Pith. sign in

REVIEW 3 major objections 6 minor 59 references

Modulation of X-ray flux by obscuration of neutron star boundary layer

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read The paper shows, through relativistic ray-tracing, that an oscillating or fragmenting inner accretion torus can periodically obscure the bright boundary layer on a neutron star's surface, amplifying X-ray flux variability enough to…

desk verdict A plausible new modulation channel for NS QPOs, but the high-amplitude assumption is doing most of the work. read the letter →

arxiv 2502.02422 v2 pith:QOY7ETIE submitted 2025-02-04 astro-ph.HE

Gabriel Török , Kateřina Klimovičová , Debora Lančová , Monika Matuszková , Eva Šrámková , Martin Urbanec , Miljenko Čemeljić , René Šprňa
show 1 more author
Vladimír Karas
This is my paper · ORCID
classification astro-ph.HE
keywords neutronstarsboundarylayerquasi-periodicoscillationsaccretiontorirelativisticraytracingX-raybinariesblackholehigh-frequencyQPOsKeplerianfrequency
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 proposes an answer to a longstanding puzzle: why the quasi-periodic oscillations (QPOs) seen in neutron-star X-ray binaries reach root-mean-square amplitudes near 30 percent, far higher than the few-percent high-frequency QPOs of black holes. The proposed mechanism is simple obscuration: an inner accretion torus that oscillates radially or vertically, or decays into an orbiting fragment, periodically hides and reveals the bright boundary layer on the neutron star's surface. Using relativistic ray-tracing that includes the star's surface and a luminous boundary layer, the authors show that this shadowing amplifies the variability of the observed X-ray flux by a large factor, while the same simulation with a black hole instead of a star produces only weak modulation. They further show that the effect naturally makes the Keplerian orbital frequency visible in the power spectrum when tori fragment. If correct, the mechanism offers a common route by which several existing QPO models could account for the high NS amplitudes.

What carries the argument

The central object is the boundary layer (BL), the bright equatorial band on a neutron star's surface where accreting matter decelerates from approximately Keplerian motion to the star's rotation, releasing roughly 60 percent of the total accretion power. In the paper's setup the BL has a Gaussian emissivity profile peaking at 190 times the thin-disc maximum, with material velocity ranging from Keplerian at the equator to zero at the poles. The mechanism is periodic geometric obscuration of this BL by an optically thick inner torus whose centre sits at 6.75 gravitational radii, oscillating with amplitudes $\Delta r = 0.75\,r_g$ radially and $\Delta\theta = 15^\circ$ vertically, or by an orbiting torus fragment.

What would settle it

A decisive test would be a systematic comparison of the predicted inclination dependence of QPO rms amplitude against a sample of neutron-star low-mass X-ray binaries with measured inclinations: the model predicts variability that grows monotonically with inclination for radial oscillations and fragments and peaks near 70 degrees for vertical oscillations, so data that are flat in amplitude against inclination would rule it out. Equally decisive would be a high-resolution GRMHD simulation of an oscillating torus showing that the assumed optically thick, large-amplitude coherent motions do not occur in realistic accretion flows.

Watch

Extended reading notes

Core claim

The central claim is that the neutron star's boundary layer acts as a flux amplifier for accretion-flow variability: periodic obscuration of this bright equatorial band by an optically thick inner torus produces the high rms amplitudes of NS kHz QPOs, whereas the same torus motions around a black hole yield only weak modulation. The paper demonstrates this with ray-tracing simulations of three kinematic cases: radial and vertical axisymmetric oscillations of a thick torus and the Keplerian motion of a torus fragment. For each case, the variability of the full NS system, dominated by the shadowing of the boundary layer, is much stronger than in the BH case, and the effect becomes significant for observer inclinations above about 20 degrees. The paper also shows that when the torus disintegrates into an orbiting fragment, the Keplerian frequency is imprinted on the light curve through obscuration, making it observable even if the disc emission itself is steady.

Load-bearing premise

The simulation's effect depends entirely on the inner torus being effectively optically thick and on its oscillating with the large, hand-picked amplitudes $\Delta r = 0.75\,r_g$ and $\Delta\theta = 15^\circ$; if real accretion flows have smaller coherent amplitudes or allow light through the torus, the boundary-layer shadowing will be much weaker and cannot by itself produce the observed strong QPOs.

Editorial extensions

If this is right

  • For observers at inclinations above about 20 degrees, boundary-layer shadowing raises the variability of the full NS system to levels consistent with the observed 10–30 percent rms of NS kHz QPOs, while the BH counterpart stays weak.
  • Vertical torus oscillations, which produce little accretion-rate modulation in existing MHD simulations, still produce strong flux variability through BL obscuration, so frequency peaks tied to the vertical epicyclic frequency can be observed.
  • When a torus decouples into an orbiting fragment, obscuration imprints the Keplerian orbital frequency onto the light curve, providing an observable signature of torus instability.
  • The mechanism is not tied to one QPO model; it can be grafted onto epicyclic, cusp-torus, and other current models to resolve their amplitude problem.
  • Radial oscillations and orbiting fragments produce variability that grows monotonically with inclination, while vertical oscillations peak near 70 degrees, giving a discriminative prediction for observations.

Reading between the lines

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

  • A testable extension: the predicted inclination dependence (monotonic for radial and fragment cases, peaked near 70 degrees for vertical oscillations) could be compared with a sample of neutron-star low-mass X-ray binaries with known orbital inclinations to discriminate the obscuration mechanism from alternatives; the paper itself does not carry out such a comparison.
  • If the obscuration picture holds, similar boundary-layer or hotspot shadowing should amplify variability in other accreting compact objects with bright surfaces, such as white dwarfs in cataclysmic variables or accreting millisecond pulsars with hotspots.
  • The assumed torus amplitudes, $\Delta r = 0.75\,r_g$ and $\Delta\theta = 15^\circ$, are large and chosen arbitrarily; a natural next step would be to derive self-consistent oscillation amplitudes from general-relativistic magnetohydrodynamic simulations to test whether the amplification survives with realistic amplitudes.
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

3 major / 6 minor

Summary. The paper uses relativistic ray tracing (the LSD code) in Schwarzschild spacetime to compute X-ray light curves from a model accreting neutron star system: a spherical NS with a bright equatorial boundary layer (BL), an inner geometrically thick torus executing rigid radial or vertical epicyclic oscillations, an outer thin disc, and, in a third scenario, an orbiting torus fragment. The central claim is that periodic obscuration of the BL by the torus or fragment amplifies flux variability, producing variation coefficients up to ~60% for high inclinations (Fig. 4), and thereby can explain the high rms amplitudes of NS kHz QPOs relative to BH high-frequency QPOs. The paper also argues that obscuration by orbiting fragments makes the Keplerian frequency observable in systems where the torus decays. The work is a forward simulation with no parameter fitting to observed QPO amplitudes or frequencies; the main inputs, including the oscillation amplitudes, torus radius, and the choice r0=6.75 rg, are stated explicitly.

Significance. If the mechanism is robust, it would offer a plausible resolution to the long-standing puzzle of why NS kHz QPO amplitudes are much larger than BH HF QPO amplitudes, and it would be applicable to several existing QPO models. The paper is a valuable proof-of-concept: it is the first to apply relativistic ray tracing to NS BL obscuration, it carefully compares NS and BH cases in the same framework, and it is transparent about its assumptions, including the arbitrary amplitude choice and constant torus luminosity. The main limitation is that the quantitative result depends sensitively on unvalidated large-amplitude coherent oscillations and on the assumption that the torus is effectively optically thick with a constant total luminosity; without sensitivity tests, the claim to explain the observed ~30% rms amplitudes is conditional.

major comments (3)
  1. [Sec. 6.2, Fig. 4] The adopted oscillation amplitudes, Δr = 0.75 rg and Δθ = 15°, are described as 'chosen arbitrarily but ... physically conceivable' and they are the primary drivers of the claimed effect. For the adopted geometry (r0 = 6.75 rg, RT = 1 rg), a vertical displacement of 15° corresponds to Δz ≈ 1.75 rg, nearly twice the torus radius, and the radial amplitude is 75% of RT, bringing the inner torus edge to within ~0.2–0.95 rg of the NS surface (RNS = 4.8 rg). These are not small epicyclic perturbations but large, coherent rigid displacements, and no hydrodynamic simulation or observational calibration is provided to show that such motions occur. Because the variation coefficients in Fig. 4 scale directly with how far the torus moves across the line of sight, the central claim that BL obscuration explains the observed ~30% rms NS QPO amplitudes is not robust to reasonable variations in amplitude. The authors should either justify the amplitudes from a physical model or present the scaling of VC with amplitude and demonstrate the amplitude range for which the mechanism still produces significant modulation.
  2. [Sec. 6.1, Sec. 9.1] The mechanism assumes the torus is effectively optically thick, that its total luminosity is constant in time, and that vertical oscillations are rigid, axisymmetric displacements. These assumptions are load-bearing: if the torus is not optically thick, or if the motion is not a coherent large-scale displacement, the obscuration signal is much weaker. The paper cites Parthasarathy et al. (2017) for the apparent absence of vertical-oscillation modulation in MHD simulations, but it does not reconcile this with the assumed coherent vertical motion. A sensitivity study that varies the torus optical depth, the torus-to-BL luminosity ratio, or the coherence of the motion would be needed to support the claim that the mechanism can resolve the high-amplitude puzzle.
  3. [Sec. 6.1] The choice r0 = 6.75 rg (so that νK = νθ = 3νr) and RT = 1 rg (the critical cusp torus size) is tied to the authors' own QPO model framework (Török et al. 2022). While the forward simulation is not circular, the conclusion that BL obscuration generally enhances NS QPO amplitudes is presented without exploring the dependence on r0, RT, or the frequency ratio. Since the effect arises from the closeness of the torus to the NS surface, the result may not hold for other plausible geometries. The authors should either discuss the generality of their setup or restrict their claims accordingly.
minor comments (6)
  1. [Sec. 4] The formula 'I = d ϕ/dS' is unclear; the symbol ϕ is not defined and likely should be a luminosity (e.g., dL/dS). The BL emissive power distribution is said to be a Gaussian but no explicit form is given.
  2. [Fig. 1] The axis label 'Δ/c70' in the top right panel appears garbled; please verify and correct the label.
  3. [Abstract/Introduction] The phrase 'the David Lynch TV series-like name' is informal and out of place in a journal article; consider removing or rewording it.
  4. [References] There are duplicate entries: Abramowicz & Kluźniak (2001a) and (2001b) are the same paper (A&A 374, L19), and Török et al. (2016) appears twice. Please consolidate the reference list.
  5. [Footnote 1] The notation 'rG = 2rg' is confusing because r_g is already defined as GM/c^2; the event horizon should be denoted with a different symbol, e.g., r_H = 2r_g.
  6. [Sec. 9.1] The phrase 'obscuration can recover the frequency peaks' is vague; consider 'can amplify the frequency peaks' or 'can produce observable peaks'.

Circularity Check

0 steps flagged · score 0.0 of 10

The BL-obscuration amplitude result is a self-contained forward ray-tracing simulation; the arbitrary high-amplitude inputs are a realism concern, not circularity.

full rationale

The paper's central claim—that periodic obscuration of the NS boundary layer by an oscillating torus or orbiting fragment can produce high-amplitude X-ray modulation—is obtained by relativistic ray tracing (LSD code) with explicitly stated geometric inputs (RNS=4.8 rg, r0=6.75 rg, RT=1 rg, Δr=0.75 rg, Δθ=15°, ΔΦ=π/3). No parameter is fitted to the observed QPO amplitudes or frequencies; the resulting variation coefficients and NS/BH contrast are genuine outputs of the geodesic calculation. The oscillation amplitudes are admittedly 'chosen arbitrarily but ... physically conceivable' (Sec. 6.2), which is an unvalidated physical premise that affects the magnitude of the effect, but it does not make the derivation circular: the high VC values are not equivalent to the inputs by construction, and the same inputs would produce different outputs for different geometries (e.g., BH vs NS). The frequency positions of the simulated PDS peaks are inherited from the input epicyclic/Keplerian frequencies, but the paper's explanatory claim concerns the amplification of these peaks via BL obscuration, which is an independent ray-tracing result. References to prior work by the same group (Bursa et al. 2004; Bakala et al. 2015; Török et al. 2022) supply methodology and motivating QPO scenarios, but no load-bearing conclusion reduces to a self-citation. The arbitrary-amplitude and optically-thick assumptions are better classified as correctness/realism risks than as circular reasoning.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The model is a forward numerical experiment built on a small set of chosen parameters and standard astrophysical assumptions. No new physical entities are postulated. The central free parameters are the torus position, size, oscillation amplitudes, and luminosity splits; they are motivated by prior QPO models but not fit to the observed data of any specific source.

free parameters (8)
  • Torus centre radius r0 = 6.75 rg
    Chosen so that νK=νθ=3νr at the torus centre, matching the 3:2 frequency ratio used in QPO models; not fit to observed data but motivated by the model framework.
  • Torus radius RT = 1 rg
    Set to the largest size allowed for a critical cusp torus at r0; a limiting case that maximizes obscuration.
  • Radial oscillation amplitude Δr = 0.75 rg
    Acknowledged as arbitrary; a high amplitude is needed for the torus to periodically cover the boundary layer.
  • Vertical oscillation amplitude Δθ = 15 degrees
    Acknowledged as arbitrary; chosen as 'quite high but still physically conceivable'.
  • Fragment opening angle ΔΦ = π/3
    Set arbitrarily; affects harmonic content but not the fundamental frequencies.
  • BL emissive peak ratio = 190 I_m
    Chosen so that boundary layer luminosity is about 60% of total, following Sunyaev and Shakura; this drives the strength of the obscuration signal.
  • Torus luminosity fraction = 10% of thin disc inner power
    Assumed lower radiative efficiency of the torus; affects the contrast between torus and boundary layer.
  • Neutron star radius RNS = 4.8 rg
    Chosen to be below ISCO and compatible with various equations of state; allows radial oscillations and the boundary layer geometry.
assumptions (6)
  • domain assumption Spacetime is Schwarzschild (non-rotating) for both NS and BH
    Adopted in Section 2; excludes frame dragging and stellar rotation, which are not modeled.
  • domain assumption NS is weakly magnetized with equatorial accretion and no accretion columns
    Section 4; this motivates the equatorial boundary layer and is typical for kHz QPO sources.
  • domain assumption Boundary layer emits about 60% of total accretion power with Gaussian latitudinal profile
    Section 4, based on Sunyaev and Shakura (1986); the profile shape is simplified.
  • domain assumption Inner torus is effectively optically thick and has constant specific angular momentum
    Section 6.1; required for the torus to cast a shadow on the BL; also used for the torus surface four-velocity.
  • ad hoc to paper Torus total luminosity is constant in time
    Section 6.1; isolates obscuration as the only variability mechanism, but real emission may vary.
  • ad hoc to paper Radial and vertical oscillations are rigid, axisymmetric displacements with epicyclic frequencies
    Section 6.2; simplified kinematics, not derived from a hydrodynamic simulation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Modulation of X-ray flux by obscuration of neutron star boundary layer." pith.science (2026). https://pith.science/paper/QOY7ETIE

@misc{pith2026250202422,
  author       = {Pith},
  title        = {Pith review of: Modulation of X-ray flux by obscuration of neutron star boundary layer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QOY7ETIE}},
  note         = {Machine review of arXiv:2502.02422}
}
read the original abstract

The quasi-periodic oscillations (QPOs) observed in the X-ray variability of both black hole (BH) and neutron star (NS) systems provide a tool for probing strong gravity and dense matter equations of state. Nevertheless, the mechanism of QPO modulation in NS systems, where the amplitudes of QPOs with frequencies approaching kHz range are very high in comparison to BH high-frequency QPOs, remains an unsolved puzzle. Relativistic ray tracing of photons emitted from the immediate vicinity of compact objects has, to date, been used to investigate various mechanisms that explain the observed weak BH QPOs. However, it has not been applied to model the NS QPO signal, which requires incorporating the NS surface and a bright boundary layer (BL) on it. Here, we explore the QPO modulation mechanisms based on the BL obscuration. Using simplified models of axisymmetric oscillations of thick accretion discs (tori), we demonstrate that the disc oscillations drive the high NS QPO amplitudes through BL obscuration, which is relevant especially for vertical oscillations. We also demonstrate that obscuration effects enable the observability of the Keplerian frequency in the case of discs that decay due to instabilities.

Figures

Figures reproduced from arXiv: 2502.02422 by the authors.

Figure 1
Figure 1. Schematics of the considered setup. Top left: An overall illustration showing components of the investigated system of accreting NS. Top right: The NS BL and radial oscillations of the torus. Bottom left: The vertical oscillations of the torus. Bottom right: The orbiting fragment of torus characterised by its opening angle ∆Φ (BL on NS surface is not shown). orbits with Keplerian velocity, at r0 = 6.75 rg. 3 Ac￾cord… view at source ↗
Figure 2
Figure 2. Snapshots from relativistic raytracing simula￾tions showing the inner regions of the accretion system of NS as seen by distant observer exploring the radially oscillating torus (top panels), the vertically oscillating torus (middle panels), and the orbiting fragment of torus (bottom panels) from the observer’s inclination angle i = 60◦ . Left: Radia￾tion intensity colour-maps. Right: Colour-maps of g-factor. investi… view at source ↗
Figure 3
Figure 3. Light curves obtained for radial (left) and vertical (middle) oscillations and for the orbiting torus fragment (right) for inclination angle i = 60◦ . The extension corresponds to one Keplerian period at r0 for the radial case and three for the vertical and fragment cases. The light curves for individual system components are shown, with the obscuration effects preserved. The dark green line corresponds to the full … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Dependence of the variation coefficient of the light curves on the inclination angle of the observer calculated for the radial and vertical oscillations and orbiting torus frag￾ment. The NS and BH configurations are compared. evant for the modulation given by the radia…
Figure 5
Figure 5. Figure 5: Simulated power density spectra for inclinations i = 80◦ (teal), i = 60◦ (orange) and i = 20◦ (maroon) for the radial and vertical oscillations and the orbiting torus. The NS and BH cases are compared. The black dashed lines denote the radial epicyclic frequency at the…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 32 canonical work pages

  1. [1]

    A., Blaes, O

    Abramowicz, M. A., Blaes, O. M., Horák, J., Kluźniak, W., & Rebusco, P. 2006, Classical and Quantum Gravity, 23, 1689, doi: 10.1088/0264-9381/23/5/014

    work page doi:10.1088/0264-9381/23/5/014 2006

  2. [2]

    A., Horák, J., & Kluzniak, W

    Abramowicz, M. A., Horák, J., & Kluzniak, W. 2007, AcA, 57, 1

    work page 2007

  3. [3]

    A., & Kluźniak, W

    Abramowicz, M. A., & Kluźniak, W. 2001a, A&A, 374, L19, doi: 10.1051/0004-6361:20010791 —. 2001b, A&A, 374, L19, doi: 10.1051/0004-6361:20010791

    doi:10.1051/0004-6361:20010791

  4. [4]

    A., & Kluźniak, W

    Abramowicz, M. A., & Kluźniak, W. 2004, in American Institute of Physics Conference Series, Vol. 714, X-ray Timing 2003: Rossi and Beyond, ed. P. Kaaret, F. K. Lamb, & J. H. Swank, 21–28, doi: 10.1063/1.1780993

    work page doi:10.1063/1.1780993 2004

  5. [5]

    Remillard, R. A. 2004, ApJL, 609, L63, doi: 10.1086/422810

    work page doi:10.1086/422810 2004

  6. [6]

    2015, A&A, 581, A35, doi: 10.1051/0004-6361/201525867

    Bakala, P., Goluchová, K., Török, G., et al. 2015, A&A, 581, A35, doi: 10.1051/0004-6361/201525867

    work page doi:10.1051/0004-6361/201525867 2015

  7. [7]

    2014, MNRAS, 439, 1933, doi: 10.1093/mnras/stu076

    Bakala, P., Török, G., Karas, V., et al. 2014, MNRAS, 439, 1933, doi: 10.1093/mnras/stu076

    work page doi:10.1093/mnras/stu076 2014

  8. [8]

    F., & Miller, M

    Barret, D., Olive, J. F., & Miller, M. C. 2005, Astronomische Nachrichten, 326, 808, doi: 10.1002/asna.200510417

    work page doi:10.1002/asna.200510417 2005

Show all 59 references
  1. [10]

    2005, MNRAS, 359, 1217, doi: 10.1111/j.1365-2966.2005.08980.x

    Beckwith, K., & Done, C. 2005, MNRAS, 359, 1217, doi: 10.1111/j.1365-2966.2005.08980.x

    2005

  2. [11]

    M., Sanna, A., & Méndez, M

    Belloni, T. M., Sanna, A., & Méndez, M. 2012, MNRAS, 426, 1701, doi: 10.1111/j.1365-2966.2012.21634.x

    2012

  3. [13]

    M., Šrámková, E., Abramowicz, M

    Blaes, O. M., Šrámková, E., Abramowicz, M. A., Kluźniak, W., & Torkelsson, U. 2007, ApJ, 665, 642, doi: 10.1086/519782

    2007 doi

  4. [14]

    2005, Astronomische Nachrichten, 326, 849, doi: 10.1002/asna.200510426

    Bursa, M. 2005, Astronomische Nachrichten, 326, 849, doi: 10.1002/asna.200510426

    2005 doi

  5. [15]

    A., Karas, V., & Kluźniak, W

    Bursa, M., Abramowicz, M. A., Karas, V., & Kluźniak, W. 2004, ApJL, 617, L45, doi: 10.1086/427167

    2004 doi

  6. [16]

    T., & Bardeen, J

    Cunningham, C. T., & Bardeen, J. M. 1973, ApJ, 183, 237, doi: 10.1086/152223 Čadež, A., Calvani, M., & Kostić, U. 2008, A&A, 487, 527, doi: 10.1051/0004-6361:200809483 de Avellar, M. G. B., Porth, O., Younsi, Z., & Rezzolla, L. 2018, MNRAS, 474, 3967, doi: 10.1093/mnras/stx3071

    1973 doi

  7. [17]

    2009, ApJ, 696, 1616, doi: 10.1088/0004-637X/696/2/1616

    Dexter, J., & Agol, E. 2009, ApJ, 696, 1616, doi: 10.1088/0004-637X/696/2/1616

    2009 doi

  8. [18]

    2006, A&A, 447, 813, doi: 10.1051/0004-6361:20052689

    Pelletier, G. 2006, A&A, 447, 813, doi: 10.1051/0004-6361:20052689

    2006 doi

  9. [19]

    C., Straub, O., & Blaes, O

    Fragile, P. C., Straub, O., & Blaes, O. 2016, MNRAS, 461, 1356, doi: 10.1093/mnras/stw1428

    2016 doi

  10. [20]

    Frank, J., King, A., & Raine, D. J. 2002, Accretion Power in Astrophysics: Third Edition (Cambridge, UK: Cambridge University Press)

    2002

  11. [21]

    2005, Astronomische Nachrichten, 326, 812, doi: 10.1002/asna.200510419

    Gilfanov, M., & Revnivtsev, M. 2005, Astronomische Nachrichten, 326, 812, doi: 10.1002/asna.200510419

    2005 doi

  12. [22]

    2003, A&A, 410, 217, doi: 10.1051/0004-6361:20031141

    Gilfanov, M., Revnivtsev, M., & Molkov, S. 2003, A&A, 410, 217, doi: 10.1051/0004-6361:20031141

    2003 doi

  13. [23]

    R., & Sunyaev, R

    Gilfanov, M. R., & Sunyaev, R. A. 2014, Physics Uspekhi, 57, 377, doi: 10.3367/UFNe.0184.201404e.0409 9

    2014

  14. [24]

    1986, MNRAS, 221, 339, doi: 10.1093/mnras/221.2.339 Goluchová, K., Török, G., Šrámková, E., et al

    Goldreich, P., Goodman, J., & Narayan, R. 1986, MNRAS, 221, 339, doi: 10.1093/mnras/221.2.339 Goluchová, K., Török, G., Šrámková, E., et al. 2019, A&A, 622, L8, doi: 10.1051/0004-6361/201834774

    1986 doi

  15. [25]

    1987, MNRAS, 225, 695, doi: 10.1093/mnras/225.3.695

    Goodman, J., Narayan, R., & Goldreich, P. 1987, MNRAS, 225, 695, doi: 10.1093/mnras/225.3.695

    1987 doi

  16. [26]

    2010, MNRAS, 405, 2447, doi: 10.1111/j.1365-2966.2010.16614.x

    Ingram, A., & Done, C. 2010, MNRAS, 405, 2447, doi: 10.1111/j.1365-2966.2010.16614.x

    2010

  17. [27]

    2016, MNRAS, 461, 1967, doi: 10.1093/mnras/stw1245

    Ingram, A., van der Klis, M., Middleton, M., et al. 2016, MNRAS, 461, 1967, doi: 10.1093/mnras/stw1245

    2016 doi

  18. [28]

    R., & Motta, S

    Ingram, A. R., & Motta, S. E. 2019, NewAR, 85, 101524, doi: 10.1016/j.newar.2020.101524

    2019

  19. [29]

    A., & Sunyaev, R

    Inogamov, N. A., & Sunyaev, R. A. 1999, Astronomy Letters, 25, 269, doi: 10.48550/arXiv.astro-ph/9904333

    1999 doi arXiv

  20. [30]

    1996, ApJ, 470, 743, doi: 10.1086/177904 —

    Karas, V. 1996, ApJ, 470, 743, doi: 10.1086/177904 —. 1999, ApJ, 526, 953, doi: 10.1086/308015

    1996 doi

  21. [31]

    2003, in Nonlinear Gravitodynamics: The Lense-Thirring Effect

    Karas, V., Semerák, O., & de Felice, F. 2003, in Nonlinear Gravitodynamics: The Lense-Thirring Effect. Edited by RUFFINI REMO & SIGISMONDI COSTANTINO. Published by World Scientific Publishing Co. Pte. Ltd, ed. R. Ruffini & C. Sigismondi, 282–287, doi: 10.1142/9789812564818_0023

    2003 doi

  22. [32]

    Karas, V., Vokrouhlický, D., & Polnarev, A. G. 1992, MNRAS, 259, 569, doi: 10.1093/mnras/259.3.569

    1992 doi

  23. [33]

    2023, Contributions of the Astronomical Observatory Skalnate Pleso, 53, 175, doi: 10.31577/caosp.2023.53.4.175

    Karas, V., Klimovičová, K., Lančová, D., et al. 2023, Contributions of the Astronomical Observatory Skalnate Pleso, 53, 175, doi: 10.31577/caosp.2023.53.4.175

    2023 doi

  24. [34]

    2001, PASJ, 53, 1, doi: 10.1093/pasj/53.1.1 —

    Kato, S. 2001, PASJ, 53, 1, doi: 10.1093/pasj/53.1.1 —. 2004, PASJ, 56, 905, doi: 10.1093/pasj/56.5.905 Kluźniak, W., & Abramowicz, M. A. 2001, Acta Physica Polonica B, 32, 3605 Kluźniak, W., & Abramowicz, M. A. 2005, in 22nd Texas Symposium on Relativistic Astrophysics, ed. P...

    2001 doi

  25. [35]

    M., & Prakash, M

    Lattimer, J. M., & Prakash, M. 2007, PhR, 442, 109, doi: 10.1016/j.physrep.2007.02.003 Matuszková, M., Török, G., Lančová, D., et al. 2024, arXiv e-prints, arXiv:2403.16226, doi: 10.48550/arXiv.2403.16226

    2007 doi arXiv

  26. [36]

    P., Zanotti, O., Sądowski, A., Mishra, B., & Kluźniak, W

    Mazur, G. P., Zanotti, O., Sądowski, A., Mishra, B., & Kluźniak, W. 2016, MNRAS, 456, 3245, doi: 10.1093/mnras/stv2890

    2016 doi

  27. [37]

    E., & Remillard, R

    McClintock, J. E., & Remillard, R. A. 2006, in Compact stellar X-ray sources, Vol. 39 (Cambridge, UK: Cambridge University Press), 157–213, doi: 10.48550/arXiv.astro-ph/0306213

    2006 doi arXiv

  28. [38]

    1995, ApJL, 445, L43, doi: 10.1086/187885

    Mineshige, S., Kusnose, M., & Matsumoto, R. 1995, ApJL, 445, L43, doi: 10.1086/187885

    1995 doi

  29. [39]

    H., Manousakis, A., et al

    Mishra, B., Vincent, F. H., Manousakis, A., et al. 2017, MNRAS, 467, 4036, doi: 10.1093/mnras/stx299

    2017 doi

  30. [40]

    J., Rezzolla, L., & Yoshida, S

    Montero, P. J., Rezzolla, L., & Yoshida, S. 2004, MNRAS, 354, 1040, doi: 10.1111/j.1365-2966.2004.08265.x

    2004

  31. [41]

    Motta, S. E. 2016, Astronomische Nachrichten, 337, 398, doi: 10.1002/asna.201612320

    2016 doi

  32. [42]

    A., & Wagoner, R

    Nowak, M. A., & Wagoner, R. V. 1991, ApJ, 378, 656, doi: 10.1086/170465

    1991 doi

  33. [43]

    Papaloizou, J. C. B., & Pringle, J. E. 1984, MNRAS, 208, 721, doi: 10.1093/mnras/208.4.721

    1984 doi

  34. [44]

    2017, MNRAS, 470, L34, doi: 10.1093/mnrasl/slx070

    Parthasarathy, V., Kluźniak, W., & Čemeljić, M. 2017, MNRAS, 470, L34, doi: 10.1093/mnrasl/slx070

    2017 doi

  35. [45]

    S., Dexter, J., Moscibrodzka, M., et al

    Prather, B. S., Dexter, J., Moscibrodzka, M., et al. 2023, ApJ, 950, 35, doi: 10.3847/1538-4357/acc586

    2023 doi

  36. [46]

    A., & McClintock, J

    Remillard, R. A., & McClintock, J. E. 2006, ARA&A, 44, 49, doi: 10.1146/annurev.astro.44.051905.092532

    2006 arXiv

  37. [48]

    2003b, MNRAS, 344, 978, doi: 10.1046/j.1365-8711.2003.07023.x

    Rezzolla, L., Yoshida, S., & Zanotti, O. 2003b, MNRAS, 344, 978, doi: 10.1046/j.1365-8711.2003.07023.x

    2003

  38. [49]

    Schnittman, J. D. 2005, ApJ, 621, 940, doi: 10.1086/427646

    2005 doi

  39. [50]

    D., & Bertschinger, E

    Schnittman, J. D., & Bertschinger, E. 2004, ApJ, 606, 1098, doi: 10.1086/383180

    2004 doi

  40. [51]

    D., Homan, J., & Miller, J

    Schnittman, J. D., Homan, J., & Miller, J. M. 2006a, ApJ, 642, 420, doi: 10.1086/500923

    doi

  41. [52]

    D., Krolik, J

    Schnittman, J. D., Krolik, J. H., & Hawley, J. F. 2006b, ApJ, 651, 1031, doi: 10.1086/507421

    doi

  42. [53]

    D., & Rezzolla, L

    Schnittman, J. D., & Rezzolla, L. 2006, ApJL, 637, L113, doi: 10.1086/500545

    2006 doi

  43. [54]

    I., & Sunyaev, R

    Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337 Sądowski, A., Lasota, J.-P., Abramowicz, M. A., &

    1973

  44. [55]

    2016, MNRAS, 456, 3915, doi: 10.1093/mnras/stv2854

    Narayan, R. 2016, MNRAS, 456, 3915, doi: 10.1093/mnras/stv2854

    2016 doi

  45. [56]

    1998, in 19th Texas Symposium on Relativistic Astrophysics and Cosmology, ed

    Stella, L., & Vietri, M. 1998, in 19th Texas Symposium on Relativistic Astrophysics and Cosmology, ed. J. Paul, T. Montmerle, & E. Aubourg, 315

    1998

  46. [57]

    1999, PhRvL, 82, 17, doi: 10.1103/PhysRevLett.82.17

    Stella, L., & Vietri, M. 1999, PhRvL, 82, 17, doi: 10.1103/PhysRevLett.82.17

    1999 doi

  47. [58]

    Stella, L., Vietri, M., & Morsink, S. M. 1999, ApJL, 524, L63, doi: 10.1086/312291

    1999 doi

  48. [59]

    2006, MNRAS, 369, 2036, doi: 10.1111/j.1365-2966.2006.10454.x

    Suleimanov, V., & Poutanen, J. 2006, MNRAS, 369, 2036, doi: 10.1111/j.1365-2966.2006.10454.x

    2006

  49. [60]

    A., & Shakura, N

    Sunyaev, R. A., & Shakura, N. I. 1986, Soviet Astronomy Letters, 12, 117 Török, G. 2009, A&A, 497, 661, doi: 10.1051/0004-6361/20079026 Török, G., Abramowicz, M. A., Kluźniak, W., & Stuchlík, Z. 2005, A&A, 436, 1, doi: 10.1051/0004-6361:20047115 10 Török, G., Goluchová, K., Ho...

    1986 doi

  50. [61]

    H., Paumard, T., Gourgoulhon, E., & Perrin, G

    Vincent, F. H., Paumard, T., Gourgoulhon, E., & Perrin, G. 2011, Classical and Quantum Gravity, 28, 225011, doi: 10.1088/0264-9381/28/22/225011

    2011 doi

  51. [62]

    Wagoner, R. V. 1999, PhR, 311, 259, doi: 10.1016/S0370-1573(98)00104-5

    1999 doi

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.