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REVIEW 3 major objections 6 minor 46 references

Connecting afterglow light curves to the GRB central engine

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that a single point on a short gamma-ray burst afterglow light curve — the jet-break time and brightness when seen on-axis, the peak when seen off-axis — determines the equivalent isotropic kinetic energy of the blast to…

desk verdict Useful inverse calibration for top-hat afterglows, but the headline accuracy claim is in-sample and conditioned on fixed microphysics. read the letter →

arxiv 2505.01158 v1 pith:RPNJHF3U submitted 2025-05-02 astro-ph.HE gr-qcnucl-th

Muhammed Diyaddin Ilhan , Kai Schwenzer This is my paper · ORCID
classification astro-ph.HEgr-qcnucl-th
keywords shortgamma-rayburstsafterglowlightcurvesforwardshockmodeljetbreakoff-axisemissionisotropickineticenergyneutronstarmergerscurveparameterization
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

Short gamma-ray bursts are thought to be powered by neutron-star mergers, and the long-lived afterglow is one of the few windows onto how much energy the merger's central engine put into the jet. This paper tries to turn that window into a measuring device. Using synthetic short-GRB afterglows from the forward-shock model, the authors fit simple broken-power-law templates to the light curves and then invert the relation between template parameters and physical inputs. Their central claim is that just two numbers read off the light curve — the time and the brightness at the jet break for on-axis bursts, or at the maximum for off-axis bursts — determine the equivalent isotropic kinetic energy of the blast to within tens of percent. If that claim is right, observers can estimate the engine's energy from a single well-defined feature of the afterglow, without modeling the messy early-time emission.

What carries the argument

The load-bearing object is a smooth broken-power-law template for the spectral-flux-density light curve, $F(t) = \left( (a t^{-\alpha})^{\nu} + (b t^{\beta})^{\nu} \right)^{-1/\nu}$, rewritten as eq. (5) for on-axis events in terms of the jet-break time $t_{jb}$ and flux $F_{jb}$, and as eq. (2) for off-axis events in terms of the maximum time $t_{\max}$ and peak flux $F_{\max}$, together with the exponents $\alpha$, $\beta$ and a smoothing parameter $\nu$. That template is fit to a dataset of synthetic afterglows generated by a relativistic hydrodynamic forward-shock simulation, and the fit parameters are mapped linearly (in log space) to the physical inputs $E_{K,\mathrm{iso}}$, $\theta_{\mathrm{obs}}$, and $n_0$ by both linear regression and a linear-activation neural network. The inverse regression — energy as a function of the light-curve parameters — is the workhorse identity of the paper, and it is the stability of its coefficients across the dataset that supports the claim that $t$ and $F$ at the break or peak carry nearly all the information.

What would settle it

Regenerate the synthetic dataset with the electron spectral index varied from the fiducial 2.43 to, say, 2.0 and 2.8 (and likewise vary the magnetic-field and electron energy fractions), refit the inverse regression, and compare the recovered $E_{K,\mathrm{iso}}$ from eqs. (17)–(18) with the true input values; if the inferred energies shift by more than the quoted tens-of-percent uncertainty, the calibration is not robust across the real burst population.

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Extended reading notes

Core claim

For a top-hat jet in the forward-shock picture, the paper establishes empirical power-law calibrations that recover the initial equivalent isotropic kinetic energy from just the break or peak position. Concretely, the on-axis estimate takes the form $E_{K,\mathrm{iso}} \propto F_{jb}^{a}\, t_{jb}^{b}\, d_{L}^{c}$ with $a \simeq 0.63$–$0.69$ and $b \simeq 1.10$–$1.12$ at x-ray and infrared frequencies (eq. 17), and the off-axis estimate replaces $F_{jb},t_{jb}$ by the corresponding peak values $F_{\max},t_{\max}$ with similar exponents (eq. 18). At radio frequencies the exponents differ, and the paper attributes that difference to spectral evolution of the on-axis light curve. The central claim is that, with the forward-shock parameters at their fiducial values, no other input — not the viewing angle, not the circumburst density, not the early-time behavior — is required to get the kinetic energy at the tens-of-percent level, and that the same two numbers also strip away most of the fitting uncertainty.

Load-bearing premise

The calibration stays valid for real bursts even though the simulation fixes the electron energy-slope and the energy fractions in magnetic fields and electrons to single representative values, and the paper does not propagate how much those quantities vary across the true population.

Editorial extensions

If this is right

  • An observer needs only the location of the jet break (on-axis) or the light-curve maximum (off-axis) to estimate $E_{K,\mathrm{iso}}$; neither the viewing angle nor the circumburst density nor early-time data are required.
  • For on-axis short GRBs, combining the inferred $E_{K,\mathrm{iso}}$ with an independently measured jet opening angle gives the total kinetic energy of the afterglow jet, and adding the prompt gamma-ray energy yields an estimate of the central engine's total energy output.
  • For off-axis events, the same calibration works from the maximum, so a nearby off-axis burst — for instance one associated with a gravitational-wave signal — can be used without knowing the viewing angle.
  • Using all five light-curve parameters pushes the synthetic-dataset uncertainty down to the few-percent level, while using only the flux or only the time fails badly, showing that the two numbers carry independent information.
  • The radio band is a partial exception: on-axis radio light curves rise before the break, the empirical exponents differ from the higher bands, and the paper treats the radio maximum as involving additional spectral-evolution physics.

Reading between the lines

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

  • An implication the authors leave implicit is that the same two-point inversion can be applied to archival afterglow light curves as a cheap consistency check: the scatter between energies from eqs. (17)–(18) and energies from full broadband fits would show how often the canonical top-hat forward-shock picture actually holds.
  • The electron spectral index $p$ is the most plausible source of population-level bias, since the paper fixes $p=2.43$ and acknowledges that theory allows $p$ to shift the power-law exponents; a natural extension is to retrain the inverse regression on synthetic light curves drawn with a distribution of $p$ values and compare the recovered energies.
  • Structured jets, which the paper does not model, have a much shallower off-axis rise than the top-hat value $\alpha \approx 5.7$, so the constants in the off-axis calibration are likely geometry-dependent; testing the same inversion on structured-jet light curves would map where the top-hat calibration breaks.
  • A multi-band joint version of the inversion could beat the single-band tens-of-percent accuracy, because the mild frequency dependence of the jet-break time adds an extra constraint linking the same $E_{K,\mathrm{iso}}$ across bands.
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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 / 6 minor

Summary. Using the AfterglowPy forward-shock code, the paper generates synthetic short-GRB afterglow light curves for a top-hat jet with three varying parameters (EK,iso, θobs, n0) and fixed microphysics (p=2.43, εe=0.1, εB=0.01, θjet=0.2), at radio, IR, and X-ray frequencies. Each light curve is fit with a smoothed broken power law (Eqs. 2 and 5) to extract break/peak flux and time, spectral slopes, and a smoothing parameter. The forward mapping from input parameters to light curve parameters is approximated by linear regression and by a single-layer linear neural network (Eq. 6). The inverse regression gives empirical power laws for EK,iso in terms of the light curve parameters (Eqs. 15-18). The paper's central claim is that only the position of the jet break (on-axis) or the maximum (off-axis) suffices to estimate EK,iso at the tens-of-percent level.

Significance. The proposed estimator is attractive because it uses a single characteristic point on the light curve and avoids full light-curve modeling. The transparent use of a public simulation code, the explicit regression tables, and the reproduction of known scalings (e.g., tjb ∝ (E/n)^{1/3}) are strengths. The paper's claim would be a useful simplification if its accuracy were confirmed on independent data. At present, the accuracy is established only as an in-sample calibration at one fiducial point in microphysical parameter space, so the significance is conditional on additional validation.

major comments (3)
  1. [Sec. IV, Tables IX-XI] The RMSE values in Tables IX-XI are residuals of inverse linear regressions evaluated on exactly the same synthetic dataset that was used to fit them; no train/test split, cross-validation, or independent simulation/observation is reported. For example, the two-parameter on-axis IR row gives RMSE=0.156, but this is a training error and generally underestimates the error on new light curves, including real afterglows. The abstract's statement that the kinetic energy is determined at the tens-of-percent level is therefore not established by the presented statistics. Please add held-out validation (e.g., cross-validation or an independent synthetic sample) and, if possible, a comparison with a few observed short-GRB afterglows with independent energy estimates, or explicitly restrict the claim to an in-sample calibration.
  2. [Sec. V, Table I] The calibration of Eqs. (15)-(18) is performed at a single fiducial point in the microphysical parameter space: p=2.43, εe=0.1, εB=0.01, θjet=0.2. The paper states in Sec. V that the electron index p can affect the power-law exponents and 'cannot be captured by our simple linear model.' Because p changes the synchrotron flux normalization and spectral indices, the fitted coefficients in Eqs. (15)-(18) are potentially biased for real bursts whose p differs from 2.43. The cancellation argument involving εe (Eq. 19) is heuristic and does not test the flux dependence. The general claim in the abstract should be either restricted to the fiducial parameters or supported by numerical runs in which p (and ideally εe and εB) are varied.
  3. [Sec. II, Table II, Note 5] The two-parameter estimators in Eqs. (17)-(18) are validated against the finite-difference position of the jet break, with uncertainty taken as half a temporal grid spacing (Note 5). Yet Table II shows that the break time obtained from the paper's own broken-power-law fit differs from this position by up to 23% for on-axis X-ray light curves and by 5-14% in other bands. In an actual observation, the break position must be identified from noisy, sparse data, either by fitting a similar model or by finite differencing of binned fluxes, so this systematic extraction uncertainty belongs in the error budget. As it stands, the 'tens of percent' claim applies to ideal dense synthetic grids, not to the practical observational procedure.
minor comments (6)
  1. [Abstract and Sec. I] The text contains multiple spacing errors ('Gammaraybursts', 'Gamma ray burst' without the space, 'Hori-zontal' in Fig. 1); please copyedit throughout.
  2. [Eq. (11)] The numerical prefactor appears incorrect: with dL=40 Mpc and H0≈70 km/s/Mpc, H0 dL/c≈0.009, giving ζ≈0.991(1+z), not 0.9999(1+z); the difference is negligible but the expression should be fixed.
  3. [Sec. III, Note 2] The fact that the neural network is essentially a linear regression is relegated to a footnote. This caveat should be in the main text so the reader does not take the two methods as independent in a strong sense.
  4. [Eqs. (15)-(18) and Tables IX-XI] Flux units are inconsistent (mJy in the tables, nJy or µJy in the formulas). Note 6 flags only the radio case; please state the unit conventions once and use them consistently.
  5. [Sec. V, Eq. (19)] The argument that εe cancels in the energy evolution is followed by Note 7 conceding that the spectral flux density depends implicitly on εe. The paragraph should be rephrased to avoid an overstrong statement of εe-independence.
  6. [Sec. II, Eq. (5)] The statement that the parametrization is also obtained from the crossing of asymptotic power laws is not shown; clarify the relationship between Eq. (4) and the crossing-time definition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the EK,iso relations are transparent empirical fits to external AfterglowPy simulations, with acknowledged parameter limitations.

full rationale

The paper's central result is an explicit calibration, not a circular derivation. Afterglow light curves are generated using the external AfterglowPy forward-shock package (Ryan et al. 2020), parametrized with broken power laws, and linear regressions are then run both from model parameters to light-curve parameters and back. The inverse relations in Eqs. (15)-(18), obtained with the quoted phrase 'we use the same data set and simply perform the linear regression the other way around,' are therefore fitted empirical approximations. Their RMSEs are in-sample training errors, which limits how strongly the 'tens of percent' claim can be extrapolated beyond the simulated distribution, but this is a statistical-validation caveat rather than a self-definitional reduction. The fixed values of p, epsilon_e, epsilon_B, and theta_jet are stated in Table I, and Sec. V explicitly concedes that p-dependence 'cannot be captured by our simple linear model'; that is a scope limitation on generalizability, not circularity. There is no load-bearing self-citation: the only self-cited entry [45] supports a peripheral remark on structured jets and is not needed for the inverse regression. Accordingly, the score is 0: the derivation chain is self-contained against an external simulation code and does not reduce to its own inputs by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new particles or physical entities. Its central claim rests on a chain of assumptions: the forward shock model is correct, the fixed microphysical parameters are representative, the broken power law parametrization captures the relevant features, and the linear log-space regression approximates the mapping. The fitted regression coefficients are free parameters tuned to the synthetic dataset, and the smoothing parameter ν is an unphysical fitting artifact. The inverse relations are therefore empirical calibrations of one specific model, not independent derivations.

free parameters (2)
  • Inverse regression coefficients for EK_iso (Eqs. 15-18) = Coefficients in Tables IX-XI
    The central estimates of EK_iso from light curve parameters are power-law fits to the same synthetic dataset, not derived from first principles. The exponents and normalizations are all fitted numbers.
  • Smoothing parameter ν in the light curve parametrization = Fitted per light curve, no physical interpretation
    An unphysical smoothing parameter introduced to capture the shape around jet break or maximum. It is needed to obtain stable fits for the other parameters, and it is poorly constrained in some bands.
assumptions (4)
  • domain assumption AfterglowPy forward shock model with a top-hat jet accurately represents short GRB afterglow emission.
    The entire synthetic dataset is generated with this model, which assumes a single-shell relativistic shock, a weakly magnetized external shock, and top-hat jet geometry. Any errors in this model propagate directly into the calibrated relations.
  • domain assumption Fixed microphysical parameters (θjet = 0.2, p = 2.43, εB = 0.01, εe = 0.1) are representative for real short GRBs and the inferred scalings are insensitive to them.
    The paper varies only EK_iso, θobs, and n, leaving all other model parameters fixed at characteristic values (Table I). The Conclusions acknowledge that p in particular could affect the power-law exponents, which would change the central estimate.
  • domain assumption The broken-power-law parametrizations in Eqs. (2) and (5) capture the physical jet-break and maximum features of the light curves.
    Fits to the synthetic light curves show systematic deviations, with RMSE from 8% to 39% depending on band and geometry. The paper notes that the fitted jet-break position can be shifted to earlier times to compensate for additional structure in the simulated curves.
  • ad hoc to paper The linear (power-law) relation in Eq. (6) holds over the parameter range, with no significant nonlinearities affecting the inverse mapping.
    The paper uses linear regression in logarithmic variables and notes that the off-axis peak flux shows sizable nonlinearities. The broadband fit across all three frequencies fails with RMSE of 34-89%, showing that the linear model is inadequate beyond narrow bands, so the validity within a band is a substantive assumption.

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Cite this review

Pith. "Pith review of Connecting afterglow light curves to the GRB central engine." pith.science (2026). https://pith.science/paper/RPNJHF3U

@misc{pith2026250501158,
  author       = {Pith},
  title        = {Pith review of: Connecting afterglow light curves to the GRB central engine},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RPNJHF3U}},
  note         = {Machine review of arXiv:2505.01158}
}
read the original abstract

Gamma ray burst (GRB) afterglow light curves have the potential to inform us about presently unobserved stages in the aftermath of a neutron star merger. Using numerical simulations of short GRB afterglows we obtain an approximate quantitative connection between key aspects of the emission mechanism and the shapes of the resulting light curves. Employing simple, but efficient, parameterizations of the light curve based on a broken power law in terms of physical parameters, fitted to a large dataset of synthetic light curves, we apply basic machine learning techniques to determine the approximate connection between key input parameters of the forward shock model and the light curve parameters. Solving then the inverse problem, we find that the strength of the central engine can be reasonably accurately estimated even with very limited information. In particular, merely the position of jet-break in the on-axis, respectively the maximum in the off-axis light curve determines the kinetic energy at the tens of percent level.

Figures

Figures reproduced from arXiv: 2505.01158 by the authors.

Figure 1
Figure 1. Fits to some exemplary infrared light curves. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

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Works this paper leans on

46 extracted references · 22 canonical work pages

  1. [1]

    R. W. Klebesadel, I. B. Strong, and R. A. Olson, Astro- phys. J. Lett.182, L85 (1973)

    work page 1973

  2. [2]

    Zhang, The Physics of Gamma-Ray Bursts (Cam- bridge University Press, 2018), ISBN 978-1-107-02761-9

    B. Zhang, The Physics of Gamma-Ray Bursts (Cam- bridge University Press, 2018), ISBN 978-1-107-02761-9

    work page 2018

  3. [3]

    Gao and P

    H. Gao and P. Mészáros, Adv. Astron. 2015, 192383 (2015), 1507.01984

    arXiv 2015

  4. [4]

    Kouveliotou, C

    C. Kouveliotou, C. A. Meegan, G. J. Fishman, N. P. Bhyat, M. S. Briggs, T. M. Koshut, W. S. Paciesas, and G. N. Pendleton, Astrophys. J. Lett.413, L101 (1993)

    work page 1993

  5. [5]

    Gehrels et al., Nature 437, 851 (2005), astro- ph/0505630

    N. Gehrels et al., Nature 437, 851 (2005), astro- ph/0505630

    work page arXiv 2005

  6. [7]

    W.-f. Fong, E. Berger, R. Margutti, and B. A. Zauderer, 12 Astrophys. J.815, 102 (2015), 1509.02922

    arXiv 2015

  7. [8]

    Abbott et al

    B. Abbott et al. (Virgo, LIGO Scientific), Phys. Rev. Lett. 119, 161101 (2017), 1710.05832

    arXiv 2017

  8. [9]

    B. P. Abbott et al. (LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRAWITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF (Deeper Wider Faster Program), AST3, CAAS- TRO, VINROUGE, MASTER,...

    arXiv 2017

Show all 46 references
  1. [10]

    B. D. Metzger, Living Rev. Rel.20, 3 (2017), 1610.09381

    2017 arXiv

  2. [11]

    Baiotti and L

    L. Baiotti and L. Rezzolla, Rept. Prog. Phys.80, 096901 (2017), 1607.03540

    2017 arXiv

  3. [12]

    M. G. Alford, L. Bovard, M. Hanauske, L. Rezzolla, and K. Schwenzer, Phys. Rev. Lett.120, 041101 (2018), 1707.09475

    2018 arXiv

  4. [13]

    M. G. Alford, S. Han, and K. Schwenzer, J. Phys. G46, 114001 (2019), 1904.05471

    2019 arXiv

  5. [14]

    Pe’er, Advances in Astronomy2015, 907321 (2015), 1504.02626

    A. Pe’er, Advances in Astronomy2015, 907321 (2015), 1504.02626

    2015 arXiv

  6. [15]

    Costa et al., Nature 387, 783 (1997), astro- ph/9706065

    E. Costa et al., Nature 387, 783 (1997), astro- ph/9706065

    1997

  7. [16]

    van Paradijs et al., Nature386, 686 (1997)

    J. van Paradijs et al., Nature386, 686 (1997)

    1997

  8. [17]

    Ruderman, inSeventh Texas Symposium on Relativis- tic Astrophysics, edited by P

    M. Ruderman, inSeventh Texas Symposium on Relativis- tic Astrophysics, edited by P. G. Bergman, E. J. Fenyves, and L. Motz (1975), vol. 262, pp. 164–180

    1975

  9. [18]

    Wang et al., Astrophys

    X.-G. Wang et al., Astrophys. J. Suppl.219, 9 (2015), 1503.03193

    2015 arXiv

  10. [19]

    Leventis, A

    K. Leventis, A. J. van der Horst, H. J. van Eerten, and R. A. M. J. Wijers, Mon. Not. Roy. Astron. Soc.431, 1026 (2013), 1302.0752

    2013 arXiv

  11. [20]

    G. Ryan, H. van Eerten, L. Piro, and E. Troja, Astro- phys. J.896, 166 (2020), 1909.11691

    2020 arXiv

  12. [21]

    Gehrels, E

    N. Gehrels, E. Ramirez-Ruiz, and D. B. Fox, Ann. Rev. Astron. Astrophys.47, 567 (2009), 0909.1531

    2009 arXiv

  13. [22]

    Berger, Annual Review of Astronomy and Astrophysic 52, 43 (2014), 1311.2603

    E. Berger, Annual Review of Astronomy and Astrophysic 52, 43 (2014), 1311.2603

    2014 arXiv

  14. [23]

    O. S. Salafia and G. Ghirlanda, Galaxies10, 93 (2022), 2206.11088

    2022 arXiv

  15. [24]

    Kumar and B

    P. Kumar and B. Zhang, Physics Reports561, 1 (2015), 1410.0679

    2015 arXiv

  16. [25]

    Rezzolla, B

    L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Lett.732, L6 (2011), 1101.4298

    2011 arXiv

  17. [26]

    R. Sari, T. Piran, and R. Narayan, Astrophys. J. Lett. 497, L17 (1998), astro-ph/9712005

    1998 arXiv

  18. [27]

    van Eerten, W

    H. van Eerten, W. Zhang, and A. MacFadyen, Astrophys. J. 722, 235 (2010), 1006.5125

    2010 arXiv

  19. [28]

    Y. Li, B. Zhang, and H.-J. Lü, Astrophys. J. Suppl.227, 7 (2016), 1608.03383

    2016 arXiv

  20. [29]

    Zhang, Y

    B. Zhang, Y. Z. Fan, J. Dyks, S. Kobayashi, P. Meszaros, D. N. Burrows, J. A. Nousek, and N. Gehrels, Astrophys. J. 642, 354 (2006), astro-ph/0508321

    2006 arXiv

  21. [30]

    X.-G. Wang, B. Zhang, E.-W. Liang, R.-J. Lu, J. Li, L. Li, and D.-B. Lin, Astrophys. J. 859, 160 (2018), 1804.02113

    2018 arXiv

  22. [31]

    Note1, note that this is merely a computational way to prevent instabilities in the fitting process and accurately fit the asymptotic power law exponents—which are al- ready clearly realized in the light curves over realistic time intervals, see fig. 1. In particular we surely...

  23. [32]

    Note2, this is surely not a surprise since in the considered simplified case the neural network effectively amounts to a mere linear regression, so that it is only the numerical optimization method that differs

  24. [33]

    Astron. Astrophys

    S. Puccetti, M. Capalbi, P. Giommi, M. Perri, G. Stratta, L. Angelini, D. N. Burrows, S. Campana, G. Chincarini, G. Cusumano, et al., "Astron. Astrophys."528, A122 (2011), 1102.4270

    2011 arXiv

  25. [34]

    Note3, it might seem more natural to rather employ the off-axis parameterization eq. (2) at radio frequencies where the light curve has a maximum (so that the spec- tral flux density and time reflect the actual values at this maximum), but to perform a consistent frequency dep...

  26. [35]

    Zhang and A

    W. Zhang and A. MacFadyen, Astrophys. J.698, 1261 (2009), 0902.2396

    2009 arXiv

  27. [36]

    (15) and (16) are formally significantly larger than the one in the 2-parameter result given below in eqs

    Note4, this is apparent since using linear error propaga- tion, the errors in the 4-parameter estimate in eqs. (15) and (16) are formally significantly larger than the one in the 2-parameter result given below in eqs. (17) and (18)

  28. [37]

    Increasing the size of temporal grid points this discretization error

    Note5, we use for the error on the position of both the jet-break and the maximum the values half a grid spac- ing away in either direction and average over all light curves. Increasing the size of temporal grid points this discretization error

  29. [38]

    Note6, note the different characteristic spectral flux den- sity ofµJy in the radio case compared tonJy in the other bands

  30. [39]

    Zhang et al., Astrophys

    B. Zhang et al., Astrophys. J.655, 989 (2007), astro- ph/0610177

    2007

  31. [40]

    clean” light curves that show a “canonical

    showing that the time of jet-break is correlated with but does not fix the kinetic energy. Correspondingly, this means that the time and the flux are not clearly corre- lated and both of them contain independent information that is required. However, observationally this is su...

  32. [41]

    L. Nava, G. Ghisellini, G. Ghirlanda, J. I. Cabrera, C. Firmani, and V. Avila-Reese, Monthly Notices of the Royal Astronomical Society377, 1464 (2007), astro- ph/0701705

    2007

  33. [42]

    Kaneko, Z

    Y. Kaneko, Z. F. Bostancı, E. Göğüş, and L. Lin, Mon. Not. Roy. Astron. Soc.452, 824 (2015), 1506.05899

    2015 arXiv

  34. [43]

    Barnes, Y

    J. Barnes, Y. L. Zhu, K. A. Lund, T. M. Sprouse, N. Vassh, G. C. McLaughlin, M. R. Mumpower, and R. Surman, Astrophys. J.918, 44 (2021), 2010.11182

    2021 arXiv

  35. [44]

    (15)-(18) explicitly depend on the spectral flux density

    Note7, the luminosity, respectively spectral flux density, in principle implicitly depends on the electron fraction, but our expressions for the isotropic kinetic energy in terms of light curve parameters eqs. (15)-(18) explicitly depend on the spectral flux density

  36. [45]

    Note8, unfortunately, such an analysis would not provide such simple analytic relations we obtain here

  37. [46]

    M. D. İlhan and M. de Pasquale, AIP Conf. Proc.2178, 030020 (2019)

    2019

  38. [47]

    D. A. Frail et al., Astrophys. J. Lett.562, L55 (2001), astro-ph/0102282

    2001 arXiv

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