Relativistic van Allen belts in magnetospheres of pulsars and white dwarfs

Maxim Lyutikov; Maxim V. Barkov

REVIEW 3 major objections 6 minor 1 cited by

Relativistic van Allen belts in magnetospheres of pulsars and white dwarfs

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read In a dipole magnetosphere, synchrotron losses split trapped relativistic particles into bouncing, freezing, and precipitating trajectories, and the beamed optical and X-ray emission encodes the field strength and viewing geometry.

desk verdict Novel classification of trapped-particle trajectories in magnetospheres, but the printed equations do not derive the integrated system; the scaling laws are model-calibrated and need a corrected derivation and code release. read the letter →

arxiv 2506.20515 v1 pith:PZUDBMRC submitted 2025-06-25 astro-ph.HE

Maxim V. Barkov , Maxim Lyutikov This is my paper · ORCID

classification astro-ph.HE

keywords relativisticvanAllenbeltspulsarmagnetosphereswhitedwarfsynchrotroncoolingmagneticmirrortrappingparticleprecipitationlight-curvemodelingARScorpii

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 argues that relativistic particles trapped in the dipole magnetospheres of neutron stars and white dwarfs—astrophysical analogs of Earth's van Allen belts—do not simply bounce forever. Once synchrotron losses are included, a trapped particle ends in one of three states: it keeps bouncing between magnetic mirrors, it freezes by shedding nearly all of its transverse motion before falling, or it precipitates onto the stellar surface while still relativistic. The authors derive approximate boundaries between these classes, $\alpha_{e,\mathrm{fl}} = 0.589\eta_c^{0.30}$ and $\alpha_{e,\mathrm{os}} = 1.079\eta_c^{0.30}$, and compute sky maps of the beamed optical and X-ray emission. If the picture is right, observed pulse shapes—single, double, flat-top, or asymmetric—can be read as diagnostics of the field strength, the injection latitude, and the viewing geometry in systems such as AR Sco, AE Aqr, and the double pulsar.

What carries the argument

The load-bearing object is the pair of dimensionless equations (Eqs. 2.27) governing $\gamma(r)$ and $\alpha(r)$ for a particle moving along a dipole field line, together with the cooling parameter $\eta_c = R_0/(c\tau_{c,0})$, the ratio of the equatorial field-line scale to the synchrotron cooling length. The dynamics is controlled by the competition between the adiabatic mirror force, which increases the pitch angle near the poles and holds the particle there, and the angle-averaged synchrotron radiation reaction, which removes transverse momentum. Near the magnetic equator the adiabatic term vanishes, so the initial motion is set purely by radiative losses; deeper in, the two forces fight, and the winner determines whether the particle bounces, freezes, or precipitates. This competition, not any exotic plasma process, is what generates the emission-pattern variety.

What would settle it

Integrate the same equations with the curvature-radiation term of Eq. (2.13) included for Lorentz factors above the threshold of Eq. (2.14): if the freezing band disappears or the boundary exponents change by more than the claimed 1%, the classification is not universal. Observationally, a phase-resolved optical and X-ray light curve of AR Sco whose peak separation or peak count does not follow the predicted dependence on $\eta_c$ and on the injection latitude (Figs. 8–9) would rule out the model as a description of that system.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the combination of magnetic bottling and synchrotron cooling in a static dipole field is rich enough to produce a sharp taxonomy of trapped-particle trajectories and a directly observable emission morphology. Solving the coupled equations for Lorentz factor and pitch angle along a field line, the authors identify oscillating, freezing, and precipitating trajectories, with the critical initial pitch angles separated according to a universal power of the dimensionless cooling parameter $\eta_c$ (Eqs. 3.3–3.4). The same calculation yields two-dimensional sky maps of synchrotron luminosity in optical and X-ray bands; the maps show that a single injection ring can produce single-peaked, double-peaked, flat-top, or asymmetric light curves depending on $\eta_c$, the injection latitude, and the observer's direction. The central practical claim is that multifrequency pulse profiles of these compact binaries are therefore invertible: they carry information about the magnetic field strength and the injection geometry of the radiating particles.

Load-bearing premise

The whole classification assumes a particle feels only the adiabatic mirror force and angle-averaged synchrotron drag in a static, non-rotating dipole field; any rotational electric field, pair cascade, wave-driven pitch-angle diffusion, or curvature radiation would change the trajectories and could erase the three classes.

Editorial extensions

If this is right

Observed single, double, flat-top, and asymmetric light curves in compact binaries can be used to estimate the magnetic field strength and the location where relativistic particles are injected.
Particles injected with pitch angles below $\alpha_{e,\mathrm{fl}}$ deposit their remaining energy directly onto the stellar surface, naturally producing the compact polar hot spots observed on white dwarfs.
Most of the synchrotron luminosity is emitted at pitch angles around $\pi/4$, so the emission cone is wide; only particles injected at very small pitch angles produce narrow beams.
In weakly cooling systems ($\eta_c \sim 10^{-5}$), emission accumulates toward specific azimuthal directions and produces two distinct peaks, whereas stronger cooling ($\eta_c \gtrsim 10^{-4}$) yields nearly constant equatorial emission.
The boundary laws $\alpha_{e,\mathrm{fl}} \propto \eta_c^{0.30}$ and $\alpha_{e,\mathrm{os}} \propto \eta_c^{0.30}$ hold for all $\eta_c < 0.1$, so the trajectory taxonomy survives across a wide range of magnetic field strengths.

Reading between the lines

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

If the same two-force competition operates in any strongly magnetized dipole, the freezing–precipitation boundary should also appear in planetary radiation belts when synchrotron cooling is artificially strong, for example in a hypothetical highly magnetized exoplanet; the maps here could be recomputed for a tilted, rotating dipole to predict phase-resolved polarization.
The model treats each particle independently, so it cannot yet predict whether radiation-reaction feedback—synchrotron photons heating the stellar surface, or pair production in pulsars—will alter the magnetosphere itself; including that feedback might make the light curves time-dependent.
The predicted boundary scaling is a clean target for a numerical experiment: a particle pusher with the full Lorentz force in a rotating dipole with an electric field would show where the static-field approximation breaks down.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

About arXiv:2506.20515: the paper gives a three-regime classification (oscillating, freezing, precipitating) for relativistic charged particles trapped in a dipole magnetosphere with synchrotron losses, and it computes optical/X-ray emission maps that could be useful for interpreting AR Sco, AE Aqr, the double pulsar, and transitional MSPs. The freezing regime, where particles radiate away transverse momentum before falling, is a genuinely interesting idea, and the qualitative argument leading to alpha_crit ~ eta^(3/10) is appealing.

The main problem is that the central equation system is not self-consistent as printed. Substituting (2.26) into (2.25) does not produce (2.27). I checked the algebra: for the energy equation you get a term eta0 gamma^2 beta sin alpha tan alpha (4-3r~)^(3/2)/(r~^6 sqrt(1-r~)) with the printed (2.25)-(2.26), while (2.27) has -2 eta0/(beta gamma) times the same factor; the ratio is not constant. For the pitch-angle radiative term the printed substitution gives a coefficient 1/4 of what (2.27) has. Also, (2.26) itself is missing a sqrt(r~) factor in the line-element conversion. Because Table 1 and the scaling laws come from integrating (2.27), those results are not grounded in the equations as presented. No code or data is shipped, so a reader cannot tell which system was actually integrated.

The scaling laws (3.3)-(3.4) are also fits to the same numerical runs that define the trajectory classes, so they are not independent predictions; the 3/10 exponent is motivated by a heuristic balance, but the coefficients are calibrated on the model itself. The emission treatment is simplified - no rotation, no pair cascades, no wave-particle diffusion, and curvature losses are dropped via a threshold - so applying the maps to real pulsars requires caution. The paper does not test its light curves against actual observations.

That said, the conceptual framework is novel and the qualitative separation of regimes is physically sensible. The paper deserves a serious referee, but not in its current form: the authors need to correct the derivation, clarify which equation set was integrated, and ideally provide the code or at least a reproducible description. If the equation issue is resolved and the scaling laws survive, this would be a useful reference for interpreting non-thermal emission from compact binary magnetospheres.

My recommendation: send it to peer review with a request for major revision. I would not cite it as-is, and I would not bring it to reading group until the equations are fixed.

Referee Report

3 major / 6 minor

Summary. The paper studies relativistic electrons trapped in a static, non-rotating dipole magnetosphere, combining adiabatic mirror force with synchrotron radiation reaction. It derives ordinary differential equations for the Lorentz factor and pitch angle along a field line (Eqs. 2.25 and 2.27), integrates them numerically, and classifies trajectories into three types: oscillating, freezing, and precipitating. It then fits critical pitch-angle boundaries as α_e,fl = 0.589 η_c^0.30 and α_e,os = 1.079 η_c^0.30, and constructs optical and X-ray synchrotron sky maps and light curves for various injection geometries. The final section applies the model qualitatively to AR Sco, AE Aqr, and transitional millisecond pulsars.

Significance. If the classification and scaling laws were supported by the equations, the paper would be a useful contribution: it formulates a tractable single-particle model of synchrotron losses in a dipole field, identifies a three-way trajectory classification, and connects it to concrete, falsifiable pulse-profile morphologies. The authors merit credit for stating the numerical method explicitly (ode15s with relative tolerance 1e-7), for giving an analytic scaling estimate α ~ η^{3/10}, and for clearly listing the main simplifying assumptions. However, because the central ODE system as printed is not derivable from the stated physics, the quantitative results — including the fitted coefficients in Eqs. (3.3)-(3.4) — are not currently established. The paper's qualitative framework may survive a corrected derivation, but the numerical claims need to be redone and verified.

major comments (3)

[2.3, Eqs. (2.25)-(2.28)] Equations (2.25) and (2.27) are inconsistent, and Eq. (2.28) is not the expansion of (2.27). Substituting Eq. (2.26) into Eq. (2.25), using sin^2θ = r̃, (3 cos 2θ + 5) = 2(4 − 3r̃), and csc^12θ = r̃^{-6}, gives dγ/dr̃ = −η0 γ^2 β sinα tanα (4−3r̃)^{3/2}/(√(1−r̃) r̃^6), whereas Eq. (2.27) has dγ/dr̃ = −2ηc (4−3r̃)^{3/2} sinα tanα/(βγ √(1−r̃) r̃^6); the ratio is 2/(γ^3β^2), not a constant. For the pitch-angle equation, the radiative term in Eq. (2.27) is four times larger than the term obtained by substituting (2.26) into the printed radiative term of (2.25), and still a factor two larger than the term from the physical equation (2.22). The adiabatic term in Eq. (2.27) does match the substitution. The starting solution (2.28) is an inconsistent hybrid: its dγ decrement has the γ^2β scaling that follows from (2.25), while its dα decrement matches (2.27). Since §3.2 and Table 1 are numerical solutions of Eq. (2.27), the three trajectory classes and the fitted boundaries (3.3)-(3.4) rest on an equation of motion that is not derived from the stated physics.
[3.2, Table 1, Eqs. (3.3)-(3.4)] The quantitative scaling laws are empirical fits to numerical solutions of Eq. (2.27), not predictions obtained independently of the integrated model. Because Eq. (2.27) is inconsistent as printed, the coefficients 0.589 and 1.079 and the exponent 0.30 in Eqs. (3.3)-(3.4) cannot be verified from the equations shown in the manuscript. No code or data is shipped to determine which system was actually integrated. The analytic estimate (3.2) involves only a rough balance of the two terms in the dα equation and cannot fix the prefactors. The authors should correct the equation of motion, rerun the integrations, and report whether the classification and the scaling laws survive; providing the integration code or trajectory data would greatly aid verification.
[1 and 4] The application claims are stronger than the idealized model supports. The model assumes a static, non-rotating dipole, no induced electric fields, no pair plasma or wave-particle pitch-angle diffusion, and no curvature radiation (with the threshold given by Eq. 2.14). In real pulsar and white dwarf magnetospheres these effects can alter the loss cone, the cooling rate, and the resulting light curves. The paper should explicitly discuss the conditions under which these omissions are justified for the target objects (AR Sco, AE Aqr, PSR J0737-3039B) and temper the statement that multi-frequency profiles 'can be used to get information about physical and geometrical properties' of these systems.

minor comments (6)

[2.1, Eq. (2.14)] Equation (2.14) is dimensionally inconsistent: γ is compared with √(cω_B/R_c), which has units of s^{-1}. The intended curvature-loss threshold should be restated with correct dimensions.
[2.3, Eq. (2.20)] The line element in Eq. (2.20) appears garbled: ds = R0 sinθ √(sin^2θ + 4 cosθ dθ) should presumably read ds = R0 sinθ √(sin^2θ + 4 cos^2θ) dθ. Please correct the notation and parenthesization.
[2.3, Eqs. (2.24)-(2.27)] The symbols η_c and η0 are used interchangeably (Eq. 2.24 defines η_c, while Eqs. 2.25, 2.27, and 3.2 use η0 or mix both). Define one symbol and use it consistently.
[2.3, Eq. (2.25)] The dθ/dt̃ equation in (2.25) does not match the physical equation (2.22): substituting sin^2θ = r̃ into (2.22) gives dθ/dt̃ = −β cosα/(√r̃ √(4−3r̃)), whereas (2.25) contains an extra factor 1/√(2r̃). Even though the trajectory integration uses Eq. (2.26) rather than the dθ equation, the inconsistency should be removed.
[3.2, Eqs. (3.3)-(3.4), Table 1] The text around Eqs. (3.3)-(3.4) is confusing: Eq. (3.3) is called the falling/precipitation boundary, Eq. (3.4) the frozen boundary, but Table 2 defines freezing as α_os ≥ α0 > α_fl. The sentence after Eq. (3.4), 'For the frozen trajectory, the pitch angle should be less when α_e,os = 1.079η_c^{0.30}', should be rephrased (probably 'less than α_e,os'). The sentence in §3.2 about 'frozen trajectories and precipitation trajectories are to keep its relative width independently of parameter η0' is incomplete and should be rewritten.
[Throughout] There are numerous typos and grammatical errors, including 'white dwarths' in the abstract, 'Combing' in §2.1, 'radaitive' in §3.1, 'in unable' in §4, and 'pith' in §4. In addition, the caption of Fig. 2 appears to mislabel the left/center/right panels relative to the figure content. A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the trajectory classification and scaling laws are derived from the stated ODEs and confirmed numerically, with only an illustrative non-load-bearing self-citation for the AR Sco parameter.

full rationale

The central derivation is self-contained: Eqs. (2.25) and (2.27) are the stated physical model (adiabatic mirror force plus synchrotron radiation reaction in a static dipole field), and the three trajectory classes are read off numerical solutions of those equations for varied η_c. The critical-angle scalings (3.3)–(3.4) are power-law fits to those numerical solutions, and the analytic estimate α_0 ∼ η_c^{3/10} in Eq. (3.2) is obtained by balancing the two competing terms in the α equation, not by assuming the exponent. The emission maps are forward-modeled from the same trajectories, so they are model predictions rather than fits to the observed light curves they are claimed to constrain. The AR Sco input η_0 = 1.25×10⁻⁴ is taken from the authors' previous work [6], but this is an illustrative parameter, not the source of the general trajectory classification; the paper scans η_c over several orders of magnitude in Table 1. No fitted parameter is renamed as a prediction, no self-citation supplies the load-bearing premise, and no ansatz is imported solely by citation. The printed algebraic inconsistency between Eqs. (2.25) and (2.27) is a correctness and reproducibility concern, not a circularity, and the absence of shipped code or data does not constitute circular reasoning. Under the hard rules, without a specific reduction of a claimed result to its own inputs, the appropriate finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard adiabatic mirror theory, the Landau-Lifshitz radiation reaction, and a static dipole field approximation. The key added inputs are the cooling parameter eta0 (borrowed from a prior AR Sco model) and the numerically fitted scaling coefficients. No new particles or forces are introduced.

free parameters (3)

eta0 (dimensionless cooling parameter) = 1.25e-4 for AR Sco; scanned over 1.25e-5 to 0.613
Central control parameter defined by Eq. (2.24); the AR Sco value is taken from the authors' prior model [6], and the scaling laws (3.3)-(3.4) are parameterized by it.
Scaling coefficients 0.589, 1.079, 234 = 0.589 eta^0.30, 1.079 eta^0.30, 234 eta^0.23
These coefficients are fitted to the numerically computed critical pitch angles in Table 1; they are not derived analytically and carry no quoted uncertainty.
Initial Lorentz factor and pitch angle grid = gamma0 in {2e3, 6e3, 2e4}; alpha0 in {0.005, 0.05, 0.5}
Chosen initial conditions for the numerical trajectory survey; emission maps use a gamma^-2 energy spectrum and uniform direction distribution.

assumptions (5)

domain assumption The first adiabatic invariant is conserved between synchrotron losses (sin alpha proportional to sqrt(B), Eq. 2.15).
This assumes the field varies slowly along the orbit and radiation reaction does not break the invariant beyond the additive term.
standard math Radiation reaction force takes the Landau-Lifshitz angle-averaged form in a magnetic field (Eq. 2.2).
Standard classical electrodynamics result; valid for gamma below the quantum critical value and for synchrotron-dominated cooling.
domain assumption Curvature emission is negligible because gamma is below the threshold in Eq. (2.14).
The authors state this regime is not achievable and neglect curvature emission.
domain assumption The magnetosphere is a static dipole with no electric fields or plasma screening.
The equations of motion (2.25), (2.27) consider only magnetic forces and radiation reaction; rotation and induced electric fields are ignored.
ad hoc to paper Particles are injected at the magnetic equator with uniform direction and dN/dgamma proportional to gamma^-2.
Injection procedure used to build emission maps; motivated by reconnection acceleration but not derived from first principles.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Relativistic van Allen belts in magnetospheres of pulsars and white dwarfs." pith.science (2026). https://pith.science/paper/PZUDBMRC

@misc{pith2026250620515,
  author       = {Pith},
  title        = {Pith review of: Relativistic van Allen belts in magnetospheres of pulsars and white dwarfs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PZUDBMRC}},
  note         = {Machine review of arXiv:2506.20515}
}

abstract

We consider dynamics and multi-frequency emission patterns of relativistic van Allen belts - particles trapped in the magnetosphere of neutron stars and white dwarths. We account for synchrotron radiative losses and effects of relativistic beaming of radiation. The system is non-Hamiltonian (non-energy conserving): this results in a wide non-scalable variety of spectral and temporal behaviors. There are three types of trapped particles' trajectories: (i) oscillating (particles experience multiple bounces between magnetic bottles); (ii) precipitating (particles fall onto the star with finite transverse momentum); (iii) freezing (particles lose their transverse motion before falling onto the star). The separation between regimes (i) and (ii) depends both on the ratio of the bounce time to cooling time at magnetic equator $\tau_{ 0} $, $\eta _0 = R_0/( c \tau_0) \leq 1$, as well as the initial pitch angle $\alpha_0$; regimes (i) and (ii) are separated at $ \alpha_{0, crit} \sim \eta_0^{3/10}$. Resulting emission patterns show large variety: single or double peaked, and/or flat hat with sharp walls. Multi-frequency profiles - in optical and X-ray bands - can be used to get information about physical (magnetic field strength, injection point) and geometrical (dipolar angle and the line of sight) properties.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Unraveling the emission mechanism powering long period radio transients from interacting white dwarf binaries via kinetic plasma simulations
astro-ph.HE 2025-09 conditional novelty 6.0 of 10

Kinetic plasma simulations show the electron cyclotron maser instability can produce efficient, narrowband, partially linearly polarized radio emission under conditions inferred for white dwarf-M dwarf binaries.

Reference graph

Works this paper leans on

16 extracted references · 12 canonical work pages · cited by 1 Pith paper

[1]

Akasofu and S

S.-I. Akasofu and S. Chapman, The Ring Current, Geomagnetic Disturbance, and the Van Allen Radiation Belts, Geophys. Res. 66 (1961) 1321

work page 1961
[2]

Alfven,Cosmical electrodynamics (1950)

H. Alfven,Cosmical electrodynamics (1950)

work page 1950
[3]

Lyutikov and C

M. Lyutikov and C. Thompson, Magnetospheric Eclipses in the Double Pulsar System PSR J0737-3039,ApJ 634 (2005) 1223 [astro-ph/0502333]

arXiv 2005
[4]

Buckley, P.J

D.A.H. Buckley, P.J. Meintjes, S.B. Potter, T.R. Marsh and B.T. Gänsicke, Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii,Nature Astronomy 1 (2017) 0029 [1612.03185]

arXiv 2017
[5]

Towards the origin of the radio emission in AR Sco, the first radio-pulsing white dwarf binary

B. Marcote, T.R. Marsh, E.R. Stanway, Z. Paragi and J.M. Blanchard, Towards the origin of the radio emission in AR Scorpii, the first radio-pulsing white dwarf binary, AAP 601 (2017) L7 [1705.00600]

work page Pith review arXiv 2017
[6]

Lyutikov, M

M. Lyutikov, M. Barkov, M. Route, D. Balsara, P. Garnavich and C. Littlefield, Magnetospheric interaction in white dwarf binaries AR Sco and AE Aqr,arXiv e-prints (2020) arXiv:2004.11474 [2004.11474]

arXiv 2020
[7]

A propeller scenario for the gamma-ray emission of low-mass X-ray binaries: The case of XSS J12270-4859

A. Papitto, D.F. Torres and J. Li, A propeller scenario for the gamma-ray emission of low-mass X-ray binaries: the case of XSS J12270-4859, MNRAS 438 (2014) 2105 [1312.0456]. – 16 –

work page Pith review arXiv 2014
[8]

A propeller model for the sub-luminous disk state of the transitional millisecond pulsar PSR J1023+0038

A. Papitto and D.F. Torres, A Propeller Model for the Sub-luminous State of the Transitional Millisecond Pulsar PSR J1023+0038, ApJ 807 (2015) 33 [1504.05029]

work page Pith review arXiv 2015

Show all 16 references

[9]

Dungey,Loss of Van Allen electrons due to whistlers,Planet

J.W. Dungey,Loss of Van Allen electrons due to whistlers,Planet. Space Sci.11 (1963) 591

1963
[10]

Abel and R.M

B. Abel and R.M. Thorne, Electron scattering loss in Earth’s inner magnetosphere 1. Dominant physical processes, Geophys. Res. 103 (1998) 2385

1998
[11]

Coroniti,Energetic Electrons in Jupiter’s Magnetosphere,ApJS, 27 (1974) 261

F.V. Coroniti,Energetic Electrons in Jupiter’s Magnetosphere,ApJS, 27 (1974) 261

1974
[12]

Horne, R.M

R.B. Horne, R.M. Thorne, Y.Y. Shprits, N.P. Meredith, S.A. Glauert, A.J. Smith et al., Wave acceleration of electrons in the Van Allen radiation belts,Nature 437 (2005) 227

2005
[13]

Landau and E.M

L.D. Landau and E.M. Lifshitz,The classical theory of fields (1975)

1975
[14]

Shampine and M.W

L.F. Shampine and M.W. Reichelt,The matlab ode suite, SIAM Journal on Scientific Computing 18 (1997) 1 [https://doi.org/10.1137/S1064827594276424]

1997 doi
[15]

Garnavich, C

P. Garnavich, C. Littlefield, M. Lyutikov and M. Barkov, Peeking Between the Pulses: The Far-UV Spectrum of the Previously Unseen White Dwarf in AR Scorpii, ApJ 908 (2021) 195 [2012.09868]

2021 arXiv
[16]

du Plessis, C

L. du Plessis, C. Venter, Z. Wadiasingh, A.K. Harding, D.A.H. Buckley, S.B. Potter et al., Probing the non-thermal emission geometry of AR Sco via optical phase-resolved polarimetry, MNRAS 510 (2022) 2998 [2112.08708]. – 17 –

2022 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Akasofu and S

S.-I. Akasofu and S. Chapman, The Ring Current, Geomagnetic Disturbance, and the Van Allen Radiation Belts, Geophys. Res. 66 (1961) 1321

work page 1961

[2] [2]

Alfven,Cosmical electrodynamics (1950)

H. Alfven,Cosmical electrodynamics (1950)

work page 1950

[3] [3]

Lyutikov and C

M. Lyutikov and C. Thompson, Magnetospheric Eclipses in the Double Pulsar System PSR J0737-3039,ApJ 634 (2005) 1223 [astro-ph/0502333]

arXiv 2005

[4] [4]

Buckley, P.J

D.A.H. Buckley, P.J. Meintjes, S.B. Potter, T.R. Marsh and B.T. Gänsicke, Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii,Nature Astronomy 1 (2017) 0029 [1612.03185]

arXiv 2017

[5] [5]

Towards the origin of the radio emission in AR Sco, the first radio-pulsing white dwarf binary

B. Marcote, T.R. Marsh, E.R. Stanway, Z. Paragi and J.M. Blanchard, Towards the origin of the radio emission in AR Scorpii, the first radio-pulsing white dwarf binary, AAP 601 (2017) L7 [1705.00600]

work page Pith review arXiv 2017

[6] [6]

Lyutikov, M

M. Lyutikov, M. Barkov, M. Route, D. Balsara, P. Garnavich and C. Littlefield, Magnetospheric interaction in white dwarf binaries AR Sco and AE Aqr,arXiv e-prints (2020) arXiv:2004.11474 [2004.11474]

arXiv 2020

[7] [7]

A propeller scenario for the gamma-ray emission of low-mass X-ray binaries: The case of XSS J12270-4859

A. Papitto, D.F. Torres and J. Li, A propeller scenario for the gamma-ray emission of low-mass X-ray binaries: the case of XSS J12270-4859, MNRAS 438 (2014) 2105 [1312.0456]. – 16 –

work page Pith review arXiv 2014

[8] [8]

A propeller model for the sub-luminous disk state of the transitional millisecond pulsar PSR J1023+0038

A. Papitto and D.F. Torres, A Propeller Model for the Sub-luminous State of the Transitional Millisecond Pulsar PSR J1023+0038, ApJ 807 (2015) 33 [1504.05029]

work page Pith review arXiv 2015