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Beaming of polarized radiation in subcritical X-ray pulsars

T0 review · 2 major / 1 minor · reviewed 2026-05-13 · grok-4.3

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Pith's one-line read Resonant Compton scattering near the cyclotron energy reduces light-curve modulation amplitude in subcritical X-ray pulsars.

desk verdict Resonant Compton scattering in the accretion column redistributes polarized radiation enough to damp modulation near the cyclotron energy, but the paper gives no numbers or tests to show how robust that damping is. read the letter →

arxiv 2604.01218 v1 submitted 2026-04-01 astro-ph.HE

I. D. Markozov , A. Y. Potekhin , A. D. Kaminker , A. A. Mushtukov This is my paper · ORCID
classification astro-ph.HE
keywords X-raypulsarscyclotronresonanceradiativetransferpolarizationneutronstarsaccretionbeaminglightcurves
checked against Foundation.ArrowOfTime
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 examines beaming of polarized radiation from subcritical X-ray pulsars, where accretion flows form channels near the neutron star surface in strong magnetic fields. It numerically solves the coupled equations of hydrodynamics and radiative transfer for two polarization modes, incorporating resonant Compton scattering and vacuum polarization. Beaming patterns emerge for varying accretion rates, photon energies, and surface radiation models, then convert to intensity and polarization light curves with general-relativistic corrections. Resonant scattering produces angular redistribution of photons around the cyclotron resonance, lowering the amplitude of intensity modulations. This matches reports of weaker pulsed fractions at those energies.

What carries the argument

Numerical solution of radiative transfer for two coupled polarization modes in the accretion channel, including resonant Compton scattering and vacuum polarization.

What would settle it

A measurement of X-ray pulsar light curves at energies matching the cyclotron resonance that shows no reduction in modulation amplitude relative to nearby energies would falsify the claimed angular redistribution.

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Extended reading notes

Core claim

In subcritical X-ray pulsars the beaming patterns are strongly affected by resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies.

Load-bearing premise

The specific models chosen for neutron star surface radiation and the numerical treatment of coupled polarization modes in the accretion channel are accurate enough to capture the dominant beaming effects.

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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript numerically solves the coupled hydrodynamic and two-mode radiative-transfer equations inside the accretion column of subcritical X-ray pulsars, incorporating resonant Compton scattering and vacuum polarization. Beaming patterns are computed for varying accretion rates, photon energies, and polarizations using different neutron-star surface emissivity models; these patterns are then folded into intensity and polarization light curves that include general-relativistic light-bending and redshift effects. The central result is that resonant scattering near the electron cyclotron energy produces angular redistribution sufficient to reduce the amplitude of the light-curve modulation, consistent with observed suppression of the pulsed fraction at those energies.

Significance. If the numerical solutions are robust, the work supplies a concrete microphysical mechanism linking cyclotron-resonant radiative transfer to the energy-dependent timing properties of X-ray pulsars. This would strengthen the physical interpretation of suppressed pulsed fractions near cyclotron lines and provide testable predictions for future polarimetric observations.

major comments (2)
  1. [Methods] Methods section (numerical integration of the two-mode RT equations): no grid-resolution convergence tests, no error estimates on the angular or frequency discretization, and no validation against limiting cases (optically thin, non-resonant, or vacuum-only regimes) are reported. Without these, it is impossible to determine whether the claimed angular redistribution near the cyclotron resonance is numerically converged or an artifact of the chosen discretization and resonance-width treatment.
  2. [Results] Results (beaming patterns and light curves): the reduction in modulation amplitude is stated only qualitatively for the authors' chosen surface-radiation models and accretion rates. No quantitative measure of the suppression (e.g., change in pulsed fraction versus energy) or sensitivity to the assumed surface emissivity and polarization boundary conditions is provided, leaving the central observational claim unsupported by the presented data.
minor comments (1)
  1. [Abstract] Abstract: the statement that beaming patterns 'are found to be strongly affected' is not accompanied by any numerical scale or reference to a specific figure or table showing the magnitude of the effect.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important aspects of numerical robustness and quantitative presentation that we will address in the revised manuscript.

read point-by-point responses

  1. Referee: [Methods] Methods section (numerical integration of the two-mode RT equations): no grid-resolution convergence tests, no error estimates on the angular or frequency discretization, and no validation against limiting cases (optically thin, non-resonant, or vacuum-only regimes) are reported. Without these, it is impossible to determine whether the claimed angular redistribution near the cyclotron resonance is numerically converged or an artifact of the chosen discretization and resonance-width treatment.

    Authors: We agree that explicit convergence tests and validations are required to establish numerical reliability. In the revised manuscript we will add a new subsection to the Methods section that reports grid-resolution convergence tests for the angular and frequency discretizations, provides quantitative error estimates, and validates the solver against the optically thin limit, the non-resonant regime, and the vacuum-polarization-only case. These additions will confirm that the angular redistribution near the cyclotron resonance is a converged physical result. revision: yes

  2. Referee: [Results] Results (beaming patterns and light curves): the reduction in modulation amplitude is stated only qualitatively for the authors' chosen surface-radiation models and accretion rates. No quantitative measure of the suppression (e.g., change in pulsed fraction versus energy) or sensitivity to the assumed surface emissivity and polarization boundary conditions is provided, leaving the central observational claim unsupported by the presented data.

    Authors: We accept that the current results are presented qualitatively. The revised manuscript will include quantitative measures of the pulsed-fraction suppression as a function of energy for the explored accretion rates. We will also add calculations for additional surface-emissivity models and polarization boundary conditions to demonstrate the sensitivity of the suppression effect. These quantitative results will directly support the observational interpretation. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: forward numerical integration of standard radiative-transfer equations

full rationale

The paper solves the coupled hydrodynamics and two-mode radiative-transfer equations numerically inside the accretion column, incorporating resonant Compton scattering, vacuum polarization, and boundary conditions from the neutron-star surface. Beaming patterns and GR-corrected light curves are direct outputs of this integration for chosen accretion rates, energies, and surface models. No parameters are fitted to observational data within the work, no self-definitional loops appear in the equations, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The central claim (resonant scattering redistributes radiation and can suppress pulsed fraction) follows from the numerical solution rather than reducing to its own inputs by construction.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The model rests on standard equations of hydrodynamics and polarized radiative transfer in magnetized plasma; no new free parameters are introduced beyond the varied inputs (accretion rate, photon energy, magnetic field).

assumptions (2)
  • standard math Equations of hydrodynamics and radiative transfer for two coupled polarization modes in a magnetized plasma
    Invoked in the numerical solution described in the abstract.
  • domain assumption Resonant Compton scattering and vacuum polarization are the dominant opacity sources near the cyclotron energy
    Central to the beaming calculation.

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Cite this review

Pith. "Pith review of Beaming of polarized radiation in subcritical X-ray pulsars." pith.science (2026). https://pith.science/paper/2604.01218

@misc{pith2026260401218,
  author       = {Pith},
  title        = {Pith review of: Beaming of polarized radiation in subcritical X-ray pulsars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.01218}},
  note         = {Machine review of arXiv:2604.01218}
}
read the original abstract

Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed in the accretion channel close to the neutron star surface. We solve equations of the hydrodynamics and radiative transfer of two coupled polarization modes in the accretion channel numerically, taking into account resonant Compton scattering and vacuum polarization. The beaming patterns are obtained for different accretion rates, photon energies and polarizations, and for different models of the neutron star surface radiation. The calculated beaming patterns are converted into light curves for both the intensity and polarization, taking into account the effects of General Relativity. These beaming patterns and light curves are found to be strongly affected by the resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies.

Figures

Figures reproduced from arXiv: 2604.01218 by the authors.

Figure 1
Figure 1. Dependence of the normalized radiant intensity QE on the polar angle θ (left panels) and corresponding beam pattern (right panel) at accretion rate M˙ = 1015 g s−1 for photon energies E = 0.2Ecyc (dotted orange lines), 0.4Ecyc (solid red lines), Ecyc (dashed green lines) and 1.5Ecyc (dot-dashed blue lines). The specific intensity IE(θ) at the surface is assumed constant (parameter b = 0). Each curve is normalized to… view at source ↗
Figure 2
Figure 2. Same as in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Same as in Figures 1 and 2 but for M˙ = 5 × 1015 g s−1 . panels, we show the corresponding beaming patterns in the polar coordinates. The surface radiation is assumed unpolarized. Each function QE(θ) is normalized to its maximum, in order to focus on the angular dependence. It should be noted that the parts of the curves with θ ≥ 90◦ cannot be observed: since the radius and height of the accretion channel are small … view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Polar diagram of outgoing radiation at M˙ = 2.5 × 1015 g s−1 (as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Polar diagram of beaming of outgoing radiation at M˙ = 2.5 × 1015 g s−1 for the unpolarized NS surface radiation, suppressed near the normal to the surface according to Equation (3) with parameter b = −1 (left panel) or b = −0.75 (right panel) [PITH_FULL_IMAGE:figures…
Figure 6
Figure 6. Figure 6: Same as in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Same as in [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Color maps of the normalized intensity of outgoing radiation as functions of the angle to the NS surface normal θ (the horizontal axis, in degrees) and photon energy E (the vertical axis, in keV). Upper panels: total intensity for both normal modes for accretion rates …
Figure 9
Figure 9. Figure 9: Light curves for the intensity and polarization degree, corresponding to the beaming patterns shown in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Same as in [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

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  1. Vacuum polarization and cyclotron resonance effects on radiative transfer and plasma deceleration in subcritical X-ray pulsars

    astro-ph.HE 2026-05 unverdicted novelty 5.0 of 10

    Simulations of subcritical X-ray pulsar accretion channels show vacuum polarization dominating plasma birefringence, enhancing cyclotron features and radiative deceleration, producing a polarization sign change above ...

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Works this paper leans on

50 extracted references · 50 canonical work pages · cited by 1 Pith paper

  1. [1]

    2024, Space-Based Multi-band Astronomical Variable Objects Monitor (SVOM), ed

    Mushtukov, A.; Tsygankov, S., Accreting strongly magnetised neutron stars: X-ray pulsars. InHandbook of X-ray and Gamma- ray Astrophysics; Bambi, C.; Santangelo, A., Eds.; Springer: Singapore, 2024; pp. 4105–4136, [arXiv:astro-ph.HE/2204.14185]. https://doi.org/10.1007/978-981-19-6960-7

    work page doi:10.1007/978-981-19-6960-7 2024

  2. [2]

    A comprehensive library of X-ray pulsars in the Small Magellanic Cloud: Time evolution of their luminosities and spin periods.Astrophys

    Yang, J.; Laycock, S.G.T.; Christodoulou, D.M.; Fingerman, S.; Coe, M.J.; Drake, J.J. A comprehensive library of X-ray pulsars in the Small Magellanic Cloud: Time evolution of their luminosities and spin periods.Astrophys. J.2017,839, 119, [arXiv:astro- ph.HE/1703.05196]. https://doi.org/10.3847/1538-4357/aa6898

    work page doi:10.3847/1538-4357/aa6898 2017

  3. [3]

    An ultraluminous X-ray source powered by an accreting neutron star

    Bachetti, M.; Harrison, F.A.; Walton, D.J.; Grefenstette, B.W.; Chakrabarty, D.; Fürst, F.; Barret, D.; Beloborodov, A.; Boggs, S.E.; Christensen, F.E.; et al. An ultraluminous X-ray source powered by an accreting neutron star.Nature2014,514, 202–204, [arXiv:astro-ph.HE/1410.3590]. https://doi.org/10.1038/nature13791

    work page doi:10.1038/nature13791

  4. [4]

    L., Belfiore, A., Stella, L., et al

    Israel, G.L.; Belfiore, A.; Stella, L.; Esposito, P .; Casella, P .; De Luca, A.; Marelli, M.; Papitto, A.; Perri, M.; Puccetti, S.; et al. An accreting pulsar with extreme properties drives an ultraluminous X-ray source in NGC 5907.Science2017,355, 817–819, [arXiv:astro-ph.HE/1609.07375]. https://doi.org/10.1126/science.aai8635

    work page doi:10.1126/science.aai8635

  5. [5]

    ULXs: Neutron stars versus black holes.Mon

    King, A.; Lasota, J.P . ULXs: Neutron stars versus black holes.Mon. Not. R. Astron. Soc.2016,458, L10–L13, [arXiv:astro- ph.HE/1601.03738]. https://doi.org/10.1093/mnrasl/slw011

    work page doi:10.1093/mnrasl/slw011 2016

  6. [6]

    , archivePrefix = "arXiv", eprint =

    King, A.; Lasota, J.P .; Klu´ zniak, W. Pulsing ULXs: tip of the iceberg?Mon. Not. R. Astron. Soc.2017,468, L59–L62, [arXiv:astro- ph.HE/1702.00808]. https://doi.org/10.1093/mnrasl/slx020

    work page doi:10.1093/mnrasl/slx020 2017

  7. [7]

    Ultraluminous X-ray sources are beamed.Mon

    Lasota, J.P .; King, A. Ultraluminous X-ray sources are beamed.Mon. Not. R. Astron. Soc.2023,526, 2506–2509, [arXiv:astro- ph.HE/2309.00034]. https://doi.org/10.1093/mnras/stad2926

    work page doi:10.1093/mnras/stad2926 2023

  8. [8]

    Bright X-ray pulsars: how outflows influence beaming, pulsations and pulse phase lags

    Mushtukov, A.A.; Portegies Zwart, S. Bright X-ray pulsars: how outflows influence beaming, pulsations and pulse phase lags. Mon. Not. R. Astron. Soc.2023,518, 5457–5464, [arXiv:astro-ph.HE/2211.08952]. https://doi.org/10.1093/mnras/stac3431

    work page doi:10.1093/mnras/stac3431 2023

Show all 50 references
  1. [9]

    Stable accretion from a cold disc in highly magnetized neutron stars.Astron

    Tsygankov, S.S.; Mushtukov, A.A.; Suleimanov, V .F.; Doroshenko, V .; Abolmasov, P .K.; Lutovinov, A.A.; Poutanen, J. Stable accretion from a cold disc in highly magnetized neutron stars.Astron. Astrophys.2017,608, A17, [arXiv:astro-ph.HE/1703.04528]. https://doi.org/10.1051/0...

    2017 doi

  2. [10]

    Study of the X-ray pulsar IGR J19294+1816 with NuSTAR: Detection of cyclotron line and transition to accretion from the cold disk.Astron

    Tsygankov, S.S.; Doroshenko, V .; Mushtukov, A.A.; Lutovinov, A.A.; Poutanen, J. Study of the X-ray pulsar IGR J19294+1816 with NuSTAR: Detection of cyclotron line and transition to accretion from the cold disk.Astron. Astrophys.2019,621, A134, [arXiv:astro-ph.HE/1811.08912]. ...

    2019 doi

  3. [11]

    Why the Number of Galactic X-ray Stars Is so Small?Astron

    Illarionov, A.F.; Sunyaev, R.A. Why the Number of Galactic X-ray Stars Is so Small?Astron. Astrophys.1975,39, 185

    1975

  4. [12]

    Cyclotron lines in highly magnetized neutron stars.Astron

    Staubert, R.; Trümper, J.; Kendziorra, E.; Klochkov, D.; Postnov, K.; Kretschmar, P .; Pottschmidt, K.; Haberl, F.; Rothschild, R.E.; Santangelo, A.; et al. Cyclotron lines in highly magnetized neutron stars.Astron. Astrophys.2019,622, A61, [arXiv:astro- ph.HE/1812.03461]. htt...

    2019 doi

  5. [13]

    The Imaging X-Ray Polarimetry Explorer (IXPE): Pre-Launch.J

    Weisskopf, M.C.; Soffitta, P .; Baldini, L.; Ramsey, B.D.; O’Dell, S.L.; Romani, R.W.; Matt, G.; Deininger, W.D.; Baumgartner, W.H.; Bellazzini, R.; et al. The Imaging X-Ray Polarimetry Explorer (IXPE): Pre-Launch.J. Astron. Telescopes, Instruments, and Systems 2022,8, 026002,...

    2022 doi

  6. [14]

    Remembering Yury N

    Heyl, J. Remembering Yury N. Gnedin at the dawn of X-ray polarimetry: Predictions of IXPE observations of neutron stars. Universe2022,8, 84. https://doi.org/10.3390/universe8020084

    doi

  7. [15]

    Determination of X-ray pulsar geometry with IXPE polarimetry.Nature Astronomy2022,6, 1433–1443, [arXiv:astro-ph.HE/2206.07138]

    Doroshenko, V .; Poutanen, J.; Tsygankov, S.S.; Suleimanov, V .F.; Bachetti, M.; Caiazzo, I.; Costa, E.; Di Marco, A.; Heyl, J.; La Monaca, F.; et al. Determination of X-ray pulsar geometry with IXPE polarimetry.Nature Astronomy2022,6, 1433–1443, [arXiv:astro-ph.HE/2206.07138]...

    doi

  8. [16]

    Maximum Accretion Efficiency in General Theory of Relativity.arXiv e-prints1998, [astro-ph/9811402]

    Mitra, A. Maximum Accretion Efficiency in General Theory of Relativity.arXiv e-prints1998, [astro-ph/9811402]. https: //doi.org/10.48550/arXiv.astro-ph/9811402

    doi arXiv

  9. [17]

    Nuclear physics of the outer layers of accreting neutron stars.J

    Meisel, Z.; Deibel, A.; Keek, L.; Shternin, P .; Elfritz, J. Nuclear physics of the outer layers of accreting neutron stars.J. Phys. G: Nuclear Physics2018,45, 093001, [arXiv:astro-ph.HE/1807.01150]. https://doi.org/10.1088/1361-6471/aad171

    doi

  10. [18]

    Accretion at a magnetic pole of a neutron star.Nature Physical Science1973,246, 1–4

    Davidson, K. Accretion at a magnetic pole of a neutron star.Nature Physical Science1973,246, 1–4. https://doi.org/10.1038/ physci246001a0

  11. [19]

    The limiting luminosity of accreting neutron stars with magnetic fields.Mon

    Basko, M.M.; Sunyaev, R.A. The limiting luminosity of accreting neutron stars with magnetic fields.Mon. Not. R. Astron. Soc. 1976,175, 395–417. https://doi.org/10.1093/mnras/175.2.395

    1976 doi

  12. [20]

    X-Ray Emission Accompanying the Accretion of Gas by a Neutron Star.Sov

    Zel’dovich, Y.B.; Shakura, N.I. X-Ray Emission Accompanying the Accretion of Gas by a Neutron Star.Sov. Astron.1969,13, 175

    1969

  13. [21]

    X-ray emission from magnetized neutron star atmospheres at low mass-accretion rates

    Sokolova-Lapa, E.; Gornostaev, M.; Wilms, J.; Ballhausen, R.; Falkner, S.; Postnov, K.; Thalhammer, P .; Fürst, F.; García, J.A.; Shakura, N.; et al. X-ray emission from magnetized neutron star atmospheres at low mass-accretion rates. I. Phase-averaged spectrum.Astron. Astroph...

    2021 doi

  14. [22]

    Accretion onto neutron stars under adiabatic shock conditions.Astrophys

    Shapiro, S.L.; Salpeter, E.E. Accretion onto neutron stars under adiabatic shock conditions.Astrophys. J.1975,198, 671–682. https://doi.org/10.1086/153645

    1975 doi

  15. [23]

    Low-luminosity accretion onto magnetized neutron stars.Astrophys

    Langer, S.H.; Rappaport, S. Low-luminosity accretion onto magnetized neutron stars.Astrophys. J.1982,257, 733–751. https://doi.org/10.1086/160028. https://doi.org/10.3390/particles1010000 Version April 2, 2026 submitted toParticles 16 of 17

    1982 doi

  16. [24]

    Dynamics of the flows accreting onto a magnetized neutron star.Astronomy Letters2004, 30, 309–318, [arXiv:astro-ph/astro-ph/0412319]

    Bykov, A.M.; Krassilchtchikov, A.M. Dynamics of the flows accreting onto a magnetized neutron star.Astronomy Letters2004, 30, 309–318, [arXiv:astro-ph/astro-ph/0412319]. https://doi.org/10.1134/1.1738153

    doi arXiv

  17. [25]

    Markozov, I.D.; Kaminker, A.D.; Potekhin, A.Y. Hydrodynamical simulation of the structure of the X-ray pulsar accretion channel: Accounting for resonant scattering.Astronomy Letters2023,49, 583–590, [arXiv:astro-ph.HE/2311.17488]. https: //doi.org/10.1134/S1063773723100031

    doi

  18. [26]

    The influence of vacuum polarization on plasma braking and radiation transfer in subcritical X-ray pulsars.Mon

    Markozov, I.D.; Potekhin, A.Y.; Kaminker, A.D.; Mushtukov, A.A. The influence of vacuum polarization on plasma braking and radiation transfer in subcritical X-ray pulsars.Mon. Not. R. Astron. Soc., to be submitted

  19. [27]

    Ginzburg, V .L.The Propagation of Electromagnetic Waves in Plasmas, 2nd ed.; Freeman and Co.: New York, 1970

    1970

  20. [28]

    The transfer equations for normal waves and radiation polarization in an anisotropic medium.Sov

    Gnedin, Y.N.; Pavlov, G.G. The transfer equations for normal waves and radiation polarization in an anisotropic medium.Sov. Phys. – JETP1974,38, 903–908

  21. [29]

    The effect of vacuum birefringence on the polarization of X-ray binaries and pulsars.Astrophys

    Novick, R.; Weisskopf, M.C.; Angel, J.R.P .; Sutherland, P .G. The effect of vacuum birefringence on the polarization of X-ray binaries and pulsars.Astrophys. J.1977,215, L117–L120. https://doi.org/10.1086/182492

    1977 doi

  22. [30]

    The effect of vacuum birefringence in a magnetic field on the polarization and beaming of X-ray pulsars.Soviet Astronomy Letters1978,4, 117–119

    Gnedin, Y.N.; Pavlov, G.G.; Shibanov, Y.A. The effect of vacuum birefringence in a magnetic field on the polarization and beaming of X-ray pulsars.Soviet Astronomy Letters1978,4, 117–119

  23. [31]

    Vacuum polarization by a magnetic field and its astrophysical manifestations.Sov

    Pavlov, G.G.; Gnedin, Y.N. Vacuum polarization by a magnetic field and its astrophysical manifestations.Sov. Sci. Rev. E: Astrophys. Space Phys. Rev.1984,3, 197

    1984

  24. [32]

    Resonant Conversion of Photon Modes Due to Vacuum Polarization in a Magnetized Plasma: Implications for X-Ray Emission from Magnetars.Astrophys

    Lai, D.; Ho, W.C.G. Resonant Conversion of Photon Modes Due to Vacuum Polarization in a Magnetized Plasma: Implications for X-Ray Emission from Magnetars.Astrophys. J.2002,566, 373–377, [arXiv:astro-ph/astro-ph/0108127]. https://doi.org/10.108 6/338074

    2002 arXiv

  25. [33]

    Atmospheres and spectra of strongly magnetized neutron stars - II

    Ho, W.C.G.; Lai, D. Atmospheres and spectra of strongly magnetized neutron stars - II. The effect of vacuum polarization.Mon. Not. R. Astron. Soc.2003,338, 233–252, [arXiv:astro-ph/astro-ph/0201380]. https://doi.org/10.1046/j.1365-8711.2003.06047.x

    2003 doi arXiv

  26. [34]

    Transfer of Polarized Radiation in Strongly Magnetized Plasmas and Thermal Emission from Magnetars: Effect of Vacuum Polarization.Astrophys

    Lai, D.; Ho, W.C.G. Transfer of Polarized Radiation in Strongly Magnetized Plasmas and Thermal Emission from Magnetars: Effect of Vacuum Polarization.Astrophys. J.2003,588, 962–974, [arXiv:astro-ph/astro-ph/0211315]. https://doi.org/10.1086/374334

    2003 doi arXiv

  27. [35]

    Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals.Mon

    van Adelsberg, M.; Lai, D. Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals.Mon. Not. R. Astron. Soc.2006,373, 1495–1522, [arXiv:astro-ph/astro-ph/0607168]. https://doi.org/10.1111/j.1365-2966. 2006.11098.x

    2006 doi arXiv

  28. [36]

    Statistical features of multiple Compton scattering in a strong magnetic field.Phys

    Mushtukov, A.A.; Markozov, I.D.; Suleimanov, V .F.; Nagirner, D.I.; Kaminker, A.D.; Potekhin, A.Y.; Portegies Zwart, S. Statistical features of multiple Compton scattering in a strong magnetic field.Phys. Rev. D2022,105, 103027, [arXiv:astro-ph.HE/2204.12271]. https://doi.org/...

    doi

  29. [37]

    Mészáros, P .High-Energy Radiation from Magnetized Neutron Stars; University of Chicago Press: Chicago, 1992

    1992

  30. [38]

    Compton and Thomson scattering in strong magnetic fields.Phys

    Herold, H. Compton and Thomson scattering in strong magnetic fields.Phys. Rev. D1979,19, 2868–2875. https://doi.org/10.110 3/PhysRevD.19.2868

  31. [39]

    LeVeque, R.J.Finite Volume Methods for Hyperbolic Problems; Cambridge Texts in Applied Mathematics, Cambridge University Press: Cambridge, 2002

    2002

  32. [40]

    The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations.J

    Colella, P .; Woodward, P .R. The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations.J. Computational Phys.1984, 54, 174–201. https://doi.org/10.1016/0021-9991(84)90143-8

    1984 doi

  33. [41]

    The thickness of accretionα-disks: Theory and observations.Astronomy Reports 2007,51, 549–562

    Suleimanov, V .F.; Lipunova, G.V .; Shakura, N.I. The thickness of accretionα-disks: Theory and observations.Astronomy Reports 2007,51, 549–562. https://doi.org/10.1134/S1063772907070049

    2007 doi

  34. [42]

    Spectrum formation in X-ray pulsars at very low mass accretion rate: Monte Carlo approach.Mon

    Mushtukov, A.A.; Suleimanov, V .F.; Tsygankov, S.S.; Portegies Zwart, S. Spectrum formation in X-ray pulsars at very low mass accretion rate: Monte Carlo approach.Mon. Not. R. Astron. Soc.2021,503, 5193–5203, [arXiv:astro-ph.HE/2006.13596]. https://doi.org/10.1093/mnras/stab811

    2021 doi

  35. [43]

    Vacuum polarization alters the spectra of accreting X-ray pulsars.Astron

    Sokolova-Lapa, E.; Stierhof, J.; Dauser, T.; Wilms, J. Vacuum polarization alters the spectra of accreting X-ray pulsars.Astron. Astrophys.2023,674, L2, [arXiv:astro-ph.HE/2305.00475]. https://doi.org/10.1051/0004-6361/202346265

    2023 doi

  36. [44]

    Rotating stars in relativity.Living Reviews in Relativity2003,6, 3, [arXiv:gr-qc/gr-qc/0302034]

    Stergioulas, N. Rotating stars in relativity.Living Reviews in Relativity2003,6, 3, [arXiv:gr-qc/gr-qc/0302034]. https://doi.org/10 .12942/lrr-2003-3

    2003

  37. [45]

    Pulse profiles of millisecond pulsars and their Fourier amplitudes.Mon

    Poutanen, J.; Beloborodov, A.M. Pulse profiles of millisecond pulsars and their Fourier amplitudes.Mon. Not. R. Astron. Soc. 2006,373, 836–844, [arXiv:astro-ph/astro-ph/0608663]. https://doi.org/10.1111/j.1365-2966.2006.11088.x

    2006 doi arXiv

  38. [46]

    Relativistic rotating vector model for X-ray millisecond pulsars.Astron

    Poutanen, J. Relativistic rotating vector model for X-ray millisecond pulsars.Astron. Astrophys.2020,641, A166, [arXiv:astro- ph.HE/2006.10448]. https://doi.org/10.1051/0004-6361/202038689

    2020 doi

  39. [47]

    Accurate analytic formula for light bending in Schwarzschild metric.Astron

    Poutanen, J. Accurate analytic formula for light bending in Schwarzschild metric.Astron. Astrophys.2020,640, A24, [arXiv:astro- ph.HE/1909.05732]. https://doi.org/10.1051/0004-6361/202037471

    2020 doi

  40. [48]

    Misner, C.W.; Thorne, K.S.; Wheeler, J.A.Gravitation; Freeman and Co.: New York, 1973

    1973

  41. [49]

    Timing characteristics of the hard X-ray emission from bright X-ray pulsars based on INTEGRAL data.Astronomy Letters2009,35, 433–456, [arXiv:astro-ph.HE/0907.4288]

    Lutovinov, A.A.; Tsygankov, S.S. Timing characteristics of the hard X-ray emission from bright X-ray pulsars based on INTEGRAL data.Astronomy Letters2009,35, 433–456, [arXiv:astro-ph.HE/0907.4288]. https://doi.org/10.1134/S1063773709070019. https://doi.org/10.3390/particles101...

    2026 doi

  42. [50]

    Energy-resolved pulse profiles of accreting pulsars: Diagnostic tools for spectral features

    Ferrigno, C.; D’Aì, A.; Ambrosi, E. Energy-resolved pulse profiles of accreting pulsars: Diagnostic tools for spectral features. Astron. Astrophys.2023,677, A103, [arXiv:astro-ph.HE/2308.03395]. https://doi.org/10.1051/0004-6361/202347062. https://doi.org/10.3390/particles1010000

    2023 doi

Pith tools

Reviewed May 13, 2026 · model on record in the stance chip above.