Dynamics of magnetoviscous warped discs around compact objects

Arthur G. Suvorov; Kostas Glampedakis

REVIEW 3 major objections 5 minor 94 references

Dynamics of magnetoviscous warped discs around compact objects

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read A vertical magnetic field from a compact object opens new unstable warp modes and cuts the perpendicular viscosity down to about 1/(α^{5/2}B^4), so tilted discs tear more easily at sub-Eddington rates.

desk verdict Novel α⊥(α) scalings for GR and magnetized warped discs, but the headline magnetic reduction depends on an undetermined sign and a missing factor 36; deserves peer review, not citation yet. read the letter →

arxiv 2601.22683 v3 pith:6MAGB4KN submitted 2026-01-30 astro-ph.HE gr-qchep-th

Arthur G. Suvorov , Kostas Glampedakis This is my paper · ORCID

classification astro-ph.HEgr-qchep-th

keywords warpedaccretiondiscsperpendicularviscosityLense-ThirringprecessiondisctearingmagneticfieldsneutronstarX-raybinariesShakura-Sunyaevparametermagnetoviscous

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 whether general-relativistic frame-dragging and a central object's magnetic field change how easily a tilted accretion disc tears into precessing rings. It argues that they do: the perpendicular viscosity that normally resists tearing is much smaller than assumed when the disc sits near a rotating compact object or in a strong vertical magnetic field. In the magnetically dominated regime the paper finds α⊥/α ~ 1/(α^{5/2} B^4), and in the relativistic regime α⊥ ≈ α/x², both well below the familiar α⊥ ≈ 1/α estimate. If correct, magnetized neutron-star systems can tear at sub-Eddington accretion rates, making warp-driven accretion episodes a more likely explanation for observed X-ray outbursts.

What carries the argument

The machinery is a pair of coupled damped oscillators for a fluid parcel in a warped disc: radial epicyclic motion δr with frequency Ω_r and damping λ, and vertical tilt ψ with frequency Ω_θ and damping λ⊥, plus a Lorentz coupling term from a vertical background field B_z. The key object is the coupled-mode dispersion relation; in the strong-field limit it yields the magnetic mode σ_B² ≈ -ε1 (c_A/H)², whose instability condition ε1 γ(r0/H)² > 1 is exactly the plasma-β<1 threshold. The α⊥(α) relation then follows from balancing perpendicular and horizontal viscous dissipation rates, using the mode amplitude derived from the same system.

What would settle it

Compute the vertical eigenfunction of the local warp mode from the linearized momentum and induction equations and evaluate ∂_z δv_x relative to δv_x/H; a negative sign (ε1 = -1) would turn the predicted σ_B² ≈ -ε1 (c_A/H)² from unstable to stable and invalidate the α⊥ reduction. A local shearing-box simulation of a tilted, vertically magnetized disc with plasma β < 1 would also show directly whether a growing warp mode exists.

Watch

Extended reading notes

Core claim

The central claim is that in a thin warped disc the ratio α⊥/α is not a fixed function of α alone: it drops steeply once either general-relativistic epicyclic detuning or a magnetic field of order 10^8–10^9 G is included. The paper's local fluid-parcel calculation shows that a vertical stellar dipole field couples the radial and tilt oscillators, creating new magnetically dominated warp modes whose real frequencies undergo avoided crossings as the field increases. Once this branch dominates, the perpendicular viscosity is suppressed as (α⊥/α)_B ∼ α^{-5/2} B^{-4}; the paper therefore concludes that intense magnetic fields significantly reduce the perpendicular viscosity at sub-Eddington accre

Load-bearing premise

The argument hinges on the sign of the vertical derivative of the perturbed radial velocity: the paper sets ∂_z δv_x ≈ +δv_x/H (ε1 = +1) in all numerical work, and the magnetic instability and associated α⊥ reduction cease to exist if the true sign is negative.

Editorial extensions

If this is right

If the magnetic branch dominates, the perpendicular viscosity falls as α^{-5/2} B^{-4}, so at B0 ~ 10^9 G the ratio α⊥/α can drop by roughly a factor of 1000 relative to the unmagnetized value.
Because α⊥ is what resists Lense-Thirring tearing, the tearing radius can extend outward (or require lower warp/tilt) in magnetized neutron-star low-mass X-ray binaries, easing the conditions for tearing-driven outbursts.
Even without magnetism, general-relativistic corrections alone give α⊥ ≈ α/x² for α ≪ x³, so warped discs in the innermost regions are less viscously stabilized than the Newtonian α⊥ ≈ 1/α estimate suggests.
Applying the model to a specific LMXB, the paper finds that a tearing radius near 115 stellar radii with a modest tilt reproduces the observed outburst luminosity factor of about 60, making disc tearing a viable explanation for that event.
For ultra-luminous X-ray pulsars with fields above 10^12 G and high accretion rates, the model cannot reproduce long giant outbursts, indicating tearing is not the mechanism there or that extra physics beyond the thin-disc treatment is required.

Reading between the lines

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

If the sign of ∂_z δv_x is actually negative (ε1 = -1), the magnetic mode is stable rather than unstable; this should be testable with a local vertical-eigenfunction calculation, and until then the predicted α⊥ suppression should be treated as conditional on the sign.
The same α⊥ suppression, if it operates in active-galactic-nucleus discs, would imply that strong central magnetic fields can trigger warp tearing without an external tidal or companion torque — a plausible route to quasi-periodic eruptions and rapid black-hole growth.
The predicted B^{-4} and α^{-3/2} scalings are sharp enough to be falsified by systematic comparisons of outburst recurrence times with dipole-field estimates in a sample of neutron-star LMXBs.
The oscillating Alfvén radius induced by magnetized warp modes, mentioned in the paper, suggests a natural mechanism for short-timescale X-ray flickering in transitional millisecond pulsars — a regime where the corrected viscosity relation matters most.

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.

Desk Editor's Note

read the letter

Dear Colleague — Here is my take on Suvorov & Glampedakis (arXiv:2601.22683). The paper does two things well. It gives a clear review of the warped-disc literature, and it extends the LP07 local oscillator by adding a damping term to the warp equation, which changes the Newtonian α⊥(α) from 1/α to α^{1/3}. That is a new, interesting toy-model result: for α≈0.1 it lowers the perpendicular viscosity from ~10 to ~0.5, which would significantly affect tearing thresholds. The addition of GR epicyclic frequencies and a stellar dipole field through a coupled-oscillator system is also new, and the avoided crossings in the mode spectrum are a legitimate curiosity. The authors are honest that the model is semi-analytic and flag the sign ambiguity in a footnote.

The soft spots are real. First, the GR asymptotic: with A_GR = Hψ0/(6x), the dissipation balance (38) gives α⊥/α = 1/(36 x^2), not α/x^2 as written in Eq. (41) and Table 1. The missing factor 36 shifts the GR-dominated regime by over an order of magnitude.

More importantly, the magnetic instability that drives the B^{-4} α^{-3/2} reduction in α⊥ requires ε1=+1 (Eqs. 89, 98). The sign of ∂z δv_x is never derived; the vertical eigenfunction is not solved, and all numerics fix ε_i=+1. With ε1=-1, the magnetic mode is stable, and the α⊥ reduction in Fig. 7 would likely change substantially. That is the core of the abstract's claim, so the paper's central quantitative prediction is not robust.

Third, the paper itself notes around Fig. 9 that the tearing radius is visually indistinguishable from the non-magnetic case except at very low α, because the direct magnetic torque dominates the α⊥ term. Thus the observational motivation for the α⊥ reduction is weaker than the abstract implies, and the SAX J1808 application is a post-hoc parameter choice.

Overall: a useful review and a genuinely new toy-model relation, but the headline magnetic result hinges on an undetermined sign and a numeric slip. It deserves a competent referee who can demand a physical derivation for ε1 and a corrected Eq. (41). I would not cite the quantitative scalings as they stand, but I would send it to peer review rather than desk-reject.

Referee Report

3 major / 5 minor

Summary. The paper analyzes warped accretion discs around compact objects by extending the local fluid-parcel model of Lodato & Pringle (2007) to include general-relativistic epicyclic frequencies and a magnetic field from the central star. It derives new scaling relations between the perpendicular and horizontal viscosities (α⊥ vs α), studies warp-mode stability, and applies the results to disc tearing in neutron-star LMXBs and ULXs. The central claim is that strong magnetic fields create new branches of warp modes and avoided crossings that reduce α⊥, making discs more prone to tearing.

Significance. If the central claim holds, the paper would provide a physical mechanism by which magnetized central objects lower the threshold for warped-disc tearing, with implications for outbursts in X-ray binaries and AGN variability. The paper is useful as a review and offers a self-consistent semianalytic framework with reproducible numerical routines. However, the magnetic result depends on an undetermined sign in the derivative-collapse approximation, and the GR regime contains a factor-36 algebraic inconsistency; these issues currently limit the reliability of the quantitative predictions.

major comments (3)

[Section 3.3, Eqs. (30), (38), (41)] Plugging the stated relativistic amplitude A_GR = Hψ0/(6x) into the dissipation balance α⊥/α = (A/(ψ0H))^2 gives α⊥/α = 1/(36x^2), i.e., α⊥ = α/(36x^2), not α⊥ = α/x^2 as written in Eq. (41) and Table 1. This factor 36 propagates into the GR-dominated regime and the stability discussion in Sec. 3.4 (e.g., Fig. 3). Please correct the algebra and any subsequent quantitative claims.
[Section 4.2, Eqs. (71)-(74), (89), (98), Fig. 5] The magnetic instability and the associated α⊥ reduction depend on the sign ε1, which is introduced as a bookkeeping parameter for ∂zδv_x but never determined from the vertical structure of the perturbation. All numerics fix ε_i = +1. From Eq. (89), σ_B^2 = -ε1(c_A/H)^2, so ε1 = -1 converts the claimed unstable magnetic mode into a stable oscillation, and the instability condition (98) cannot be satisfied. Footnote 2 acknowledges the derivative approximation is 'oblivious to the sign,' yet the central magnetic result of the abstract—reduced α⊥ and easier tearing—hinges on ε1 = +1. A physical derivation of ε1 from the vertical eigenfunction is required before this result can be accepted.
[Section 3, Eqs. (17)-(18)] The new damping term λ⊥ψ̇ in the warp equation is introduced without a microphysical derivation, and it drives the non-magnetic result α⊥ ≈ α^{1/3} (Eq. 39), which differs from the PP83/Ogilvie hydrodynamical value α⊥ ≈ 1/(2α) and the LP07 result. Please justify this term from the fluid equations or, if it is a model assumption, show how the conclusions change if the term is omitted, since the comparison with the literature in Table 1 depends on it.

minor comments (5)

[Eq. (47)] The 3x3 determinant in Eq. (47) is difficult to read; please present the Q_i definitions and the matrix more clearly.
[Table 1] The LP07 entry (α⊥ = 1/α) should be accompanied by a more precise reference to the equation in Lodato & Pringle (2007); the text cites the paper generally.
[Sec. 4.1, Eq. (49)] The derivation of the magnetic torque formula is compressed; the appearance of the (H/r)^{-1} factor is not obvious. An intermediate step would improve clarity.
[Fig. 5 caption] The caption states ε_i=1 for all i; consider adding a panel with ε1=-1 to demonstrate the sensitivity of the stability boundary to this choice.
[Sec. 3.3, after Eq. (39)] The statement 'α⊥ ≈ 0.5−10 for α≈0.1' should be reconciled with α⊥ = α^{1/3} ≈ 0.46; as written it appears to overstate the lower end of the range.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the α⊥ scaling is the self-consistent output of the coupled system (79)/(100); self-citations are minor and the ε1 sign issue is a robustness caveat, not a circular reduction.

full rationale

The central perpendicular-viscosity result is not a fitted input. Equation (100) follows from the dissipation balance (33) and the amplitude (99), and it is solved simultaneously with the dispersion relation (79)/(96). The magnetic branch, avoided crossings, and the derived B^{-4}/α^{-3/2} scaling (Fig. 7, Eq. 102) are outputs of this fixed-point system, not pre-assumed values. The SAX J1808.4-3658 application uses the observed differential-precession timescale to fix r_t and treats the inclination as a free or independently constrained parameter; it is a plausibility demonstration rather than a fit of the central scaling. Self-citations (Glampedakis & Suvorov 2021; Suvorov & Melatos 2019, 2020; Stefanou, Suvorov & Pons 2025) are used for standard dipole/Alfvén-radius and source parameters, and the paper even flags a typo in the authors' earlier formula (footnote 4), so the cited prior work is not carrying the main derivation. The principal caveat is the undetermined sign ε1: footnote 2 admits the derivative approximations are 'oblivious to the sign of the actual derivative', Eq. (71) introduces ε1 as a bookkeeping sign, Eq. (89) gives σ_B² = -ε1(c_A/H)², and Fig. 5 fixes ε_i = +1. If ε1 = -1, the magnetic mode is stable and the predicted α⊥ reduction would not occur. This is a genuine validity/robustness concern, but it is not circularity: the paper's claim is conditional on an unevaluated sign, not equivalent to its own input by construction.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The model is a hierarchy of assumptions. The standard Shakura-Sunyaev relations (Eq. 1) and Kerr epicyclic frequencies (15)-(16) are imported background. The paper's own premises are: (i) a damping term λ⊥ψ̇ in the warp equation (Eq. 18) — the source of the α^{1/3} result; (ii) the dissipation-balance ansatz (33) that equates time-averaged shear dissipation in the two directions — the machinery that converts response amplitudes into α⊥; (iii) the derivative collapse ∂z≈1/H, ∂x≈ψ0/H with sign bookkeeping ε_i=+1 (Eqs. 71-74) — the load-bearing choice for the magnetic instability; (iv) a purely vertical dipole magnetic field. No new particles or entities are introduced; the 'magnetic modes' are a family of solutions of the coupled oscillator system, not new physics. All claimed scalings (39), (41), (89), (102) are consequences of these choices.

free parameters (7)

α (Shakura-Sunyaev viscosity) = scanned 10^-3–0.5
Not fitted; explored as free over the range relevant to observed discs (Sec. 5.1).
B0 (stellar surface dipole field) = scanned 10^7–10^10 G; 2×10^8 G chosen for SAX J1808
Free parameter of the model; bounds from neutron-star spin-down/cyclotron observations constrain the range.
H0 = H/r (aspect ratio) = ≈10^-2 in most figures; for SAX J1808 set by Eq. (111)
Kept 'effectively free' in Sec. 2.1; in the application it is implicitly adjusted so the predicted tear radius matches the observed precession timescale.
β (tilt angle) = 0.03 chosen for SAX J1808 (Eq. 113)
Chosen after the fact so the predicted luminosity ratio L≈47 ≈ 60 matches the observed outburst; roughly consistent with an independent colatitude estimate 4–10° but not fixed by it.
ξ (Alfvén-radius prefactor) = ≈0.1 (Eq. 106)
Footnote 4: 'often treated as a free parameter'; imported from Glampedakis & Suvorov 2021.
ε_i bookkeeping signs = +1 for all i (Eqs. 71-74, Fig. 5)
Hand-chosen; the magnetic instability condition (98) requires ε1=+1; no derivation of the sign is given.
ψ0 (warp amplitude) = 0.3 for applications (Figs. 9-10)
Free parameter; small-warp approximation assumed.

assumptions (8)

domain assumption Standard Shakura-Sunyaev thin-disc structure relations (Σ=ρH, Mdot≈νΣ, c_s≈HΩ, ν≈αHc_s), Eq. (1).
Used throughout; presumes a thin Keplerian alpha disc.
domain assumption Local test-body model with linear Stokes drag f_visc = -mλv (Eq. 12), laminar subsonic flow.
Standard in LP07-style linear stability; validity limited to laminar flow.
ad hoc to paper The warp equation includes a perpendicular damping term λ⊥ψ̇ (Eq. 18), unlike LP07.
The central amendment; its absence yields the LP07 result α⊥=1/α, its presence yields α⊥≈α^{1/3}.
ad hoc to paper Viscous dissipation balance ν⊥⟨(∂rδvz)²⟩ = ν⟨(∂zδvr)²⟩ (Eq. 33).
Ansatz connecting the alpha parameters to the response amplitudes; not derived from the Navier-Stokes system.
ad hoc to paper Derivative collapse ∂z≈1/H, ∂x≈ψ0/H with bookkeeping signs ε_i (Eqs. 71-74).
Replaces the vertical structure by signs; results depend on ε1=+1.
domain assumption Purely vertical background magnetic field (B_y=0) and dipole profile B_z=-B0(R/r)³.
Simplifies induction; toroidal-field case explicitly deferred.
standard math Kerr epicyclic frequencies (15)-(16) for orbital motion; O(q) truncation for neutron stars.
Standard geodesic perturbation theory (Appendix A).
standard math Hydrodynamical Q_i coefficients (44)-(46) from Ogilvie 1999 / Doğan et al. 2018 for an isothermal Γ=5/3 polytrope.
Imported into the local-model stability determinant (47); regime matching unquantified.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Dynamics of magnetoviscous warped discs around compact objects." pith.science (2026). https://pith.science/paper/6MAGB4KN

@misc{pith2026260122683,
  author       = {Pith},
  title        = {Pith review of: Dynamics of magnetoviscous warped discs around compact objects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6MAGB4KN}},
  note         = {Machine review of arXiv:2601.22683}
}

read the original abstract

Accretion discs that are tilted with respect to their compact hosts can warp out-of-plane through general relativistic frame-dragging. Warp influences disc dynamics in ways that have been studied extensively, especially as regards instabilities that might lead to rapid angular-momentum cancellation between neighboring rings of fluid and mass infall. We provide a review of warped-disc phenomena here, revisiting key hydrodynamical assumptions that impact calculations of the shear viscosity controlling instability thresholds. Relativistic effects at the level of gas-parcel orbits are included, as are external Lorentz forces applied by the compact primary's magnetic field. Semianalytic analysis reveals that intense magnetic fields can bring about new branches of warp modes and avoided crossings that significantly reduce the perpendicular viscosity at sub-Eddington accretion rates. Critical strengths required for misaligned torques to tear a thin disc may thus relax for systems like neutron star X-ray binaries or radio-loud active galactic nuclei.

Figures

Figures reproduced from arXiv: 2601.22683 by the authors.

**Figure 1.** Schematic of a tilted accretion disc around a compact object. If sufficiently magnetised, truncation of the disc occurs at the Alfv´en radius, RA, where magnetic pressure balances the ram pressure of circulating material (left; see Sec. 4.2 for a definition). In cases of dynamical capture, young systems, or where the BP effect is not at work, there is no further expectation of any existing disc-object symmetry: the … view at source ↗

**Figure 2.** Ratio of the perpendicular viscosity coefficient, determined using the amplitude (22) and expression (38), to the Newtonian prediction (39) as a function of α for q = 0.2 and x = 1/6 (blue) or x = 1/20 (red). The horizontal line marks equality, reached after α ≈ 0.1 for the less compact case. Solutions asymptote to this value for large α. examine how the adjusted amplitude (22) affects the stability of a disc us… view at source ↗

**Figure 3.** shows the instability region as a function of viscosity (α) and warp (|ψ0|) for a compact case with x = 1/6 and q = 0.2 as compared to the Newtonian limit (x → 0). Even for these relatively extreme parameter choices, we see that the two regions largely overlap except at large warps where the scheme breaks down. In general though, GR terms make the system more unstable: for ψ0 ≈ 1, a viscosity of α ≲ 0.06 leads to i… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Dimensionless magnetic parameter γ(r0/H) 2 from expression (95) as a function of radius for H/r0 = 10−2 , α = 0.1, R = 10 km, M = 1.4M⊙, B0 = 2 × 108 G, and M˙ = 10−6M˙ edd (solid blue curve). The solid, vertical lines depict the limiting values associated with total…

**Figure 6.** Figure 6: Real parts of normalised mode frequencies, ˜σR, determined by solving equations (79) and (100) simultaneously as a function of B8 = B0/108 G, of which there are four in general (coloured curves). We fix M = 1.4M⊙, R = 10 km, M˙ = 10−4M˙ edd, ψ0 = 0.3, H/r0 = 10−2 , α…

**Figure 8.** Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: Tearing radii (rt) in units of R, as a function of B0 and α, for fixed parameter choices M = 1.4M⊙, R = 10 km, H/r0 = 10−2 , q = 0.2, and β = |ψ| = 0.3 for either M˙ = 10−4M˙ edd (left) or M˙ = 10−3M˙ edd (right). Above the respective white contours (with the lower and…

**Figure 10.** Figure 10: Tearing radius rt in units of the stellar radius for parameters appropriate to SAX J1808.4–3658 (see text), as a function of viscosity and disc thickness (in units of H−3 = 103 ×H/r0). The white contour corresponds to rt = 115R, as anticipated from matching timescal…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

94 extracted references · 1 linked inside Pith

[1]

J., Desoer C

Anagnost J. J., Desoer C. A., 1991, Circuits Systems and Signal Processing, 10, 101

1991
[2]

Arrabal Haro P. et al. , 2023, , 622, 707

2023
[3]

Bachetti M. et al. , 2020, , 891, 44

2020
[4]

Baglio M. C. et al. , 2023, , 677, A30

2023
[5]

Bahramian A., Degenaar N., 2023, in Handbook of X-ray and Gamma-ray Astrophysics, p. 120

2023
[6]

A., Hawley J

Balbus S. A., Hawley J. F., 1998, Reviews of Modern Physics, 70, 1

1998
[7]

M., Petterson J

Bardeen J. M., Petterson J. A., 1975, , 195, L65

1975
[8]

M., Press W

Bardeen J. M., Press W. H., Teukolsky S. A., 1972, , 178, 347

1972

Show all 94 references

[9]

S., Ruzmaikin A

Bisnovatyi-Kogan G. S., Ruzmaikin A. A., 1976, , 42, 401

1976
[10]

Brandenburg A., 2008, Physica Scripta Volume T, 130, 014016

2008
[11]

Campana S., Coti Zelati F., D'Avanzo P., 2013, , 432, 1695

2013
[12]

O . F., Ertan \

C oban \"O . F., Ertan \"U ., 2024, , 961, 252

2024
[13]

Celora T., Palenzuela C., Vigan \`o D., Aguilera-Miret R., 2025, arXiv e-prints, arXiv:2505.01208

2025
[14]

Chashkina A., Abolmasov P., Poutanen J., 2017, , 470, 2799

2017
[15]

J., Wadiasingh Z., 2024, , 533, 2133

Cooper A. J., Wadiasingh Z., 2024, , 533, 2133

2024
[16]

Curd B., Anantua R., West H., Duran J., 2025, , 540, 1215

2025
[17]

De Luca V., Del Grosso L., Franciolini G., Kritos K., Berti E., D'Orazio D., Silk J., 2025, arXiv e-prints, arXiv:2512.19666

2025
[18]

D \' az Trigo M. et al. , 2018, , 616, A23

2018
[19]

Doroshenko V. et al. , 2022, Nature Astronomy, 6, 1433

2022
[20]

Doroshenko V., Tsygankov S., Santangelo A., 2018, , 613, A19

2018
[21]

J., 2015, , 449, 1251

Do g an S., Nixon C., King A., Price D. J., 2015, , 449, 1251

2015
[22]

J., King A

Do g an S., Nixon C. J., King A. R., Pringle J. E., 2018, , 476, 1519

2018
[23]

M., Lasota J

Dubus G., Hameury J. M., Lasota J. P., 2001, , 373, 251

2001
[24]

C., Liska M., 2025, in New Frontiers in GRMHD Simulations, Bambi C., Mizuno Y., Shashank S., Yuan F., eds., pp

Fragile P. C., Liska M., 2025, in New Frontiers in GRMHD Simulations, Bambi C., Mizuno Y., Shashank S., Yuan F., eds., pp. 361--387

2025
[25]

C., Mathews G

Fragile P. C., Mathews G. J., Wilson J. R., 2001, , 553, 955

2001
[26]

Frank J., King A., Raine D., 1992, Accretion power in astrophysics. , Vol. 21

1992
[27]

P., 2006, , 457, 343

Fromang S., Nelson R. P., 2006, , 457, 343

2006
[28]

G., 2021, , 508, 2399

Glampedakis K., Suvorov A. G., 2021, , 508, 2399

2021
[29]

M., Lasota J

Hameury J. M., Lasota J. P., 2020, , 643, A171

2020
[30]

M., Patruno A., Chakrabarty D., Markwardt C

Hartman J. M., Patruno A., Chakrabarty D., Markwardt C. B., Morgan E. H., van der Klis M., Wijnands R., 2009, , 702, 1673

2009
[31]

O., Zheng J., Maccarone T

Heinke C. O., Zheng J., Maccarone T. J., Degenaar N., Bahramian A., Sivakoff G. R., Toor S., 2025, , 279, 57

2025
[32]

R., Greenhill L

Herrnstein J. R., Greenhill L. J., Moran J. M., 1996, , 468, L17

1996
[33]

Hurley-Walker N. et al. , 2022, , 601, 526

2022
[34]

Ibragimov A., Poutanen J., 2009, , 400, 492

2009
[35]

J., Poutanen J., Krawczynski H., 2015, , 807, 53

Ingram A., Maccarone T. J., Poutanen J., Krawczynski H., 2015, , 807, 53

2015
[36]

Ingram A., van der Klis M., 2013, , 434, 1476

2013
[37]

J., Pattie E

Kashyap U., Maccarone T. J., Pattie E. C., Ng M., Ravi S., Marshall H. L., 2025, , 992, 66

2025
[38]

C., Gilbaum S., 2023, , 524, 1269

Kaur K., Stone N. C., Gilbaum S., 2023, , 524, 1269

2023
[39]

R., Pringle J

King A. R., Pringle J. E., Livio M., 2007, , 376, 1740

2007
[40]

u ng \"o r C., Sa g lam M. T., G \

Kocab y k T., G \"u ng \"o r C., Sa g lam M. T., G \"u ver T., Bostanc Z. F., 2025, , 537, 500

2025
[41]

Kong L.-D. et al. , 2022, , 933, L3

2022
[42]

Krawczynski H. et al. , 2022, Science, 378, 650

2022
[43]

D., Raadu M

Kuijpers J., Fletcher L., Abada-Simon M., Horne K. D., Raadu M. A., Ramsay G., Steeghs D., 1997, , 322, 242

1997
[44]

E., 1985, , 213, 435

Kumar S., Pringle J. E., 1985, , 213, 435

1985
[45]

Lambrides E. et al. , 2024, arXiv e-prints, arXiv:2409.13047

2024 arXiv
[46]

D., Nelson R

Larwood J. D., Nelson R. P., Papaloizou J. C. B., Terquem C., 1996, , 282, 597

1996
[47]

B., Van Moer M., 2021, , 507, 983

Liska M., Hesp C., Tchekhovskoy A., Ingram A., van der Klis M., Markoff S. B., Van Moer M., 2021, , 507, 983

2021
[48]

Liska M. T. P., Kaaz N., Musoke G., Tchekhovskoy A., Porth O., 2023, , 944, L48

2023
[49]

J., 2010, , 405, 1212

Lodato G., Price D. J., 2010, , 405, 1212

2010
[50]

E., 2007, , 381, 1287

Lodato G., Pringle J. E., 2007, , 381, 1287

2007
[51]

Ludlam R. M. et al. , 2021, , 911, 123

2021
[52]

Miniutti G. et al. , 2019, , 573, 381

2019
[53]

M., Martin E

Montgomery M. M., Martin E. L., 2010, , 722, 989

2010
[54]

P., Remillard R

Muno M. P., Remillard R. A., Chakrabarty D., 2002, , 568, L35

2002
[55]

V., Abramowicz M

Narayan R., Igumenshchev I. V., Abramowicz M. A., 2003, , 55, L69

2003
[56]

J., Nixon C

Nealon R., Price D. J., Nixon C. J., 2015, , 448, 1526

2015
[57]

Nixon C., 2015, , 450, 2459

2015
[58]

Nixon C., King A., Price D., Frank J., 2012, , 757, L24

2012
[59]

J., King A

Nixon C. J., King A. R., 2012, , 421, 1201

2012
[60]

I., 1999, , 304, 557

Ogilvie G. I., 1999, , 304, 557

1999
[61]

I., Latter H

Ogilvie G. I., Latter H. N., 2013, , 433, 2403

2013
[62]

V., Degenaar N., Wijnands R., Parikh A

Page D., Homan J., Nava-Callejas M., Cavecchi Y., Beznogov M. V., Degenaar N., Wijnands R., Parikh A. S., 2022, , 933, 216

2022
[63]

Pan X., Li S.-L., Cao X., Miniutti G., Gu M., 2022, , 928, L18

2022
[64]

Papaloizou J. C. B., Pringle J. E., 1983, , 202, 1181

1983
[65]

Papaloizou J. C. B., Terquem C., 1995, , 274, 987

1995
[66]

T., Robba N

Papitto A., Di Salvo T., D'A \` A., Iaria R., Burderi L., Riggio A., Menna M. T., Robba N. R., 2009, , 493, L39

2009
[67]

Pappas G., 2017, , 466, 4381

2017
[68]

B., Ogilvie G

Paris J. B., Ogilvie G. I., 2018, , 477, 2406

2018
[69]

Patruno A., Haskell B., Andersson N., 2017, , 850, 106

2017
[70]

A., Boyd P

Phillipson R. A., Boyd P. T., Smale A. P., 2018, , 477, 5220

2018
[71]

E., 1992, , 258, 811

Pringle J. E., 1992, , 258, 811

1992
[72]

E., 1996, , 281, 357

Pringle J. E., 1996, , 281, 357

1996
[73]

Qu Y., Zhang B., 2025, , 981, 34

2025
[74]

J., 2021, , 909, 82

Raj A., Nixon C. J., 2021, , 909, 82

2021
[75]

J., Do g an S., 2021, , 909, 81

Raj A., Nixon C. J., Do g an S., 2021, , 909, 81

2021
[76]

Sanna A. et al. , 2017, , 471, 463

2017
[77]

Scheuer P. A. G., Feiler R., 1996, , 282, 291

1996
[78]

M., D \"o nmez C

Serim M. M., D \"o nmez C . K., Serim D., Ducci L., Baykal A., Santangelo A., 2023, , 522, 6115

2023
[79]

I., Sunyaev R

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

1973
[80]

Starling R. L. C., Siemiginowska A., Uttley P., Soria R., 2004, , 347, 67

2004
[81]

G., Pons J

Stefanou P., Suvorov A. G., Pons J. A., 2025, , 543, 273

2025
[82]

G., Dehman C., Pons J

Suvorov A. G., Dehman C., Pons J. A., 2025 a , arXiv e-prints, arXiv:2505.05373

2025
[83]

G., Dehman C., Pons J

Suvorov A. G., Dehman C., Pons J. A., 2025 b , , 991, 134

2025
[84]

G., Melatos A., 2019, , 484, 1079

Suvorov A. G., Melatos A., 2019, , 484, 1079

2019
[85]

G., Melatos A., 2020, , 499, 3243

Suvorov A. G., Melatos A., 2020, , 499, 3243

2020
[86]

Tao L., Feng H., Zhang S., Bu Q., Zhang S., Qu J., Zhang Y., 2019, , 873, 19

2019
[87]

W., 2014, , 441, 1408

Tremaine S., Davis S. W., 2014, , 441, 1408

2014
[88]

van der Klis M., 1998, Advances in Space Research, 22, 925

1998
[89]

E., Stella L., 1988, , 231, 325

White N. E., Stella L., 1988, , 231, 325

1988
[90]

Wijers R. A. M. J., Pringle J. E., 1999, , 308, 207

1999
[91]

Wijnands R., van der Klis M., 1998, , 394, 344

1998
[92]

Wilson-Hodge C. A. et al. , 2018, , 863, 9

2018
[93]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence a...
[94]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

J., Desoer C

Anagnost J. J., Desoer C. A., 1991, Circuits Systems and Signal Processing, 10, 101

1991

[2] [2]

Arrabal Haro P. et al. , 2023, , 622, 707

2023

[3] [3]

Bachetti M. et al. , 2020, , 891, 44

2020

[4] [4]

Baglio M. C. et al. , 2023, , 677, A30

2023

[5] [5]

Bahramian A., Degenaar N., 2023, in Handbook of X-ray and Gamma-ray Astrophysics, p. 120

2023

[6] [6]

A., Hawley J

Balbus S. A., Hawley J. F., 1998, Reviews of Modern Physics, 70, 1

1998

[7] [7]

M., Petterson J

Bardeen J. M., Petterson J. A., 1975, , 195, L65

1975

[8] [8]

M., Press W

Bardeen J. M., Press W. H., Teukolsky S. A., 1972, , 178, 347

1972