Pith. sign in

REVIEW 4 major objections 6 minor 71 references

Spectral Energy Correlations of Gamma-Ray Bursts from Structured Jets

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Gamma-ray burst spectrum–energy correlations are viewing-angle dependent: converting a 148-burst sample from off-axis to in-axis jet geometry steepens all three fitted relations and makes the resulting Hubble diagrams tighter as distance in

desk verdict The steepening claim is mostly built into the conversion rule, but the out-axis fits are careful and the paper is honest about its circularity. read the letter →

arxiv 2508.04487 v1 pith:TBPAGPYD submitted 2025-08-06 astro-ph.HE astro-ph.CO

X. L. Zhang , Z. B. Zhang , Y. F. Huang , D. Li , X. J. Li , L. M. Song This is my paper · ORCID
classification astro-ph.HEastro-ph.CO
keywords gamma-rayburstsstructuredjetsviewinganglespectrum-energycorrelationsAmatirelationYonetokuGhirlandaHubblediagram
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 asks whether the three empirical spectrum–energy correlations that turn gamma-ray bursts into distance indicators are systematically flattened by the angle at which each burst's jet is viewed. Treating all 148 bursts as off-axis (out-axis) observers of a power-law structured jet, the authors convert each observed quantity to the hypothetical on-axis value. The converted in-axis correlations are universally steeper: the peak-energy versus isotropic-energy slope rises from 0.40 to 0.61, versus peak luminosity from 0.37 to 0.57, and versus jet-corrected energy from 0.29 to 0.47, with the in-axis indices matching synchrotron-radiation predictions. In-axis isotropic energies are about an order of magnitude larger than out-axis ones for long and short bursts, and the in-axis Hubble diagrams are tighter. If correct, much of the scatter that has limited GRB cosmology is a viewing-angle artefact, and correcting for it makes GRBs better high-redshift standard candles.

What carries the argument

The carrying mechanism is the out-axis to in-axis conversion of Eqs. (5)–(9), based on a power-law structured jet: outside a uniform core ($\theta_c=3^\circ$), energy density scales as $(\theta/\theta_c)^{-2}$ and Lorentz factor as $(\theta/\theta_c)^{-\kappa}$ with $\kappa=2$ for every burst. Each in-axis quantity is the out-axis value times the same factor $(\theta/\theta_c)^2$ — $E_{\rm iso}$, $L_{\rm p}$, $E_\gamma$, and $\Gamma$ alike — and $E_{\rm pi,in}=(\Gamma_{\rm in}/\Gamma_{\rm out})E_{\rm pi,out}$. In log-log space this is one common shift $s=2\log(\theta/\theta_c)$ added to both axes, the structure that biases fitted slopes upward when viewing angle varies. Lorentz factors come

What would settle it

Recompute the three correlations on the same 148 bursts with a surface-integrated structured-jet model — integrate Doppler-weighted emissivity over the visible jet, with independent power-law indices for the energy and Lorentz-factor profiles — instead of multiplying every quantity by $(\theta/\theta_c)^2$. If the in-axis slopes are no longer universally steeper than the out-axis ones, the claim fails. Observationally: measure viewing angles independently (gravitational-wave counterparts, high-resolution afterglow imaging) and check whether each burst's shift tracks $(\theta/\theta_c)^2$ burst

Watch

Extended reading notes

Core claim

The paper claims the empirical GRB spectrum–energy relations are viewing-angle dependent: an off-axis observer inside a structured power-law jet sees systematically lower energies and luminosities, flattening fitted slopes. Rescaling 148 out-axis bursts to in-axis geometry — $E_{\rm in}=E_{\rm out}(\theta/\theta_c)^2$ for $E_{\rm iso}$, $L_{\rm p}$, $E_\gamma$, and $E_{\rm pi,in}=(\Gamma_{\rm in}/\Gamma_{\rm out})E_{\rm pi,out}$ — steepens all three relations (slopes 0.40→0.61, 0.37→0.57, 0.29→0.47), matching synchrotron-radiation predictions, and tightens the in-axis Hubble diagrams. The out-axis effect, the authors conclude, is the main scatter source in previous GRB correlations, and GRBs

Load-bearing premise

The result rests on the assumption that for every burst the in-axis energy, luminosity, and Lorentz factor are simply the out-axis values multiplied by the same factor $(\theta/\theta_c)^2$, with one fixed core angle ($\theta_c=3^\circ$) and one fixed index ($\kappa=2$) imposed on all 148 bursts; if a realistic jet breaks that common-shift symmetry, the universal steepening is not assured.

Editorial extensions

If this is right

  • The in-axis power-law indices (≈0.61, 0.57, 0.47) sit close to the value expected from synchrotron radiation, strengthening the case that synchrotron emission powers both in-axis and out-axis bursts.
  • In-axis isotropic energies are roughly an order of magnitude larger than out-axis ones for long and short GRBs, implying previous energy estimates are systematically low for bursts viewed off-axis.
  • Hubble diagrams built from the in-axis relations are tighter and track the standard ΛCDM model, so corrected GRB correlations are better cosmological distance indicators at high redshift.
  • The larger scatter seen in earlier GRB correlations can be largely attributed to the out-axis viewing effect.
  • Short and supernova-associated GRBs follow the same relations with larger scatter, and the circularity problem in GRB cosmology remains independent of the jet model.

Reading between the lines

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

  • Because the conversion adds the same logarithmic shift $s=2\log(\theta/\theta_c)$ to both axes, the steepening is to first order a mathematical corollary of the common-shift assumption: the fitted slope moves from $\eta$ toward $\beta' = \eta + (1-\eta)[\mathrm{Cov}(x,s)+\mathrm{Var}(s)]/\mathrm{Var}(x+s)$, which exceeds $\eta$ whenever the out-axis slope is below 1 and the shift varies across bur
  • The same algebra predicts the direction of the correction depends on the fitted slope: for a hypothetical underlying relation steeper than unity the common shift would flatten it, so 'universally steeper' is a property of these particular correlations, not of the correction procedure in general.
  • A surface-integrated forward model with independent power-law indices for energy and Lorentz factor would show whether the steepening survives; this is testable on the same 148 bursts and would decide whether the claim is physical or an artefact of Eqs. (5)–(9).
  • If the steepening holds, the corrected in-axis relations offer a path to calibrate high-redshift GRBs against low-redshift anchors, potentially extending standard-candle cosmology beyond $z\approx1.7$; a joint fit with supernovae would reveal whether the tighter correlations actually reduce cosmological parameter errors.
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.

Referee Report

4 major / 6 minor

Summary. The paper assembles a sample of 148 out-axis GRBs (128 long, 8 short, 12 SN-associated) with viewing angles and half-opening angles taken from the literature. Assuming a power-law structured jet with core half-angle θ_c=3° and Lorentz-factor index κ=2, the authors convert the observed out-axis quantities E_iso, L_p, E_γ and E_p to 'in-axis' quantities via Eqs. (5)–(9), refit the three spectral-energy correlations with a maximum-likelihood method that includes intrinsic scatter, and report that the in-axis relations are universally steeper (Eqs. 14–19). They then construct Hubble diagrams from the out-axis and in-axis relations and conclude that the in-axis diagrams are better cosmological indicators.

Significance. If the conversion were physically realistic and the steepening robust, correcting for structured-jet viewing angle would be a valuable step toward sharper GRB correlations and more precise high-redshift distance indicators. The compilation of 148 bursts, the use of MLE with intrinsic scatter, and the clear presentation of fitted slopes and dispersions in Table 3 are strengths. However, the central claim is tied to a single ad hoc transformation of the same data, so the analysis as presented does not establish the claimed universality. The paper is useful as a model-dependent exploration, but the headline conclusion needs substantial reframing and additional tests.

major comments (4)
  1. [§3.2, Table 3] The conversion rule multiplies every in-axis quantity by the same factor (θ/θ_c)^2. In log-log space this is a common shift s=2log(θ/θ_c) added to both the ordinate and the abscissa. For an out-axis relation y_out=η x_out+ε, the in-axis slope is β' = η + (1−η)[Cov(x_out,s)+Var(s)]/Var(x_out+s). With η<1 and a positive numerator, β'>η automatically. The reported steepening (0.40→0.61, 0.37→0.57, 0.29→0.47) is therefore a remapping of the same 148 bursts, not an independently measured property of in-axis GRBs. The claim of 'universal steepening' needs to be tested against a surface-integrated structured-jet model in which E_iso, L_p, E_γ and E_p transform with different powers of (θ/θ_c); otherwise it is a corollary of the equal-shift assumption.
  2. [Table 3] The out-axis fits use 128 LGRBs, while the in-axis fits use 114 LGRBs with available Γ. The slope comparison is therefore not performed on the same sample. The difference 0.40±0.04 vs 0.61±0.05 could be affected by the subset selection. The authors should refit the out-axis relations using the same 114 LGRBs and verify that the steepening persists. This is a necessary control for the central quantitative claim.
  3. [§3.3] The conclusion that in-axis Hubble diagrams are 'better cosmological indicators' is not supported by the reported scatter. The intrinsic dispersion σ_s in Table 3 increases from out-axis to in-axis for the E_pi−E_iso relation (0.31→0.41) and the E_pi−L_p relation (0.32→0.39), and only decreases slightly for E_pi−E_γ (0.34→0.33). The Hubble diagrams are built from the same correlations fitted to the same sample, so the comparison is self-calibrated; the smaller χ²/dof largely reflects the reduced sample size. A quantitative comparison of distance-modulus residuals, or a simulation/out-of-sample test, is needed before claiming that in-axis GRBs are better cosmological indicators.
  4. [§2.1–2.2] The adopted values θ_c=3° and κ=2 are fixed for all bursts with no validation, and the viewing angles θ_v and half-opening angles θ_j are taken from afterglow fits that assumed a top-hat jet (Ryan et al. 2015; Hu et al. 2019; Aksulu et al. 2020). The conversion Eqs. (5)–(9) are then applied as if these angles were measured under the power-law structured-jet model. This is a model mismatch that affects every derived in-axis quantity. A realistic structured-jet conversion should integrate emissivity over the visible jet surface with Doppler weighting, and the exponent for E_p (linked to δ∝Γ) need not equal the exponent for E_iso (linked to δ^3 ε). The robustness of the steepening to these choices should be demonstrated.
minor comments (6)
  1. [Abstract/Summary] The slopes quoted in the Summary differ slightly from Eqs. (14)–(19): out-axis L_p slope is 0.36 vs 0.37, E_γ slope is 0.28 vs 0.29, and in-axis E_iso slope is 0.62 vs 0.61. Please unify the numbers.
  2. [Throughout] Typos include 'structrured', 'imprirical', 'realitivistic', and 'aixs' (Summary and Secs. 2.2, 3.2). The manuscript would benefit from a careful proofreading pass.
  3. [Figures 6–9] Axis labels are garbled with slash notation (e.g., '/s45', '/s52'). Please replace with clear, standard mathematical notation so the figures are readable.
  4. [Eq. (11) and surrounding text] The text says C=4(4−k)/(5−4), which appears to be a typo for a factor involving (5−k). Please check the formula against Granot & Sari (2002) and correct.
  5. [§3.3] The text refers to 'spectrum-energy relations of Equations (1)-(6)' but the fitted relations are Eqs. (14)–(19). Please update the cross-reference.
  6. [Table 1 and §2.1] Sample-size statements are inconsistent: Table 1 mentions 132 GRBs with both θ_v and Γ, while the text says Γ is available for 114 long, 8 short and 10 SN/GRBs, and 135 GRBs have good t_b. Please clarify the exact numbers used for each fit.

Circularity Check

3 steps flagged · score 7.0 of 10

In-axis correlations are constructed by the equal-shift conversion (Eqs. 5-9); the 'universal steepening' is a remapping of the same data, and the X23 'confirmation' is a self-cited structured-jet model.

  1. self definitional [Sec. 2.2, Eqs. (5)-(9); results in Sec. 3.2, Eqs. (14)-(19)]
    "For simplicity, we follow Rossi et al. (2002) to take θc = 3◦ and κ=2 for all bursts in our sample. ... We also assume the two in-axis parameters to hold the similar power-law relations as Eiso,in = ... Eiso,out(θ/θc)^2 (θc < θ ≤ θj), (5) ... Lp,in = ... Lp,out(θ/θc)^2 ... (7) ... Eγ,in = ... Eγ,out(θ/θc)^2 ... (8) ... Epi,in ≡ νin/νout Epi,out ≃ Γin/Γout Epi,out. (9)"

    All four in-axis quantities are defined as the out-axis quantity times the same per-burst factor (θ/θc)^2 for bursts outside the core. In log-log space this adds the same shift s=2log(θ/θc) to both the ordinate and abscissa of the Epi-Eiso, Epi-Lp, and Epi-Eγ relations. The refitted slope is therefore not a new observable: for an out-axis slope η it is β' = η + (1-η)[Cov(x,s)+Var(s)]/Var(x+s). The steepening reported in Eqs. (14)-(19) (0.40→0.61, 0.37→0.57, 0.29→0.47) is a mathematical consequence of this equal-shift transformation plus the covariance of the adopted viewing angles with the data, not an independent empirical discovery. The values θc=3° and κ=2 are imposed for all bursts with no validation, so the 'universally steeper' conclusion is built into the conversion rule.

  2. self citation load bearing [Sec. 3.2 (after Eq. 25) and Sec. 4 Summary; X23 = Xu et al. 2023, A&A 673, A20]
    "all the in-axis spectrum-energy relations are ubiquitously steeper than the corresponding out-axis ones, which is in good agreement with the recent results of other groups (Farinelli et al. 2021, X23). Interestingly, this phenomenon can be satisfactorily explained in the framework of the synchrotron radiation mechanism by considering the variation of the Lorentz factor and the corresponding relativistic boosting effect (X23)."

    X23 is Xu et al. (2023), whose author list includes Y.-F. Huang, a co-author of this paper. The paper uses X23 as the theoretical justification that the steepened in-axis slopes are the synchrotron expectation. But X23 is itself a structured-jet model calculation using the same power-law angular profile family that the present paper adopts (the paper even cites the power-law jet as favored by Xu et al. 2005). Invoking X23 therefore does not provide an external, assumption-independent check: it re-imports the same ansatz that generated the steepening. The agreement is consistency with a self-cited model, not an independent confirmation.

1 more flagged steps
  1. other [Sec. 3.3, last paragraph]
    "However, the circularity problem (e.g. Kodama et al. 2008) is independent of the adoption of the jet model, which may prevent the effective application of these empirical energy relations in cosmology."

    The paper constructs Hubble diagrams using the same spectrum-energy relations (Eqs. 27-29) that were fitted from the same sample, and then claims the in-axis diagrams are 'better cosmological indicators' because they are tighter. This is the standard GRB circularity problem: the calibrator and the test use the same data. The passage explicitly acknowledges the problem. It does not invalidate the earlier slope comparison, but it means the Hubble-diagram claim is not an independent validation.

full rationale

The core result of the paper is that in-axis GRB correlations are 'universally steeper' (Abstract; Eqs. 14-19). The in-axis variables are not observed; they are generated from the out-axis data by Eqs. (5)-(9), which multiply Eiso, Lp, Eγ and Epi by the same factor (θ/θc)^2 for bursts viewed outside the core. In log space this is a common shift to both axes, so the refitted slopes are deterministic functions of the original slopes, the viewing-angle distribution, and the assumed θc and κ. The slope increases 0.40→0.61, 0.37→0.57, 0.29→0.47 therefore follow from the conversion assumption rather than from any new, independent measurement. This is a self-definitional circularity: the 'in-axis' relations are defined in terms of the 'out-axis' relations, and the claimed discovery is a property of that definition. The situation is not improved by the appeal to X23, a co-authored structured-jet model that shares the same power-law ansatz; it is presented as independent confirmation ('other groups') but is a self-citation. Finally, the Hubble-diagram comparison is affected by the standard circularity problem, which the paper itself acknowledges in Sec. 3.3. Because the central quantitative claim reduces to the equal-shift conversion, a score of 7 is appropriate; the paper's data handling and MLE fitting are otherwise transparent.

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

The paper is a reanalysis of literature data under an assumed jet profile. The five numbers above are adopted by hand and directly control the magnitudes of all corrections: theta_c and the two power-law indices set the common (theta/theta_c)^2 factor, while omega and zeta shape the Lorentz factors entering Epi,in. The per-burst viewing angles are inputs inherited from prior MCMC fits, so their uncertainties are not propagated either. Nothing is fit to first principles.

free parameters (5)
  • Jet core half-opening angle theta_c = 3 degrees
    Adopted for all 148 bursts 'for simplicity' (Sec. 2.2, Eq. 3 note). It sets the normalization of every correction factor (theta/theta_c)^2 and hence the magnitude of the slope bias; no uncertainty or burst-to-burst variation is included.
  • Lorentz factor power-law index kappa = 2
    Adopted as the upper limit of the 1.5-2 range from Zhang & Meszaros (2002). It sets Gamma_in/Gamma_out and therefore the Epi,in correction in Eq. (9).
  • Energy density power-law index = 2
    Assumed in Eq. (3). Together with kappa = 2 it makes all four conversions share the same (theta/theta_c)^2 factor, producing the uniform upward bias of the fitted slopes.
  • X-ray light curve smoothness parameter omega = 3
    Assumed in Eq. (10) when fitting the broken power law to X-ray afterglows; affects the derived plateau break time and hence the Lorentz factors used in the conversion.
  • Exponent zeta in dEiso/dlnu ~ u^zeta = 1.5
    Taken from Granot & Kumar (2006) in Eq. (13) to estimate initial Lorentz factors from the plateau break; propagates into Epi,in and Gamma_in.
assumptions (5)
  • domain assumption GRB jets follow the two-segment power-law structured profile of Eqs. (3)-(4): a uniform core out to theta_c, then energy density ~ (theta/theta_c)^-2 and Lorentz factor ~ (theta/theta_c)^-k with kappa = 2.
    The entire out-axis versus in-axis distinction and all conversions in Eqs. (5)-(9) rest on this profile. Only one burst (170817A) is outside the jet, so every other burst is interpreted through this model. Power-law jets are a prior from the literature, not established here.
  • ad hoc to paper Every in-axis quantity is obtained from its out-axis value by the same multiplicative factor, Eqs. (5)-(9).
    These relations are assumed, not derived from an integral over the jet surface or a radiative transfer calculation. Because the same log-space shift is applied to both axes of each correlation, the fitted slope is strongly biased upward, so the headline steepening is largely a consequence of this assumption.
  • domain assumption Viewing angles theta_v and opening angles theta_j measured from top-hat-jet afterglow fits (Ryan 2015, Hu 2019, Aksulu 2020) are transferable to the power-law structured jet.
    Section 2.1 imports all angles from ScaleFit MCMC fits that assume a top-hat jet, justified only by a conditional sentence. No structured-jet validation is performed.
  • domain assumption The fiducial cosmology H0 = 70 km/s/Mpc, Omega_m = 0.27, Omega_Lambda = 0.73 is used to compute luminosity distances and then again as the model against which the Hubble diagrams are judged.
    Standard practice in the GRB-correlation literature, but it makes the 'better cosmological indicator' comparison circular; the paper explicitly acknowledges the circularity problem in Sec. 3.3.
  • domain assumption Synchrotron radiation theory as applied by X23 predicts the on/off-axis correlation slopes and is used to interpret the measured in-axis indices.
    The interpretation is imported from Xu et al. (2023); the paper does not derive the synchrotron slopes itself. Because the steepening is biased by construction, agreement with X23 is weaker evidence than the paper implies.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Spectral Energy Correlations of Gamma-Ray Bursts from Structured Jets." pith.science (2026). https://pith.science/paper/TBPAGPYD

@misc{pith2026250804487,
  author       = {Pith},
  title        = {Pith review of: Spectral Energy Correlations of Gamma-Ray Bursts from Structured Jets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TBPAGPYD}},
  note         = {Machine review of arXiv:2508.04487}
}
read the original abstract

Using 148 out-axis gamma-ray bursts, we build their spectrum-energy relations of peak energy versus isotropic energy, peak energy versus peak luminosity and peak energy versus jet-calibrated energy which are corrected for a structured jet model. These relations are found to depend on the observer's viewing angle as long as the observer is within the jet cone. After converting the out-axis energy relations to the in-axis situations, we find that the corresponding in-axis energy relations are universally steeper, of which all of them can be roughly interpreted by the Synchrotron radiation mechanism as shown in Xu et al.. Meanwhile, we notice that the in-axis means of isotropic energies are about one order of magnitude larger than the out-axis means for both short and long bursts except the Supernova-associated gamma-ray bursts. Furthermore, we apply all the newly-found energy relations to construct the Hubble diagrams of out/in-axis bursts. It is found that the in-axis Hubble diagrams are better cosmological indicators.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 22 canonical work pages

  1. [1]

    D., Wijers, R

    Aksulu, M. D., Wijers, R. A. M. J., van Eerten, H. J., & van der Horst, A. J. 2020, MNRAS, 497, 4672, doi: 10.1093/mnras/staa2297

    work page doi:10.1093/mnras/staa2297 2020

  2. [3]

    2012, in International Journal of Modern Physics Conference Series, Vol

    Amati, L. 2012, in International Journal of Modern Physics Conference Series, Vol. 12, International Journal of Modern Physics Conference Series, 19–27, doi: 10.1142/S2010194512006228

    work page doi:10.1142/s2010194512006228 2012

  3. [4]

    2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056 Energy correlations of in- and out-axis GRBs27

    Amati, L., D’Agostino, R., Luongo, O., Muccino, M., & Tantalo, M. 2019, MNRAS, 486, L46, doi: 10.1093/mnrasl/slz056 Energy correlations of in- and out-axis GRBs27

    doi:10.1093/mnrasl/slz056 2019

  4. [5]

    2008, MNRAS, 391, 577, doi: 10.1111/j.1365-2966.2008.13943.x

    Amati, L., Guidorzi, C., Frontera, F., et al. 2008, MNRAS, 391, 577, doi: 10.1111/j.1365-2966.2008.13943.x

    arXiv 2008

  5. [6]

    S., & Della Valle, M

    Amati, L., Sawant, D. S., & Della Valle, M. 2016, Astronomical and Astrophysical Transactions, 29, 193

    work page 2016

  6. [7]

    2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

    Amati, L., Frontera, F., Tavani, M., et al. 2002, A&A, 390, 81, doi: 10.1051/0004-6361:20020722

    doi:10.1051/0004-6361:20020722 2002

  7. [8]

    B., Price, P

    Berger, E., Fox, D. B., Price, P. A., et al. 2007, ApJ, 664, 1000, doi: 10.1086/518762

    doi:10.1086/518762 2007

  8. [9]

    D., & McKee, C

    Blandford, R. D., & McKee, C. F. 1976, Physics of Fluids, 19, 1130, doi: 10.1063/1.861619

    doi:10.1063/1.861619 1976

Show all 71 references
  1. [10]

    J., Fox, D

    Cucchiara, A., Levan, A. J., Fox, D. B., et al. 2011, ApJ, 736, 7, doi: 10.1088/0004-637X/736/1/7 D’Agostini, G. 2005, arXiv e-prints, physics/0511182, doi: 10.48550/arXiv.physics/0511182

    2011 doi arXiv

  2. [11]

    G., & Gou, L

    Dai, Z. G., & Gou, L. J. 2001, ApJ, 552, 72, doi: 10.1086/320463 de Ugarte Postigo, A., Izzo, L., Kann, D. A., et al. 2017, The Astronomer’s Telegram, 11038, 1

    2001 doi

  3. [12]

    2011, MNRAS, 415, 3580, doi: 10.1111/j.1365-2966.2011.18975.x

    Demianski, M., & Piedipalumbo, E. 2011, MNRAS, 415, 3580, doi: 10.1111/j.1365-2966.2011.18975.x

    2011

  4. [13]

    Dermer, C. D. 2004, ApJ, 614, 284, doi: 10.1086/426532

    2004 doi

  5. [14]

    2021, MNRAS, 501, 5723, doi: 10.1093/mnras/staa4048

    Frontera, F. 2021, MNRAS, 501, 5723, doi: 10.1093/mnras/staa4048

    2021 doi

  6. [15]

    S., & Bloom, J

    Friedman, A. S., & Bloom, J. S. 2005, ApJ, 627, 1, doi: 10.1086/430292

    2005 doi

  7. [16]

    2004, ApJ, 616, 331, doi: 10.1086/424913

    Ghirlanda, G., Ghisellini, G., & Lazzati, D. 2004, ApJ, 616, 331, doi: 10.1086/424913

    2004 doi

  8. [17]

    S., Paragi, Z., et al

    Ghirlanda, G., Salafia, O. S., Paragi, Z., et al. 2019, Science, 363, 968, doi: 10.1126/science.aau8815

    2019 doi

  9. [18]

    2017, ApJL, 848, L14, doi: 10.3847/2041-8213/aa8f41

    Goldstein, A., Veres, P., Burns, E., et al. 2017, ApJL, 848, L14, doi: 10.3847/2041-8213/aa8f41

    2017 doi

  10. [19]

    2017, ApJL, 850, L24, doi: 10.3847/2041-8213/aa991d

    Granot, J., Guetta, D., & Gill, R. 2017, ApJL, 850, L24, doi: 10.3847/2041-8213/aa991d

    2017 doi

  11. [20]

    2006, MNRAS, 366, L13, doi: 10.1111/j.1745-3933.2005.00121.x

    Granot, J., & Kumar, P. 2006, MNRAS, 366, L13, doi: 10.1111/j.1745-3933.2005.00121.x

    2006

  12. [21]

    Granot, J., Panaitescu, A., Kumar, P., & Woosley, S. E. 2002, ApJL, 570, L61, doi: 10.1086/340991

    2002 doi

  13. [22]

    2002, ApJ, 568, 820, doi: 10.1086/338966

    Granot, J., & Sari, R. 2002, ApJ, 568, 820, doi: 10.1086/338966

    2002 doi

  14. [23]

    2020, ApJ, 894, 11, doi: 10.3847/1538-4357/ab84e7

    Guo, Q., Wei, D., & Wang, Y. 2020, ApJ, 894, 11, doi: 10.3847/1538-4357/ab84e7

    2020 doi

  15. [24]

    D., et al

    Hajela, A., Margutti, R., Alexander, K. D., et al. 2019, ApJL, 886, L17, doi: 10.3847/2041-8213/ab5226

    2019 doi

  16. [25]

    D., Oates, S

    Hu, Y. D., Oates, S. R., Lipunov, V. M., et al. 2019, A&A, 632, A100, doi: 10.1051/0004-6361/201834959

    2019 doi

  17. [26]

    F., Dai, Z

    Huang, Y. F., Dai, Z. G., & Lu, T. 2000, MNRAS, 316, 943, doi: 10.1046/j.1365-8711.2000.03683.x

    2000

  18. [27]

    2018, Progress of Theoretical and Experimental Physics, 2018, 043E02, doi: 10.1093/ptep/pty036 —

    Ioka, K., & Nakamura, T. 2018, Progress of Theoretical and Experimental Physics, 2018, 043E02, doi: 10.1093/ptep/pty036 —. 2019, MNRAS, 487, 4884, doi: 10.1093/mnras/stz1650 28Zhang et al

    2018 doi

  19. [28]

    2020, Nature Astronomy, 4, 77, doi: 10.1038/s41550-019-0892-y

    Jin, Z.-P., Covino, S., Liao, N.-H., et al. 2020, Nature Astronomy, 4, 77, doi: 10.1038/s41550-019-0892-y

    2020 doi

  20. [29]

    2008, MNRAS, 391, L1, doi: 10.1111/j.1745-3933.2008.00508.x

    Kodama, Y., Yonetoku, D., Murakami, T., et al. 2008, MNRAS, 391, L1, doi: 10.1111/j.1745-3933.2008.00508.x

    2008

  21. [30]

    R., Djorgovski, S

    Kulkarni, S. R., Djorgovski, S. G., Odewahn, S. C., et al. 1999, Nature, 398, 389, doi: 10.1038/18821

    1999 doi

  22. [31]

    2023, JCAP, 2023, 021, doi: 10.1088/1475-7516/2023/07/021

    Mukherjee, A. 2023, JCAP, 2023, 021, doi: 10.1088/1475-7516/2023/07/021

    2023 doi

  23. [32]

    2008, ApJ, 680, 92, doi: 10.1086/529582

    Li, H., Xia, J.-Q., Liu, J., et al. 2008, ApJ, 680, 92, doi: 10.1086/529582

    2008 doi

  24. [33]

    2024, ApJ, 962, 117, doi: 10.3847/1538-4357/ad18a8

    Li, X.-J., Zhang, Z.-B., Huang, Y.-F., & Xu, F. 2024, ApJ, 962, 117, doi: 10.3847/1538-4357/ad18a8

    2024 doi

  25. [34]

    J., Zhang, Z

    Li, X. J., Zhang, Z. B., & Zhang, K. 2022, A&A, 657, A124, doi: 10.1051/0004-6361/202140747

    2022 doi

  26. [35]

    J., Zhang, Z

    Li, X. J., Zhang, Z. B., Zhang, X. L., & Zhen, H. Y. 2021, ApJS, 252, 16, doi: 10.3847/1538-4365/abd3fd

    2021 doi

  27. [36]

    M., & Ramirez-Ruiz, E

    Lloyd-Ronning, N. M., & Ramirez-Ruiz, E. 2002, ApJ, 576, 101, doi: 10.1086/341723

    2002 doi

  28. [37]

    2021, Galaxies, 9, 77, doi: 10.3390/galaxies9040077

    Luongo, O., & Muccino, M. 2021, Galaxies, 9, 77, doi: 10.3390/galaxies9040077

    2021 doi

  29. [38]

    D., Lamb, G

    Lyman, J. D., Lamb, G. P., Levan, A. J., et al. 2018, Nature Astronomy, 2, 751, doi: 10.1038/s41550-018-0511-3

    2018 doi

  30. [39]

    2021, ApJ, 907, 60, doi: 10.3847/1538-4357/abd2be

    Maity, B., & Chandra, P. 2021, ApJ, 907, 60, doi: 10.3847/1538-4357/abd2be

    2021 doi

  31. [40]

    I., & Hidalgo, J

    Montiel, A., Cabrera, J. I., & Hidalgo, J. C. 2021, MNRAS, 501, 3515, doi: 10.1093/mnras/staa3926

    2021 doi

  32. [41]

    2006, A&A, 450, 471, doi: 10.1051/0004-6361:20054211

    Nava, L., Ghisellini, G., Ghirlanda, G., Tavecchio, F., & Firmani, C. 2006, A&A, 450, 471, doi: 10.1051/0004-6361:20054211

    2006 doi

  33. [42]

    P., & Bonnell, J

    Norris, J. P., & Bonnell, J. T. 2006, ApJ, 643, 266, doi: 10.1086/502796

    2006 doi

  34. [43]

    P., Bonnell, J

    Norris, J. P., Bonnell, J. T., Kazanas, D., et al. 2005, ApJ, 627, 324, doi: 10.1086/430294

    2005 doi

  35. [44]

    A., Kouveliotou, C., Grupe, D., et al

    Nousek, J. A., Kouveliotou, C., Grupe, D., et al. 2006, ApJ, 642, 389, doi: 10.1086/500724

    2006 doi

  36. [45]

    Rhoads, J. E. 1999, ApJ, 525, 737, doi: 10.1086/307907

    1999 doi

  37. [46]

    Rossi, E., Lazzati, D., & Rees, M. J. 2002, MNRAS, 332, 945, doi: 10.1046/j.1365-8711.2002.05363.x

    2002

  38. [48]

    2015, ApJ, 799, 3, doi: 10.1088/0004-637X/799/1/3

    Zhang, B.-B. 2015, ApJ, 799, 3, doi: 10.1088/0004-637X/799/1/3

    2015 doi

  39. [49]

    Q., Graziani, C., et al

    Sakamoto, T., Lamb, D. Q., Graziani, C., et al. 2004, ApJ, 602, 875, doi: 10.1086/381232

    2004 doi

  40. [50]

    1998, ApJL, 497, L17, doi: 10.1086/311269

    Sari, R., Piran, T., & Narayan, R. 1998, ApJL, 497, L17, doi: 10.1086/311269

    1998 doi

  41. [51]

    Schaefer, B. E. 2007, ApJ, 660, 16, doi: 10.1086/511742

    2007 doi

  42. [52]

    I., Sokolov, I

    Shirokov, S. I., Sokolov, I. V., Lovyagin, N. Y., et al. 2020, MNRAS, 496, 1530, doi: 10.1093/mnras/staa1548 Energy correlations of in- and out-axis GRBs29

    2020 doi

  43. [53]

    2020, MNRAS, 497, 1217, doi: 10.1093/mnras/staa1984

    Takahashi, K., & Ioka, K. 2020, MNRAS, 497, 1217, doi: 10.1093/mnras/staa1984

    2020 doi

  44. [54]

    2019, ApJS, 245, 1, doi: 10.3847/1538-4365/ab4711

    Tang, C.-H., Huang, Y.-F., Geng, J.-J., & Zhang, Z.-B. 2019, ApJS, 245, 1, doi: 10.3847/1538-4365/ab4711

    2019 doi

  45. [55]

    J., Becerra González, J., et al

    Troja, E., Castro-Tirado, A. J., Becerra González, J., et al. 2019, MNRAS, 489, 2104, doi: 10.1093/mnras/stz2255

    2019 doi

  46. [56]

    2013, MNRAS, 431, 1398, doi: 10.1093/mnras/stt262

    Takahashi, K., & Morihara, Y. 2013, MNRAS, 431, 1398, doi: 10.1093/mnras/stt262

    2013 doi

  47. [57]

    2013, MNRAS, 431, 3301, doi: 10.1093/mnras/stt409

    Velten, H., Montiel, A., & Carneiro, S. 2013, MNRAS, 431, 3301, doi: 10.1093/mnras/stt409

    2013 doi

  48. [58]

    2020, ApJ, 893, 77, doi: 10.3847/1538-4357/ab0a86

    Wang, F., Zou, Y.-C., Liu, F., et al. 2020, ApJ, 893, 77, doi: 10.3847/1538-4357/ab0a86

    2020 doi

  49. [59]

    M., & Gao, W

    Wei, D. M., & Gao, W. H. 2003, MNRAS, 345, 743, doi: 10.1046/j.1365-8711.2003.06971.x

    2003

  50. [60]

    M., & Jin, Z

    Wei, D. M., & Jin, Z. P. 2003, A&A, 400, 415, doi: 10.1051/0004-6361:20030007

    2003 doi

  51. [61]

    2023, A&A, 673, A20, doi: 10.1051/0004-6361/202245414

    Xu, F., Huang, Y.-F., Geng, J.-J., et al. 2023, A&A, 673, A20, doi: 10.1051/0004-6361/202245414

    2023 doi

  52. [62]

    F., & Dai, Z

    Xu, L., Wu, X. F., & Dai, Z. G. 2005, ApJ, 634, 1155, doi: 10.1086/497102

    2005 doi

  53. [63]

    2002, ApJL, 571, L31, doi: 10.1086/341225

    Yamazaki, R., Ioka, K., & Nakamura, T. 2002, ApJL, 571, L31, doi: 10.1086/341225

    2002 doi

  54. [64]

    2004, ApJ, 609, 935, doi: 10.1086/421285

    Yonetoku, D., Murakami, T., Nakamura, T., et al. 2004, ApJ, 609, 935, doi: 10.1086/421285

    2004 doi

  55. [65]

    2018, The Physics of Gamma-Ray Bursts, doi: 10.1017/9781139226530

    Zhang, B. 2018, The Physics of Gamma-Ray Bursts, doi: 10.1017/9781139226530

    2018 doi

  56. [66]

    2002, ApJ, 571, 876, doi: 10.1086/339981

    Zhang, B., & Mészáros, P. 2002, ApJ, 571, 876, doi: 10.1086/339981

    2002 doi

  57. [67]

    2020a, Research in Astronomy and Astrophysics, 20, 201, doi: 10.1088/1674-4527/20/12/201

    Zhang, X.-L., Zhang, C.-T., Li, X.-J., et al. 2020a, Research in Astronomy and Astrophysics, 20, 201, doi: 10.1088/1674-4527/20/12/201

    doi

  58. [68]

    Z., Deng, J

    Zhang, Z., Xie, G. Z., Deng, J. G., & Jin, W. 2006a, MNRAS, 373, 729, doi: 10.1111/j.1365-2966.2006.11058.x

    2006

  59. [69]

    B., Chen, D

    Zhang, Z. B., Chen, D. Y., & Huang, Y. F. 2012, ApJ, 755, 55, doi: 10.1088/0004-637X/755/1/55

    2012 doi

  60. [70]

    2006b, ChJA&A, 6, 312, doi: 10.1088/1009-9271/6/3/06

    Zhang, Z.-B., Deng, J.-G., Lu, R.-J., & Gao, H.-F. 2006b, ChJA&A, 6, 312, doi: 10.1088/1009-9271/6/3/06

    doi

  61. [71]

    B., Jiang, M., Zhang, Y., et al

    Zhang, Z. B., Jiang, M., Zhang, Y., et al. 2020b, ApJ, 902, 40, doi: 10.3847/1538-4357/abb400

    doi

  62. [72]

    B., Xie, G

    Zhang, Z. B., Xie, G. Z., Deng, J. G., & Wei, B. T. 2007, Astronomische Nachrichten, 328, 99, doi: 10.1002/asna.200610666

    2007 doi

  63. [73]

    B., Zhang, C

    Zhang, Z. B., Zhang, C. T., Zhao, Y. X., et al. 2018, PASP, 130, 054202, doi: 10.1088/1538-3873/aaa6af

    2018 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.