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Modelling the multi-wavelength emission and polarisation signatures of the novel white-dwarf pulsar system AR Sco

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A magnetic mirror fit to AR Sco's SED sets the white-dwarf surface field at 250–300 million gauss and the electron index near 2.9.

desk verdict A genuinely novel gyro-resolved emission code applied to AR Sco, with a plausible but under-determined SED fit whose headline B-field constraint shifts by a factor ~2.5 if you use the alternative TK17 normalisation. read the letter →

arxiv 2505.08567 v1 pith:YXEMTDEI submitted 2025-05-13 astro-ph.HE astro-ph.SR

Louis du Plessis This is my paper · ORCID
classification astro-ph.HEastro-ph.SR
keywords ARScowhitedwarfpulsarmagneticmirrormodelradiationreactionforcesAristotelianelectrodynamicssynchro-curvaturespectralenergydistributionfield
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

AR Scorpii is the first white-dwarf pulsar, and this thesis tries to show that its pulsed radio-to-X-ray emission can be explained by a magnetic mirror: electrons injected from the M-dwarf companion travel along the white dwarf's magnetic field, mirror near the pole, and radiate most of their energy there. The author reports that a gyro-resolved particle code with classical radiation reaction reproduces the observed spectral energy distribution, including the recent NICER pulsed X-ray points, with a white-dwarf surface field of $B_{\rm S}=(2.5-3.0)\times10^{8}$ G and an injected electron power-law index $p\sim2.9$. The thesis also claims that the solver converges to the Aristotelian Electrodynamics radiation-reaction limit, reproduces the emission maps of an independent pulsar model after calibration, and shows that mirror points and spectra depend strongly on field strength, perpendicular electric field, pitch angle, and Lorentz factor. If correct, this turns the magnetic mirror from a qualitative proposal into a quantitative, SED-based constraint on the white dwarf's field and particle injection physics.

What carries the argument

The carrying mechanism is the magnetic mirror itself: particles launched at the companion midpoint with an energy distribution $f(\gamma)\propto\gamma^{-p}$ and a uniform pitch-angle distribution $\theta_p\in[0^\circ,90^\circ]$ travel inward along one field line, lose energy through synchro-curvature radiation, and are turned around by the mirror force before reaching the white dwarf. The load-bearing numerical instrument is the Dormand–Prince 8(7) adaptive integrator, which solves the Lorentz force plus the classical radiation-reaction force under the assumption that the parallel electric field is screened; radiation is then accumulated along the $\mathbf{E}\times\mathbf{B}$-drifted trajectory using the synchro-curvature spectrum written in terms of an effective perpendicular field $\tilde{B}_\perp$, the calibration chapter's preferred prescription, rather than standard synchrotron formulas that assume no electric field. This machinery ties the SED to $B_{\rm S}$ and $p$: the field sets the mirror height, the particle index sets the spectral slope, and the radiation-reaction limit caps the particle energy.

What would settle it

Measure the Zeeman splitting of the white dwarf's Lyman-$\alpha$ (or surface cyclotron) lines: a surface field of $2.5\times10^{8}$ G would produce a measurable splitting, while the thesis notes that the existing non-detection already sets an upper limit near $10^{8}$ G, so a confirmed Zeeman limit below $2.5\times10^{8}$ G would rule out the fitted field unless the absorbing region is hidden. A complementary check is to compute the model's orbital-phase-resolved polarisation position angle from the emission maps and compare it directly with the Potter & Buckley polarimetry that the geometric fit used.

Watch

Extended reading notes

Core claim

In the author's own terms, the central result is that the magnetic mirror scenario proposed for AR Sco can be fitted to the observed multi-wavelength SED, including the recent NICER pulsed X-ray spectrum, and that the fit selects a white-dwarf surface dipole field of $B_{\rm S}=(2.5-3.0)\times10^{8}$ G together with an electron power-law index $p\sim2.9$; the implied synchrotron spectral index $(p-1)/2\sim0.95$ falls within the observationally estimated optical/UV range of 0.8–1.4. The fit is produced by solving the full equations of motion with the classical Landau–Lifshitz radiation-reaction force, following the particle's $\mathbf{E}\times\mathbf{B}$-drifted trajectory, and computing synchro-curvature radiation along that curve instead of applying standard synchrotron formulas that assume no electric field. A second reported result is that particles in strong $\mathbf{E}_\perp$-fields and radiation reaction enter the Aristotelian Electrodynamics radiation-reaction limit, confirming both the solver and the AE framework in outward-moving pulsar cases, while the AE trajectory equations are shown not to apply to inward-moving mirror particles.

Load-bearing premise

The fit assumes particles are injected along a single magnetic field line from the companion midpoint with a power-law energy spectrum, a uniform pitch-angle distribution, and a fully screened electric field parallel to $\mathbf{B}$; if those injection assumptions are wrong, the inferred surface field and electron index change.

Editorial extensions

If this is right

  • If the fit is right, AR Sco's white dwarf must carry a surface field of $250$–$300$ MG, strong enough to power the non-thermal emission by spin-down without invoking accretion.
  • Mirror points and radiative losses depend strongly on $\mathbf{E}_\perp$ and initial pitch angle, so earlier mirror models with decoupled transport equations mis-place the X-ray emission region.
  • The synchro-curvature radiation must be computed along the particle's $\mathbf{E}\times\mathbf{B}$-drifted curve; standard synchrotron formulas are not applicable in the high-$\mathbf{E}_\perp$ regime present here.
  • The radiation-reaction limit of Aristotelian Electrodynamics is reached in uniform and force-free pulsar fields, but not for inward-moving mirroring particles, so AE trajectories should not be used for the infall phase of a mirror model.
  • Orbital-phase-resolved polarimetry implies $\alpha$ varies by about $10^\circ$ and $\zeta$ by about $30^\circ$ across the orbit, with spin-coupled emission dominant at phases 0.1–0.6 and beat-coupled emission dominant at 0.6–1.1; self-consistent emission maps should reproduce this behaviour.

Reading between the lines

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

  • The quoted $B_{\rm S}$ range should be read as a first forward-modelling estimate: injecting over a bundle of field lines or a finite companion spot could shift the fitted field and index, so the range is not a uniqueness bound.
  • If the reported 40–100 yr precession of the white dwarf is real, the magnetic inclination angle drifts on that timescale; archival SEDs separated by decades could reveal a secular shift in mirror depth and spectral shape.
  • Running the same code on J1912-4410, the second white-dwarf pulsar, would test whether the same magnetic mirror parameters explain both sources or whether a different injection geometry is needed.
  • If the parallel electric field is only partially screened, the added acceleration would push mirror points deeper and harden the X-ray tail; this hardening could be searched for in the NICER pulsed spectrum as a function of orbital phase.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. This PhD-thesis manuscript develops a gyro-resolved particle-dynamics and emission code that includes classical radiation-reaction forces, validates it against Aristotelian Electrodynamics (AE) solutions and against the Harding/Kalapotharakos pulsar emission models, and then applies the code to the white-dwarf pulsar AR Sco in the magnetic-mirror scenario of Takata et al. (2017). The central claim is that the model can fit the multi-wavelength spectral energy distribution, including the recent NICER pulsed X-ray spectrum, thereby constraining the white-dwarf surface field to B_S = (2.5–3.0) × 10^8 G and the electron power-law index to p ≈ 2.9. The thesis also presents geometric rotating-vector-model fits to phase-resolved polarimetry and a Lomb-Scargle analysis separating spin- and beat-coupled emission, and it studies the effect of B-field, E⊥-field, initial pitch angle, and initial Lorentz factor on mirror points, spectra, and emission maps.

Significance. If the central SED constraint is robust, the result would be important for the newly established white-dwarf-pulsar class, because it would provide an independent, non-Zeeman estimate of the AR Sco magnetic field in a regime that is otherwise difficult to probe. The paper's validation strategy is a genuine strength: the particle solver is benchmarked against the AE radiation-reaction limit and against an independent gyro-centric pulsar emission code, and the comparison of the Cerutti/Kelner and Viganò synchro-curvature radiation methods is a useful practical contribution. The manuscript is also transparent about ambiguities in the Takata et al. (2017, 2019) setup, and it explicitly flags the non-independence of its normalisation equations. However, the headline B_S and p values are not yet backed by a quantitative fit statistic, and they depend on several load-bearing modelling choices whose sensitivity is not demonstrated. The exploratory nature of Chapter 6 is acknowledged, but the strength of the abstract's claim currently exceeds what the presented analysis supports.

major comments (4)
  1. [§6.2, Eqs. (6.2)–(6.5)] The normalisation of the modelled synchrotron flux is degenerate in a way that directly moves the headline B_S value. Equation (6.5) is explicitly not independent of Eq. (6.2) — the manuscript itself states this — and the two conditions give substantially different particle injection rates. For p = 2.9, γ_min = 50, and γ_max = 3.4 × 10^6, Eq. (6.2) yields ˙N_e ≈ 3 × 10^36 s^−1 while Eq. (6.5) yields ≈ 5 × 10^35 s^−1, a factor of roughly 6–7. Since the synchrotron flux scales with the injection rate at fixed B, matching the observed NICER flux with the adopted Eq. (6.5) normalisation requires B_S approximately √(6–7) ≈ 2.5 times larger than with the kinetic-power normalisation of Eq. (6.2). The quoted B_S = (2.5–3.0) × 10^8 G could therefore shift toward ≈ 1 × 10^8 G, near the Zeeman upper limit of ≤ 100 MG quoted in Chapter 1. The central B-field constraint is not robust until this choice is justified or the two normalisations are reconciled.
  2. [§6.3.1 and Abstract] The claim that the SED and NICER spectrum are fitted 'well' is not supported by any quantitative goodness-of-fit measure. No residuals, uncertainties, χ²/dof values, or comparison statistics are provided for the fits, and the setup adopts post hoc choices — orbital phase 0.25, α = 60° or 80°, ζ = 60° — rather than presenting a systematic parameter search or confidence intervals. As it stands, the stated constraints B_S = (2.5–3.0) × 10^8 G and p ≈ 2.9 are illustrative values from a single exploratory configuration, not demonstrated best-fit parameters with associated errors.
  3. [§6.1 and §6.2] The model is explicitly restricted to one magnetic field line ('I will thus start by modelling one field line in this exploratory work'), with injection from the companion midpoint, a power-law γ distribution, and a uniform pitch-angle distribution. Section 6.2 also notes that there is no indication how TK17/TK19 set up their particles or which field lines they used. Because the mirroring height, the emission pattern, and the SED normalisation all depend on these choices, the inferred B_S is conditional on an unvalidated injection geometry. The manuscript should either demonstrate insensitivity to field-line choice and orbital phase, or state the B-field constraint as conditional on the single-field-line assumption.
  4. [§6.1 and §6.2] The fully screened E_parallel assumption is adopted from Geng et al. (2016) without a sensitivity test. If E_parallel is not completely screened in the AR Sco magnetosphere, the particle acceleration and radiation-reaction balance change, which would alter the emitted spectra and therefore the fitted B_S and p. The paper correctly notes that only E_parallel is screened while E⊥ remains, but it does not explore even a small residual parallel electric field. A sensitivity study with a non-zero E_parallel should be included before the B-field constraint is presented as conclusive.
minor comments (4)
  1. [Chapter 5/6 cross-references] The text refers to 'Equations (21) in Chapter 4' and 'Equation (7) in Chapter 4'; these cross-references should give explicit equation numbers or be reformatted for the standalone article version.
  2. [§6.2 vs. Abstract] The displayed fits are described as using p = 3.0 from TK19, while the abstract and conclusions quote p ≈ 2.9; please reconcile the quoted power-law index with the value actually used in the fits.
  3. [Figure 6.1] The SED figure would be much easier to assess if each model curve were labelled with its B_S, p, α, ζ, and normalisation choice, and if the NICER pulsed points were visually distinguished from the XMM-Newton points and the upper limits.
  4. [General presentation] There are numerous typographical and formatting inconsistencies (for example, 'Du Plessis' vs 'du Plessis' in citations and '10% the B-field strength of Vela'); a careful language and reference pass would improve readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the AR Sco B-field and spectral index are fitted to external SED/NICER data, and the AE/calibration results are checked against independent analytic and code benchmarks.

full rationale

The central claim of the thesis (abstract and Section 6.3) is that the modelled SED, including the NICER pulsed X-ray spectrum, can be fitted with a white-dwarf surface field B_S = (2.5-3.0) x 10^8 G and electron index p ~ 2.9. This is an explicit forward-model fit: B_S and p are scanned model parameters selected by matching the observed multi-wavelength SED, not quantities derived from the model alone. No equation defines B_S in terms of the SED or vice versa, so there is no self-definitional reduction. The only coupling that could be mistaken for circularity is the spectral normalisation discussed in Section 6.2: the thesis quotes Equation (6.5) and immediately states 'A problem with this approach is that Equation (6.5) is not independent from Equation (6.2) since they use L_B to calculate Ndot_e.' This is a disclosed model degeneracy: the absolute flux normalisation is anchored to the magnetic dissipation power L_B, which itself scales with the assumed B-field, so the inferred B_S is conditional on the adopted normalisation convention. That is a genuine caveat about robustness, but not a hidden circular step, because the SED data are external and the fit does not rename an input as a prediction. The AE convergence tests are validated against the analytic Aristotelian-Electrodynamics expressions of Gruzinov (2012) and Kelner et al. (2015), and the Harding et al. calibration is an independent gyro-centric code; neither validation is equivalent to the present paper's own assumptions. Self-citations to du Plessis et al. (2022, 2024) are methodological (RVM fitting and particle-dynamics solver) and are not load-bearing for the AR Sco spectral fit. The screening of E_parallel is adopted from the external Geng et al. (2016) work; whether that screening is correct is a physical assumption, not a circularity. Overall, the derivation chain is self-contained against external benchmarks, and the disclosed normalisation ambiguity should be weighed as a modelling uncertainty rather than as circularity.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a forward model with several free parameters (B-field, particle index, angles) and explicit physical assumptions (screened E_parallel, single field line, power-law injection). These are all stated in the thesis, but the first three are not derived from first principles, controlling the strength of the SED constraint.

free parameters (7)
  • WD surface magnetic field B_S = 2.5 - 3.0 x 10^8 G
    Varied in the magnetic mirror model to fit the observed SED; the reported constraint is a fitted range, not a first-principles prediction.
  • Electron power-law index p = ~2.9
    Varied to match the optical/UV to X-ray SED; p=2.5 from TK17 produced too hard a spectrum, so p=3.0 was used (consistent with TK19).
  • Magnetic inclination angle alpha = 60 deg (also 80 deg)
    Adopted from TK17's estimate, with an alternative case at 80 degrees; not fitted to the SED.
  • Observer angle zeta = 60 deg
    Adopted from TK17; not fitted, though other observer angles are mentioned.
  • Orbital phase = 0.25
    Selected because Potter & Buckley (2018b) found maximum linear polarisation between orbital phases 0.2 and 0.5; this choice affects the geometry of the modelled emission.
  • gamma_min, gamma_max = 50, 3.4 x 10^6
    Adopted from TK17 and Geng et al. (2016) without re-derivation; the gamma_max comes from balancing acceleration and SR cooling.
  • Pitch-angle distribution = uniform 0-90 deg, step 5 deg
    Uniform pitch-angle prior in the particle injection, as in TK17.
assumptions (5)
  • domain assumption The classical Landau-Lifshitz radiation reaction force (with the field-gradient term neglected) is valid for the modelled regimes.
    Invoked in Chapter 4/5 when integrating equations of motion; the paper checks that the experienced E-field stays below the Schwinger limit for the AR Sco cases, but the neglect of the gradient term is an approximation used in most PIC codes.
  • ad hoc to paper The E_parallel field is fully screened in the AR Sco magnetosphere (Geng et al. 2016), so no parallel acceleration operates.
    Adopted from Geng et al. (2016) and TK17 without independent verification; if E_parallel is not screened, particle acceleration and emission would change significantly, altering the fitted parameters.
  • ad hoc to paper Particles are injected from the companion midpoint and propagate along a single magnetic field line.
    Chosen due to computational cost and because TK17's implementation is vague; the thesis notes this causes low-statistic emission maps and that multiple field lines are not sampled.
  • domain assumption The WD magnetosphere is described by a retarded dipole field inside 0.2 R_LC and a force-free FIDO field outside the ramp region.
    Used in the calibration (Chapter 5); for AR Sco, the retarded dipole field is used without the FF grid, which is an idealization.
  • ad hoc to paper The particle injection rate is normalised using the magnetic dissipation luminosity LB, which scales as mu^2, and the charge-conservation condition from TK17.
    The normalisation couples the fitted B-field to the overall flux; if the magnetic dissipation estimate is wrong, the spectral normalisation changes.

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Cite this review

Pith. "Pith review of Modelling the multi-wavelength emission and polarisation signatures of the novel white-dwarf pulsar system AR Sco." pith.science (2026). https://pith.science/paper/YXEMTDEI

@misc{pith2026250508567,
  author       = {Pith},
  title        = {Pith review of: Modelling the multi-wavelength emission and polarisation signatures of the novel white-dwarf pulsar system AR Sco},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YXEMTDEI}},
  note         = {Machine review of arXiv:2505.08567}
}
abstract

The reclassification of AR Scorpii (AR Sco) from a delta Scuti variable star to a white dwarf binary system has initiated an in-depth exploration of this novel system. The main aim of this work was to develop a general emission code to concurrently model the emission maps, light curves, and spectra at various orbital phases for AR Sco. For the development of the emission code, I solved the general equations of motion with included classical radiation reaction forces (RRF) by implementing the Dormand-Prince 8(7) numerical integrator with adaptive time-step methods. This yielded improved accuracy and computational time vs. the commonly used Vay symplectic integrator, particularly for the high $B$-fields, $E_{\perp}$-fields, and RRF needed for pulsar and pulsar-like magnetospheres. Additionally, I demonstrated the novel result of the particles entering and conforming to the radiation reaction limit regime of Aristotelian Electrodynamics. As calibration for the radiation calculations, emission maps, and spectra I compared my model output with results from the code of the pulsar emission model of Harding and collaborators for a pulsar with $10\%$ the $B$-field strength of Vela and how my results converged to theirs. Next, I showed my exploratory modelling of the magnetic mirror scenario proposed for AR Sco. I demonstrate I could fit the observational spectral energy distribution including the recent \textit{NICER} pulsed X-ray spectrum well, constraining the white dwarf $B$-field to $B_{\rm S} = (2.5 - 3.0) \times 10^{8} \, \rm{G}$. Finally, I showed the effect the $B$-field, $E_{\perp}$-field, initial pitch angle, and initial particle Lorentz factor have on the mirror points, RRF, emission maps, and spectra. This demonstrates how crucial it is to include the general particle dynamics to accurately model the micro-physics present in magnetic mirror models.

Figures

Figures reproduced from arXiv: 2505.08567 by the authors.

Figure 2.1
Figure 2.1. Equipotential surfaces of a binary system where the stellar bodies are shown by the black dots marked 1 and 2 and centre of mass as an x (Carroll & Ostlie, 2017). The inner La￾grangian point is located at the intersecting point numbered 1. A close binary system can now be defined as a system where the two stars in the system share a common envelope. If we assume the binary system has a circular orbit, then using New… view at source ↗
Figure 2.2
Figure 2.2. PsP˙ s diagram where the positive-slope dashed lines indicate the age of the pulsar and the negative-slope dashed lines indicate the surface B-field strength (Gotthelf et al., 2013). assumed, with the interior B-field being Bin = BS⃗ez ∥ µ (Padmanabhan, 2001). Since inside the conductor E · B = 0, Goldreich & Julian (1969) showed that the Maxwell equations yield Ein + (Ω × r) c × Bin = 0 Ein = − B0Ωr sin θ c (sin θe… view at source ↗
Figure 2.3
Figure 2.3. A pulsar magnetosphere showing the light cylinder and the slant dashed line indicating where Ω · B = 0 (ρGJ = 0) from Goldreich & Julian (1969). acceleration component, assuming a∥ = 0. Using the Lamour formula and substituting the frame￾invariant scalar product of the four-vector acceleration a · a yields P = 2e 2a · a 3c 3 = 2e 2γ 4 3c 3  a 2 ⊥ + γ 2 a 2 ∥  = 2e 2γ 4 3c 3 ωgv 2 ⊥ = 2e 2γ 4 3c 3  eB γmc2 (v sin… view at source ↗
Figures from the paper (46 more)
Figure 2.4
Figure 2.4. Figure 2.4: The principal axis of the polarisation ellipse where the E-field components are rotated by an angle χ (Rybicki & Lightman, 2008). we may write in the case of elliptical polarisation: E ′ x = ξ0 cos β cos ωt, E′ y = −ξ0 sin β cos ωt, (2.43) [PITH_FULL_IMAGE:figures/f…
Figure 2.5
Figure 2.5. Figure 2.5: Schematic of the radio emission beam of a pulsar, indicating all the geomet￾ric angles associated with the emission beam (Lorimer & Kramer, 2005) [PITH_FULL_IMAGE:figures/full_fig_p025_2_5.png]
Figure 1
Figure 1. Figure 1: Emission maps generated using the code from AH15; BH22, and using the parameters discussed in Section 2.3, and for a photon energy range of 100 MeV − 50 GeV and 𝐵S = 8 × 1012 G. Panel a) shows the CR emission map using the unscreened 𝑟ovc region between 𝑟ovc : 0.9 − 0.…
Figure 2
Figure 2. Figure 2: Calibration case using 𝐵S = 8 × 1010 G, showing ∇ · B in red and the 𝐸-field experienced by the particle normalised by the Schwinger field in blue [PITH_FULL_IMAGE:figures/full_fig_p071_2.png]
Figure 3
Figure 3. Figure 3: Vela-like calibration case using 𝐵S = 8 × 1011 G, showing ∇ · B in red and the 𝐸-field experienced by the particle normalised by the Schwinger field in blue. case and not the 𝐵S = 8 × 1012 G case included in the Appendix is mentioned in the previous section and will be…
Figure 4
Figure 4. Figure 4: Particle position plot for the Vela-like calibration case using 𝐵S = 8 × 1011 G, where the red line represents our model results without RRF, the magenta line the case with RRF, and the blue line the position components of the BH22 model. In panel a) we show the 𝑥-comp…
Figure 5
Figure 5. Figure 5: Components of particle direction for the same case as in [PITH_FULL_IMAGE:figures/full_fig_p073_5.png]
Figure 6
Figure 6. Figure 6: Results for the Vela-like case as in [PITH_FULL_IMAGE:figures/full_fig_p074_6.png]
Figure 7
Figure 7. Figure 7: Calibration case of [PITH_FULL_IMAGE:figures/full_fig_p075_7.png]
Figure 8
Figure 8. Figure 8: The AE convergence results for the case as in [PITH_FULL_IMAGE:figures/full_fig_p076_8.png]
Figure 9
Figure 9. Figure 9: Results for the Vela-like case as in [PITH_FULL_IMAGE:figures/full_fig_p076_9.png]
Figure 10
Figure 10. Figure 10: Results for the 𝜌c values for the 𝐵S = 8 × 1010 G case. All the results are calculated using our model using the different equations from Section 2, except for the black curve. Our model results are shown in red, the 𝜌c from the BH22 model in black, 𝜌eff from KP15 in …
Figure 11
Figure 11. Figure 11: The single-particle spectra for the same case as [PITH_FULL_IMAGE:figures/full_fig_p078_11.png]
Figure 12
Figure 12. Figure 12: The single-particle spectra for an SR-dominant case using RD fields with 𝐵S = 8×106 G, 𝑅 min acc = 4.0×10−4cm−1 , 𝑅 max acc = 2.5×10−3cm−1 , 𝛾0 = 1×106 , and initial 𝜃p = 60◦ . We have plotted the standard CR spectrum in orange and the standard SR spectrum in blue. Th…
Figure 13
Figure 13. Figure 13: The single-particle spectra for the same case as [PITH_FULL_IMAGE:figures/full_fig_p078_13.png]
Figure 14
Figure 14. Figure 14: CR emission maps produced by our model for the Vela-like 𝐵S = 8 × 1011 G case discussed in Section 3.2. In panels a), c) and e), we show emission maps using 𝑟ovc = 0.96 and in panels b), d) and f), we show emission maps using the slot gap between 𝑟ovc = 0.9 and 𝑟ovc =…
Figure 15
Figure 15. Figure 15: Emission maps using our model parameters for the Vela-like 𝐵S = 8 × 1010 G case, discussed in Section 3.1. In panels a), c) and e), we show emission maps using 𝑟ovc = 0.96, and in panels b), d) and f), we show emission maps using the slot gap between 𝑟ovc = 0.9 and 𝑟o…
Figure 16
Figure 16. Figure 16: Spectra for the Vela-like 𝐵S = 8 × 1011 G case using 𝑅 min acc = 4.0 × 10−2 cm−1 and 𝑅 max acc = 2.5 × 10−1 cm−1 . The spectra in this figure are produced with our model using the different radiation calculations from Section 2. The CR spectrum is plotted in orange, t…
Figure 17
Figure 17. Figure 17: Emission maps generated using the code from BH22 for the parameters discussed in Section 2.3. Panels a) and b) are similar to those in [PITH_FULL_IMAGE:figures/full_fig_p085_17.png]
Figure 19
Figure 19. Figure 19: Vela calibration case using 𝐵S = 8 × 1012 G, showing ∇ · B in red and the 𝐸-field experienced by the particle normalised by the Schwinger field in blue. panel d) is also above that of their model, but starts to converge to their result at 2.0𝑅LC. For the AE convergenc…
Figure 20
Figure 20. Figure 20: Vela-like calibration case using 𝐵S = 8 × 1011 G, when limiting with 𝛾𝑐, showing the corrected observer emission phase in panel a), normalised particle velocity components in panel b), 𝜌c in panel c), and 𝛾 in panel d). Here DPM represents our results and BHM the AH15…
Figure 21
Figure 21. Figure 21: The AE convergence results for the Vela-like case using 𝐵S = 8 × 1011 G, when limiting with 𝛾𝑐. In this plot DPM labels our model results, AE those of Gruzinov (2012), and AE-k those of KP15 where these curves overlap. Panel a) shows the particle 𝑥-direction, panel b)…
Figure 22
Figure 22. Figure 22: Results for the Vela-like case using 𝐵S = 8 × 1011 G, with panel a) showing our 𝛾 results in red 𝛾c in blue, and 𝛾SRR in green. Panel b) shows our particle 𝜌c in red and the effective 𝜌c from KP15 in blue. Panel c) shows the different force components, namely the Lore…
Figure 23
Figure 23. Figure 23: Vela calibration case using 𝐵S = 8 × 1012 G when limiting with 𝛾𝑐, showing the observer-corrected emission phase in panel a), normalised particle velocity components in panel b), 𝜌c in panel c), and 𝛾 in panel d). Here DPM labels our results and BHM the AH15 model res…
Figure 24
Figure 24. Figure 24: The AE convergence results for the Vela case using 𝐵S = 8 × 1012 G. In this plot DPM labels our model results, AE those of Gruzinov (2012), and AE-k those of KP15 where these curves overlap. Panel a) shows the particle 𝑥-direction, panel b) the 𝑦-direction, and panel …
Figure 25
Figure 25. Figure 25: Results for the Vela case using 𝐵S = 8 × 1012 G, with panel a) showing our 𝛾 results in red, 𝛾c in blue, and 𝛾SRR in green. Panel b) shows our particle 𝜌c in red and the effective 𝜌c from KP15 in blue. Panel c) shows the different force components, namely the Lorentz …
Figure 26
Figure 26. Figure 26: The AE convergence results for the RD case using 𝐵S = 8 × 108 G. In this plot DPM labels is our model results, AE those of Gruzinov (2012), and AE-k those of KP15. Panel a) shows the particle 𝑥-direction, panel b) the 𝑦-direction and panel c), the 𝑧-direction. In pane…
Figure 27
Figure 27. Figure 27: In this plot for a mirror scenario, DPM labels our model results, AE those of Gruzinov (2012), and AE-k those of KP15. Panel a) shows the particle 𝑥-direction, panel b) the 𝑦-direction, and panel c) the 𝑧-direction. In panel d) we show the various angles discussed in …
Figure 28
Figure 28. Figure 28: Results for the case as shown in [PITH_FULL_IMAGE:figures/full_fig_p091_28.png]
Figure 29
Figure 29. Figure 29: CR emission map using our model’s own 𝜌c with a similar setup to [PITH_FULL_IMAGE:figures/full_fig_p092_29.png]
Figure 6.1
Figure 6.1. Figure 6.1: AR Sco magnetic mirror model SED using a power-law index of p = 3.0, ζ = 60◦ , and plotted with the multi-wavelength observational data. The spectra include are, the BS = 4.0 × 108 G and α = 60◦ case (TK19 “best-fit parameters”) plotted in pale blue, the BS = 6.0 × 1…
Figure 6.2
Figure 6.2. Figure 6.2: The particle trajectories for various initial γ and θp values using BS = 6.0 × 107 G and BS = 3.0 × 108 G for the high B-field case. The initial particle parameters are as shown in the legend where the blue, red, purple and brown curves are overlapping. The axis is n…
Figure 6.3
Figure 6.3. Figure 6.3: The same initial particle parameters used in [PITH_FULL_IMAGE:figures/full_fig_p101_6_3.png]
Figure 6.4
Figure 6.4. Figure 6.4: I have plotted the non-normalised single-particle spectra using BS = 4.0 × 108 G, α = 60◦ , and ζ = 60◦ . For the first set of spectra, I show the spectrum for 4 particle pitch angles with γ ∼ 5 × 105 namely, θp = 5◦ plotted in blue, θp = 15◦ plotted in orange, θp = …
Figure 6.5
Figure 6.5. Figure 6.5: The same as in [PITH_FULL_IMAGE:figures/full_fig_p103_6_5.png]
Figure 6.6
Figure 6.6. Figure 6.6: AR Sco emission map produced using BS = 6 × 108 G, α = 60◦ , and p = 3.0. I show the ζ = 60◦ cut in purple used to concurrently produce the spectra in [PITH_FULL_IMAGE:figures/full_fig_p104_6_6.png]
Figure 6.7
Figure 6.7. Figure 6.7: AR Sco emission map produced using BS = 4 × 108 G, α = 60◦ , and p = 3.0. I show the ζ = 60◦ cut in purple used to concurrently produce the spectra in [PITH_FULL_IMAGE:figures/full_fig_p105_6_7.png]
Figure 6.8
Figure 6.8. Figure 6.8: AR Sco emission map produced using BS = 2.5 × 108 G, α = 60◦ , p = 3.0, and γmin = 10. I show the ζ = 60◦ cut in purple used to concurrently produce the spectra in [PITH_FULL_IMAGE:figures/full_fig_p105_6_8.png]
Figure 6.9
Figure 6.9. Figure 6.9: AR Sco emission map produced using BS = 4 × 108 G, α = 60◦ , and p = 3.0 with the E⊥-field excluded. I show the ζ = 60◦ cut in purple used to concurrently produce the spectra in [PITH_FULL_IMAGE:figures/full_fig_p107_6_9.png]
Figure 6.10
Figure 6.10. Figure 6.10: AR Sco emission map produced using BS = 4 × 108 G, α = 80◦ and p = 3.0. I show the ζ = 60◦ cut in purple used to concurrently produce the spectra in [PITH_FULL_IMAGE:figures/full_fig_p107_6_10.png]
Figure 6.11
Figure 6.11. Figure 6.11: AR Sco emission map produced using the same parameters as [PITH_FULL_IMAGE:figures/full_fig_p108_6_11.png]
Figure 6.12
Figure 6.12. Figure 6.12: AR Sco emission map for the same scenario as [PITH_FULL_IMAGE:figures/full_fig_p109_6_12.png]
Figure 6.13
Figure 6.13. Figure 6.13: AR Sco emission map for the same scenario as [PITH_FULL_IMAGE:figures/full_fig_p109_6_13.png]
Figure 6.14
Figure 6.14. Figure 6.14: AR Sco emission map for the same scenario as [PITH_FULL_IMAGE:figures/full_fig_p110_6_14.png]
Figure 6.16
Figure 6.16. Figure 6.16: AR Sco light curve produced from the emission map in [PITH_FULL_IMAGE:figures/full_fig_p110_6_16.png]
Figure 6.17
Figure 6.17. Figure 6.17: AR Sco light curve produced from the emission map in [PITH_FULL_IMAGE:figures/full_fig_p111_6_17.png]

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  1. Towards Modelling AR Sco: Calibration -- Reproducing High-Energy Pulsar Emission and Testing Convergence to Aristotelian Electrodynamics

    astro-ph.HE 2025-06 conditional novelty 6.0 of 10

    A gyro-phase-resolved pulsar emission code calibrated against a gyro-centric model reproduces its curvature radiation maps and spectra for a Vela-like pulsar and converges to the Aristotelian Electrodynamics limit.

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Works this paper leans on

77 extracted references · 27 canonical work pages · cited by 1 Pith paper

  1. [1]

    1983, ApJ, 266, 215, doi:10.1086/160771

    Arons, J. 1983, ApJ, 266, 215, doi:10.1086/160771

    doi:10.1086/160771 1983

  2. [2]

    K., Kalapotharakos, C., & Johnson, T

    Barnard, M., Venter, C., Harding, A. K., Kalapotharakos, C., & Johnson, T. J. 2022, ApJ, 925, 184, doi:10.3847/1538-4357/ac2a3d

    doi:10.3847/1538-4357/ac2a3d 2022

  3. [3]

    2018, MNRAS, 476, L10, doi:10.1093/mnrasl/sly022

    Bednarek, W. 2018, MNRAS, 476, L10, doi:10.1093/mnrasl/sly022

    work page doi:10.1093/mnrasl/sly022 2018

  4. [4]

    Belyaev, M. A. 2015, MNRAS, 449, 2759, doi:10.1093/mnras/stv468 Ben´ aˇ cek, J., Timokhin, A., Mu˜ noz, P. A., et al. 2024, arXiv e-prints, arXiv:2405.20866, doi:10. 48550/arXiv.2405.20866

    arXiv doi:10.48550/arxiv.2405.20866 2015

  5. [5]

    G., & Ikhsanov, N

    Beskrovnaya, N. G., & Ikhsanov, N. R. 2024, Astrophysical Bulletin, 79, 104, doi:10.1134/ S1990341323600254

    work page 2024

  6. [6]

    R., & Gould, R

    Blumenthal, G. R., & Gould, R. J. 1970, Reviews of Modern Physics, 42, 237 B¨ ottcher, M., Harris, D. E., & Krawczynski, H. 2012, Relativistic Jets from Active Galactic Nuclei, Vol. 1 (Wiley Online Library)

    work page 1970

  7. [7]

    N., Harding, A

    Brambilla, G., Kalapotharakos, C., Timokhin, A. N., Harding, A. K., & Kazanas, D. 2018, ApJ, 858, 81, doi:10.3847/1538-4357/aab3e1

    doi:10.3847/1538-4357/aab3e1 2018

  8. [8]

    Buckley, D. A. H., Meintjes, P. J., Potter, S. B., Marsh, T. R., & G¨ ansicke, B. T. 2017, Nature Astronomy, 1, 0029, doi:10.1038/s41550-016-0029

    doi:10.1038/s41550-016-0029 2017

Show all 77 references
  1. [9]

    E., & Paschalidis, V

    Cai, Y., Gralla, S. E., & Paschalidis, V. 2023, Phys. Rev. D, 108, 063018, doi:10.1103/PhysRevD. 108.063018

    2023 doi

  2. [10]

    W., & Ostlie, D

    Carroll, B. W., & Ostlie, D. A. 2017, An introduction to modern astrophysics (Cambridge University Press)

    2017

  3. [11]

    Cerutti, B., Mortier, J., & Philippov, A. A. 2016a, MNRAS, 463, L89, doi:10.1093/mnrasl/slw162

    doi

  4. [12]

    2015, MNRAS, 448, 606, doi:10.1093/ mnras/stv042 120 Louis du Plessis 121

    Cerutti, B., Philippov, A., Parfrey, K., & Spitkovsky, A. 2015, MNRAS, 448, 606, doi:10.1093/ mnras/stv042 120 Louis du Plessis 121

    2015

  5. [13]

    A., & Spitkovsky, A

    Cerutti, B., Philippov, A. A., & Spitkovsky, A. 2016b, MNRAS, 457, 2401, doi:10.1093/mnras/ stw124

    doi

  6. [15]

    Y., & Beloborodov, A

    Chen, A. Y., & Beloborodov, A. M. 2014, ApJ, 795, L22, doi:10.1088/2041-8205/795/1/L22

    2014 doi

  7. [16]

    F., et al

    Chen, F. F., et al. 1984, Introduction to plasma physics and controlled fusion, Vol. 1 (Springer), doi:10.1007/978-3-319-22309-4

    1984 doi

  8. [17]

    1999, The Astrophysical Journal, 511, 351, doi:10

    Contopoulos, I., Kazanas, D., & Fendt, C. 1999, The Astrophysical Journal, 511, 351, doi:10. 1086/306652

    1999

  9. [18]

    K., & Harding, A

    Daugherty, J. K., & Harding, A. K. 1982, Astrophys. J, 252, 337, doi:10.1086/159561 —. 1983, The Astrophysical Journal, 273, 761, doi:10.1086/161411 Du Plessis, L. 2020, PhD thesis, North-West University (South Africa) Du Plessis, L., Venter, C., Harding, A. K., et al. 2024, M...

    1982 doi

  10. [19]

    1966, Reviews of Modern Physics, 38, 626

    Erber, T. 1966, Reviews of Modern Physics, 38, 626

    1966

  11. [20]

    1989, A&A, 225, 479

    Finkbeiner, B., Herold, H., Ertl, T., & Ruder, H. 1989, A&A, 225, 479

    1989

  12. [21]

    2019, ApJ, 872, 67, doi:10.3847/1538-4357/aafb2c

    Garnavich, P., Littlefield, C., Kafka, S., et al. 2019, ApJ, 872, 67, doi:10.3847/1538-4357/aafb2c

    2019 doi

  13. [22]

    2021, ApJ, 908, 195, doi:10.3847/ 1538-4357/abd4db

    Garnavich, P., Littlefield, C., Lyutikov, M., & Barkov, M. 2021, ApJ, 908, 195, doi:10.3847/ 1538-4357/abd4db

    2021

  14. [23]

    B., Buckley, D

    Garnavich, P., Potter, S. B., Buckley, D. A. H., et al. 2023, ApJ, 958, L22, doi:10.3847/2041-8213/ ad0be7

    2023 doi

  15. [24]

    2016, Astrophys

    Geng, J.-J., Zhang, B., & Huang, Y.-F. 2016, Astrophys. J. Lett., 831, L10, doi:10.3847/ 2041-8205/831/1/L10

    2016

  16. [25]

    1968, in Pulsating Stars (Springer), 74–75

    Gold, T. 1968, in Pulsating Stars (Springer), 74–75

    1968

  17. [26]

    Goldreich, P., & Julian, W. H. 1969, Astrophys. J, 157, 869, doi:10.1086/150119

    1969 doi

  18. [27]

    V., Halpern, J

    Gotthelf, E. V., Halpern, J. P., & Alford, J. 2013, Astrophys. J, 765, 58, doi:10.1088/0004-637X/ 765/1/58

    2013 doi

  19. [28]

    Gruzinov, A. 2008, J. Cosmology Astropart. Phys., 2008, 002, doi:10.1088/1475-7516/2008/11/ 002 —. 2012, arXiv e-prints, arXiv:1205.3367, doi:10.48550/arXiv.1205.3367

    2008 doi arXiv

  20. [29]

    K., & Kalapotharakos, C

    Harding, A. K., & Kalapotharakos, C. 2015, ApJ, 811, 63, doi:10.1088/0004-637X/811/1/63 Louis du Plessis 122 —. 2017, ApJ, 840, 73, doi:10.3847/1538-4357/aa6ead

    2015 doi

  21. [30]

    K., & Preece, R

    Harding, A. K., & Preece, R. 1987, ApJ, 319, 939, doi:10.1086/165510

    1987 doi

  22. [31]

    K., Tademaru, E., & Esposito, L

    Harding, A. K., Tademaru, E., & Esposito, L. W. 1978, Astrophysical Journal, 225, 226, doi:10. 1086/156486

    1978

  23. [32]

    K., Usov, V

    Harding, A. K., Usov, V. V., & Muslimov, A. 2005, arXiv e-prints, astro.https://arxiv.org/ abs/astro-ph/0510135

    2005 arXiv

  24. [33]

    K., Venter, C., & Kalapotharakos, C

    Harding, A. K., Venter, C., & Kalapotharakos, C. 2021, ApJ, 923, 194, doi:10.3847/1538-4357/ ac3084

    2021 doi

  25. [34]

    Hartle, J. B. 2003, Gravity: An introduction to Einstein’s general relativity, AAPT

    2003

  26. [35]

    Jackson, J. D. 1962, Classical Electrodynamics (John Wiley and Sons)

    1962

  27. [36]

    K., & Kazanas, D

    Kalapotharakos, C., Brambilla, G., Timokhin, A., Harding, A. K., & Kazanas, D. 2018, ApJ, 857, 44, doi:10.3847/1538-4357/aab550

    2018 doi

  28. [37]

    2009, A&A, 496, 495, doi:10.1051/0004-6361:200810281

    Kalapotharakos, C., & Contopoulos, I. 2009, A&A, 496, 495, doi:10.1051/0004-6361:200810281

    2009 doi

  29. [38]

    K., & Kazanas, D

    Kalapotharakos, C., Harding, A. K., & Kazanas, D. 2014, The Astrophysical Journal, 793, 97, doi:10.1088/0004-637x/793/2/97

    2014 doi

  30. [39]

    2012, ApJ, 749, 2, doi:10.1088/ 0004-637X/749/1/2

    Kalapotharakos, C., Kazanas, D., Harding, A., & Contopoulos, I. 2012, ApJ, 749, 2, doi:10.1088/ 0004-637X/749/1/2

    2012

  31. [40]

    K., & Kazanas, D

    Kalapotharakos, C., Wadiasingh, Z., Harding, A. K., & Kazanas, D. 2023, ApJ, 954, 204, doi:10. 3847/1538-4357/ace972

    2023

  32. [41]

    Katz, J. I. 2017, ApJ, 835, 150, doi:10.3847/1538-4357/835/2/150

    2017 doi

  33. [42]

    R., Prosekin, A

    Kelner, S. R., Prosekin, A. Y., & Aharonian, F. A. 2015, AJ, 149, 33, doi:10.1088/0004-6256/ 149/1/33

    2015 doi

  34. [43]

    Komissarov, S. S. 2002, MNRAS, 336, 759, doi:10.1046/j.1365-8711.2002.05313.x

    2002

  35. [44]

    D., & Lifshitz, E

    Landau, L. D., & Lifshitz, E. M. 1975, The classical theory of fields

    1975

  36. [45]

    2012, ApJ, 746, 60, doi:10.1088/0004-637X/746/1/60

    Li, J., Spitkovsky, A., & Tchekhovskoy, A. 2012, ApJ, 746, 60, doi:10.1088/0004-637X/746/1/60

    2012 doi

  37. [46]

    Longair, M. S. 1983, High energy astrophysics, Vol. 199 (Cambridge university press Cambridge)

    1983

  38. [47]

    R., & Kramer, M

    Lorimer, D. R., & Kramer, M. 2005, Handbook of pulsar astronomy, Vol. 4 (Cambridge university press)

    2005

  39. [48]

    Luo, Q., Shibata, S., & Melrose, D. B. 2000, Mon. Not. Roy. Astron. Soc., 318, 943, doi:10.1046/ j.1365-8711.2000.03791.x

    2000

  40. [49]

    2020, arXiv e-prints, arXiv:2004.11474.https:// arxiv.org/abs/2004.11474

    Lyutikov, M., Barkov, M., Route, M., et al. 2020, arXiv e-prints, arXiv:2004.11474.https:// arxiv.org/abs/2004.11474

    2020 arXiv

  41. [50]

    R., G¨ ansicke, B

    Marsh, T. R., G¨ ansicke, B. T., H¨ ummerich, S., et al. 2016, Nature, 537, 374, doi:10.1038/ nature18620

    2016

  42. [51]

    1983, MNRAS, 202, 495, doi:10.1093/mnras/202.2.495 Louis du Plessis 123

    Morini, M. 1983, MNRAS, 202, 495, doi:10.1093/mnras/202.2.495 Louis du Plessis 123

    1983 doi

  43. [52]

    2024, A&A, 684, A115, doi:10.1051/0004-6361/202347692

    Mottez, F. 2024, A&A, 684, A115, doi:10.1051/0004-6361/202347692

    2024 doi

  44. [53]

    G., & Harding, A

    Muslimov, A. G., & Harding, A. K. 2003, The Astrophysical Journal, 588, 430, doi:10.1086/368162

    2003 doi

  45. [54]

    P., & Gunn, J

    Ostriker, J. P., & Gunn, J. E. 1969, Astrophys. J, 157, 1395, doi:10.1086/150160 Paczy´ nski, B. 1971, ARA&A, 9, 183, doi:10.1146/annurev.aa.09.090171.001151

    1969

  46. [55]

    2001, Theoretical Astrophysics: Volume 2, Stars and Stellar Systems (Cambridge University Press)

    Padmanabhan, T. 2001, Theoretical Astrophysics: Volume 2, Stars and Stellar Systems (Cambridge University Press)

    2001

  47. [56]

    R., Buckley, D

    Pelisoli, I., Marsh, T. R., Buckley, D. A. H., et al. 2023, Nature Astronomy, 7, 931, doi:10.1038/ s41550-023-01995-x

    2023

  48. [57]

    2024, MNRAS, 527, 3826, doi:10.1093/mnras/stad3442 P´ etri, J

    Pelisoli, I., Sahu, S., Lyutikov, M., et al. 2024, MNRAS, 527, 3826, doi:10.1093/mnras/stad3442 P´ etri, J. 2023, A&A, 677, A72, doi:10.1051/0004-6361/202346515

    2024 doi

  49. [58]

    A., & Spitkovsky, A

    Philippov, A. A., & Spitkovsky, A. 2014, ApJ, 785, L33, doi:10.1088/2041-8205/785/2/L33 —. 2018, ApJ, 855, 94, doi:10.3847/1538-4357/aaabbc

    2014 doi

  50. [59]

    A., Spitkovsky, A., & Cerutti, B

    Philippov, A. A., Spitkovsky, A., & Cerutti, B. 2015, ApJ, 801, L19, doi:10.1088/2041-8205/ 801/1/L19

    2015 doi

  51. [60]

    B., & Buckley, D

    Potter, S. B., & Buckley, D. A. H. 2018a, Mon. Not. Roy. Astron. Soc., 478, L78, doi:10.1093/ mnrasl/sly078 —. 2018b, Mon. Not. Roy. Astron. Soc., doi:10.1093/mnras/sty2407

    doi

  52. [61]

    Radhakrishnan, V., & Cooke, D. J. 1969, Astrophys. J. Lett., 3, 225

    1969

  53. [62]

    W., & Yadigaroglu, I

    Romani, R. W., & Yadigaroglu, I. A. 1995, ApJ, 438, 314, doi:10.1086/175076

    1995 doi

  54. [63]

    B., & Lightman, A

    Rybicki, G. B., & Lightman, A. P. 2008, Radiative processes in astrophysics (John Wiley & Sons)

    2008

  55. [64]

    R., Belloni, D., G¨ ansicke, B

    Schreiber, M. R., Belloni, D., G¨ ansicke, B. T., Parsons, S. G., & Zorotovic, M. 2021, Nature Astronomy, 5, 648, doi:10.1038/s41550-021-01346-8

    2021 doi

  56. [65]

    K., Meintjes, P

    Singh, K. K., Meintjes, P. J., Kaplan, Q., Ramamonjisoa, F. A., & Sahayanathan, S. 2020, arXiv e-prints, arXiv:2006.12950.https://arxiv.org/abs/2006.12950

    2020 arXiv

  57. [66]

    2024, arXiv e-prints, arXiv:2406.14512, doi:10.48550/ arXiv.2406.14512

    Soudais, A., Cerutti, B., & Contopoulos, I. 2024, arXiv e-prints, arXiv:2406.14512, doi:10.48550/ arXiv.2406.14512

    2024 doi arXiv

  58. [67]

    2006, ApJ, 648, L51, doi:10.1086/507518

    Spitkovsky, A. 2006, ApJ, 648, L51, doi:10.1086/507518

    2006 doi

  59. [68]

    A., Littlefield, C., Garnavich, P., et al

    Stiller, R. A., Littlefield, C., Garnavich, P., et al. 2018, ArXiv e-prints.https://arxiv.org/abs/ 1802.04323

    2018 arXiv

  60. [69]

    Sturrock, P. A. 1971, Astrophys. J, 164, 529, doi:10.1086/150865

    1971 doi

  61. [70]

    1982, The Astrophysical Journal, 258, 335, doi:10.1086/160082

    Svensson, R. 1982, The Astrophysical Journal, 258, 335, doi:10.1086/160082

    1982 doi

  62. [71]

    Takata, J., & Cheng, K. S. 2019, ApJ, 875, 119, doi:10.3847/1538-4357/ab1259

    2019 doi

  63. [72]

    Takata, J., Hu, C.-P., Lin, L. C. C., et al. 2018, ApJ, 853, 106, doi:10.3847/1538-4357/aaa23d

    2018 doi

  64. [73]

    F., Wang, H

    Takata, J., Wang, X. F., Wang, H. H., et al. 2021, ApJ, 907, 115, doi:10.3847/1538-4357/abd0f8 Louis du Plessis

    2021 doi

  65. [74]

    Takata, J., Yang, H., & Cheng, K. S. 2017, Astrophys. J, 851, 143, doi:10.3847/1538-4357/aa9b33

    2017 doi

  66. [75]

    2014, Journal of Korean Astronomical Society, 47, 15, doi:10.5303/JKAS.2014.47.1

    Trippe, S. 2014, Journal of Korean Astronomical Society, 47, 15, doi:10.5303/JKAS.2014.47.1. 015

    2014 doi

  67. [76]

    Venter, C., & De Jager, O. C. 2010, ApJ, 725, 1903, doi:10.1088/0004-637X/725/2/1903 Vigan` o, D., Torres, D. F., Hirotani, K., & Pessah, M. E. 2015, MNRAS, 447, 1164, doi:10.1093/ mnras/stu2456

    2010 doi

  68. [77]

    L., Fonseca, R

    Vranic, M., Martins, J. L., Fonseca, R. A., & Silva, L. O. 2016, Computer Physics Communications, 204, 141, doi:10.1016/j.cpc.2016.04.002

    2016 doi

  69. [78]

    2018, ApJ, 864, L16, doi:10.3847/2041-8213/aada4f

    Yang, Y.-P., & Zhang, B. 2018, ApJ, 864, L16, doi:10.3847/2041-8213/aada4f

    2018 doi

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