Anisotropic electron populations in BL Lac jets: consequences for the observed emission

E. Sobacchi; F. Tavecchio

REVIEW 3 major objections 5 minor 2 cited by

Anisotropic electron populations in BL Lac jets: consequences for the observed emission

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that if the most energetic electrons in BL Lac jets keep small pitch angles, the observed spectrum of Mkn 421 can be fitted with the magnetic field in equipartition with the electrons, and that a hard TeV inverse-Compton…

desk verdict A useful proof-of-concept: anisotropic pitch-angle distributions can get Mkn 421 to equipartition, but the result leans entirely on the adopted theta_max(gamma) ansatz. read the letter →

arxiv 1908.02183 v2 pith:SDUTFLEU submitted 2019-08-06 astro-ph.HE

F. Tavecchio , E. Sobacchi This is my paper · ORCID

classification astro-ph.HE

keywords BLLacobjectssynchrotronself-Comptonpitch-angleanisotropyspectralenergydistributionequipartitionrelativisticjetsTeVgamma-raysMkn421

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 tries to show that the two long-standing tensions in the standard one-zone synchrotron self-Compton model of BL Lac jets—the inferred magnetic field is far below the electron energy density, and the electrons radiate inefficiently—disappear if the most energetic electrons have an anisotropic momentum distribution. Using the BL Lac object Mkn 421 as a representative case, the authors build an anisotropic one-zone SSC model and find that the observed spectral energy distribution can be reproduced under equipartition between the magnetic field and relativistic electrons, with magnetic fields around 1 G rather than 0.1 G. The same electron anisotropy also predicts a harder inverse-Compton continuum at TeV energies, which is proposed as an observable test. A sympathetic reader should care because equipartition is what is expected if jets are launched as Poynting-dominated flows, while the standard isotropic scenario requires a magnetically weak, radiatively inefficient jet.

What carries the argument

The load-bearing element is the phenomenological pitch-angle distribution of Eq. (2): electrons with Lorentz factor $\gamma$ below $\gamma_{\rm iso} \sim 10^4$ keep an isotropic distribution ($\theta_{\max} = \pi/2$), whereas above $\gamma_{\rm iso}$ their maximum pitch angle shrinks as $\theta_{\max} \propto (\gamma/\gamma_{\rm iso})^{-\eta}$. Since the local magnetic field is tangled, the electron population is locally anisotropic but globally isotropic, so only the pitch-angle-dependent synchrotron process is modified, while the inverse-Compton emissivity keeps the isotropic treatment. This energy-dependent anisotropy suppresses the synchrotron emissivity of the highest-energy electrons, shifting the synchrotron peak to the electrons at $\gamma_{\rm iso}$ while the inverse-Compton peak remains at $\gamma_{\rm b}$, and it lengthens the synchrotron cooling time above $\gamma_{\rm iso}$ by roughly $1/\theta_{\max}^2$, making the cooling time grow as $\gamma^{2\eta-1}$. The same ingredient changes the synchrotron spectral index above the frequency emitted by the $\gamma_{\rm iso}$ electrons to $\alpha = (n-1+\eta)/(2-\eta)$, which is what allows a harder electron slope $n_2 \simeq 3$ and the construction of a self-consistent cooled distribution.

What would settle it

Measure the TeV spectrum of Mkn 421 during a low state: the anisotropic model predicts a distinctly hard inverse-Compton continuum with fluxes a factor 2–3 higher at a few TeV than the standard isotropic model, so a measured spectrum as soft as the isotropic prediction would rule the mechanism out for this source.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the broadband SED of Mkn 421, previously fit by the isotropic one-zone model with $B$ around 0.06 G and a magnetic-to-electron energy ratio of about 0.05, is reproduced equally well when electrons above $\gamma_{\rm iso} \sim 10^4$ have pitch angles that shrink as $\theta_{\max} \propto \gamma^{-\eta}$ with $\eta = 0.5$. In this anisotropic model the synchrotron peak is produced by electrons around $\gamma_{\rm iso}$ rather than by the same particles that make the inverse-Compton peak, the magnetic field can be raised to about 1 G, and the magnetic-to-electron energy density ratio reaches $U_B/U_e \sim 1.3$ to $2.1$, i.e. equipartition. A self-consistent cooling calculation, in which injection and radiative losses balance and synchrotron cooling is suppressed by the small pitch angles, also reproduces the SED under equipartition when inverse-Compton losses are effective around $\gamma_{\rm iso}$. The paper further claims that the anisotropic model predicts a harder SSC spectrum at very high energies, with fluxes larger by a factor of 2–3 at a few TeV, and proposes that hard spectrum as a discriminating test.

Load-bearing premise

The central claim rests on the assumed pitch-angle law $\theta_{\max} \propto \gamma^{-\eta}$ for $\gamma > \gamma_{\rm iso}$ and on the existence of a physical mechanism that maintains that anisotropy, which the paper itself says is not established.

Editorial extensions

If this is right

BL Lac emission-site parameters shift from low magnetisation to equipartition, removing the conflict with jets launched as Poynting-dominated flows.
The high-energy electron slope can be $n_2 \simeq 3$ with continuous injection and cooling, in place of the very soft slope $n_2 \simeq 4$ to $4.2$ required by the isotropic model.
The smaller Doppler factor allowed by the anisotropic fits implies a larger radiation energy density in the emission site, with consequences for TeV transparency and for the multimessenger role of high-peaked BL Lacs.
A hard, potentially detectable TeV inverse-Compton spectrum, with fluxes 2–3 times higher at a few TeV than the isotropic prediction, becomes a direct observational test.

Reading between the lines

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

If the anisotropic picture is right, the same equipartition fit should work for other well-sampled high-peaked BL Lacs, so applying it to objects such as Mrk 501 and PKS 2155-304 would reveal whether equipartition is a general property of the class or a special fit for Mkn 421.
The low-energy isotropisation invoked by the model requires a proton component, and that same baryon load may be the population responsible for BL Lac neutrino associations, connecting this SED model to high-energy neutrino detections.
The model predicts a spectral break in the synchrotron continuum at the frequency emitted by the $\gamma_{\rm iso}$ electrons, which could be searched for in existing optical and X-ray data as a way to distinguish anisotropic from standard cooling breaks.

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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

Colleague,

The paper puts a quantitative framework under Sobacchi & Lyubarsky's idea that relativistic electrons in BL Lac jets have pitch angles that shrink with energy. It shows that with that anisotropy you can fit the Mkn 421 SED with B around 1 G and electron energy density comparable to the magnetic one, which the standard isotropic one-zone SSC model cannot do without a low B and low radiative efficiency. That is a clean demonstration that the tension is not inherent to one-zone SSC, provided the anisotropy is real.

What's genuinely new: the analytic synchrotron emissivity for a power-law angular distribution (Eq. A4), the angle-averaged cooling rate (Eqs. 6-8), and the time-dependent cooling calculations that let them construct a self-consistent electron distribution. These are useful tools for anyone wanting to test anisotropic emission. The application to Mkn 421 is careful, and the predicted hard tail in the VHE SSC component is a concrete observable. The authors also state plainly in Section 4 that the pitch-angle distribution is phenomenological and the scenario is not fully self-consistent.

The soft spot is exactly the one the authors admit. The whole equipartition result flows from Eq. (2): a specific theta_max(gamma) = (gamma/gamma_iso)^-eta for gamma > gamma_iso with eta = 0.5 and gamma_iso ~ 1e4, plus the assumption that the distribution inside the cone is uniform. Change the functional form, change the intra-cone angular distribution, and the derived B and K will shift; equipartition is not guaranteed. The fits are single-object and by eye, with roughly ten free parameters, so they do not validate the ansatz independently. The self-consistent model also leans on IC cooling near gamma_iso to make the standard gamma^-2 tail, another condition that is not derived from first principles. The hard TeV spectrum is a real prediction, but it is tied to the fitted electron slope, so it is not a sharp, model-independent test.

None of this kills the paper. The authors are transparent about what is assumed, and a proof-of-concept that anisotropic pitch angles can restore equipartition is worth having on the table. It gives the reconnection/plasma community a concrete target: compute theta_max(gamma) from kinetic simulations and see if the SED still works.

My recommendation is to send it to peer review. A good referee should ask for a sensitivity study around the ansatz, not for an entirely new paper. For readers working on blazar jet modeling or particle acceleration, this is a useful and honest piece.

Referee Report

3 major / 5 minor

Summary. The paper presents a one-zone SSC model for BL Lac SEDs in which the electron momentum distribution is anisotropic, with a maximum pitch angle θmax(γ) = π/2 for γ < γiso and θmax ∝ γ^{-η} for γ > γiso, following Sobacchi & Lyubarsky (2019). The model is applied to the low-state SED of Mkn 421 in two variants: a phenomenological broken power-law electron distribution (Section 2) and a time-dependent injection-plus-cooling distribution (Section 3). The authors claim that both variants reproduce the observed SED with magnetic-to-electron energy density ratios UB/Ue ~ 1.3–2.1, i.e., near equipartition, in contrast to the standard isotropic model which requires low magnetization and low radiative efficiency. They further predict a hard inverse-Compton spectrum at TeV energies as a test of the anisotropic scenario.

Significance. If the central claim holds, the paper offers a way to reconcile one-zone SSC fits of BL Lacs with Poynting-flux-dominated jet models, addressing a long-standing tension in blazar modeling. The hard-TeV spectral prediction is falsifiable with CTA-class instruments, and the cooling-rate derivation for anisotropic electrons (Eqs. 6–8) together with the spectral slope derivation in Appendix A are useful, internally plausible technical contributions. The manuscript is also unusually honest in acknowledging its limitations, explicitly stating in Section 4 that the pitch-angle distribution is purely phenomenological and the scenario is not fully self-consistent. However, the result is a proof-of-concept: it rests on the unvalidated ansatz of Eq. (2), and the SED fits are performed by eye with a large number of free parameters, so the significance is real but conditional.

major comments (3)

[§2, Eq. (2) and §4] The equipartition conclusion (Table 1, UB/Ue = 1.30–2.1) and the hard-TeV prediction (Fig. 2) rest entirely on the assumed functional form θmax(γ) = (π/2)(γ/γiso)^{-η} for γ > γiso, with η = 0.5 and γiso ~ 10^4. The authors themselves acknowledge in Section 4 that this choice is 'purely phenomenological' and that the scenario 'is not fully self-consistent.' Because γiso, η, and the uniform-in-cone angular distribution used in Eqs. (3) and (6) are not derived from a physical model or independently constrained, the central claim is conditional: a different θmax(γ) or a different intra-cone angular distribution could erase the equipartition result. I ask for either a physical derivation of θmax(γ) from pitch-angle scattering rates or kinetic simulations, or a sensitivity study showing how UB/Ue and the predicted TeV spectrum vary for plausible alternative forms of the ansatz.
[§2, Fig. 1 and Table 1] The statement that the SED is 'satisfactorily reproduced' is supported only by visual inspection; no goodness-of-fit statistic, parameter uncertainties, or degeneracy analysis is provided. With roughly ten free parameters in Table 1 (γmin, γb, γmax, γiso, n1, n2, η, B, K, R, δ), the two models shown are not uniquely determined, and the derived UB/Ue values are therefore not robust. A quantitative fit, such as a chi-square or likelihood scan with confidence regions on the key parameters (at least B, K, γiso, and η), is needed to substantiate the claim that the anisotropic model achieves equipartition.
[§3, Fig. 5] The self-consistent scenario requires IC cooling to be effective for electrons with γ ≳ γiso; the authors explicitly state in Section 4 that the Sobacchi–Lyubarsky mechanism can operate only in this case. In the numerical calculation, the IC losses are computed using the synchrotron photon field from the phenomenological model of Section 2 (as described in the discussion of Fig. 4) rather than from the time-dependent electron distribution being evolved. This partial self-consistency should be stated more prominently in Section 3, and the sensitivity of the derived UB/Ue = 2.1 to the assumed photon field should be discussed.

minor comments (5)

[§3, Eq. (7)] The displayed formula for A(γ) is ambiguous; it should be written as A(γ) = 1 − μ/2 − μ²/2.
[§3, Eq. (5)] There is a typo: 'pith angle' should be 'pitch angle.'
[Table 1] The caption lists the last column as the magnetic-to-electron energy density ratio; it would be helpful to note that 'equipartition' is used loosely for ratios of order unity, since the self-consistent model gives UB/Ue = 2.1.
[Fig. 2] The VHE zoom would benefit from explicit axis labels (νFν versus photon energy) and a shaded band indicating the factor 2–3 flux difference mentioned in the text.
[§1] The statement that 'reconnection is unlikely to produce such a universal energy distribution' would benefit from a direct citation to kinetic simulation results, rather than relying on the preceding discussion alone.

Circularity Check

1 steps flagged · score 3.0 of 10

Main equipartition claim is a genuine forward fit to an external SED; the 'hard TeV spectrum' prediction reduces to the fitted electron index n2, and the anisotropic input itself is an acknowledged phenomenological ansatz.

fitted input called prediction [Section 2, paragraph 'A last point concerns the IC spectrum' (text around Fig. 2), with parameters in Table 1.]
"Since in the anisotropic case the underlying electron distribution required to produce the high-energy tail of the synchrotron peak is harder than in the isotropic case, one expects a harder SSC spectrum at high-energy (i.e. after the SSC peak). Indeed, harder spectra are predicted in the VHE by the anisotropic model (Fig. 2). Quite interestingly, in this case, fluxes differences by a factor 2−3 are expected at few TeV, a prediction that could be easily tested by the upcoming Cherenkov Telescope Array."

The VHE IC slope is set by the same electron index n2 that is chosen to reproduce the synchrotron continuum: the paper states that the anisotropic scenario 'allows us to use a harder slope, n2≃ 3', while n2 is constrained by 'the observed slope of the optical-UV and X-ray continua'. In the one-zone SSC model the synchrotron and IC branches are produced by the same N(γ), so the IC spectral hardness is an algebraic consequence of the fitted n2, not an independent output of the pitch-angle anisotropy (the anisotropy affects only the synchrotron emissivity through Eq. 3, not the IC emissivity). Thus the 'hard TeV spectrum' advertised as a testable prediction is forced by the fit input rather than being an independent model prediction.

full rationale

The central equipartition claim is not circular by construction: B and K are free parameters, and the reported UB/Ue ratios (1.30, 1.35, 2.1 in Table 1 and Section 3) are computed after fitting the SED of Mkn 421, not imposed as constraints. The fit is checked against external observational data (Abdo et al. 2011), so the main result has independent content. The model's input pitch-angle function (Eq. 2) is an assumption, and the paper explicitly labels it 'purely phenomenological' and says the scenario 'is not fully self-consistent'; this is a robustness limitation, not an equation-level circularity. The same holds for the choice γiso ~ 10^4, taken to be 'consistent with the value suggested by Sobacchi & Lyubarsky (2019)': this is a self-citation that supplies an input parameter, but the paper also tests the fit against the external SED, so the citation is not the sole justification. The one genuine circular element is the VHE 'prediction': the hard IC spectrum is the forced SSC consequence of the n2 index fitted to the lower-energy continuum, so presenting it as a potential test of the anisotropic model overstates its independence. No uniqueness theorem, no renaming of a known result, and no definitional identity between input and output are present. Score 3 reflects one secondary fitted-input-called-prediction while the central equipartition claim remains externally anchored.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The model is a parametric forward model with many free parameters; the key ad hoc input is the pitch-angle distribution of Eq. (2). No new physical entities such as particles, fields, or dimensions are introduced.

free parameters (8)

gamma_iso = 1.2e4 - 2.8e4 (models 1, 2); 1.5e4 (self-consistent)
Lorentz factor below which electrons are isotropic; chosen so the synchrotron peak is produced by gamma_iso electrons, a central ingredient of the model.
eta = 0.5
Slope of the pitch-angle distribution above gamma_iso; chosen to reproduce the observed spectral shapes; must be < 2 for the emissivity to decline with frequency.
n1, n2 = n1 = 2.0 - 2.2, n2 = 3.0 - 3.2 (phenomenological); self-consistent model uses injection slopes
Electron energy distribution slopes below and above gamma_b; constrained by optical-UV and X-ray/TeV spectral indices.
B = 1.25 G (models 1, 2); 0.9 G (self-consistent)
Magnetic field strength; chosen to match SED peak frequencies and fluxes and to reach equipartition.
K = 7e4 cm^-3 (model 1); 1.3e4 cm^-3 (model 2)
Normalization of the electron energy distribution; chosen to match the observed total flux.
R = 2.65e16 cm (models 1, 2); 4e15 cm (self-consistent)
Radius of the emission region; adopted from standard one-zone SSC values and adjusted to the fit.
delta = 15 (models 1, 2); 10.5 (self-consistent)
Doppler factor; chosen to match peak frequencies and fluxes.
gamma_inj, n_inj, t_inj = gamma_inj = 5e4 - 6e4, n_inj = 2.5 - 2.75, t_inj = 2R/c
Injection parameters for the self-consistent model; chosen to reproduce the SED under cooling.

assumptions (5)

domain assumption The electron momentum distribution is locally anisotropic but globally isotropic in the emission region because the magnetic field is tangled on small scales.
Invoked in Section 2 to justify computing synchrotron emission with the local pitch-angle distribution while treating IC emission as isotropic.
ad hoc to paper The pitch-angle distribution follows Eq. (2): theta_max = pi/2 for gamma < gamma_iso and theta_max proportional to gamma^{-eta} for gamma > gamma_iso.
Phenomenological ansatz, acknowledged as not derived; central to the predicted spectral shape and equipartition result.
domain assumption Gyro-resonant scattering isotropizes electrons below gamma_iso, while the highest-energy electrons retain small pitch angles.
Taken from Sobacchi & Lyubarsky (2019); requires a proton component and energy-dependent scattering, which is uncertain for BL Lacs.
domain assumption The standard one-zone SSC geometry applies: a single spherical emission region of radius R, Doppler factor delta, with co-spatial electrons and synchrotron photons.
Adopted from Maraschi & Tavecchio (2003); the paper modifies this framework but retains its geometry.
domain assumption Inverse Compton scattering does not significantly diffuse the electron pitch angles.
The authors estimate in Appendix B that the pitch-angle variation per IC scattering is at most 1/gamma, so it is neglected; this preserves the assumed anisotropy.

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Cite this review

Pith. "Pith review of Anisotropic electron populations in BL Lac jets: consequences for the observed emission." pith.science (2026). https://pith.science/paper/SDUTFLEU

@misc{pith2026190802183,
  author       = {Pith},
  title        = {Pith review of: Anisotropic electron populations in BL Lac jets: consequences for the observed emission},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SDUTFLEU}},
  note         = {Machine review of arXiv:1908.02183}
}

read the original abstract

We investigate the impact on the properties of high-energy emitting BL Lac objects of a population of electrons with an anisotropic momentum distribution. We adopt a simple phenomenological description of the anisotropy, in which the most energetic electrons have a small pitch angle and the least energetic electrons are isotropic, as proposed by Sobacchi \& Lyubarsky (2019). We explore (i) a simple model that assumes a phenomenological shape for the electron energy distribution, and (ii) a self-consistent scheme in which the electrons follow a distribution which is the result of the balance between injection and radiative losses (we include the effects of the anisotropy on the synchrotron cooling rate). Considering the BL Lac object Mkn 421 as representative of the entire class, we show that in both cases the emission can be satisfactorily reproduced under equipartition between the magnetic field and the relativistic electrons. This is in better agreement with the idea that jets are launched as Poynting dominated flows with respect to the standard isotropic scenario, which requires both a low magnetization and a low radiative efficiency to reproduce the observed emission. The hard spectrum predicted for the inverse Compton continuum at TeV energies could be used as a potential test of the anisotropic model.

Figures

Figures reproduced from arXiv: 1908.02183 by the authors.

**Figure 1.** Spectral energy distribution of Mkn 421 (black filled circles) obtained during the campaign reported in Abdo et al. (2011) reproduced with the anisotropic electron distribution model assuming a phenomenological electron energy distribution (orange solid: model 1; blue long-dashed: model 2). The parameters are listed in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 3.** Synchrotron cooling time as a function of the Lorentz factor for electrons with isotropic (long-dashed cyan) and anisotropic (η = 0.5, solid blue; η = 1, dashed red) momentum distribution. We assume γiso = 104 and B = 2 G. is dominated by the inverse Compton (γ˙IC γ˙s) and the KleinNishina effects are not too strong. If γ˙tot ∝ γ2 at all γ, the solution of Eq. (9) is N(γ) ∝ γ−2 at γ < γinj and N(γ) ∝ γ−(ninj+1) at … view at source ↗

**Figure 5.** [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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

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In relativistic pair-plasma turbulence, particles are first injected by parallel electric fields at plasmoid-mediated reconnecting current sheets, then accelerated stochastically by perpendicular electric fields, yiel...

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Works this paper leans on

38 extracted references · 33 canonical work pages · cited by 2 Pith papers

[1]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 '...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....
[3]

Abdo A. A. et al. , 2011, , 736, 131

work page 2011
[4]

Barniol Duran R., Tchekhovskoy A., Giannios D., 2017, , 469, 4957

work page 2017
[5]

D., Znajek R

Blandford R. D., Znajek R. L., 1977, , 179, 433

work page 1977
[6]

Bromberg O., Tchekhovskoy A., 2016, , 456, 1739

work page 2016
[7]

S., Cooper G., 1970, Journal of Computational Physics, 6, 1

Chang J. S., Cooper G., 1970, Journal of Computational Physics, 6, 1

work page 1970
[8]

Chiaberge M., Ghisellini G., 1999, , 306, 551

work page 1999

Show all 38 references

[9]

M., Petropoulou M., Sironi L., Giannios D., 2019, arXiv e-prints, arXiv:1908.02764

Christie I. M., Petropoulou M., Sironi L., Giannios D., 2019, arXiv e-prints, arXiv:1908.02764

2019 arXiv
[10]

Comisso L., Sironi L., 2018, Physical Review Letters, 121, 255101

2018
[11]

Costamante L., Bonnoli G., Tavecchio F., Ghisellini G., Tagliaferri G., Khangulyan D., 2018, , 477, 4257

2018
[12]

Fossati G., Maraschi L., Celotti A., Comastri A., Ghisellini G., 1998, , 299, 433

1998
[13]

Ghisellini G., 1989, , 236, 341

1989
[14]

Ghisellini G., Celotti A., Fossati G., Maraschi L., Comastri A., 1998, , 301, 451

1998
[15]

Ghisellini G., Righi C., Costamante L., Tavecchio F., 2017, , 469, 255

2017
[16]

Ghisellini G., Tavecchio F., 2010, , 409, L79

2010
[17]

Ghisellini G., Tavecchio F., Foschini L., Ghirlanda G., Maraschi L., Celotti A., 2010, , 402, 497

2010
[18]

Ghisellini G., Tavecchio F., Maraschi L., Celotti A., Sbarrato T., 2014, , 515, 376

2014
[19]

Guo F., Li H., Daughton W., Liu Y.-H., 2014, Physical Review Letters, 113, 155005

2014
[20]

, 2018, Science, 361, eaat1378

IceCube Collaboration et al. , 2018, Science, 361, eaat1378

2018
[21]

T., 2016, , 828, 13

Inoue Y., Tanaka Y. T., 2016, , 828, 13

2016
[22]

S., Vlahakis N., K \"o nigl A., Barkov M

Komissarov S. S., Vlahakis N., K \"o nigl A., Barkov M. V., 2009, , 394, 1182

2009
[23]

E., 2010, , 402, 353

Lyubarsky Y. E., 2010, , 402, 353

2010
[24]

Maraschi L., Tavecchio F., 2003, , 593, 667

2003
[25]

Nalewajko K., Gupta M., 2017, , 606, A44

2017
[26]

Petropoulou M., Sironi L., Spitkovsky A., Giannios D., 2019, , 880, 37

2019
[27]

B., Lightman A

Rybicki G. B., Lightman A. P., 1979, Radiative processes in astrophysics . Wiley, New York

1979
[28]

C., Rees M

Sikora M., Begelman M. C., Rees M. J., 1994, , 421, 153

1994
[29]

M., 2000, , 534, 109

Sikora M., Madejski G. M., 2000, , 534, 109

2000
[30]

M., 2009, , 704, 38

Sikora M., Stawarz ., Moderski R., Nalewajko K., Madejski G. M., 2009, , 704, 38

2009
[31]

Sironi L., Spitkovsky A., 2014, , 783, L21

2014
[32]

E., 2019, , 484, 1192

Sobacchi E., Lyubarsky Y. E., 2019, , 484, 1192

2019
[33]

Tavecchio F., Ghisellini G., 2016, , 456, 2374

2016
[34]

Tavecchio F., Ghisellini G., Ghirlanda G., Foschini L., Maraschi L., 2010, , 401, 1570

2010
[35]

Tavecchio F., Maraschi L., Ghisellini G., 1998, , 509, 608

1998
[36]

Tavecchio F., Oikonomou F., Righi C., 2019, , 1890

2019
[37]

M., Padovani P., 1995, , 107, 803

Urry C. M., Padovani P., 1995, , 107, 803

1995
[38]

R., Uzdensky D

Werner G. R., Uzdensky D. A., 2017, , 843, L27

2017

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 '...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

[3] [3]

Abdo A. A. et al. , 2011, , 736, 131

work page 2011

[4] [4]

Barniol Duran R., Tchekhovskoy A., Giannios D., 2017, , 469, 4957

work page 2017

[5] [5]

D., Znajek R

Blandford R. D., Znajek R. L., 1977, , 179, 433

work page 1977

[6] [6]

Bromberg O., Tchekhovskoy A., 2016, , 456, 1739

work page 2016

[7] [7]

S., Cooper G., 1970, Journal of Computational Physics, 6, 1

Chang J. S., Cooper G., 1970, Journal of Computational Physics, 6, 1

work page 1970

[8] [8]

Chiaberge M., Ghisellini G., 1999, , 306, 551

work page 1999