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arxiv: 2605.18122 · v1 · pith:2CQ3WUS5new · submitted 2026-05-18 · 🌌 astro-ph.HE

Spectral energy-loss bump and γ-ray pulsar halos

Kun Fang This is my paper

Pith reviewed 2026-05-20 09:06 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords pulsar halosgamma-ray spectraenergy-loss bumpspectral curvaturediffusion coefficientmagnetic fieldelectron injectionGeminga
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The pith

A time-dependent energy-loss bump in electron spectra unifies the gamma-ray observations of young and old pulsar halos.

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

The paper interprets the strongly curved spectrum measured for the young pulsar halo LHAASO J0248+6021 as the point where the energy-loss feature in the injected electrons still sits close to the original high-energy cutoff. This single picture also accounts for the much softer spectrum seen around the older Geminga pulsar, where the same feature has moved to lower energies. A sympathetic reader would care because the model removes the need for separate explanations for halos of different ages and ties the observed curvature directly to the time since electrons were injected and the strength of the surrounding magnetic field. The approach therefore offers a consistent description of how high-energy electrons evolve and radiate in these extended structures.

Core claim

The broadband spectra of young and old pulsar halos find a unified interpretation in the picture of a time-dependent energy-loss bump. For LHAASO J0248+6021 the large curvature arises because the bump in the parent electron spectrum has not yet significantly departed from the high-energy cutoff; this requires either a lower-than-typical ambient magnetic field or an electron injection age much shorter than the pulsar characteristic age. For the much older Geminga pulsar the expected bump has shifted below 100 GeV, in excellent agreement with Fermi-LAT measurements.

What carries the argument

the time-dependent energy-loss bump in the parent electron spectrum, which moves to lower energies as the pulsar ages and thereby produces the observed spectral curvature at different energies for young versus old halos.

If this is right

  • The spectral data constrain only the combination of magnetic field strength and electron injection age rather than either quantity separately.
  • Uncertainty in the magnetic field produces an order-of-magnitude spread in the diffusion coefficient that fits the halo size.
  • Future X-ray observations of the same region can break the degeneracy between field strength and injection age.
  • The model predicts that older halos will show the energy-loss feature shifted to lower gamma-ray energies, as already seen for Geminga.

Where Pith is reading between the lines

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

  • If the required low magnetic field is confirmed, it would imply that some young pulsars sit in atypical local environments that affect how their halos evolve.
  • The same time-dependent bump mechanism could be searched for in other extended gamma-ray sources once more halos are detected.
  • Improved constraints on diffusion coefficients from multiple halos would feed into broader models of cosmic-ray electron transport through the interstellar medium.

Load-bearing premise

The ambient magnetic field near the young pulsar is either weaker than typical interstellar values or the electrons were injected well before the pulsar's current characteristic age.

What would settle it

X-ray observations of synchrotron emission from the same electron population that would directly measure the local magnetic field strength and show whether it is low enough or the injection history short enough to keep the energy-loss bump at the observed energies.

Figures

Figures reproduced from arXiv: 2605.18122 by Kun Fang.

Figure 1
Figure 1. Figure 1: Initial fit of the LHAASO J0248+6021 spectrum. The ambient magnetic field strength and effective initial spin-down timescale are fixed as B = 3 µG and ˜τ0 = 10 kyr, respectively. The model clearly failed to capture the characteristics of the measurements. characteristic age τc = 62.4 kyr are given by the ATNF catalog (Manchester et al., 2005). The validity of Eq. (3) depends on the pulsar braking index bei… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Spatially integrated parent-electron spectrum of a pulsar halo at various injection ages, where [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: Fits to the spectrum of LHAASO J0248 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left: Fits to the one-dimensional γ-ray surface brightness of LHAASO J0248+6021. The diffusion coefficient is determined from the fit, while other parameters are taken from the best-fit models of the spectral fits shown in the left panel of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Isotropic synchrotron emission predicted by the best-fit models in the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

LHAASO J0248$+$6021, a possible $\gamma$-ray pulsar halo associated with PSR J0248$+$6021 (J0248), exhibits a highly curved spectrum as revealed by LHAASO and Fermi-LAT measurements. We propose a direct interpretation of this large curvature: the energy-loss bump in the parent electron spectrum has not yet significantly departed from the high-energy cutoff. This requires either that the ambient magnetic field strength $B$ around J0248 be lower than the typical value in the interstellar medium, or that the electron injection age be significantly shorter than the pulsar characteristic age. For the much older Geminga pulsar, the expected energy-loss bump in its $\gamma$-ray halo spectrum has shifted below $100\ \text{GeV}$, in excellent agreement with Fermi-LAT measurements. Thus, the broadband spectra of young and old pulsar halos find a unified interpretation in the picture of a time-dependent energy-loss bump. Meanwhile, the spectral measurements of LHAASO J0248$+$6021 only constrain the combination of $B$ and electron injection age. The uncertainty in $B$ leads to an order-of-magnitude variation in the fitted diffusion coefficient. Future X-ray observations are expected to break the degeneracies.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The paper interprets the highly curved gamma-ray spectrum of LHAASO J0248+6021 (associated with PSR J0248+6021) as arising from a time-dependent energy-loss bump in the parent electron spectrum that has not yet separated from the high-energy injection cutoff. This framework is extended to the older Geminga pulsar halo, where the bump is predicted to have shifted below 100 GeV in agreement with Fermi-LAT data, providing a unified picture for young and old pulsar halos. The model notes a degeneracy between ambient magnetic field B and electron injection age t_inj that constrains only their product, leading to order-of-magnitude uncertainty in the fitted diffusion coefficient, and suggests future X-ray observations to resolve it.

Significance. If the central interpretation holds, the work supplies a compact, time-dependent explanation for spectral curvature across pulsar halos of different ages without invoking new physics. It highlights how the position of the cooling break relative to the injection cutoff can unify apparently disparate spectra and correctly flags the B-t_inj degeneracy as the dominant uncertainty. The suggestion of X-ray follow-up is a concrete path to falsifiability, though the absence of quantitative model equations, error budgets, or auxiliary constraints in the current manuscript limits the immediate strength of the unification claim.

major comments (3)
  1. [Abstract] Abstract and model description: the central claim that the observed curvature is a direct signature of an energy-loss bump still coincident with the injection cutoff is presented qualitatively, but no explicit derivation of the bump position, no analytic expression for the electron spectrum, and no chi-squared or likelihood fit to the LHAASO+Fermi data are supplied; the agreement is therefore post-hoc and the required B or t_inj values remain unquantified.
  2. [Geminga discussion] Geminga comparison: the statement of 'excellent agreement' with Fermi-LAT data for the older halo relies on the same energy-loss framework used to interpret J0248+6021; because the spectral data only constrain the product B² t_inj, the claimed confirmation is circular and does not independently validate the time-dependent bump picture.
  3. [Discussion of uncertainties] Parameter degeneracy: the manuscript acknowledges that spectral measurements constrain only the combination of B and injection age, yet provides no auxiliary observable (rotation-measure map, X-ray synchrotron upper limit, or proper-motion age) that could break the degeneracy; without such a constraint the order-of-magnitude spread in the diffusion coefficient remains unaddressed and undermines quantitative predictions.
minor comments (2)
  1. [Model setup] Notation for the diffusion coefficient and its energy dependence should be defined explicitly when first introduced, including whether it is assumed constant or energy-dependent.
  2. [Abstract] The abstract states that future X-ray observations will break the degeneracies; a short paragraph outlining the expected synchrotron signature or flux limit would strengthen the claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments on our manuscript. We address each of the major comments in detail below, indicating the revisions we plan to make to improve the quantitative rigor of the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract and model description: the central claim that the observed curvature is a direct signature of an energy-loss bump still coincident with the injection cutoff is presented qualitatively, but no explicit derivation of the bump position, no analytic expression for the electron spectrum, and no chi-squared or likelihood fit to the LHAASO+Fermi data are supplied; the agreement is therefore post-hoc and the required B or t_inj values remain unquantified.

    Authors: We agree with the referee that the current manuscript presents the central interpretation in a qualitative manner. To address this, we will revise the manuscript to include an explicit analytic derivation of the position of the energy-loss bump relative to the injection cutoff. We will also provide the analytic expression for the time-dependent electron spectrum. Furthermore, we will perform a quantitative chi-squared fit to the LHAASO and Fermi-LAT spectral data for LHAASO J0248+6021 and report the best-fit values for B and t_inj along with their uncertainties. This will transform the agreement from post-hoc to a proper statistical comparison. revision: yes

  2. Referee: [Geminga discussion] Geminga comparison: the statement of 'excellent agreement' with Fermi-LAT data for the older halo relies on the same energy-loss framework used to interpret J0248+6021; because the spectral data only constrain the product B² t_inj, the claimed confirmation is circular and does not independently validate the time-dependent bump picture.

    Authors: We do not believe the comparison is circular. The key point is the time evolution: the model predicts that as the system ages, the energy-loss bump shifts to lower energies relative to the cutoff. Applying the same framework to the older Geminga pulsar naturally places the bump below 100 GeV, matching the Fermi-LAT data. This is an independent test of the time-dependent aspect using a different pulsar with a different characteristic age. We will revise the text to emphasize this predictive aspect and clarify that the agreement supports the unified picture without relying on circular reasoning. revision: partial

  3. Referee: [Discussion of uncertainties] Parameter degeneracy: the manuscript acknowledges that spectral measurements constrain only the combination of B and injection age, yet provides no auxiliary observable (rotation-measure map, X-ray synchrotron upper limit, or proper-motion age) that could break the degeneracy; without such a constraint the order-of-magnitude spread in the diffusion coefficient remains unaddressed and undermines quantitative predictions.

    Authors: We acknowledge this limitation. The manuscript already highlights the degeneracy between B and t_inj and the resulting uncertainty in the diffusion coefficient. We will expand the discussion section to explore potential auxiliary observables in more detail, including the possibility of using X-ray synchrotron observations to constrain B, as suggested. We will also check for any available rotation measure data or proper motion constraints for PSR J0248+6021. However, we note that such data may not be immediately available, and the primary path forward remains future targeted observations. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the time-dependent energy-loss bump interpretation.

full rationale

The paper interprets the curved spectrum of LHAASO J0248+6021 as the energy-loss bump remaining close to the injection cutoff, which requires either sub-typical B or t_inj much less than the spin-down age; it then notes that the same framework places the bump below 100 GeV for the older Geminga pulsar, matching Fermi-LAT data. This is a consistency check using standard synchrotron/IC loss timescales applied to known pulsar ages rather than a self-referential fit. The manuscript explicitly flags the B–t_inj degeneracy and the resulting spread in diffusion coefficient, without renaming a fitted quantity as a prediction or relying on load-bearing self-citations for the core claim. The derivation therefore remains self-contained against external spectral measurements and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The interpretation rests on standard cosmic-ray energy-loss physics and pulsar injection assumptions, with free parameters for magnetic field and diffusion coefficient adjusted to match spectral curvature; no new entities are introduced.

free parameters (2)
  • ambient magnetic field B
    Adjusted below typical ISM value or traded against injection age to keep the energy-loss bump near the cutoff
  • diffusion coefficient
    Fitted to spectral data; varies by an order of magnitude due to B-age degeneracy
axioms (2)
  • standard math Electrons lose energy via synchrotron and inverse-Compton processes at rates that produce a time-dependent spectral bump
    Core mechanism invoked to explain curvature evolution with age
  • domain assumption Pulsars inject electrons with a power-law spectrum extending to a high-energy cutoff
    Standard assumption for the parent particle population

pith-pipeline@v0.9.0 · 5750 in / 1609 out tokens · 59471 ms · 2026-05-20T09:06:33.649954+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · 17 internal anchors

  1. [1]

    2015, , 579, A101

    Aladro, R., Martín, S., Riquelme, D., et al. 2015, , 579, A101

    work page 2015

  2. [2]

    author Abeysekara, A. , et al. ( collaboration HAWC ), year 2017 . title Extended gamma-ray sources around pulsars constrain the origin of the positron flux at Earth . journal Science volume 358 , pages 911--914 . :10.1126/science.aan4880, http://arxiv.org/abs/1711.06223 arXiv:1711.06223

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1126/science.aan4880 2017

  3. [3]

    author Aharonian, F. , et al. ( collaboration LHAASO ), year 2021 . title Extended Very-High-Energy Gamma-Ray Emission Surrounding PSR J0622 + 3749 Observed by LHAASO-KM2A . journal Phys. Rev. Lett. volume 126 , pages 241103 . :10.1103/PhysRevLett.126.241103, http://arxiv.org/abs/2106.09396 arXiv:2106.09396

    work page doi:10.1103/physrevlett.126.241103 2021

  4. [4]

    author Albert, A. , et al. ( collaboration HAWC ), year 2023 . title HAWC Detection of a TeV Halo Candidate Surrounding a Radio-quiet Pulsar . journal Astrophys. J. Lett. volume 944 , pages L29 . :10.3847/2041-8213/acb5ee, http://arxiv.org/abs/2301.04646 arXiv:2301.04646

    work page doi:10.3847/2041-8213/acb5ee 2023

  5. [5]

    author Albert, A. , et al. ( collaboration HAWC ), year 2024 . title Precise Measurements of TeV Halos around Geminga and Monogem Pulsars with HAWC . journal Astrophys. J. volume 974 , pages 246 . :10.3847/1538-4357/ad738e

    work page doi:10.3847/1538-4357/ad738e 2024

  6. [6]

    , et al., year 2025

    author Albert, A. , et al., year 2025 . title Extended TeV Halos May Commonly Exist around Middle-Aged Pulsars . journal Phys. Rev. Lett. volume 134 , pages 171005 . :10.1103/PhysRevLett.134.171005, http://arxiv.org/abs/2505.00175 arXiv:2505.00175

    work page doi:10.1103/physrevlett.134.171005 2025

  7. [7]

    , et al., year 2026

    author Alfaro, R. , et al., year 2026 . title The Fourth HAWC Catalog of Very-High-Energy Gamma-Ray Sources http://arxiv.org/abs/2602.00263 arXiv:2602.00263

    work page arXiv 2026

  8. [8]

    Diffusive propagation of UHECR and the propagation theorem

    author Aloisio, R. , author Berezinsky, V. , year 2004 . title Diffusive propagation of UHECR and the propagation theorem . journal Astrophys. J. volume 612 , pages 900--913 . :10.1086/421869, http://arxiv.org/abs/astro-ph/0403095 arXiv:astro-ph/0403095

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/421869 2004

  9. [9]

    , author Recchia, S

    author Amato, E. , author Recchia, S. , year 2024 . title Gamma-ray halos around pulsars: impact on pulsar wind physics and galactic cosmic ray transport . journal Riv. Nuovo Cim. volume 47 , pages 399--452 . :10.1007/s40766-024-00059-8, http://arxiv.org/abs/2409.00659 arXiv:2409.00659

    work page doi:10.1007/s40766-024-00059-8 2024

  10. [10]

    author Amenomori, M. , et al. ( collaboration Tibet AS * ), year 2026 . title Constraining the magnetohydrodynamic turbulence around Geminga by observing the -ray halo beyond 100 TeV . journal Sci. Adv. volume 12 , pages adv8173 . :10.1126/sciadv.adv8173

    work page doi:10.1126/sciadv.adv8173 2026

  11. [11]

    Pulsar wind nebulae with bow shocks: non-thermal radiation and cosmic ray leptons

    author Bykov, A.M. , author Amato, E. , author Petrov, A.E. , author Krassilchtchikov, A.M. , author Levenfish, K.P. , year 2017 . title Pulsar wind nebulae with bow shocks: non-thermal radiation and cosmic ray leptons . journal Space Sci. Rev. volume 207 , pages 235--290 . :10.1007/s11214-017-0371-7, http://arxiv.org/abs/1705.00950 arXiv:1705.00950

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s11214-017-0371-7 2017

  12. [12]

    author Cao, Z. , et al. ( collaboration LHAASO ), year 2025 . title LHAASO detection of very-high-energy -ray emission surrounding PSR J0248+6021 . journal Sci. China Phys. Mech. Astron. volume 68 , pages 279504 . :10.1007/s11433-024-2508-5, http://arxiv.org/abs/2410.04425 arXiv:2410.04425

    work page doi:10.1007/s11433-024-2508-5 2025

  13. [13]

    , year 2026

    author De Sarkar, A. , year 2026 . title Investigating the emission signatures of pulsar halo candidate HESS J1813-126 . journal Astron. Astrophys. volume 706 , pages A378 . :10.1051/0004-6361/202557618, http://arxiv.org/abs/2601.21689 arXiv:2601.21689

    work page doi:10.1051/0004-6361/202557618 2026

  14. [14]

    , author Dalessandro , E

    author Della Croce , A. , author Dalessandro , E. , author Vesperini , E. , author Bellazzini , M. , author Fanelli , C. , author Origlia , L. , author Sanna , N. , year 2025 . title Tracing the W3/W4/W5 and Perseus complex dynamical evolution with star clusters . journal Astron. Astrophys. volume 698 , pages A142 . :10.1051/0004-6361/202553840, http://ar...

    work page doi:10.1051/0004-6361/202553840 2025

  15. [15]

    and Abolmasov, Pavel , month = may, year =

    author Dempsey, P. , author Duffy, P. , year 2007 . title Radiative losses and cut-offs of energetic particles at relativistic shocks . journal Mon. Not. Roy. Astron. Soc. volume 378 , pages 625--634 . :10.1111/j.1365-2966.2007.11800.x, http://arxiv.org/abs/0704.0168 arXiv:0704.0168

    work page doi:10.1111/j.1365-2966.2007.11800.x 2007

  16. [16]

    , author Manconi, S

    author Di Mauro, M. , author Manconi, S. , author Donato, F. , year 2019 . title Detection of a -ray halo around Geminga with the Fermi -LAT data and implications for the positron flux . journal Phys. Rev. D volume 100 , pages 123015 . :10.1103/PhysRevD.104.089903, http://arxiv.org/abs/1903.05647 arXiv:1903.05647 . note [Erratum: Phys.Rev.D 104, 089903 (2021)]

    work page doi:10.1103/physrevd.104.089903 2019

  17. [17]

    , author Manconi, S

    author Di Mauro, M. , author Manconi, S. , author Donato, F. , year 2020 . title Evidences of low-diffusion bubbles around Galactic pulsars . journal Phys. Rev. D volume 101 , pages 103035 . :10.1103/PhysRevD.101.103035, http://arxiv.org/abs/1908.03216 arXiv:1908.03216

    work page doi:10.1103/physrevd.101.103035 2020

  18. [18]

    Origin of the Cosmic Ray Galactic Halo Driven by Advected Turbulence and Self-Generated Waves

    author Evoli, C. , author Blasi, P. , author Morlino, G. , author Aloisio, R. , year 2018 . title Origin of the Cosmic Ray Galactic Halo Driven by Advected Turbulence and Self-Generated Waves . journal Phys. Rev. Lett. volume 121 , pages 021102 . :10.1103/PhysRevLett.121.021102, http://arxiv.org/abs/1806.04153 arXiv:1806.04153

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.121.021102 2018

  19. [19]

    , author Walter , F.M

    author Faherty , J. , author Walter , F.M. , author Anderson , J. , year 2007 . title The trigonometric parallax of the neutron star Geminga . journal Astrophys. Space Sci. volume 308 , pages 225--230 . :10.1007/s10509-007-9368-0

    work page doi:10.1007/s10509-007-9368-0 2007

  20. [20]

    , year 2022

    author Fang, K. , year 2022 . title Gamma-ray pulsar halos in the Galaxy . journal Front. Astron. Space Sci. volume 9 , pages 1022100 . :10.3389/fspas.2022.1022100, http://arxiv.org/abs/2209.13294 arXiv:2209.13294

    work page doi:10.3389/fspas.2022.1022100 2022

  21. [21]

    PHECT: A lightweight computation tool for pulsar halo emission

    author Fang, K. , year 2026 . title Lightweight computation tool for pulsar halo emission . journal Phys. Rev. D volume 113 , pages 083018 . :10.1103/lxmg-75p8, http://arxiv.org/abs/2508.13667 arXiv:2508.13667

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/lxmg-75p8 2026

  22. [22]

    , author Bi, X.J

    author Fang, K. , author Bi, X.J. , author Lin, S.J. , author Yuan, Q. , year 2021 . title Klein Nishina Effect and the Cosmic Ray Electron Spectrum . journal Chin. Phys. Lett. volume 38 , pages 039801 . :10.1088/0256-307X/38/3/039801, http://arxiv.org/abs/2007.15601 arXiv:2007.15601

    work page doi:10.1088/0256-307x/38/3/039801 2021

  23. [23]

    , author Xi, S.Q

    author Fang, K. , author Xi, S.Q. , author Bao, L.Z. , author Bi, X.J. , author Chen, E.S. , year 2022 . title Features of the gamma-ray pulsar halo HESS J1831-098 . journal Phys. Rev. D volume 106 , pages 123017 . :10.1103/PhysRevD.106.123017, http://arxiv.org/abs/2207.13533 arXiv:2207.13533

    work page doi:10.1103/physrevd.106.123017 2022

  24. [24]

    Measuring Average Treatment Effect from Heavy-tailed Data

    author Gaensler, B.M. , author Slane, P.O. , year 2006 . title The evolution and structure of pulsar wind nebulae . journal Ann. Rev. Astron. Astrophys. volume 44 , pages 17--47 . :10.1146/annurev.astro.44.051905.092528, http://arxiv.org/abs/astro-ph/0601081 arXiv:astro-ph/0601081

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.astro.44.051905.092528 2006

  25. [25]

    , author Mitchell, A

    author Giacinti, G. , author Mitchell, A. , author L\'opez-Coto, R. , author Joshi, V. , author Parsons, R. , author Hinton, J. , year 2020 . title Halo fraction in TeV-bright pulsar wind nebulae . journal Astron. Astrophys. volume 636 , pages A113 . :10.1051/0004-6361/201936505, http://arxiv.org/abs/1907.12121 arXiv:1907.12121

    work page doi:10.1051/0004-6361/201936505 2020

  26. [26]

    , author Yuan, Q

    author Guo, Y.Y. , author Yuan, Q. , year 2024 . title Impact of electron spectra on morphology of pulsar halos at ultra-high energies . journal JHEAp volume 43 , pages 227--230 . :10.1016/j.jheap.2024.07.006, http://arxiv.org/abs/2407.10705 arXiv:2407.10705

    work page doi:10.1016/j.jheap.2024.07.006 2024

  27. [27]

    Escape from Vela X

    author Hinton, J. , author Funk, S. , author Parsons, R.D. , author Ohm, S. , year 2011 . title Escape from Vela X . journal Astrophys. J. Lett. volume 743 , pages L7 . :10.1088/2041-8205/743/1/L7, http://arxiv.org/abs/1111.2036 arXiv:1111.2036

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/743/1/l7 2011

  28. [28]

    , author Linden, T

    author John, I. , author Linden, T. , year 2023 . title Pulsars do not produce sharp features in the cosmic-ray electron and positron spectra . journal Phys. Rev. D volume 107 , pages 103021 . :10.1103/PhysRevD.107.103021, http://arxiv.org/abs/2206.04699 arXiv:2206.04699

    work page doi:10.1103/physrevd.107.103021 2023

  29. [29]

    , author Becker, W

    author Khokhriakova, A. , author Becker, W. , author Ponti, G. , author Sasaki, M. , author Li, B. , author Liu, R.Y. , year 2024 . title Searching for X-ray counterparts of degree-wide TeV halos around middle-aged pulsars with SRG/eROSITA . journal Astron. Astrophys. volume 683 , pages A180 . :10.1051/0004-6361/202347311, http://arxiv.org/abs/2310.10454 ...

    work page doi:10.1051/0004-6361/202347311 2024

  30. [30]

    , et al., year 2026

    author Krivonos, R. , et al., year 2026 . title A wide-field X-ray search for the Geminga pulsar halo with SRG/ART-XC . journal Astron. Astrophys. volume 705 , pages A107 . :10.1051/0004-6361/202555650, http://arxiv.org/abs/2512.13846 arXiv:2512.13846

    work page doi:10.1051/0004-6361/202555650 2026

  31. [31]

    Using HAWC to Discover Invisible Pulsars

    author Linden, T. , author Auchettl, K. , author Bramante, J. , author Cholis, I. , author Fang, K. , author Hooper, D. , author Karwal, T. , author Li, S.W. , year 2017 . title Using HAWC to discover invisible pulsars . journal Phys. Rev. D volume 96 , pages 103016 . :10.1103/PhysRevD.96.103016, http://arxiv.org/abs/1703.09704 arXiv:1703.09704

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.96.103016 2017

  32. [32]

    , year 2022

    author Liu, R.Y. , year 2022 . title The physics of pulsar halos: Research progress and prospect . journal Int. J. Mod. Phys. A volume 37 , pages 2230011 . :10.1142/S0217751X22300113, http://arxiv.org/abs/2207.04011 arXiv:2207.04011

    work page doi:10.1142/s0217751x22300113 2022

  33. [33]

    Constraining the magnetic field in the TeV halo of Geminga with X-ray Observation

    author Liu, R.Y. , author Ge, C. , author Sun, X.N. , author Wang, X.Y. , year 2019 . title Constraining the Magnetic Field in the TeV Halo of Geminga with X-Ray Observations . journal Astrophys. J. volume 875 , pages 149 . :10.3847/1538-4357/ab125c, http://arxiv.org/abs/1904.11438 arXiv:1904.11438

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab125c 2019

  34. [34]

    , author de O\ na Wilhelmi, E

    author L\'opez-Coto, R. , author de O\ na Wilhelmi, E. , author Aharonian, F. , author Amato, E. , author Hinton, J. , year 2022 . title Gamma-ray haloes around pulsars as the key to understanding cosmic-ray transport in the Galaxy . journal Nature Astron. volume 6 , pages 199--206 . :10.1038/s41550-021-01580-0, http://arxiv.org/abs/2202.06899 arXiv:2202.06899

    work page doi:10.1038/s41550-021-01580-0 2022

  35. [35]

    The ATNF Pulsar Catalogue

    author Manchester, R.N. , author Hobbs, G.B. , author Teoh, A. , author Hobbs, M. , year 2005 . title The Australia Telescope National Facility pulsar catalogue . journal Astron. J. volume 129 , pages 1993 . :10.1086/428488, http://arxiv.org/abs/astro-ph/0412641 arXiv:astro-ph/0412641

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/428488 2005

  36. [36]

    , author Woo, J

    author Manconi, S. , author Woo, J. , author Shang, R.Y. , author Krivonos, R. , author Tang, C. , author Di Mauro, M. , author Donato, F. , author Mori, K. , author Hailey, C.J. , year 2024 . title Geminga s pulsar halo: An X-ray view . journal Astron. Astrophys. volume 689 , pages A326 . :10.1051/0004-6361/202450242, http://arxiv.org/abs/2403.10902 arXi...

    work page doi:10.1051/0004-6361/202450242 2024

  37. [37]

    , author de Guillebon, L

    author Martin, P. , author de Guillebon, L. , author Collard, E. , author Mertz, I. , author Mohrmann, L. , author Principe, G. , author Lemoine-Goumard, M. , author Marcowith, A. , author Terrier, R. , author Filipovi \'c , M.D. , year 2024 . title Extended gamma-ray emission from particle escape in pulsar wind nebulae - Application to HESS J1809 193 and...

    work page doi:10.1051/0004-6361/202450254 2024

  38. [38]

    , author Liang, Y.F

    author Meng, Y. , author Liang, Y.F. , author Zhu, B.Y. , author Sun, X.N. , author Liang, E.W. , year 2026 . title Revisiting the Geminga halo at GeV energies with Fermi-LAT data . journal Phys. Rev. D volume 113 , pages 063027 . :10.1103/qlyv-qh6r, http://arxiv.org/abs/2602.20882 arXiv:2602.20882

    work page doi:10.1103/qlyv-qh6r 2026

  39. [39]

    Observations of three young gamma-ray pulsars with the Gran Telescopio Canarias

    author Mignani, R.P. , author Rea, N. , author Testa, V. , author Marelli, M. , author De Luca, A. , author Pierbattista, M. , author Shearer, A. , author Torres, D.F. , author de Ona Wilhelmi, E. , year 2016 . title Observations of three young -ray pulsars with the Gran Telescopio Canarias . journal Mon. Not. Roy. Astron. Soc. volume 461 , pages 4317--43...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stw1629 2016

  40. [40]

    , author Linden, T

    author Mukhopadhyay, P. , author Linden, T. , year 2022 . title Self-generated cosmic-ray turbulence can explain the morphology of TeV halos . journal Phys. Rev. D volume 105 , pages 123008 . :10.1103/PhysRevD.105.123008, http://arxiv.org/abs/2111.01143 arXiv:2111.01143

    work page doi:10.1103/physrevd.105.123008 2022

  41. [41]

    Initial spin periods of neutron stars in supernova remnants

    author Popov, S.B. , author Turolla, R. , year 2012 . title Initial spin periods of neutron stars in supernova remnants . journal Astrophys. Space Sci. volume 341 , pages 457--464 . :10.1007/s10509-012-1100-z, http://arxiv.org/abs/1204.0632 arXiv:1204.0632

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10509-012-1100-z 2012

  42. [42]

    Geminga's puzzling pulsar wind nebula

    author Posselt, B. , author Pavlov, G. , author Slane, P. , author Romani, R. , author Bucciantini, N. , author Bykov, A. , author Kargaltsev, O. , author Weisskopf, M. , author Ng, C.Y. , year 2017 . title Geminga's puzzling pulsar wind nebula . journal Astrophys. J. volume 835 , pages 66 . :10.3847/1538-4357/835/1/66, http://arxiv.org/abs/1611.03496 arX...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/835/1/66 2017

  43. [43]

    , author Bamba, A

    author Suzuki, H. , author Bamba, A. , author Shibata, S. , year 2021 . title Quantitative Age Estimation of Supernova Remnants and Associated Pulsars . journal Astrophys. J. volume 914 , pages 103 . :10.3847/1538-4357/abfb02, http://arxiv.org/abs/2104.10052 arXiv:2104.10052

    work page doi:10.3847/1538-4357/abfb02 2021

  44. [44]

    PSRs J0248+6021 and J2240+5832: Young Pulsars in the Northern Galactic Plane. Discovery, Timing, and Gamma-ray observations

    author Theureau, G. , et al., year 2011 . title PSRs J0248+6021 and J2240+5832: Young Pulsars in the Northern Galactic Plane. Discovery, Timing, and Gamma-ray observations . journal Astron. Astrophys. volume 525 , pages A94 . :10.1051/0004-6361/201015317, http://arxiv.org/abs/1010.4230 arXiv:1010.4230

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201015317 2011

  45. [45]

    Absorption of Very High Energy Gamma Rays in the Milky Way

    author Vernetto, S. , author Lipari, P. , year 2016 . title Absorption of very high energy gamma rays in the Milky Way . journal Phys. Rev. D volume 94 , pages 063009 . :10.1103/PhysRevD.94.063009, http://arxiv.org/abs/1608.01587 arXiv:1608.01587

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.94.063009 2016

  46. [46]

    , author Mitchell, A.M.W

    author Wach, T. , author Mitchell, A.M.W. , year 2025 . title TeV Emission from PSR B1055-52 with HESS: Evidence for a Pulsar Halo . journal PoS volume ICRC2025 , pages 874 . :10.22323/1.501.0874, http://arxiv.org/abs/2510.02802 arXiv:2510.02802

    work page doi:10.22323/1.501.0874 2025

  47. [47]

    , author Li, C.M

    author Wu, Q.Z. , author Li, C.M. , author Liang, X.H. , author Ge, C. , author Liu, R.Y. , year 2024 . title Diagnosing the Particle Transport Mechanism in the Pulsar Halo via X-Ray Observations . journal Astrophys. J. volume 969 , pages 9 . :10.3847/1538-4357/ad43e1, http://arxiv.org/abs/2401.17982 arXiv:2401.17982

    work page doi:10.3847/1538-4357/ad43e1 2024

  48. [48]

    GeV observations of the extended pulsar wind nebulae constrain the pulsar interpretations of the cosmic-ray positron excess

    author Xi, S.Q. , author Liu, R.Y. , author Huang, Z.Q. , author Fang, K. , author Wang, X.Y. , year 2019 . title GeV observations of the extended pulsar wind nebulae constrain the pulsar interpretations of the cosmic-ray positron excess . journal Astrophys. J. volume 878 , pages 104 . :10.3847/1538-4357/ab20c9, http://arxiv.org/abs/1810.10928 arXiv:1810.10928

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab20c9 2019

  49. [49]

    Discrete treatment of inverse Compton scattering: implications on parameter estimation in gamma-ray astronomy

    author Xia, J. , author Lv, X. , author Fang, K. , author Liu, S. , year 2025 . title Discrete treatment of inverse Compton scattering: Implications on parameter estimation in gamma-ray astronomy . journal Phys. Rev. D volume 111 , pages 123048 . :10.1103/g41m-jzfj, http://arxiv.org/abs/2503.15052 arXiv:2503.15052

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/g41m-jzfj 2025

  50. [50]

    , et al., year 2025

    author Yuan, W. , et al., year 2025 . title Science objectives of the Einstein Probe mission . journal Sci. China Phys. Mech. Astron. volume 68 , pages 239501 . :10.1007/s11433-024-2600-3, http://arxiv.org/abs/2501.07362 arXiv:2501.07362

    work page doi:10.1007/s11433-024-2600-3 2025

  51. [51]

    , author Wang, Z

    author Zheng, D. , author Wang, Z. , year 2024 . title Finding Candidate TeV Halos among Very-high-energy Sources . journal Astrophys. J. volume 968 , pages 117 . :10.3847/1538-4357/ad496d, http://arxiv.org/abs/2403.16074 arXiv:2403.16074

    work page doi:10.3847/1538-4357/ad496d 2024

  52. [52]

    , author Yu, Z.H

    author Zhou, G.Y. , author Yu, Z.H. , author Yuan, Q. , author Zhang, H.H. , year 2022 . title Geminga contribution to the cosmic-ray positron excess according to the gamma-ray observations . journal Commun. Theor. Phys. volume 74 , pages 105403 . :10.1088/1572-9494/ac7cd6, http://arxiv.org/abs/2205.07038 arXiv:2205.07038

    work page doi:10.1088/1572-9494/ac7cd6 2022