermediate field strength; chosen to vary MRI stress level.
  • initial plasma beta for MHD-beta1 = 10
    Strongest initial field; chosen to produce the strongest MRI stresses and highest eccentricity.
  • orbital Mach number M = 20 or 40 depending on run
    Sets the locally isothermal temperature profile (T ~ 1/r). Values chosen per run; no fit to outcome.
  • initial disk outer radius in MHD-beta runs = 16.53 white dwarf radii
    Chosen to place the initial disk beyond the 3:1 resonance radius (15.2 R_WD) so the resonance is populated; this selection directly enables the positive result.
  • accretion stream width in stream-fed runs = 0.5 white dwarf radii
    Gaussian width of injected stream; setup choice, not fitted.
assumptions (6)
  • domain assumption Locally isothermal equation of state with temperature proportional to 1/r, fixing orbital Mach number
    Used in all runs (Sec. 2). Removes realistic thermodynamics and disk cooling; could affect dense-ring formation and eccentricity evolution.
  • domain assumption Vertical stratification and vertical component of gravity are neglected; domain is vertically periodic
    Sec. 2. This is the load-bearing simplification; in real disks MRI turbulence and eccentricity profiles have vertical structure, as shown by Chan et al. (2023).
  • domain assumption Ideal MHD with an imposed net vertical poloidal magnetic flux
    No explicit resistivity or field topology beyond net vertical flux; real disks may have more complex fields and non-ideal effects.
  • domain assumption Alpha viscosity model for Hydro-alpha (Shakura-Sunyaev) with alpha=0.1
    Hydro-alpha comparison uses a parameterized viscous model as a stand-in for turbulence; this is not a faithful representation of MHD turbulence but is the established baseline.
  • domain assumption Inflow boundary at inner radius and outflow boundary at outer radius
    Sec. 2. Inflow inner boundary permits mass loss through the inner edge and is required for the eccentric void; a stellar boundary layer would differ, as the paper notes.
  • domain assumption No accretion stream in the successful MHD-beta runs
    Sec. 2 and Discussion. Removing the stream avoids its damping of eccentricity (Lubow 1994; Kley et al. 2008), so the results isolate the resonance+MRI interaction but not stream-fed systems.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Simulations of Eccentricity Growth in Compact Binary Accretion Disks with MHD Turbulence." pith.science (2026). https://pith.science/paper/LQ3NEMT3

@misc{pith2026241115325,
  author       = {Pith},
  title        = {Pith review of: Simulations of Eccentricity Growth in Compact Binary Accretion Disks with MHD Turbulence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQ3NEMT3}},
  note         = {Machine review of arXiv:2411.15325}
}
read the original abstract

We present the results of four magnetohydrodynamic simulations and one alpha-disk simulation of accretion disks in a compact binary system, neglecting vertical stratification and assuming a locally isothermal equation of state. We demonstrate that in the presence of net vertical field, disks that extend out to the 3:1 mean motion resonance grow eccentricity in full MHD in much the same way as in hydrodynamical disks. Hence turbulence due to the magnetorotational instability (MRI) does not impede the tidally-driven growth of eccentricity in any meaningful way. However, we find two important differences with alpha-disk theory. First, in MHD, eccentricity builds up in the inner disk with a series of episodes of radial disk breaking into two misaligned eccentric disks, separated by a region of circular orbits. Standing eccentric waves are often present in the inner eccentric disk. Second, the successful spreading of an accretion disk with MRI turbulence out to the resonant radius is nontrivial, and much harder than spreading an alpha-disk. This is due to the tendency to develop over-dense rings in which tidal torques overwhelm MRI transport and truncate the disk too early. We believe that the inability to spread the disk sufficiently was the reason why our previous attempt to excite eccentricity via the 3:1 mean motion resonance with MHD failed. Exactly how MHD disks successfully spread outward in compact binary systems is an important problem that has not yet been understood.

Figures

Figures reproduced from arXiv: 2411.15325 by the authors.

Figure 1
Figure 1. Time evolution of the spatially averaged plasma beta (left), Maxwell stress parameter (middle), and Reynolds stress parameter (right) in each of the four simulations. Horizontal dashed lines indicate time-averages after 35 binary orbital periods. The full evolution of all simulations can be viewed here. α = R σrϕrdrdϕdz R Pgasrdrdϕdz (1) Here Pgas is the gas pressure, PB is the magnetic pressure, ρ is the density, a… view at source ↗
Figure 2
Figure 2. Radial dependence of vertically and azimuthally-averaged density (left panel) and tidal and turbulent torques (right panel) in MHD-stream at 28.64 (upper left), 54.41 (upper right), and 114.54 (bottom) binary orbital periods after the start of the simulation. Outward radial spreading of the disk stalled, due to the overwhelming tidal torques on the density spike in the outer disk. Because the disk was unable to reac… view at source ↗
Figure 3
Figure 3. Radial profiles of vertically and azimuthally-averaged density, time-averaged over ten (49.9-59.9) binary orbits. The left panel shows the actual density profiles, while the right panel renormalizes the density so that the disks all have the same total mass. The resonance radius is indicated by the vertical dashed line. approximately 50 and 60 binary orbits across all the MHD simulations. While all the simulations h… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Evolution of eccentricity for simulation MHD-β4. The left and right columns of panels refer to the eccentricity magnitude and direction (in terms of the Laplace-Runge-Lenz vector, measured in a non-rotating frame with origin r = 0). The top panels show the overall evol…
Figure 5
Figure 5. Figure 5: Late time evolution of an MHD simulation (MHD-β4, left group of four panels) and the stream-fed alpha disk (Hydro-α, right group of panels). The 3:1 mean motion resonance is indicated by the white lines in all the figure panels. Going clockwise from the upper left in e…
Figure 6
Figure 6. Figure 6: Density in the z = 0 midplane (left), and its deviation from the vertically- and azimuthally- (shell) averaged density (right) in MHD-β4. Spiral waves in the outer radial regions, and eccentric standing modes in the inner radial regions, are apparent in the right hand …
Figure 7
Figure 7. Figure 7: Left panels: local rate of work done by magnetic forces and the local Maxwell stress torque times local angular velocity (top), vertically and azimuthally-averaged as well as time-averaged over epochs 65-75 orbits in simulation MHD-β4. The predicted eccentricity growth…
Figure 8
Figure 8. Figure 8: Midplane (z = 0) density (upper left), Maxwell stress alpha parameter (upper right), magnetic pressure (lower left), and plasma beta (lower right) in MHD-β4 at the same epoch as shown in [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Late time snapshot of the magnetic field configuration of MHD-β4. The upper row shows z = 0 midplane slices, and the bottom row shows y = 0 vertical slices, of (left to right) density, the radial magnetic field component, the azimuthal magnetic field component, the ver…
Figure 10
Figure 10. Figure 10: Evolution of the magnitude of mass weighted average eccentricity across all the simulations. MHD-β3 in that the disk breaks and an inner void forms in all the ways discussed previously. However, unlike the weaker magnetic field simulations which began with low eccentr…
Figure 11
Figure 11. Figure 11: Evolution of eccentricity for simulation MHD-β1. As in [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 8 canonical work pages

  1. [1]

    A., & Hawley, J

    Balbus, S. A., & Hawley, J. F. 1998, Reviews of Modern Physics, 70, 1, doi: 10.1103/RevModPhys.70.1

    doi:10.1103/revmodphys.70.1 1998

  2. [2]

    J., & Ogilvie, G

    Barker, A. J., & Ogilvie, G. I. 2014, MNRAS, 445, 2637, doi: 10.1093/mnras/stu1939

    doi:10.1093/mnras/stu1939 2014

  3. [3]

    H., & Piran, T

    Chan, C.-H., Krolik, J. H., & Piran, T. 2018, ApJ, 856, 12, doi: 10.3847/1538-4357/aab15c

    doi:10.3847/1538-4357/aab15c 2018

  4. [4]

    Chan, C.-H., Piran, T., & Krolik, J. H. 2022, ApJ, 933, 81, doi: 10.3847/1538-4357/ac68f3 —. 2023, arXiv e-prints, arXiv:2312.06775, doi: 10.48550/arXiv.2312.06775

    work page Pith review arXiv doi:10.48550/arxiv.2312.06775 2022

  5. [5]

    W., Latter, H

    Dewberry, J. W., Latter, H. N., Ogilvie, G. I., & Fromang, S. 2020, MNRAS, 497, 451, doi: 10.1093/mnras/staa1898

    work page doi:10.1093/mnras/staa1898 2020

  6. [6]

    M., et al

    Fontaine, G., Brassard, P., Green, E. M., et al. 2011, ApJ, 726, 92, doi: 10.1088/0004-637X/726/2/92

    doi:10.1088/0004-637x/726/2/92 2011

  7. [7]

    Fromang, S., Latter, H., Lesur, G., & Ogilvie, G. I. 2013, A&A, 552, A71, doi: 10.1051/0004-6361/201220016

    doi:10.1051/0004-6361/201220016 2013

  8. [8]

    Kley, W., Papaloizou, J. C. B., & Ogilvie, G. I. 2008, A&A, 487, 671, doi: 10.1051/0004-6361:200809953

    doi:10.1051/0004-6361:200809953 2008

Show all 24 references
  1. [9]

    1997, MNRAS, 289, 889, doi: 10.1093/mnras/289.4.889

    Kunze, S., Speith, R., & Riffert, H. 1997, MNRAS, 289, 889, doi: 10.1093/mnras/289.4.889

    1997 doi

  2. [10]

    J., Bloemen, S., et al

    Kupfer, T., Groot, P. J., Bloemen, S., et al. 2015, MNRAS, 453, 483, doi: 10.1093/mnras/stv1609

    2015 doi

  3. [11]

    Lubow, S. H. 1991, ApJ, 381, 259, doi: 10.1086/170647 —. 1994, ApJ, 432, 224, doi: 10.1086/174563

    1991 doi

  4. [12]

    M., & Dewberry, J

    Lynch, E. M., & Dewberry, J. W. 2023, MNRAS, 526, 2673, doi: 10.1093/mnras/stad2678

    2023 doi

  5. [13]

    Murray, J. R. 1998, MNRAS, 297, 323, doi: 10.1046/j.1365-8711.1998.01504.x 16 O’Donoghue, D., & Charles, P. A. 1996, MNRAS, 282, 191, doi: 10.1093/mnras/282.1.191

    1998

  6. [14]

    I., & Lynch, E

    Ogilvie, G. I., & Lynch, E. M. 2018, Monthly Notices of the Royal Astronomical Society, 483, 4453, doi: 10.1093/mnras/sty3436

    2018 doi

  7. [15]

    2021, MNRAS, 505, 1, doi: 10.1093/mnras/stab1212

    Oyang, B., Jiang, Y.-F., & Blaes, O. 2021, MNRAS, 505, 1, doi: 10.1093/mnras/stab1212

    2021 doi

  8. [16]

    Papaloizou, J. C. B. 2005a, A&A, 432, 743, doi: 10.1051/0004-6361:20041947 —. 2005b, A&A, 432, 757, doi: 10.1051/0004-6361:20041948

    doi

  9. [17]

    R., & Diaz, M

    Patterson, J., Thomas, G., Skillman, D. R., & Diaz, M. 1993, ApJS, 86, 235, doi: 10.1086/191777

    1993 doi

  10. [18]

    I., & Sunyaev, R

    Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337

    1973

  11. [19]

    M., Tomida, K., White, C

    Stone, J. M., Tomida, K., White, C. J., & Felker, K. G. 2020, ApJS, 249, 4, doi: 10.3847/1538-4365/ab929b

    2020 doi

  12. [20]

    K., & Inutsuka, S.-i

    Suzuki, T. K., & Inutsuka, S.-i. 2009, ApJL, 691, L49, doi: 10.1088/0004-637X/691/1/L49

    2009 doi

  13. [21]

    1975, MNRAS, 170, 219, doi: 10.1093/mnras/170.1.219

    Warner, B. 1975, MNRAS, 170, 219, doi: 10.1093/mnras/170.1.219

    1975 doi

  14. [22]

    1988, MNRAS, 232, 35, doi: 10.1093/mnras/232.1.35 —

    Whitehurst, R. 1988, MNRAS, 232, 35, doi: 10.1093/mnras/232.1.35 —. 1994, MNRAS, 266, 35, doi: 10.1093/mnras/266.1.35

    1988 doi

  15. [23]

    1991, MNRAS, 249, 25, doi: 10.1093/mnras/249.1.25

    Whitehurst, R., & King, A. 1991, MNRAS, 249, 25, doi: 10.1093/mnras/249.1.25

    1991 doi

  16. [24]

    2002, MNRAS, 333, 791, doi: 10.1046/j.1365-8711.2002.05450.x

    Zurita, C., Casares, J., Shahbaz, T., et al. 2002, MNRAS, 333, 791, doi: 10.1046/j.1365-8711.2002.05450.x

    2002

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.