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Forward and Reverse Shock Emission from Relativistic Jets with Arbitrary Angular and Stratified Radial Profiles

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Standard analytic models overestimate reverse-shock optical flashes from thin-shell gamma-ray burst jets by more than three orders of magnitude, with the neglected ejecta velocity gradient accounting for about two of those orders.

desk verdict A genuinely useful code paper with a plausible but unanchored central claim: the factor-of-10^3 thin-shell reverse-shock suppression needs a full-hydro benchmark before it becomes quantitative. read the letter →

arxiv 2507.15311 v1 pith:E45JDTCR submitted 2025-07-21 astro-ph.HE

Hao Wang , Hao Zhou , Yi-Zhong Fan , Da-Ming Wei This is my paper
classification astro-ph.HE
keywords gamma-rayburstsreverseshockafterglowstructuredjetsjetradialstructureenergyconservationGRB990123refreshedshocks
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

This paper extends a numerical afterglow code, jetsimpy, to include the layered radial structure of gamma-ray burst (GRB) ejecta, not just its angular profile. Using the upgraded code, the authors argue that standard analytic models of the reverse shock—the shock that travels backward into the still-moving ejecta—significantly overestimate the early optical flash. In the thin-shell regime, where the ejecta has stretched into a homogeneous speed distribution, the analytic peak luminosity is too bright by more than three orders of magnitude; the neglected velocity gradient alone accounts for about two of those orders. In the thick-shell regime the overestimate is roughly one order of magnitude. If these results hold, early optical flashes from GRBs are intrinsically rarer and fainter than previously expected, and reverse-shock emission cannot be used to infer jet parameters without accounting for the full radial structure.

What carries the argument

The load-bearing object is the radially integrated conservation scheme: the paper integrates the Euler equations over the thin blast region between the forward and reverse shocks, treating the two shocked regions as one thermodynamic system whose total energy is strictly conserved, with a single uniform velocity for the whole blast region. The reverse-shock jump conditions relate the post-shock quantities to the relative Lorentz factor $\Gamma_{34}=\Gamma\Gamma_{\rm ej}(1-\beta\beta_{\rm ej})$, and the ejecta density at the reverse shock is derived from two profile functions, the launch luminosity $L_{\rm iso}(\tau)$ and the energy-per-log-velocity distribution $dE_{\rm iso}/d\log u$, which automatically enforce that outer layers are fast and inner layers slow. A phenomenological cooling coefficient $g$ handles the post-crossing rarefaction. The pressure-balance assumption used by earlier analytic models is replaced by energy conservation, and lateral expansion is driven only by the forward-shock pressure term, a choice the paper tests by comparing light curves with the full expression.

What would settle it

Run a full relativistic hydrodynamic simulation of a thin-shell top-hat jet with $E_{\rm iso}=10^{52}$ erg, $\Gamma_0=300$, $n_0=1$ cm$^{-3}$, and $T_{90}\approx 0$, then compare the reverse-shock peak flux. If the simulated peak lands within an order of magnitude of the analytic curve rather than roughly three orders below it, the central claim would be refuted.

Watch

Extended reading notes

Core claim

The paper's central claim is that closing the forward-reverse shock system with global energy conservation, rather than the usual pressure balance at the contact discontinuity, changes the predicted reverse-shock emission dramatically. The energy-conservation prescription makes the blastwave decelerate earlier, lowers the relative Lorentz factor $\Gamma_{34}$ between ejecta and shocked region, and exposes the velocity gradient inside the ejecta that analytic thin-shell models ignore. Together these effects make the thin-shell reverse-shock peak flux more than three orders of magnitude fainter than the analytic benchmark (and about an order fainter in thick shells). The paper also claims that in structured jets an off-axis observer can see a thin-to-thick transition, but that its light-curve shape is practically indistinguishable from pure thin or thick shell cases, and that the same framework naturally describes refreshed shocks and kilonova afterglows. Fitting the GRB 990123 optical flash, the paper finds agreement with data and infers that the ejecta in that burst is at least mildly magnetized.

Load-bearing premise

The forward-reverse shock system is closed by assuming a single uniform velocity throughout the blast region and by neglecting the reverse shock's pressure in lateral expansion; if that simplified velocity and pressure structure is not accurate, the computed reverse-shock luminosity could shift by the claimed orders of magnitude.

Editorial extensions

If this is right

  • Thin-shell GRB jets should not generally be expected to produce bright reverse-shock optical flashes, which naturally explains why such flashes are rarely detected.
  • Analytic thin-shell reverse-shock light curves are not self-consistent, because neglecting the ejecta velocity gradient violates energy conservation in the blast region.
  • Thick-shell reverse-shock peak fluxes are still overestimated by about an order of magnitude, which shifts the inferred jet parameters in existing fits.
  • For structured jets, off-axis observers may see a thin-to-thick transition, but it is very hard to detect because it demands long jet durations and fine-tuned viewing angles.
  • The same code reproduces refreshed-shock and kilonova-afterglow light curves, where the reverse-shock radio emission can outshine the forward shock for high microphysical parameters.

Reading between the lines

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

  • If the three-orders-of-magnitude overestimate is correct, archival searches for GRB optical flashes should be re-evaluated with fainter reverse-shock templates, making non-detections less constraining than previously thought.
  • The paper's claim implies that bright optical flashes such as GRB 990123's require either magnetization of the ejecta or an unusual energy-injection history; a direct measurement of ejecta magnetization from polarization observations could discriminate between these.
  • A full two-dimensional special-relativistic hydrodynamic simulation of a thin-shell structured jet would provide a direct numerical check of the energy-conservation blastwave dynamics, which the paper does not benchmark against full simulations.
  • The unified radial profile used for structured jets mixes a thick-shell luminosity with a thin-shell velocity distribution; testing other profile shapes would show how much the predicted light-curve morphology depends on that choice.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper extends the public jetsimpy afterglow code to jets with arbitrary axisymmetric two-dimensional structure by adding a stratified radial ejecta profile. The forward-reverse shock system is closed with a total-energy-conservation prescription rather than pressure balance at the contact discontinuity, leading to the paper's central claim: analytic reverse-shock models overestimate thin-shell peak emission by more than three orders of magnitude and thick-shell peak emission by about one order. The paper also studies off-axis emission from structured jets, models kilonova afterglows as refreshed shocks, and fits the optical/X-ray afterglow of GRB 990123. The authors report internal consistency checks, including convergence of blastwave energy to the forward-shock-only case and agreement with analytic kilonova afterglow slopes.

Significance. If the central claim is correct, the paper is an important correction to the standard analytic reverse-shock light-curve framework: early optical flashes from homogeneous thin-shell GRB ejecta would be far fainter than usually predicted, which would help explain the rarity of detected reverse-shock components. The code extension itself is valuable: it is a public tool, handles arbitrary angular and radial profiles including GRMHD-derived inputs, and the paper shows several nontrivial consistency checks (energy convergence, kilonova slope agreement, and a multi-band GRB fit). The main quantitative claim, however, rests on a new closure that is not benchmarked against full hydrodynamic simulations, and the GRB 990123 fit is not an independent test because a magnetic-energy fraction is a free parameter driven to near unity.

major comments (3)
  1. [§2.2, Eq. (25)] The central suppression claim in §3.1 and summary point 4 depends on the energy-conservation closure with a single uniform blast-region Lorentz factor Γ and on the manual truncation of the reverse-shock pressure in lateral expansion (P_b ≡ β²M_fs/3). The text states that this adjustment leaves the light curves unchanged, but no comparison is shown, and the authors themselves caution that in regimes where reverse-shock pressure is non-negligible, full hydrodynamic simulations should be preferred. The thin-shell case is precisely such a regime, since the reverse-shock region carries a large fraction of the blast energy and Γ34 is small. Without a benchmark of Γ34(t), the blastwave energy, and the reverse-shock light curve against a 1D relativistic hydrodynamic solver for the same thin- and thick-shell initial conditions, the factor-of-10³ overestimation is not empirically anchored. I would ask the authors to add such a benchmark and to display the light curves with the original P_b expression versus the truncated one.
  2. [§3.1, Eqs. (42)–(44)] The claim that the neglected ejecta velocity gradient alone accounts for about two orders of magnitude of the suppression rests on the assumed thin-shell energy distribution dE_iso/dlogu = E_iso (Γ/Γ0)^{-2} β/β0. This profile is chosen so that the energy is spatially uniform and the total energy is E_iso, but it is not derived from a microphysical spreading model, and it is not validated against hydrodynamics. Since this assumption is a load-bearing part of the factor-of-10³ conclusion, the authors should test the sensitivity of the peak reverse-shock flux to the shape of the velocity distribution (for example, by varying the power-law index or by using a distribution obtained from pressure-driven spreading of a cold shell), and should state whether the two-order contribution is robust to such variations.
  3. [§4, Table 1] The GRB 990123 fit is presented as a validation of the new modeling, but it does not independently test the central thin-shell suppression claim. The fit assumes a thick shell, fixes ϵ_e,rs = 0.5 and p_rs = 2.5, and leaves ϵ_B,rs free; the best fit drives log10 ϵ_B,rs ≈ −0.06 (ϵ_B,rs ≈ 0.86), so the reverse-shock brightness can be adjusted by a near-unity magnetic energy fraction. The inferred ϵ_e,rs + ϵ_B,rs ≈ 1.4 also violates the usual sum constraint, which the text acknowledges. The fit is useful as a demonstration of the code's flexibility, but it should not be described as validating the new closure; I recommend the authors either add a hydro-benchmark validation or explicitly limit the role of this fit in the paper's conclusions.
minor comments (4)
  1. [§2.3] The sentence "To realize this second difficulty" should read "To resolve this second difficulty," and "adopts" in the interpolation equation should be "adopt."
  2. [Eq. (31)] The quantity M_ej is used in Eq. (31) but is not defined; please define it explicitly (presumably the total mass of the ejecta shell) and distinguish it from the reverse-shock mass M_rs.
  3. [Fig. 3 caption] The lower-panel caption "thin shell (T90 0 s)" is ambiguous; please write "thin shell (T90 → 0)" or "T90 ≈ 0" to avoid implying an unphysical zero duration.
  4. [§3.2, Eq. (48)] The sentence "the jet energy distribution in velocity space follows the thin shell case (see eq. 42)" appears to reference the wrong equation; the relevant thin-shell energy distribution is Eq. (43), not Eq. (42).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central suppression claim is a model-to-model comparison under stated conservation-law closures, not a fit renamed as prediction.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The dynamics are obtained from the Euler conservation equations (Eqs. 10-11) and the trans-relativistic shock jump conditions (Eqs. 1-9), which are taken from external references (Uhm 2011; Mignone & McKinney 2007). The new element is the energy-conservation closure for the blast region, Eq. 22-24, which is explicitly contrasted with the pressure-balance prescription in Eq. 45. The central quantitative claim, that analytic thin-shell reverse-shock peak fluxes are overestimated by more than three orders of magnitude, is a comparison between two model closures using the same microphysical parameters for both the new model and the analytic comparison (Fig. 3 caption fixes epsilon_B,rs = 0.5 for both). The 'two orders of magnitude' attributed to the neglected velocity gradient is likewise a difference between the full thin-shell velocity-gradient treatment (Eqs. 43-44) and the 'simplified' uniform-velocity thin-shell case, not a fitted parameter renamed as a prediction. The GRB 990123 fit leaves epsilon_B,rs as a free parameter, but the paper explicitly frames it as 'only a test to our code' and does not use that fit to derive the overestimate claim. Self-citations to Wang et al. 2024 are references to a public numerical code and its documented scheme, not to an unverified uniqueness theorem, and the code is machine-available for independent reproduction. The authors' caution that their pressure-truncation closure (Eq. 25) should be checked against full hydrodynamic simulations in regimes where reverse-shock pressure matters is an acknowledged validation limitation, not a circular reduction of the result to its own inputs. No step was found in which an output quantity equals an input quantity by definition, or in which a load-bearing claim reduces to a self-citation chain. The appropriate finding is therefore no significant circularity.

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

No new physical particles, fields, or conserved quantities are introduced. The 'imagined tail' is a numerical device, not a physical entity. The free parameters listed are the model choices that most directly affect the reverse shock emission and the validation fit.

free parameters (5)
  • g (reverse shock cooling coefficient) = 1.934 (+0.044, -0.086) in the GRB 990123 fit; set to 1 in case studies
    Phenomenological cooling exponent in the imagined-tail velocity decay (Eq. 29). Controls post-crossing reverse shock behavior; values of order 1 are asserted to be of interest (Section 2.3). Not derived from first principles.
  • Thin-shell velocity energy-distribution index (Eq. 43) = 2 (chosen)
    dE/dlogu is set proportional to (Gamma/Gamma0)^-2 to give a uniform spatial energy distribution for a shell of thickness r/Gamma0^2. The functional form is assumed, not measured; it drives the two-orders-of-magnitude velocity-gradient correction.
  • E_iso (GRB 990123 fit) = 1e55 erg (fixed)
    Fixed by hand to break degeneracies, motivated by E_gamma,iso ~ 3e54 erg (Section 4). Affects the validation fit.
  • epsilon_e,rs and p_rs (GRB 990123 fit) = 0.5, 2.5 (fixed)
    Fixed because the early flash is only observed in one band; they shape the reverse-shock spectrum but are not independently constrained.
  • epsilon_B,rs (GRB 990123 fit) = ~0.86 (log10 = -0.063)
    Fitted free parameter that directly sets the reverse-shock peak flux; high value is needed to match the bright flash, so the fit success is not an independent validation.
assumptions (7)
  • standard math Relativistic shock jump conditions with a trans-relativistic equation of state
    Eqs. (1)-(9); adopted from Uhm 2011 / Mignone & McKinney 2007, not rederived.
  • domain assumption Ambient medium is cold and at rest; ejecta is cold (internal energy converted to kinetic) and unmagnetized
    Section 2.1; excludes hot/magnetized ejecta, which could change reverse shock emission.
  • domain assumption Blast region is a uniform-velocity, infinitely thin surface; radial profiles are delta functions
    Section 2.2; enables radial integration of Euler equations, valid in the ultra-relativistic limit.
  • domain assumption Reverse shock pressure is neglected in lateral expansion (Eq. 25)
    Section 2.2; stated to stabilize numerics with no shown comparison; authors caution it may fail for slow outflows.
  • ad hoc to paper Imagined zero-density tail with velocity decay (Eq. 29) models post-crossing reverse shock
    Section 2.3; phenomenological workaround with free exponent g.
  • domain assumption Constant ambient density (k=0) in the central case studies
    Section 3.1; claim demonstrated only for k=0.
  • ad hoc to paper Unified radial profile (Eq. 48) smoothly connects thin and thick shell cases
    Section 3.2; assumed to construct a structured jet with both regimes.

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Cite this review

Pith. "Pith review of Forward and Reverse Shock Emission from Relativistic Jets with Arbitrary Angular and Stratified Radial Profiles." pith.science (2026). https://pith.science/paper/E45JDTCR

@misc{pith2026250715311,
  author       = {Pith},
  title        = {Pith review of: Forward and Reverse Shock Emission from Relativistic Jets with Arbitrary Angular and Stratified Radial Profiles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E45JDTCR}},
  note         = {Machine review of arXiv:2507.15311}
}
read the original abstract

Gamma-ray bursts are expected to be generated by structured jets, whose profiles significantly impact their afterglow emission. Previously, we developed a numerical code jetsimpy, to model the afterglow of jets with arbitrary angular profiles. In this study, we extend the code to incorporate a stratified radial profile, enabling it to model jets with arbitrary axisymmetric two-dimensional structures. The radial profile leads to the formation of a reverse shock. We modeled the shock system using an energy conservation prescription, which differs from the pressure balance approach. This leads to remarkably different predictions for reverse shock emission. In particular, we find that the reverse shock emission in the thin shell case is significantly overestimated in analytic models. We also explore the off-axis reverse shock emission from structured jets, where the cores belong to thick shell cases and the wings belong to thin shell cases. We have confirmed the prediction that off-axis observers may see a thin-to-thick transition, but we find that the light curve morphology is hard to distinguish from pure thin or thick shell cases. A radial profile also introduces hydrodynamic energy injection. As such, our code can naturally apply to refreshed shock cases, where the modeling of kilonova afterglows is demonstrated as an example. To validate our method, we fit the optical flash of GRB 990123, showing good agreement with the data. The upgraded jetsimpy provides unprecedented flexibility in modeling the afterglow emission of jets with various profiles, including those derived from general relativistic magnetohydrodynamic simulations.

Figures

Figures reproduced from arXiv: 2507.15311 by the authors.

Figure 1
Figure 1. An illustration of the forward-reverse shock sys￾tem and the labeling of the relevant thermodynamic quanti￾ties. The boundary condition of the blast region is deter￾mined by the shock jump conditions. Here, we follow Uhm 2011, who derived the jump conditions assuming a trans-relativistic equation of state (Mignone & McK￾inney 2007; see also Weaver et al. 1977; Sari & Piran 1995; Pe’er et al. 2017). At the forward sh… view at source ↗
Figure 2
Figure 2. The evolution of blastwave properties in the forward-reverse shock system. The parameters for these sim￾ulations are: Eiso = 1052 erg, Γ0 = 300, n0 = 1 cm−3 , θc = 0.1 rad, T90 = 100 s, g = 1. Upper panel: Evolution of the isotropic equivalent energy for the forward shock-only case, the thick shell case, and the thin shell case. For com￾parison, the result of the simplified thin shell case is also shown. Middle Pane… view at source ↗
Figure 3
Figure 3. The optical light curves of forward and reverse shock emission in the thin and thick shell cases predicted by our model. The simulation parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Off-axis reverse shock emission at optical wave￾band for a structured jet. The angular structure follows a power-law profile with a half-opening angle of θc = 0.1 and a slope of s = 4. The parameters for the jet simulation are: Ec = 1052 erg, Γc = 300, n0 = 10 cm−3 , a…
Figure 5
Figure 5. Figure 5: The kilonova afterglow emission predicted by our model. For comparison, the forward shock only case is also shown to demonstrate the consistency of our model. The parameters for the ejecta are Eiso = 1051 erg and umin = 0.2. The parameters for the forward and reverse s…
Figure 6
Figure 6. Figure 6: The best fitting optical and X-ray light curves for GRB 990123 afterglow. The optical data are converted to AB magnitude and are corrected for galactic extinction. Our fitting shows good agreement with the observa￾tional data, as illustrated in [PITH_FULL_IMAGE:figure…
Figure 7
Figure 7. Figure 7: The parameter estimation results for GRB 990123 afterglow. The parameter uncertainties are in 1-σ level, and the contour plots show 1-σ and 2-σ levels. duced by structured jets. In addition to the previously studied angular profile, we introduce a stratified radial pro…

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Reference graph

Works this paper leans on

95 extracted references · 7 canonical work pages · cited by 1 Pith paper

  1. [1]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017a, PhRvL, 119, 161101, doi: 10.1103/PhysRevLett.119.161101 —. 2017b, ApJL, 848, L12, doi: 10.3847/2041-8213/aa91c9 —. 2017c, ApJL, 848, L13, doi: 10.3847/2041-8213/aa920c

    doi:10.1103/physrevlett.119.161101

  2. [2]

    Reverse and forward shock afterglow emission from steep jets viewed off axis

    Abdikamalov, E., & Beniamini, P. 2025, arXiv e-prints, arXiv:2502.12757, doi: 10.48550/arXiv.2502.12757

    work page Pith review arXiv doi:10.48550/arxiv.2502.12757 2025

  3. [3]

    K., Beniamini, P., & Hotokezaka, K

    Acharya, S. K., Beniamini, P., & Hotokezaka, K. 2025, A&A, 693, A108, doi: 10.1051/0004-6361/202452290

    doi:10.1051/0004-6361/202452290 2025

  4. [4]

    2021, MNRAS, 507, 1788, doi: 10.1093/mnras/stab2000

    Ai, S., & Zhang, B. 2021, MNRAS, 507, 1788, doi: 10.1093/mnras/stab2000

    work page doi:10.1093/mnras/stab2000 2021

  5. [5]

    1999, Nature, 398, 400, doi: 10.1038/18837

    Akerlof, C., Balsano, R., Barthelmy, S., et al. 1999, Nature, 398, 400, doi: 10.1038/18837

    doi:10.1038/18837 1999

  6. [6]

    D., Berger, E., Fong, W., et al

    Alexander, K. D., Berger, E., Fong, W., et al. 2017, ApJL, 848, L21, doi: 10.3847/2041-8213/aa905d

    doi:10.3847/2041-8213/aa905d 2017

  7. [7]

    D., Margutti, R., Blanchard, P

    Alexander, K. D., Margutti, R., Blanchard, P. K., et al. 2018, ApJL, 863, L18, doi: 10.3847/2041-8213/aad637

    doi:10.3847/2041-8213/aad637 2018

  8. [8]

    2019, Astrophys

    Ashton, G., et al. 2019, Astrophys. J. Suppl., 241, 27, doi: 10.3847/1538-4365/ab06fc Barniol Duran, R., Nakar, E., Piran, T., & Sari, R. 2015, MNRAS, 448, 417, doi: 10.1093/mnras/stv011

    doi:10.3847/1538-4365/ab06fc 2019

Show all 95 references
  1. [9]

    M., & Uhm, Z

    Beloborodov, A. M., & Uhm, Z. L. 2006, ApJL, 651, L1, doi: 10.1086/508807

    2006 doi

  2. [10]

    2022, MNRAS, 515, 555, doi: 10.1093/mnras/stac1821

    Beniamini, P., Gill, R., & Granot, J. 2022, MNRAS, 515, 555, doi: 10.1093/mnras/stac1821

    2022 doi

  3. [11]

    2020, MNRAS, 493, 3521, doi: 10.1093/mnras/staa538

    Beniamini, P., Granot, J., & Gill, R. 2020, MNRAS, 493, 3521, doi: 10.1093/mnras/staa538

    2020 doi

  4. [12]

    2016, MNRAS, 457, L108, doi: 10.1093/mnrasl/slw003

    Beniamini, P., & Kumar, P. 2016, MNRAS, 457, L108, doi: 10.1093/mnrasl/slw003

    2016 doi

  5. [13]

    2019, MNRAS, 482, 5430, doi: 10.1093/mnras/sty3110

    Beniamini, P., & Nakar, E. 2019, MNRAS, 482, 5430, doi: 10.1093/mnras/sty3110

    2019 doi

  6. [14]

    L., Larson, D., Weiland, J

    Bennett, C. L., Larson, D., Weiland, J. L., & Hinshaw, G. 2014, ApJ, 794, 135, doi: 10.1088/0004-637X/794/2/135

    2014 doi

  7. [15]

    2011, ApJ, 740, 100, doi: 10.1088/0004-637X/740/2/100

    Bromberg, O., Nakar, E., Piran, T., & Sari, R. 2011, ApJ, 740, 100, doi: 10.1088/0004-637X/740/2/100

    2011 doi

  8. [16]

    2014, A&A, 564, A125, doi: 10.1051/0004-6361/201322971

    Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, A&A, 564, A125, doi: 10.1051/0004-6361/201322971

    2014 doi

  9. [17]

    J., Zapatero-Osorio, M

    Castro-Tirado, A. J., Zapatero-Osorio, M. R., Caon, N., et al. 1999, Science, 283, 2069, doi: 10.1126/science.283.5410.2069

    1999

  10. [18]

    C., & Laskar, T

    Duffell, P. C., & Laskar, T. 2018, ApJ, 865, 94, doi: 10.3847/1538-4357/aadb9c

    2018 doi

  11. [19]

    C., & MacFadyen, A

    Duffell, P. C., & MacFadyen, A. I. 2013, ApJ, 775, 87, doi: 10.1088/0004-637X/775/2/87

    2013 doi

  12. [20]

    2002, ChJA&A, 2, 449, doi: 10.1088/1009-9271/2/5/449

    Fan, Y.-Z., Dai, Z.-G., Huang, Y.-F., & Lu, T. 2002, ChJA&A, 2, 449, doi: 10.1088/1009-9271/2/5/449

    2002 doi

  13. [21]

    Z., Wei, D

    Fan, Y. Z., Wei, D. M., & Wang, C. F. 2004, A&A, 424, 477, doi: 10.1051/0004-6361:20041115

    2004 doi

  14. [22]

    Z., Zhang, B., Kobayashi, S., & M´ esz´ aros, P

    Fan, Y. Z., Zhang, B., Kobayashi, S., & M´ esz´ aros, P. 2005, ApJ, 628, 867, doi: 10.1086/430339

    2005 doi

  15. [23]

    K., Alexander, K

    Fong, W., Blanchard, P. K., Alexander, K. D., et al. 2019, ApJL, 883, L1, doi: 10.3847/2041-8213/ab3d9e

    2019 doi

  16. [24]

    Giannios, D., Mimica, P., & Aloy, M. A. 2008, A&A, 478, 747, doi: 10.1051/0004-6361:20078931

    2008 doi

  17. [25]

    2023, MNRAS, 524, L78, doi: 10.1093/mnrasl/slad075

    Gill, R., & Granot, J. 2023, MNRAS, 524, L78, doi: 10.1093/mnrasl/slad075

    2023 doi

  18. [26]

    2021, MNRAS, 500, 3511, doi: 10.1093/mnras/staa3501 18

    Gottlieb, O., Nakar, E., & Bromberg, O. 2021, MNRAS, 500, 3511, doi: 10.1093/mnras/staa3501 18

    2021 doi

  19. [27]

    2024, MNRAS, 531, 1704, doi: 10.1093/mnras/stae1224

    Govreen-Segal, T., & Nakar, E. 2024, MNRAS, 531, 1704, doi: 10.1093/mnras/stae1224

    2024 doi

  20. [28]

    2018, MNRAS, 481, 2711, doi: 10.1093/mnras/sty2454

    Granot, J., De Colle, F., & Ramirez-Ruiz, E. 2018, MNRAS, 481, 2711, doi: 10.1093/mnras/sty2454

    2018 doi

  21. [29]

    2003, ApJ, 591, 1086, doi: 10.1086/375489

    Granot, J., & Kumar, P. 2003, ApJ, 591, 1086, doi: 10.1086/375489

    2003 doi

  22. [30]

    2003, Nature, 426, 138, doi: 10.1038/426138a

    Granot, J., Nakar, E., & Piran, T. 2003, Nature, 426, 138, doi: 10.1038/426138a

    2003 doi

  23. [31]

    2012, MNRAS, 421, 570, doi: 10.1111/j.1365-2966.2011.20335.x

    Granot, J., & Piran, T. 2012, MNRAS, 421, 570, doi: 10.1111/j.1365-2966.2011.20335.x

    2012

  24. [32]

    J., et al

    Haggard, D., Nynka, M., Ruan, J. J., et al. 2017, ApJL, 848, L25, doi: 10.3847/2041-8213/aa8ede

    2017 doi

  25. [33]

    D., et al

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

    2019 doi

  26. [34]

    2018, ApJ, 867, 95, doi: 10.3847/1538-4357/aadf92

    Piran, T. 2018, ApJ, 867, 95, doi: 10.3847/1538-4357/aadf92

    2018 doi

  27. [35]

    F., & Cheng, K

    Huang, Y. F., & Cheng, K. S. 2003, MNRAS, 341, 263, doi: 10.1046/j.1365-8711.2003.06430.x

    2003

  28. [36]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    2007 doi

  29. [37]

    2018, ApJ, 857, 128, doi: 10.3847/1538-4357/aab76d

    Jin, Z.-P., Li, X., Wang, H., et al. 2018, ApJ, 857, 128, doi: 10.3847/1538-4357/aab76d

    2018 doi

  30. [38]

    2018, MNRAS, 473, L121, doi: 10.1093/mnrasl/slx175

    Kathirgamaraju, A., Barniol Duran, R., & Giannios, D. 2018, MNRAS, 473, L121, doi: 10.1093/mnrasl/slx175

    2018 doi

  31. [39]

    2019, MNRAS, 487, 3914, doi: 10.1093/mnras/stz1564

    Kathirgamaraju, A., Giannios, D., & Beniamini, P. 2019, MNRAS, 487, 3914, doi: 10.1093/mnras/stz1564

    2019 doi

  32. [40]

    2000, ApJ, 545, 807, doi: 10.1086/317869

    Kobayashi, S. 2000, ApJ, 545, 807, doi: 10.1086/317869

    2000 doi

  33. [41]

    1999, ApJ, 513, 669, doi: 10.1086/306868

    Kobayashi, S., Piran, T., & Sari, R. 1999, ApJ, 513, 669, doi: 10.1086/306868

    1999 doi

  34. [42]

    2000, ApJ, 542, 819, doi: 10.1086/317021

    Kobayashi, S., & Sari, R. 2000, ApJ, 542, 819, doi: 10.1086/317021

    2000 doi

  35. [43]

    2003, ApJ, 597, 455, doi: 10.1086/378283

    Kobayashi, S., & Zhang, B. 2003, ApJ, 597, 455, doi: 10.1086/378283

    2003 doi

  36. [44]

    2003, ApJ, 591, 1075, doi: 10.1086/375186

    Kumar, P., & Granot, J. 2003, ApJ, 591, 1075, doi: 10.1086/375186

    2003 doi

  37. [45]

    P., Lyman, J

    Lamb, G. P., Lyman, J. D., Levan, A. J., et al. 2019a, ApJL, 870, L15, doi: 10.3847/2041-8213/aaf96b

    doi

  38. [46]

    P., Tanvir, N

    Lamb, G. P., Tanvir, N. R., Levan, A. J., et al. 2019b, ApJ, 883, 48, doi: 10.3847/1538-4357/ab38bb

    doi

  39. [47]

    2015, ApJ, 814, 1, doi: 10.1088/0004-637X/814/1/1

    Laskar, T., Berger, E., Margutti, R., et al. 2015, ApJ, 814, 1, doi: 10.1088/0004-637X/814/1/1

    2015 doi

  40. [48]

    D., Berger, E., et al

    Laskar, T., Alexander, K. D., Berger, E., et al. 2018, ApJ, 862, 94, doi: 10.3847/1538-4357/aacbcc

    2018 doi

  41. [49]

    J., et al

    Lazzati, D., Perna, R., Morsony, B. J., et al. 2018, PhRvL, 120, 241103, doi: 10.1103/PhysRevLett.120.241103

    2018 doi

  42. [50]

    K., Murphy, T., Lenc, E., et al

    Leung, J. K., Murphy, T., Lenc, E., et al. 2023, MNRAS, 523, 4029, doi: 10.1093/mnras/stad1670

    2023 doi

  43. [51]

    2005, A&A, 438, 821, doi: 10.1051/0004-6361:20042534

    Maiorano, E., Masetti, N., Palazzi, E., et al. 2005, A&A, 438, 821, doi: 10.1051/0004-6361:20042534

    2005 doi

  44. [52]

    2021, ARA&A, 59, 155, doi: 10.1146/annurev-astro-112420-030742

    Margutti, R., & Chornock, R. 2021, ARA&A, 59, 155, doi: 10.1146/annurev-astro-112420-030742

    2021 doi

  45. [53]

    2017, ApJL, 848, L20, doi: 10.3847/2041-8213/aa9057

    Margutti, R., Berger, E., Fong, W., et al. 2017, ApJL, 848, L20, doi: 10.3847/2041-8213/aa9057

    2017 doi

  46. [54]

    D., Xie, X., et al

    Margutti, R., Alexander, K. D., Xie, X., et al. 2018, ApJL, 856, L18, doi: 10.3847/2041-8213/aab2ad M´ esz´ aros, P., & Rees, M. J. 1999, MNRAS, 306, L39, doi: 10.1046/j.1365-8711.1999.02800.x M´ esz´ aros, P., Rees, M. J., & Wijers, R. A. M. J. 1998, ApJ, 499, 301, doi: 10.10...

    2018

  47. [55]

    Mignone, A., & McKinney, J. C. 2007, MNRAS, 378, 1118, doi: 10.1111/j.1365-2966.2007.11849.x

    2007

  48. [56]

    P., Deller, A

    Mooley, K. P., Deller, A. T., Gottlieb, O., et al. 2018, Nature, 561, 355, doi: 10.1038/s41586-018-0486-3

    2018 doi

  49. [57]

    2023, MNRAS, 525, 5224, doi: 10.1093/mnras/stad2594

    Guiriec, S. 2023, MNRAS, 525, 5224, doi: 10.1093/mnras/stad2594

    2023 doi

  50. [58]

    2011, Nature, 478, 82, doi: 10.1038/nature10365

    Nakar, E., & Piran, T. 2011, Nature, 478, 82, doi: 10.1038/nature10365

    2011 doi

  51. [59]

    2002, ApJ, 579, 699, doi: 10.1086/342791

    Nakar, E., Piran, T., & Granot, J. 2002, ApJ, 579, 699, doi: 10.1086/342791

    2002 doi

  52. [60]

    2013, MNRAS, 433, 2107, doi: 10.1093/mnras/stt872

    Nava, L., Sironi, L., Ghisellini, G., Celotti, A., & Ghirlanda, G. 2013, MNRAS, 433, 2107, doi: 10.1093/mnras/stt872

    2013 doi

  53. [61]

    2023, MNRAS, 520, 2727, doi: 10.1093/mnras/stad175

    Menegazzi, L. 2023, MNRAS, 520, 2727, doi: 10.1093/mnras/stad175

    2023 doi

  54. [62]

    Panaitescu, A., M´ esz´ aros, P., & Rees, M. J. 1998, ApJ, 503, 314, doi: 10.1086/305995

    1998 doi

  55. [63]

    2024a, MNRAS, 528, 2066, doi: 10.1093/mnras/stae197 —

    Pang, S.-L., & Dai, Z.-G. 2024a, MNRAS, 528, 2066, doi: 10.1093/mnras/stae197 —. 2024b, ApJ, 977, 123, doi: 10.3847/1538-4357/ad9007 Pe’er, A., Long, K., & Casella, P. 2017, ApJ, 846, 54, doi: 10.3847/1538-4357/aa80df

    2017 doi

  56. [64]

    A., Ho, A

    Perley, D. A., Ho, A. Y. Q., Fausnaugh, M., et al. 2025, MNRAS, 537, 2362, doi: 10.1093/mnras/staf125

    2025 doi

  57. [65]

    2013, MNRAS, 430, 2121, doi: 10.1093/mnras/stt037

    Piran, T., Nakar, E., & Rosswog, S. 2013, MNRAS, 430, 2121, doi: 10.1093/mnras/stt037

    2013 doi

  58. [66]

    2018, ApJ, 869, 130, doi: 10.3847/1538-4357/aaf054

    Radice, D., Perego, A., Hotokezaka, K., et al. 2018, ApJ, 869, 130, doi: 10.3847/1538-4357/aaf054

    2018 doi

  59. [67]

    J., & M´ esz´ aros, P

    Rees, M. J., & M´ esz´ aros, P. 1998, ApJL, 496, L1, doi: 10.1086/311244

    1998 doi

  60. [68]

    Rhoads, J. E. 1997, ApJL, 487, L1, doi: 10.1086/310876 —. 1999, ApJ, 525, 737, doi: 10.1086/307907

    1997 doi

  61. [69]

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

    2002

  62. [70]

    2020, ApJ, 896, 166, doi: 10.3847/1538-4357/ab93cf

    Ryan, G., van Eerten, H., Piro, L., & Troja, E. 2020, ApJ, 896, 166, doi: 10.3847/1538-4357/ab93cf

    2020 doi

  63. [71]

    2000, ApJL, 535, L33, doi: 10.1086/312689 19

    Sari, R., & M´ esz´ aros, P. 2000, ApJL, 535, L33, doi: 10.1086/312689 19

    2000 doi

  64. [72]

    1995, ApJL, 455, L143, doi: 10.1086/309835

    Sari, R., & Piran, T. 1995, ApJL, 455, L143, doi: 10.1086/309835

    1995 doi

  65. [73]

    Sari, R., Piran, T., & Halpern, J. P. 1999, ApJL, 519, L17, doi: 10.1086/312109

    1999 doi

  66. [74]

    F., & Finkbeiner, D

    Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103, doi: 10.1088/0004-637X/737/2/103

    2011 doi

  67. [75]

    2013, ApJ, 778, 107, doi: 10.1088/0004-637X/778/2/107

    Sironi, L., & Giannios, D. 2013, ApJ, 778, 107, doi: 10.1088/0004-637X/778/2/107

    2013 doi

  68. [76]

    P., Perley, D

    Srinivasaragavan, G. P., Perley, D. A., Ho, A. Y. Q., et al. 2025, MNRAS, 538, 351, doi: 10.1093/mnras/staf290

    2025 doi

  69. [77]

    2017, Nature, 551, 71, doi: 10.1038/nature24290

    Troja, E., Piro, L., van Eerten, H., et al. 2017, Nature, 551, 71, doi: 10.1038/nature24290

    2017 doi

  70. [78]

    2018, MNRAS, 478, L18, doi: 10.1093/mnrasl/sly061

    Troja, E., Piro, L., Ryan, G., et al. 2018, MNRAS, 478, L18, doi: 10.1093/mnrasl/sly061

    2018 doi

  71. [79]

    2020, MNRAS, 498, 5643, doi: 10.1093/mnras/staa2626

    Troja, E., van Eerten, H., Zhang, B., et al. 2020, MNRAS, 498, 5643, doi: 10.1093/mnras/staa2626

    2020 doi

  72. [80]

    Uhm, Z. L. 2011, ApJ, 733, 86, doi: 10.1088/0004-637X/733/2/86

    2011 doi

  73. [81]

    L., & Beloborodov, A

    Uhm, Z. L., & Beloborodov, A. M. 2007, ApJL, 665, L93, doi: 10.1086/519837 van Eerten, H., van der Horst, A., & MacFadyen, A. 2012, ApJ, 749, 44, doi: 10.1088/0004-637X/749/1/44 van Eerten, H., Zhang, W., & MacFadyen, A. 2010, ApJ, 722, 235, doi: 10.1088/0004-637X/722/1/235

    2007 doi

  74. [82]

    G., Giannios, D., & Duffell, P

    Wang, H., Dastidar, R. G., Giannios, D., & Duffell, P. C. 2024, ApJS, 273, 17, doi: 10.3847/1538-4365/ad4d9d

    2024 doi

  75. [83]

    Y., Dai, Z

    Wang, X. Y., Dai, Z. G., & Lu, T. 2000, MNRAS, 319, 1159, doi: 10.1046/j.1365-8711.2000.03922.x

    2000

  76. [84]

    1977, ApJ, 218, 377, doi: 10.1086/155692

    Weaver, R., McCray, R., Castor, J., Shapiro, P., & Moore, R. 1977, ApJ, 218, 377, doi: 10.1086/155692

    1977 doi

  77. [85]

    Willmer, C. N. A. 2018, ApJS, 236, 47, doi: 10.3847/1538-4365/aabfdf

    2018 doi

  78. [86]

    2019, ApJL, 880, L23, doi: 10.3847/2041-8213/ab2fd4

    Wu, Y., & MacFadyen, A. 2019, ApJL, 880, L23, doi: 10.3847/2041-8213/ab2fd4

    2019 doi

  79. [87]

    2013, ApJ, 776, 120, doi: 10.1088/0004-637X/776/2/120

    Yi, S.-X., Wu, X.-F., & Dai, Z.-G. 2013, ApJ, 776, 120, doi: 10.1088/0004-637X/776/2/120

    2013 doi

  80. [88]

    2022, in Handbook of X-ray and Gamma-ray Astrophysics, ed

    Yuan, W., Zhang, C., Chen, Y., & Ling, Z. 2022, in Handbook of X-ray and Gamma-ray Astrophysics, ed. C. Bambi & A. Sangangelo (Springer, Singapore), 86, doi: 10.1007/978-981-16-4544-0 151-1

    2022 doi

  81. [89]

    2018, The Physics of Gamma-Ray Bursts (Cambridge University Press), doi: 10.1017/9781139226530

    Zhang, B. 2018, The Physics of Gamma-Ray Bursts (Cambridge University Press), doi: 10.1017/9781139226530

    2018 doi

  82. [90]

    Z., Dyks, J., et al

    Zhang, B., Fan, Y. Z., Dyks, J., et al. 2006, ApJ, 642, 354, doi: 10.1086/500723

    2006 doi

  83. [91]

    2005, ApJ, 628, 315, doi: 10.1086/429787

    Zhang, B., & Kobayashi, S. 2005, ApJ, 628, 315, doi: 10.1086/429787

    2005 doi

  84. [92]

    2003a, ApJ, 595, 950, doi: 10.1086/377363

    Zhang, B., Kobayashi, S., & M´ esz´ aros, P. 2003a, ApJ, 595, 950, doi: 10.1086/377363

    doi

  85. [93]

    2009, ApJ, 698, 1261, doi: 10.1088/0004-637X/698/2/1261

    Zhang, W., & MacFadyen, A. 2009, ApJ, 698, 1261, doi: 10.1088/0004-637X/698/2/1261

    2009 doi

  86. [94]

    E., & MacFadyen, A

    Zhang, W., Woosley, S. E., & MacFadyen, A. I. 2003b, ApJ, 586, 356, doi: 10.1086/367609

    doi

  87. [95]

    2022, MNRAS, 513, 4887, doi: 10.1093/mnras/stac1198

    Zhang, Z.-L., Liu, R.-Y., Geng, J.-J., Wu, X.-F., & Wang, X.-Y. 2022, MNRAS, 513, 4887, doi: 10.1093/mnras/stac1198

    2022 doi

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