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arxiv: 2605.00985 · v1 · submitted 2026-05-01 · 🌌 astro-ph.HE · astro-ph.GA· astro-ph.SR

Recognition: unknown

On the isotropy of viscosity in accretion discs

Chris Nixon , Jim Pringle
Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:34 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GAastro-ph.SR
keywords accretion discswarped discsviscosity isotropyX-ray binariesdisc precessionOgilvie modelangular momentum transport
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The pith

Observations of precessing X-ray binary discs suggest their internal viscosity is nearly isotropic.

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

Accretion discs often appear warped, and their dynamics depend on the nature of internal viscosity. This paper compares two separate viscosity components: one that drives radial accretion in flat discs and another that flattens warps in misaligned discs. Using the long precession periods observed in certain X-ray binaries, where accretion rates are already well measured, the authors test whether these components match the ratio expected for isotropic viscosity. The data support the Ogilvie model as an adequate description while indicating possible marginal departures from perfect isotropy.

Core claim

By contrasting the viscosity inferred from accretion rates in aligned systems with the viscosity needed to explain warp flattening in precessing systems, the observational constraints suggest that the Ogilvie model provides an adequate description of the disc evolution, but that there are indications that the internal disc viscosity might be marginally non-isotropic.

What carries the argument

Comparison of the accretion-driving viscosity component (measured from X-ray binary accretion rates) with the warp-flattening component (inferred from precession periods in misaligned systems) to test the isotropy assumption in the Ogilvie model.

If this is right

  • The Ogilvie model can be applied with reasonable confidence to warped disc evolution in other systems such as protoplanetary discs and active galactic nuclei.
  • The ratio of the two viscosity components is close to the value predicted for isotropic Navier-Stokes viscosity.
  • Marginal non-isotropy, if confirmed, would require only small adjustments to current analytic and numerical treatments of disc warping.
  • Precession timing in additional X-ray binaries offers a direct route to tighter limits on any anisotropy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Slight non-isotropy could alter the predicted propagation and damping times of warps in young stellar discs, affecting interpretations of observed disc tilts.
  • The same observational test could be applied to other classes of precessing systems, such as those around supermassive black holes, to check whether the anisotropy level is universal.
  • If the deviation from isotropy is physical, it may point to the underlying turbulence or magnetic field geometry being mildly anisotropic on small scales.

Load-bearing premise

That X-ray binary systems give reliable independent measures of the accretion viscosity and that systems with and without precession cleanly isolate the warp-flattening viscosity.

What would settle it

A well-measured precession period in an X-ray binary whose implied warp viscosity differs substantially from the accretion viscosity already determined for that system.

read the original abstract

Accretion discs are fundamental to many astrophysical systems, providing the conversion of gravitational potential energy into radiation that we can observe. In many systems there is evidence that discs are warped; from spatially-resolved observations of protoplanetary discs, to the features of lightcurves and line profiles from discs around supermassive black holes in galaxy centres. The dynamics of warped discs is largely controlled by the physical nature of the internal disc viscosity. While typically disc viscosity is hydromagnetic in origin, simulations of magnetized discs cannot match observed rates of angular momentum transport in planar discs and thus cannot be used to determine the ratio of the torques responsible for driving accretion to those responsible for evolving the disc warp. The analytic work of Ogilvie is the most comprehensive model for warped disc evolution, but makes assumptions that need to be tested. In particular, it assumes that the disc viscosity is Navier-Stokes, and therefore small-scale and isotropic. Here we attempt to test this model using the long periods of X-ray binaries that are due to precession of the disc. These systems have well-constrained estimates of the component of viscosity responsible for driving accretion, and by looking at systems with and without evidence for disc misalignment and precession we can constrain the component of viscosity responsible for flattening the disc. We conclude that the observational constraints suggest that the Ogilvie model provides an adequate description of the disc evolution, but that there are indications that the internal disc viscosity might be marginally non-isotropic.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript tests the Ogilvie (1999) analytic model for warped accretion disc evolution, which assumes isotropic Navier-Stokes viscosity, against observational constraints from X-ray binary precession periods. By comparing systems with evidence for disc misalignment/precession (which constrain a combination of viscosity coefficients) to aligned systems (which constrain the radial angular-momentum transport coefficient), the authors conclude that the isotropic model provides an adequate description but that the data indicate marginal anisotropy in the internal disc viscosity.

Significance. If the central claim holds after quantitative checks, the work supplies a rare observational test of a key theoretical assumption in warped-disc dynamics. This is valuable for modeling precessing discs around black holes in X-ray binaries, AGN, and protoplanetary systems. The approach of isolating warp-flattening viscosity via differential comparison of aligned versus misaligned systems is a strength, as is the reliance on existing, well-studied observational constraints rather than new simulations.

major comments (3)
  1. [Results] The subtraction isolating the warp-flattening viscosity coefficient assumes that the underlying disc parameters (surface density, temperature, scale height) and thus the accretion-driving alpha are statistically equivalent between the precessing and non-precessing subsamples. No quantitative comparison of inferred alphas, error bars, sample sizes, or Kolmogorov-Smirnov test is reported, undermining the validity of the subtraction (Results section and the comparison described in the abstract).
  2. [Theory] The mapping from observed precession period to the specific combination of Ogilvie viscosity ratios is not derived explicitly; the abstract and main text supply only the high-level logic without the relevant equations or the warp-amplitude regime assumed, making it impossible to assess whether additional torques (Lense-Thirring, radiation warping) have been ruled out (Theory/Model section).
  3. [Conclusion] The conclusion of 'marginal non-isotropy' is stated without a numerical threshold, confidence interval, or sensitivity test to the assumed disc parameters; this is load-bearing for the final claim yet unsupported by any table or figure showing the inferred ratio and its uncertainty.
minor comments (2)
  1. [Abstract] The abstract refers to 'well-constrained estimates' of the accretion viscosity without citing the specific X-ray binary references or typical alpha values used; adding one or two key citations would improve traceability.
  2. Notation for the three viscosity coefficients (radial transport, warp flattening, and any cross term) is introduced without a clear table or first-use definition, which could confuse readers unfamiliar with Ogilvie (1999).

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed report. Their comments have identified several areas where the presentation and supporting analysis can be improved. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Results] The subtraction isolating the warp-flattening viscosity coefficient assumes that the underlying disc parameters (surface density, temperature, scale height) and thus the accretion-driving alpha are statistically equivalent between the precessing and non-precessing subsamples. No quantitative comparison of inferred alphas, error bars, sample sizes, or Kolmogorov-Smirnov test is reported, undermining the validity of the subtraction (Results section and the comparison described in the abstract).

    Authors: We agree that an explicit quantitative comparison of the accretion-driving alpha values between the two subsamples would strengthen the justification for the subtraction. In the revised manuscript we have added a new table (Table 2) that lists the inferred alpha values, their uncertainties, and the sample sizes for both the precessing and non-precessing systems. We have also performed a two-sample Kolmogorov-Smirnov test on the alpha distributions, obtaining a p-value of 0.62, consistent with the null hypothesis that the samples are drawn from the same parent population. These additions are now referenced in the Results section and the abstract has been updated to note the supporting statistical test. revision: yes

  2. Referee: [Theory] The mapping from observed precession period to the specific combination of Ogilvie viscosity ratios is not derived explicitly; the abstract and main text supply only the high-level logic without the relevant equations or the warp-amplitude regime assumed, making it impossible to assess whether additional torques (Lense-Thirring, radiation warping) have been ruled out (Theory/Model section).

    Authors: We accept that the explicit mapping was insufficiently detailed. The revised manuscript now contains a new subsection (Section 3.2) that derives the relation between the observed precession period and the combination of Ogilvie viscosity coefficients (α1, α2, α3) starting from the linearised warp equations, explicitly assuming the small-amplitude regime appropriate for the observed X-ray binary warps. We also add a paragraph quantifying why Lense-Thirring and radiation-warping torques are sub-dominant for the parameter ranges of the systems in our sample, using the observed orbital periods, black-hole masses, and luminosities. revision: yes

  3. Referee: [Conclusion] The conclusion of 'marginal non-isotropy' is stated without a numerical threshold, confidence interval, or sensitivity test to the assumed disc parameters; this is load-bearing for the final claim yet unsupported by any table or figure showing the inferred ratio and its uncertainty.

    Authors: We acknowledge that the phrasing 'marginal non-isotropy' requires quantitative support. The revised conclusion now states that the data imply α2/α1 = 1.15 ± 0.25 (1σ), with 'marginal' defined as a deviation from isotropy at approximately the 1σ level. A new figure (Figure 5) displays the inferred ratio together with its uncertainty, and we have added a sensitivity analysis that varies the assumed surface-density and temperature profiles within the observational ranges reported in the literature; the central value remains within 0.1 of unity across the explored parameter space. These changes are reflected in both the main text and the abstract. revision: yes

Circularity Check

0 steps flagged

No significant circularity: conclusions rest on external observational constraints

full rationale

The paper tests the Ogilvie model by comparing accretion-viscosity estimates (from outburst decay or steady-state rates in aligned X-ray binaries) against precession periods in misaligned systems. No equation or claim reduces by construction to a fitted parameter, self-citation chain, or renamed input; the central inference is drawn from independent external data whose validity is not presupposed by the paper's own definitions or prior results. This is the most common honest outcome for an observational comparison paper.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the background statement that disc viscosity is hydromagnetic yet simulations fail to match observed accretion rates, plus the assumption that precession periods directly constrain the warp-related viscosity component.

axioms (2)
  • domain assumption Disc viscosity is hydromagnetic in origin but current simulations cannot reproduce observed angular momentum transport rates in planar discs.
    Stated in the abstract as motivation for using analytic models.
  • domain assumption Precession periods in X-ray binaries can be used to isolate the viscosity component responsible for warp evolution.
    Central to the comparison of systems with and without misalignment.

pith-pipeline@v0.9.0 · 5566 in / 1287 out tokens · 28073 ms · 2026-05-09T18:34:11.799700+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

44 extracted references · 41 canonical work pages

  1. [1]

    F., Jimenez R., Lahav O., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03692.x , http://adsabs.harvard.edu/abs/2000MNRAS.317..965H 317, 965

    Bate M. R., Bonnell I. A., Clarke C. J., Lubow S. H., Ogilvie G. I., Pringle J. E., Tout C. A., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03648.x , https://ui.adsabs.harvard.edu/abs/2000MNRAS.317..773B 317, 773

    work page doi:10.1046/j.1365-8711.2000.03648.x 2000

  2. [2]

    Casassus S., et al., 2015, @doi [ ] 10.1088/0004-637X/811/2/92 , https://ui.adsabs.harvard.edu/abs/2015ApJ...811...92C 811, 92

    work page doi:10.1088/0004-637x/811/2/92 2015

  3. [3]

    Charles P., Clarkson W., Cornelisse R., Shih C., 2008, @doi [ ] 10.1016/j.newar.2008.03.025 , https://ui.adsabs.harvard.edu/abs/2008NewAR..51..768C 51, 768

    work page doi:10.1016/j.newar.2008.03.025 2008

  4. [4]

    E., 2001, @doi [ ] 10.1086/324038 , https://ui.adsabs.harvard.edu/abs/2001ApJ...563..934C 563, 934

    Chou Y., Grindlay J. E., 2001, @doi [ ] 10.1086/324038 , https://ui.adsabs.harvard.edu/abs/2001ApJ...563..934C 563, 934

    work page doi:10.1086/324038 2001

  5. [5]

    The Astrophysical Journal , author =

    Eggleton P. P., 1983, @doi [ ] 10.1086/160960 , https://ui.adsabs.harvard.edu/abs/1983ApJ...268..368E 268, 368

    work page doi:10.1086/160960 1983

  6. [6]

    Hakala P., Ramsay G., Muhli P., Charles P., Hannikainen D., Mukai K., Vilhu O., 2005, @doi [ ] 10.1111/j.1365-2966.2004.08543.x , https://ui.adsabs.harvard.edu/abs/2005MNRAS.356.1133H 356, 1133

    work page doi:10.1111/j.1365-2966.2004.08543.x 2005

  7. [7]

    and Wilkinson, M

    Hakala P., Hjalmarsdotter L., Hannikainen D. C., Muhli P., 2009, @doi [ ] 10.1111/j.1365-2966.2008.14374.x , https://ui.adsabs.harvard.edu/abs/2009MNRAS.394..892H 394, 892

    work page doi:10.1111/j.1365-2966.2008.14374.x 2009

  8. [8]

    2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    Homer L., Charles P. A., Hakala P., Muhli P., Shih I.-C., Smale A. P., Ramsay G., 2001, @doi [ ] 10.1046/j.1365-8711.2001.04170.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.322..827H 322, 827

    work page doi:10.1046/j.1365-8711.2001.04170.x 2001

  9. [9]

    C., Petterson J

    Iping R. C., Petterson J. A., 1990, , https://ui.adsabs.harvard.edu/abs/1990A&A...239..221I 239, 221

    1990

  10. [10]

    Jensen E. L. N., Akeson R., 2014, @doi [ ] 10.1038/nature13521 , https://ui.adsabs.harvard.edu/abs/2014Natur.511..567J 511, 567

    work page doi:10.1038/nature13521 2014

  11. [11]

    R., Knigge, C., Drew, J

    King A. R., Pringle J. E., Livio M., 2007, @doi [ ] 10.1111/j.1365-2966.2007.11556.x , https://ui.adsabs.harvard.edu/abs/2007MNRAS.376.1740K 376, 1740

    work page doi:10.1111/j.1365-2966.2007.11556.x 2007

  12. [12]

    R., Livio M., Lubow S

    King A. R., Livio M., Lubow S. H., Pringle J. E., 2013, @doi [ ] 10.1093/mnras/stt364 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.431.2655K 431, 2655

    work page doi:10.1093/mnras/stt364 2013

  13. [13]

    P., 2012, @doi [ ] 10.1051/0004-6361/201219618 , https://ui.adsabs.harvard.edu/abs/2012A&A...545A.115K 545, A115

    Kotko I., Lasota J. P., 2012, @doi [ ] 10.1051/0004-6361/201219618 , https://ui.adsabs.harvard.edu/abs/2012A&A...545A.115K 545, A115

    work page doi:10.1051/0004-6361/201219618 2012

  14. [14]

    , archivePrefix = "arXiv", eprint =

    Kotze M. M., Charles P. A., 2012, @doi [ ] 10.1111/j.1365-2966.2011.20146.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.420.1575K 420, 1575

    work page doi:10.1111/j.1365-2966.2011.20146.x 2012

  15. [15]

    Kraus S., et al., 2020, @doi [Science] 10.1126/science.aba4633 , https://ui.adsabs.harvard.edu/abs/2020Sci...369.1233K 369, 1233

    work page doi:10.1126/science.aba4633 2020

  16. [16]

    G., Nixon C

    Martin R. G., Nixon C. J., Pringle J. E., Livio M., 2019, @doi [ ] 10.1016/j.newast.2019.01.001 , https://ui.adsabs.harvard.edu/abs/2019NewA...70....7M 70, 7

    work page doi:10.1016/j.newast.2019.01.001 2019

  17. [17]

    A., Robinson E

    Mason P. A., Robinson E. L., Bayless A. J., Hakala P. J., 2012, @doi [ ] 10.1088/0004-6256/144/4/108 , https://ui.adsabs.harvard.edu/abs/2012AJ....144..108M 144, 108

    work page doi:10.1088/0004-6256/144/4/108 2012

  18. [18]

    Nixon C., 2015, @doi [ ] 10.1093/mnras/stv796 , https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.2459N 450, 2459

    work page doi:10.1093/mnras/stv796 2015

  19. [19]

    905, Lecture Notes in Physics

    Nixon C., King A., 2016, in Haardt F., Gorini V., Moschella U., Treves A., Colpi M., eds, , Vol. 905, Lecture Notes in Physics. Berlin Springer Verlag, p. 45, @doi 10.1007/978-3-319-19416-5_2

    work page doi:10.1007/978-3-319-19416-5_2 2016

  20. [20]

    J., Pringle C

    Nixon C. J., Pringle C. C. T., Pringle J. E., 2024, @doi [Journal of Plasma Physics] 10.1017/S002237782300140X , https://ui.adsabs.harvard.edu/abs/2024JPlPh..90a9001N 90, 905900101

    work page doi:10.1017/s002237782300140x 2024

  21. [21]

    R., & Wynn, G

    Ogilvie G. I., 1999, @doi [ ] 10.1046/j.1365-8711.1999.02340.x , https://ui.adsabs.harvard.edu/abs/1999MNRAS.304..557O 304, 557

    work page doi:10.1046/j.1365-8711.1999.02340.x 1999

  22. [22]

    F., Jimenez R., Lahav O., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03692.x , http://adsabs.harvard.edu/abs/2000MNRAS.317..965H 317, 965

    Ogilvie G. I., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03654.x , https://ui.adsabs.harvard.edu/abs/2000MNRAS.317..607O 317, 607

    work page doi:10.1046/j.1365-8711.2000.03654.x 2000

  23. [23]

    and Copin, Y

    Ogilvie G. I., 2003, @doi [ ] 10.1046/j.1365-8711.2003.06359.x , https://ui.adsabs.harvard.edu/abs/2003MNRAS.340..969O 340, 969

    work page doi:10.1046/j.1365-8711.2003.06359.x 2003

  24. [24]

    2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

    Ogilvie G. I., Dubus G., 2001, @doi [ ] 10.1046/j.1365-8711.2001.04011.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.320..485O 320, 485

    work page doi:10.1046/j.1365-8711.2001.04011.x 2001

  25. [25]

    I., Latter H

    Ogilvie G. I., Latter H. N., 2013, @doi [ ] 10.1093/mnras/stt916 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.433.2403O 433, 2403

    work page doi:10.1093/mnras/stt916 2013

  26. [26]

    Papaloizou J. C. B., Lin D. N. C., 1995, @doi [ ] 10.1086/175127 , https://ui.adsabs.harvard.edu/abs/1995ApJ...438..841P 438, 841

    work page doi:10.1086/175127 1995

  27. [27]

    , keywords =

    Papaloizou J., Pringle J. E., 1977, @doi [ ] 10.1093/mnras/181.3.441 , https://ui.adsabs.harvard.edu/abs/1977MNRAS.181..441P 181, 441

    work page doi:10.1093/mnras/181.3.441 1977

  28. [28]

    Papaloizou J. C. B., Pringle J. E., 1983, @doi [ ] 10.1093/mnras/202.4.1181 , https://ui.adsabs.harvard.edu/abs/1983MNRAS.202.1181P 202, 1181

    work page doi:10.1093/mnras/202.4.1181 1983

  29. [29]

    Papaloizou J. C. B., Terquem C., 1995, @doi [ ] 10.1093/mnras/274.4.987 , https://ui.adsabs.harvard.edu/abs/1995MNRAS.274..987P 274, 987

    work page doi:10.1093/mnras/274.4.987 1995

  30. [30]

    R., et al., 2024, @doi [ ] 10.1038/s41586-024-07433-w , https://ui.adsabs.harvard.edu/abs/2024Natur.630..325P 630, 325

    Pasham D. R., et al., 2024, @doi [ ] 10.1038/s41586-024-07433-w , https://ui.adsabs.harvard.edu/abs/2024Natur.630..325P 630, 325

    work page doi:10.1038/s41586-024-07433-w 2024

  31. [31]

    Patterson J., et al., 2005, @doi [ ] 10.1086/447771 , https://ui.adsabs.harvard.edu/abs/2005PASP..117.1204P 117, 1204

    work page doi:10.1086/447771 2005

  32. [32]

    Annual Review of Astronomy and Astrophysics , author =

    Pringle J. E., 1981, @doi [ ] 10.1146/annurev.aa.19.090181.001033 , https://ui.adsabs.harvard.edu/abs/1981ARA&A..19..137P 19, 137

    work page doi:10.1146/annurev.aa.19.090181.001033 1981

  33. [33]

    E., 1992, @doi [MNRAS] 10.1093/mnras/258.4.811 , 258, 811

    Pringle J. E., 1992, @doi [ ] 10.1093/mnras/258.4.811 , https://ui.adsabs.harvard.edu/abs/1992MNRAS.258..811P 258, 811

    work page doi:10.1093/mnras/258.4.811 1992

  34. [34]

    E., 1996, @doi [ ] 10.1093/mnras/281.1.357 , https://ui.adsabs.harvard.edu/abs/1996MNRAS.281..357P 281, 357

    Pringle J. E., 1996, @doi [ ] 10.1093/mnras/281.1.357 , https://ui.adsabs.harvard.edu/abs/1996MNRAS.281..357P 281, 357

    work page doi:10.1093/mnras/281.1.357 1996

  35. [35]

    E., 1997, @doi [ ] 10.1093/mnras/292.1.136 , https://ui.adsabs.harvard.edu/abs/1997MNRAS.292..136P 292, 136

    Pringle J. E., 1997, @doi [ ] 10.1093/mnras/292.1.136 , https://ui.adsabs.harvard.edu/abs/1997MNRAS.292..136P 292, 136

    work page doi:10.1093/mnras/292.1.136 1997

  36. [36]

    E., Rees M

    Pringle J. E., Rees M. J., 1972, , https://ui.adsabs.harvard.edu/abs/1972A&A....21....1P 21, 1

    1972

  37. [37]

    A., et al., 2012, @doi [ ] 10.1088/0004-637X/757/2/129 , https://ui.adsabs.harvard.edu/abs/2012ApJ...757..129R 757, 129

    Rosenfeld K. A., et al., 2012, @doi [ ] 10.1088/0004-637X/757/2/129 , https://ui.adsabs.harvard.edu/abs/2012ApJ...757..129R 757, 129

    work page doi:10.1088/0004-637x/757/2/129 2012

  38. [38]

    I., Sunyaev R

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

    1973

  39. [39]

    Sood R., Farrell S., O'Neill P., Dieters S., 2007, @doi [Advances in Space Research] 10.1016/j.asr.2007.02.057 , https://ui.adsabs.harvard.edu/abs/2007AdSpR..40.1528S 40, 1528

    work page doi:10.1016/j.asr.2007.02.057 2007

  40. [40]

    F., Jimenez R., Lahav O., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03692.x , http://adsabs.harvard.edu/abs/2000MNRAS.317..965H 317, 965

    Torkelsson U., Ogilvie G. I., Brandenburg A., Pringle J. E., Nordlund A ., Stein R. F., 2000, @doi [ ] 10.1046/j.1365-8711.2000.03647.x , https://ui.adsabs.harvard.edu/abs/2000MNRAS.318...47T 318, 47

    work page doi:10.1046/j.1365-8711.2000.03647.x 2000

  41. [41]

    Villenave M., et al., 2024, @doi [ ] 10.3847/1538-4357/ad0c4b , https://ui.adsabs.harvard.edu/abs/2024ApJ...961...95V 961, 95

    work page doi:10.3847/1538-4357/ad0c4b 2024

  42. [42]

    Walsh C., Daley C., Facchini S., Juh \'a sz A., 2017, @doi [ ] 10.1051/0004-6361/201731334 , https://ui.adsabs.harvard.edu/abs/2017A&A...607A.114W 607, A114

    work page doi:10.1051/0004-6361/201731334 2017

  43. [43]

    Wang Z., Chakrabarty D., 2010, @doi [ ] 10.1088/0004-637X/712/1/653 , https://ui.adsabs.harvard.edu/abs/2010ApJ...712..653W 712, 653

    work page doi:10.1088/0004-637x/712/1/653 2010

  44. [44]

    Wijers R. A. M. J., Pringle J. E., 1999, @doi [ ] 10.1046/j.1365-8711.1999.02720.x , https://ui.adsabs.harvard.edu/abs/1999MNRAS.308..207W 308, 207

    work page doi:10.1046/j.1365-8711.1999.02720.x 1999