Pith. sign in

REVIEW 4 major objections 5 minor 262 references

Self-organized critical characteristics of teraelectronvolt photons from GRB 221009A

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read This paper argues that the 172 TeV photons from GRB 221009A show waiting-time statistics characteristic of a self-organized critical process, with power-law slopes and scale-invariant Tsallis q values.

desk verdict A statistically careful but physically overreaching paper: the power-law WTD and q-Gaussian fits are plausible, but the SOC claim is undercut by an untested nonstationary-Poisson null that the authors themselves cite. read the letter →

arxiv 2412.16052 v2 pith:YDQGIIRN submitted 2024-12-20 astro-ph.HE

Wen-Long Zhang , Shuang-Xi Yi , Yuan-Chuan Zou , Fa-Yin Wang , Cheng-Kui Li , Sheng-Lun Xie This is my paper · ORCID
classification astro-ph.HE
keywords GRB221009Ateraelectronvoltphotonsself-organizedcriticalitywaitingtimedistributionTsallisq-GaussianpowerlawscaleinvarianceLHAASO
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 analyzes the arrival-time gaps, or waiting times, of 172 teraelectronvolt photons from GRB 221009A, the brightest gamma-ray burst on record, as recorded by the LHAASO-KM2A observatory. It finds that the waiting-time distribution is not exponential: it follows a threshold power law with slope about 1.67 for the full sample and 2.10 for the main-afterglow subsample, and that Tsallis q-Gaussian fits keep q nearly constant across time scales (mean q about 2.6 and 2.5). The authors interpret the power-law form plus scale invariance as signs of a self-organized critical process in the generation of teraelectronvolt photons, while the mismatch with the theoretical $\alpha$--$q$ relation indicates the photons are not fully independent. If correct, the highest-energy afterglow emission of the brightest burst is produced by avalanche-like, correlated processes rather than independent random events, giving a new probe of jet magnetization and energy injection in gamma-ray bursts.

What carries the argument

The machinery is the pair of statistical fits used as self-organized-criticality fingerprints. The waiting time is defined as $T_{\rm wait} = T_{i+1} - T_i$; the cumulative waiting-time distribution is fit by a threshold power law (a generalized Pareto type II distribution), and the rescaled aggregated waiting times $x_n = X_n/\sigma_{X_n}$ are fit by the Tsallis q-Gaussian $f(x_n) = A[1-B(1-q)x_n^2]^{1/(1-q)}$. The paper uses the fitted $\alpha_x$ and $q$ to test two theoretical predictions: the SOC avalanche slope $\alpha_T = (S+1)/2$ for Euclidean dimensions $S=1,2,3$, and the relation $\alpha = 2/(q-1)$ linking the power-law slope to the q-Gaussian index. The deviation from the second relation is the load-bearing signal that the photons are interdependent rather than independent arrivals.

What would settle it

Simulate a Poisson process whose rate follows the LHAASO-KM2A count-rate history of GRB 221009A, then run the same WTD and Tsallis q-Gaussian fits on the synthetic photon list; if the synthetic sample reproduces the observed slopes ($\alpha_x \approx 1.67$ and $2.10$) and mean q values ($\approx 2.5$--$2.6$), the waiting-time data do not require self-organized criticality.

Watch

Extended reading notes

Core claim

The paper's central claim is that the 172 TeV photons from GRB 221009A behave statistically like an avalanche system: the cumulative waiting-time distribution fits a threshold power law, $N_{\rm cum}(>x) = A + B(x+x_0)^{1-\alpha_x}$, with $\alpha_x = 1.67^{+0.04}_{-0.04}$ for Sample I and $\alpha_x = 2.10^{+0.10}_{-0.08}$ for Sample II, and the rescaled aggregated wait times obey Tsallis q-Gaussian fits with mean $q = 2.60^{+0.14}_{-0.14}$ and $q = 2.53^{+0.14}_{-0.14}$ that stay roughly constant as the time scale n runs from 1 to 50. The paper argues that this combination is evidence of self-organized criticality, noting that a Poisson process would give an exponential waiting-time distribution and that the power-law form is also consistent with a nonstationary process such as a time-varying shock. The fitted $\alpha_x$ and $q$ lie off the theoretical line $\alpha = 2/(q-1)$; the paper reads this deviation as a sign that the photons are not completely independent and that the emission is not a standard Markovian avalanche. It proposes that a partially magnetically dominated jet component with continued central-engine energy injection can produce these self-organized critical characteristics.

Load-bearing premise

The load-bearing premise is that a power-law waiting-time distribution plus an approximately constant Tsallis q is evidence for self-organized criticality, rather than simply what a nonstationary Poisson process with a time-varying rate looks like; the paper cites that alternative but never fits such a null model to the observed light curve.

Editorial extensions

If this is right

  • If the self-organized-criticality interpretation holds, the TeV afterglow of GRB 221009A was generated by an avalanche-like process rather than a smooth external-shock phase, meaning the central engine kept injecting energy and a partially magnetized component shaped the emission.
  • The non-exponential waiting-time distribution implies that future TeV light curves of bright GRBs should not be modeled as independent photon arrivals; correlated, bursty emission should be expected.
  • The near-constant q across time scales makes scale invariance a quantitative observable that can be compared across GRBs and with waiting-time statistics from solar flares or magnetars.
  • The measured deviation from $\alpha = 2/(q-1)$ predicts that photon arrivals in high-rate intervals are more strongly correlated, and that longer baselines would reveal the same q with steeper or shallower power-law slopes depending on injection activity.

Reading between the lines

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

  • The SOC conclusion would be stronger if tested against a nonstationary Poisson null model driven by the actual LHAASO count-rate history; without such a test, the observed power-law waiting-time distribution may simply reflect the burst's time-varying rate rather than avalanche physics.
  • A testable extension is to apply the same waiting-time and Tsallis analysis to other LHAASO-detected GRBs or to the prompt megaelectronvolt emission of the same burst, asking whether the $\alpha$--$q$ deviation, not just the power law, is a universal signature of very-high-energy production.
  • If the non-independence interpretation is correct, the departures from the $\alpha = 2/(q-1)$ line could serve as a diagnostic of engine activity, with larger departures marking stronger energy injection or higher magnetization.
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 / 5 minor

Summary. The paper analyzes the waiting times of 172 TeV photons from GRB 221009A detected by LHAASO-KM2A. It defines waiting times as intervals between adjacent photon arrival times, builds two samples (all 172 photons, and 143 photons in the main emission interval 230–900 s), and fits the cumulative waiting-time distribution with an exponential and with a threshold power-law (Eq. 3). The power-law fits give slopes alpha_x = 1.67 (Sample I) and 2.10 (Sample II), and the paper argues that the WTD significantly deviates from exponential behavior. It then fits Tsallis q-Gaussian distributions (Eq. 5) to rescaled sums of waiting times at scales n = 1 to 50, reporting roughly constant q values (average q about 2.60 and 2.53). Using the theoretical relation alpha = 2/(q - 1) (Eq. 6) from Celikoglu et al. (2010), the paper finds that the fitted (alpha, q) points deviate from this relation and interprets this as evidence that the TeV photons are not completely independent. The paper concludes that the power-law and scale-free features imply self-organized critical characteristics in the generation of TeV photons, possibly related to a magnetized jet component and central-engine energy injection.

Significance. The empirical material is valuable: the LHAASO photon arrival-time list is a unique dataset, and the paper makes a concrete, falsifiable statistical claim about the WTD and q-Gaussian behavior. If the interpretation were supported, it would add an interesting data point to the debate on whether GRB high-energy emission is a self-organized critical process. The paper also has strengths: it uses publicly available data, applies two complementary statistical tools, and is honest enough to cite Wheatland et al. (1998) and Aschwanden & McTiernan (2010) as showing that a power-law WTD is consistent with a nonstationary process. However, the central inference is underdetermined because the nonstationary Poisson null is invoked but never fitted or simulated against the actual LHAASO light curve. The reported fits also lack the statistical tests needed to distinguish a genuine power law and a constant q from finite-sample artifacts or from a time-varying Poisson rate. The SOC conclusion is therefore plausible but not yet established.

major comments (4)
  1. [Section 4] The central claim that a power-law WTD implies SOC is undercut by the paper's own caveat in Section 4: "The power-law distribution is consistent with a nonstationary process, as was discussed by Wheatland et al. (1998) and Aschwanden & McTiernan (2010)." For a Poisson process with a time-varying rate lambda(t), the marginal waiting-time distribution is a mixture of exponentials and can approximate a power law over a finite range. The paper never constructs this null model from the LHAASO light curve, never simulates waiting times from it, and never compares its WTD or q(n) to the observed data. A concrete test would be to estimate lambda(t) from the binned LHAASO light curve, simulate 172 independent photons, and compare the resulting WTD slope and q values with the observed ones. Until this is done, the power-law WTD and the approximate constancy of q cannot distinguish SOC from a nonstationary independent-emission process.
  2. [Section 3.1, Eq. (4)] The evidence that the WTD is power-law rather than exponential rests on reduced chi-square values of 0.77 and 1.02, with no p-values, no confidence intervals, and no model-comparison statistic. The cumulative distribution is fitted in log-bins, so the data points are strongly correlated, and Eq. (4) is not a standard goodness-of-fit test for such correlated cumulative counts. With 172 and 143 events and several free parameters (amplitude, k, x0, alpha_x), the fitted power law is not convincingly distinguished from other heavy-tailed forms or from the mixture-of-exponentials expected under a nonstationary Poisson process. The authors should report an unbinned test (e.g., Kolmogorov-Smirnov or Anderson-Darling), a likelihood-ratio test between the exponential and power-law models, and a bootstrap or simulation-based calibration of the fit statistic.
  3. [Section 3.2, Fig. 2] The scale-invariance claim is based on five fitted q values per sample, but the q values show visible scatter: Sample I has q = 2.31 at n = 20, and Sample II has q = 2.09 at n = 20, with quoted uncertainties of about 0.1. The paper says q remains "relatively stable" without performing a formal test of constancy across n. A chi-square fit of a constant-q model to the five q values should be reported, and the correlation among the fitted q values should be addressed if the sums X_n are constructed from overlapping windows (the paper does not state whether the windows are independent). Without this, the claim of scale invariance is a visual impression rather than a demonstrated property.
  4. [Section 4, Eq. (6) and Fig. 3] The deviation from the theoretical relation alpha = 2/(q - 1) is interpreted as evidence that the photons are not independent. However, Eq. (6) is derived for a specific class of systems (Celikoglu et al. 2010), and the fitted (alpha, q) pair can deviate for several other reasons: finite-sample bias, the presence of the threshold parameter x0 in Eq. (3), detector dead-time and effective-area effects, or a time-varying rate that produces a superstatistical q. The paper needs to show, for example by simulation of the nonstationary Poisson model, that the observed deviation cannot be reproduced by such a null. Merely noting that the fitted point lies off the curve does not establish photon-photon correlations.
minor comments (5)
  1. [Section 2.1.2] The text says "Nenv refers to the total number of events" in the context of Eq. (3), but Eq. (3) does not contain Nenv; the constants A and B are not defined in the text. Please clarify or remove this phrase.
  2. [Section 2.1.2, Eq. (4)] The symbol chi_cum is written with a square-root sign and is then called the reduced chi-square. Either the formula or the terminology should be corrected, and the number of degrees of freedom (nx - npar) should be stated explicitly.
  3. [Section 2.2] The definition of X_n is unclear: the text says "S_i is the scale size of the ith waiting time" and then defines X_n = S_{i+n} - S_i. Presumably S_i is a cumulative waiting time, but the notation should be defined precisely, and it should be stated whether overlapping or non-overlapping windows are used.
  4. [Figure 2] The y-axis label "Number (Rescaled)" in the left panel is confusing because the fitted quantity is a probability density or a normalized count. Please use a clear label such as "Probability density (rescaled)" and describe the rescaling factors in the caption.
  5. [Section 5] The abstract and conclusions use the phrase "self-organized critical characteristics" and "imply a self-organized critical process." Given the analysis in Section 4 and the missing nonstationary-Poisson test, the wording should be tempered to "consistent with" or "suggestive of" rather than "imply." This is a presentation issue, but it matters for the interpretation presented to the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fitted WTD and q-Gaussian parameters are compared against external analytic relations, and the paper's own nonstationary-process caveat is an underdetermination rather than a definitional reduction.

full rationale

The paper's derivation chain is a sequence of fits to the same 172-photon data set (threshold power-law slopes alpha_x and Tsallis q values) followed by comparisons with external relations. The alpha_x values are fitted with Eq. (3); the q values are fitted with Eq. (5); and the comparison in Fig. 3 uses the independent theoretical relation alpha = 2/(q-1) from Celikoglu et al. (2010). No fitted parameter is relabeled as a prediction, and no equation is defined in terms of the conclusion it is used to support. The conclusion that the photon arrival process is non-Poisson and eventually that the system shows self-organized critical characteristics is an interpretation, not a quantity derived by construction. The paper itself concedes the central degeneracy: 'The power-law distribution is consistent with a nonstationary process' (Section 4), citing Wheatland et al. (1998) and Aschwanden & McTiernan (2010). Failing to test that null against the LHAASO light curve weakens the SOC inference and is a substantive scientific limitation, but it is a model-competition or underdetermination problem rather than circular reasoning. Self-citations in the introduction (e.g., Zhang et al. 2022, 2023; Yi et al. 2016, 2017) are contextual and do not carry the load-bearing argument; the decisive theory citations are external. Accordingly, the strict circularity score is 0.

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

The paper's claims rest on fitted statistical parameters (alpha, q, x0, amplitudes) and on external theoretical relations (Celikoglu 2010, Wheatland 1998) that are applied without a quantitative null model. No new physical entities are introduced; the proposed magnetically dominated component and energy injection are borrowed from prior work.

free parameters (5)
  • k (exponential decay rate) = not reported
    Free amplitude and decay rate fitted to WTD with Equation 1; used only as a null comparison.
  • x0 (threshold parameter) = not reported
    Fitted with Equation 3 for both samples; absorbs incomplete sampling and background, per Section 2.1.2.
  • alpha_x (power-law slope) = 1.67 (Sample I), 2.10 (Sample II)
    Central fitted parameter of the WTD; fitted via MCMC.
  • q (Tsallis q parameter) = 2.60 (Sample I), 2.53 (Sample II)
    Fitted to rescaled X_n distributions with Equation 5; scale-invariance claim rests on its near-constancy.
  • A, B (amplitudes) = not reported
    Nuisance parameters in cumulative and q-Gaussian fits.
assumptions (5)
  • standard math Waiting times of a constant-rate Poisson process are exponentially distributed and serve as the null hypothesis.
    Used in Section 2.1.1 to test randomness of photon arrival.
  • domain assumption The theoretical relation alpha = 2/(q-1) from Celikoglu et al. (2010) applies to this system.
    Used in Section 2.2 and Figure 3 to interpret the fitted alpha and q values; the validity of applying this SOC-avalanche relation to TeV photon waiting times is assumed.
  • domain assumption The nonstationary Poisson process model (Wheatland et al. 1998) predicts power-law WTDs and is a competing explanation.
    Invoked in Section 4 as an alternative interpretation but never fitted as a null model, undermining the SOC claim.
  • domain assumption The q-Gaussian form (Equation 5) is the correct functional model for rescaled fluctuations X_n/sigma; deviations are attributed to non-independence.
    No goodness-of-fit tests or alternative distributions are compared for the X_n distributions.
  • domain assumption The 172 reconstructed photons form an unbiased representation of the true TeV photon arrival process, unaffected by detector dead time or background.
    Section 2.1 takes arrival times from Cao et al. (2023) at face value; Sample II is used to reduce background but no background model is quantified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Self-organized critical characteristics of teraelectronvolt photons from GRB 221009A." pith.science (2026). https://pith.science/paper/YDQGIIRN

@misc{pith2026241216052,
  author       = {Pith},
  title        = {Pith review of: Self-organized critical characteristics of teraelectronvolt photons from GRB 221009A},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YDQGIIRN}},
  note         = {Machine review of arXiv:2412.16052}
}
read the original abstract

The very high-energy afterglow in GRB 221009A, known as the ``brightest of all time'' (BOAT), has been thoroughly analyzed in previous studies. In this paper, we conducted a statistical analysis of the waiting time behavior of 172 TeV photons from the BOAT observed by LHAASO-KM2A. The following results were obtained: (I) The waiting time distribution (WTD) of these photons deviates from the exponential distribution. (II) The behavior of these photons exhibits characteristics resembling those of a self-organized critical system, such as a power-law distribution and scale-invariance features in the WTD. The power-law distribution of waiting times is consistent with the prediction of a nonstationary process. (III) The relationship between the power-law slopes of the WTD and the scale-invariant characteristics of the Tsallis q-Gaussian distribution deviates from existing theory. We suggest that this deviation is due to the photons not being completely independent of each other. In summary, the power-law and scale-free characteristics observed in these photons imply a self-organized critical process in the generation of teraelectronvolt photons from GRB 221009A. Based on other relevant research, we propose that the involvement of a partially magnetically dominated component and the continuous energy injection from the central engine can lead to deviations in the generation of teraelectronvolt afterglow from the simple external shock-dominated process, thereby exhibiting the self-organized critical characteristics mentioned above.

Figures

Figures reproduced from arXiv: 2412.16052 by the authors.

Figure 1
Figure 1. Waiting time distributions and fitting results. The two panels depict the cumulative distributions of waiting time for Sample I and Sample II, which have been fit with an exponential (Eq. 1) and a threshold power law (Eq. 3). The solid lines represent the best-fitting results for each function, while the regions between the two dash-dotted lines indicate the 95% confidence level for each. Additionally, the dashed li… view at source ↗
Figure 2
Figure 2. Data (xn) distributions and fitting results about q-Gauss. The left panel shows several examples of xn distributions for different values of n and corresponding fitting curves (which have been rescaled to distinguish each sample). The right panel shows the evolution between the best-fitting results of q (with 1-σ error) and n of PDFs. SOC systems can be defined for Euclidean space dimensions S = 1, 2, 3. Aschwanden … view at source ↗
Figure 3
Figure 3. Comparison between theoretical predictions and fitting results. The dashed blue line in the figure represents the relationship curve pro￾posed by Celikoglu et al. (2010). The other data points correspond to the fitting results of two samples. that the appearance of each teraelectronvolt photon is not com￾pletely random. The most important conclusion is that, although power-law distributions and scale invariance feat… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

262 extracted references · 32 canonical work pages

  1. [1]

    Anand, N., Shahid, M., & Resmi, L., 2018, MNRAS, 481, 4332

    2018

  2. [2]

    2012, ApJL, 757, L31

    Axelsson, M., Baldini, L., Barbiellini, G., et al. 2012, ApJL, 757, L31

    2012

  3. [3]

    of SPIE, 5165, 175

    Barthelmy, S.D., 2004, Proc. of SPIE, 5165, 175

    2004

  4. [4]

    Beniamini, P., & Giannios, D., 2017, MNRAS, 468, 3202

    2017

  5. [5]

    2005, Natur, 438, 988

    Berger, E., Price, P.A., Cenko, S.B., et al. 2005, Natur, 438, 988

    2005

  6. [6]

    2013, ApJ, 775, 67

    Bernardini, M.G., Campana, S., Ghisellini, G., et al. 2013, ApJ, 775, 67

    2013

  7. [7]

    2014, ApJ, 784, 17

    Burgess, J.M., Preece, R.D., Connaughton, V., et al. 2014, ApJ, 784, 17

    2014

  8. [8]

    2008, ApJ, 685, L19

    Burlon, D., Ghirlanda, G., Ghisellini, G., et al. 2008, ApJ, 685, L19

    2008

Show all 262 references
  1. [9]

    2009, A&A, 505, 569

    Burlon, D., Ghirlanda, G., Ghisellini, G., et al. 2009, A&A, 505, 569

    2009

  2. [10]

    2005, Science, 309, 1833

    Burrows, D.N., Romano,P., Falcone, A., et al. 2005, Science, 309, 1833

    2005

  3. [11]

    Bostanc , Z.F., Kaneko, Y., & G\" o g \" u s , E., 2013, MNRAS, 428, 1623

    2013

  4. [12]

    Charisi, M., Marka, S., & Bartos, I., 2015, MNRAS, 448, 2624

    2015

  5. [13]

    Chen, W., Song, L.M., Zheng, S.J. et al. 2020, Sci. China-Phys. Mech. Astron. 50, 129512

    2020

  6. [14]

    Coppin, P., de Vries, K. D. & van Eijndhoven, N. 2020, Physical Review D, 102, 103014

    2020

  7. [15]

    Colgate, S.A., 1974, ApJ, 187, 333

    1974

  8. [16]

    Cohen, E., Katz, J.I., Piran, T. et al. 1997, ApJ, 488, 330

    1997

  9. [17]

    1997, ApJL, 479, L39

    Crider, A., Liang, E.P., Smith, I.A., et al. 1997, ApJL, 479, L39

    1997

  10. [18]

    Daigne, F., & Mochkovitch, R., 1998, MNRAS, 296, 275

    1998

  11. [19]

    Deng, W., & Zhang, B., 2014, ApJ, 785, 112

    2014

  12. [20]

    2015, ApJ, 805, 163

    Deng, W., Li, H., Zhang, B., et al. 2015, ApJ, 805, 163

    2015

  13. [21]

    Dereli-B \'e gu \'e , H., Pe'er, A., & Ryde, F., 2020, ApJ, 897, 145

    2020

  14. [22]

    1989, Nature, 340, 126

    Eichler, D., Livio, M., Piran, T., et al. 1989, Nature, 340, 126

    1989

  15. [23]

    2004, ApJ, 611, 1005

    Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005

    2004

  16. [24]

    & Celotti, A., 2004, A&A, 422, L55

    Ghirlanda, G., Ghisellini, G. & Celotti, A., 2004, A&A, 422, L55

    2004

  17. [25]

    Ghirlanda, G., Celotti, A., & Ghisellini, G., 2003, A&A, 406, 879

    2003

  18. [26]

    Celotti, A., & Ghisellini, G., 2002, A&A, 393, 409

    Ghirlanda, G. Celotti, A., & Ghisellini, G., 2002, A&A, 393, 409

    2002

  19. [27]

    Ghisellini, G., & Celotti, A., 1999, ApJL, 511, L93

    1999

  20. [28]

    2017, ApJL, 848, L14

    Goldstein, A., Veres, P., Burns, E., et al. 2017, ApJL, 848, L14

    2017

  21. [29]

    2015, ApJ, 807, 148

    Guiriec, S., Kouveliotou, C., Daigne, F., et al. 2015, ApJ, 807, 148

    2015

  22. [30]

    Hakkila, J., Horv\' a th, I., Hofesmann, E. et al. 2018, ApJ, 855, 101

    2018

  23. [31]

    2014, ApJ, 789, 145

    Hu, Y.-D., Liang, E.-W., Xi, S.-Q., et al. 2014, ApJ, 789, 145

    2014

  24. [32]

    2015, ApJ, 811, 4

    Kagawa, Y., Yonetoku, D., Sawano, T., et al. 2015, ApJ, 811, 4

    2015

  25. [33]

    2006, ApJS, 166, 298

    Kaneko, Y., Preece, R.D., Briggs, M.S., et al. 2006, ApJS, 166, 298

    2006

  26. [34]

    2015, MNRAS, 452, 824

    Kaneko, Y., Bostanc , Z.F., G\" o g \" u s , E., et al. 2015, MNRAS, 452, 824

    2015

  27. [35]

    2020, ApJ, 889, 110

    Katsukura, D., Sakamoto, T., Tashiro, M.S., et al. 2020, ApJ, 889, 110

    2020

  28. [36]

    Katz, J.I., 1994, ApJ, 422, 248

    1994

  29. [37]

    Kocevski, D., Ryde, F., & Liang, E., 2003, ApJ, 596, 389

    2003

  30. [38]

    Kouveliotou, C., Meegan, C.A., Fishman, G.J. et al. 1993, ApJL, 413, L101

    1993

  31. [39]

    1995, ApJ, 452, 145

    Koshut, T.M., Konveliotou, C., Paciesas, S.W., et al. 1995, ApJ, 452, 145

    1995

  32. [40]

    2018, ApJ, 862, 155

    Lan, L., L\" u , H.-J., Zhong, S.-Q., et al. 2018, ApJ, 862, 155

    2018

  33. [41]

    Lan, L., Lu, R.-J., L\" u , H.-J. et al. 2020, MNRAS, 492, 3622

    2020

  34. [42]

    Lazarian, A., Zhang, B., & Xu, S., 2019, ApJ, 882, 184

    2019

  35. [43]

    Lazzati, D., 2005, MNRAS, 357, 722

    2005

  36. [44]

    Li, L., 2019, ApJS, 242, 16

    2019

  37. [45]

    Li, L., 2019, ApJS, 245, 7

    2019

  38. [46]

    Liao, J.Y., Luo, Q., Zhu, Y. et al. 2020, Sci. China-Phys. Mech. Astron. 50, 129510

    2020

  39. [47]

    2016, ApJ, 829, 7

    Lien, A., Sakamoto, T., Barthelmy, S.D., et al. 2016, ApJ, 829, 7

    2016

  40. [48]

    Liu, C.Z., Zhang, Y.F. Li, X. F., et al. 2020, Sci. China-Phys. Mech. Astron. 63, 249503

    2020

  41. [49]

    Acuner, F

    Z. Acuner, F. Ryde, A. Pe'er, D. Mortlock, and B. Ahlgren, ApJ, 893, 128 (2020)

    2020

  42. [50]

    J. W. He, W. Li, H. B. Wang, S. J. Yu, and R. F. Su, SPIE, 11444, 1144438 (2020)

    2020

  43. [51]

    2020, ApJ, 892, 113

    Li, X.J., Zhang, Z.B., Zhang, C.T., et al. 2020, ApJ, 892, 113

    2020

  44. [52]

    Li, Y., Zhang, B., & Yuan, Q., 2020, ApJ, 897, 154

    2020

  45. [53]

    2021, ApJS, 252, 16

    Li, X.J., Zhang, Z.B., Zhang, X.L., et al. 2021, ApJS, 252, 16

    2021

  46. [54]

    & Usov, V.V., 2000, ApJ, 543, L129

    Lyutikov, M. & Usov, V.V., 2000, ApJ, 543, L129

    2000

  47. [55]

    1974, ApJL, 194, L19

    Metzger, A.E., Parker, R.H., Gilman, D., et al. 1974, ApJL, 194, L19

    1974

  48. [56]

    2018, ApJ, 860, 72

    Meng, Y.-Z., Geng, J.-J., Zhang, B.-B., et al. 2018, ApJ, 860, 72

    2018

  49. [57]

    2019, ApJ, 882, 26

    Meng, Y.-Z., Liu, L.-D., Wei, J.-J., et al. 2019, ApJ, 882, 26

    2019

  50. [58]

    Meszaros, P., Rees, M.J., & Papathanassiou, H., 1994, ApJ, 432, 181

    1994

  51. [59]

    & Piran, T., 1992, ApJL, 395, L83

    Narayan, R., Paczynski, B. & Piran, T., 1992, ApJL, 395, L83

    1992

  52. [60]

    Norris, J.P.,& Bonnell, J.T., 2006, ApJ, 643, 266

    2006

  53. [61]

    Norris, J.P., Gehrels, N., & Scargle, J.D., 2010, ApJ, 717, 411

    2010

  54. [62]

    Norris, J.P., Gehrels, N., & Scargle, J.D., 2011, ApJ, 735, 23

    2011

  55. [63]

    2019, A&A, 628, A59

    Oganesyan, G., Nava, L., Ghirlanda, G., et al. 2019, A&A, 628, A59

    2019

  56. [64]

    1986, ApJL, 308, L43

    Paczynski, B. 1986, ApJL, 308, L43

    1986

  57. [65]

    1998, ApJL, 506, L23

    Preece, R.D., Briggs, M.S., Mallozzi, R.S., et al. 1998, ApJL, 506, L23

    1998

  58. [66]

    Rees, M.J., & Meszaros, P., 1994, ApJL, 430, L93

    1994

  59. [67]

    2005, ssr, 120, 95

    Roming, P.W.A., Kennedy, T.E., Mason, K.O.,et al. 2005, ssr, 120, 95

    2005

  60. [68]

    2019, MNRAS, 484, 1912

    Ryde, F., Yu, H.-F., Dereli-B \'e gu \'e , H., et al. 2019, MNRAS, 484, 1912

    2019

  61. [69]

    2009, ApJ, 693, 922

    Sakamoto, T., Sato, G., Barbier, L., et al. 2009, ApJ, 693, 922

    2009

  62. [70]

    2011, ApJS, 195, 2

    Sakamoto, T., Barthelmy, S.D., Baumgartner, W.H., et al. 2011, ApJS, 195, 2

    2011

  63. [71]

    2017, ApJL, 848, L15

    Savchenko, V., Ferrigno, C., Kuulkers, E., et al. 2017, ApJL, 848, L15

    2017

  64. [72]

    1998, ApJL, 497, L17

    Sari, R., Piran, T., & Narayan, R. 1998, ApJL, 497, L17

    1998

  65. [73]

    Song, X.Y., Xiong, S.L., Luo, Q. et al. 2020, Sci. China-Phys. Mech. Astron. 50, 129511

    2020

  66. [74]

    Thompson, C., 1994, MNRAS, 270, 480

    1994

  67. [75]

    Troja, E., Rosswog, S., & Gehrels, N., 2010, ApJ, 723, 1711

    2010

  68. [76]

    P., Bonnell, J

    Norris, J. P., Bonnell, J. T., Kazanas, D., et al. ApJ, 627, 324 (2005)

    2005

  69. [77]

    S., Paciesas, W

    Mallozzi, R. S., Paciesas, W. S., Pendleton, G. N., et al. ApJ, 454, 597 (1995)

    1995

  70. [78]

    M., Petrosian, V., & Mallozzi, R

    Lloyd, N. M., Petrosian, V., & Mallozzi, R. S. ApJ, 534, 227 (2000)

    2000

  71. [79]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. ApJL, 848, L13 (2017)

    2017

  72. [80]

    A. S. Pozanenko, M. V. Barkov, P. Yu. Minaev, A. A. Volnova, E. D. Mazaeva, A. S. Moskvitin, M. A. Krugov, V. A. Samodurov, V. M. Loznikov, and M. Lyutikov, ApJL, 852, L30 (2018)

    2018

  73. [81]

    von Kienlin, P

    A. von Kienlin, P. Veres, O. J. Roberts, R. Hamburg, E. Bissaldi , M. S. Briggs, E. Burns, A. Goldstein,

  74. [82]

    Zhang, E.-W

    B.-B. Zhang, E.-W. Liang, and B. Zhang, ApJ, 666, 1002 (2007)

    2007

  75. [83]

    2012, MNRAS, 424, 2821

    Virgili, F.J., Qin, Y., Zhang, B., et al. 2012, MNRAS, 424, 2821

    2012

  76. [84]

    2020, ApJ, 893, 46

    von Kienlin, A., Meegan, C.A., Paciesas, W.S., et al. 2020, ApJ, 893, 46

    2020

  77. [85]

    2020, ApJ, 893, 77

    Wang, F.-F., Zou, Y.-C., Liu, F.-X., et al. 2020, ApJ, 893, 77

    2020

  78. [86]

    Wei, J., Cordier, B., Antier, S. et al. arXiv:1610.06892

    arXiv

  79. [87]

    Woosley, S.E., 1993, ApJ, 405, 273

    1993

  80. [88]

    Zhang, Z.B., & Qin, Y.P., 2005, MNRAS, 363, 1290

    2005

  81. [89]

    Zhang, B., 2006, Natur, 444, 1010

    2006

  82. [90]

    2007, ApJL, 655, L25

    Zhang, B., Zhang, B.-B., Liang, E.-W., et al. 2007, ApJL, 655, L25

    2007

  83. [91]

    2007, ApJ, 655, 989

    Zhang, B., Liang, E.W., Page, K.L., et al. 2007, ApJ, 655, 989

    2007

  84. [92]

    & Choi, C.S

    Zhang, Z.B. & Choi, C.S. 2008, A&A, 484, 293

    2008

  85. [93]

    2009, ApJ, 703, 1696

    Zhang, B., Zhang, B.-B., Virgili, F.J., et al. 2009, ApJ, 703, 1696

    2009

  86. [94]

    2011, ApJ, 730, 141

    Zhang, B.-B., Zhang, B., Liang, E.-W., et al. 2011, ApJ, 730, 141

    2011

  87. [95]

    Zhang, B., & Yan, H.R., 2011, ApJ, 726, 90

    2011

  88. [96]

    Zhang, Z.B., Zhang, C.T., Zhao, Y.X. et al. 2018, PASP, 130, 054202

    2018

  89. [97]

    2018, Nature Communications, 9, 447

    Zhang, B.-B., Zhang, B., Sun, H.,et al. 2018, Nature Communications, 9, 447

    2018

  90. [98]

    2018, NatAs, 2, 69

    Zhang, B.-B., Zhang, B., Castro-Tirado, A.J., et al. 2018, NatAs, 2, 69

    2018

  91. [99]

    2019, ApJ, 884, 25

    Zhong, S.-Q., Dai, Z.-G., Cheng, J.-G., et al. 2019, ApJ, 884, 25

    2019

  92. [100]

    2020, RAA, 20, 201

    Zhang, X.L., Zhang, C.T., Li, X.J., et al. 2020, RAA, 20, 201

    2020

  93. [101]

    2020, ApJ, 902, 40

    Zhang, Z.B., Jiang, M., Zhang, Y., et al. 2020, ApJ, 902, 40

    2020

  94. [102]

    2020, Sci

    Zhang, S.-N., Li, T.P., Lu, F.J., et al. 2020, Sci. China-Phys. Mech. Astron. 63, 249502

    2020

  95. [103]

    2019, , 575, 464, 10.1038/s41586-019-1743-9

    Abdalla , H., Adam , R., Aharonian , F., et al. 2019, , 575, 464, 10.1038/s41586-019-1743-9

    2019 doi

  96. [104]

    2023, arXiv e-prints, arXiv:2303.01203, 10.48550/arXiv.2303.01203

    An , Z.-H., Antier , S., Bi , X.-Z., et al. 2023, arXiv e-prints, arXiv:2303.01203, 10.48550/arXiv.2303.01203

    2023 doi

  97. [105]

    Arnold, B. C. 2008, Pareto and Generalized Pareto Distributions, ed. D. Chotikapanich (New York, NY: Springer New York), 119--145, 10.1007/978-0-387-72796-7_7

    2008 doi

  98. [106]

    Aschwanden , M. J. 2012, , 539, A2, 10.1051/0004-6361/201118237

    2012 doi

  99. [107]

    2015, , 814, 19, 10.1088/0004-637X/814/1/19

    ---. 2015, , 814, 19, 10.1088/0004-637X/814/1/19

    2015 doi

  100. [108]

    2019, , 880, 105, 10.3847/1538-4357/ab29f4

    ---. 2019, , 880, 105, 10.3847/1538-4357/ab29f4

    2019 doi

  101. [109]

    J., & McTiernan , J

    Aschwanden , M. J., & McTiernan , J. M. 2010, , 717, 683, 10.1088/0004-637X/717/2/683

    2010 doi

  102. [110]

    1989, , 94, 15,635, 10.1029/JB094iB11p15635

    Bak , P., & Tang , C. 1989, , 94, 15,635, 10.1029/JB094iB11p15635

    1989 doi

  103. [111]

    1988, , 38, 364, 10.1103/PhysRevA.38.364

    Bak , P., Tang , C., & Wiesenfeld , K. 1988, , 38, 364, 10.1103/PhysRevA.38.364

    1988 doi

  104. [112]

    2023, , 946, L31, 10.3847/2041-8213/acc39c

    Burns , E., Svinkin , D., Fenimore , E., et al. 2023, , 946, L31, 10.3847/2041-8213/acc39c

    2023 doi

  105. [113]

    2023, Science Advances, 9, eadj2778, 10.1126/sciadv.adj2778

    Cao , Z., Aharonian , F., An , Q., et al. 2023, Science Advances, 9, eadj2778, 10.1126/sciadv.adj2778

    2023 doi

  106. [114]

    X., et al

    Cao , Z., Aharonian , F., Axikegu , Bai, Y. X., et al. 2024, , 133, 071501, 10.1103/PhysRevLett.133.071501

    2024 doi

  107. [115]

    Carenza , P., & Marsh , M. C. D. 2022, arXiv e-prints, arXiv:2211.02010, 10.48550/arXiv.2211.02010

    2022 doi arXiv

  108. [116]

    2007, , 75, 055101, 10.1103/PhysRevE.75.055101

    Caruso , F., Pluchino , A., Latora , V., Vinciguerra , S., & Rapisarda , A. 2007, , 75, 055101, 10.1103/PhysRevE.75.055101

    2007 doi

  109. [117]

    Celikoglu , A., Tirnakli , U., & Queir \'o s , S. M. D. 2010, , 82, 021124, 10.1103/PhysRevE.82.021124

    2010 doi

  110. [118]

    2017, Chinese Physics C, 41, 065104, 10.1088/1674-1137/41/6/065104

    Chang , Z., Lin , H.-N., Sang , Y., & Wang , P. 2017, Chinese Physics C, 41, 065104, 10.1088/1674-1137/41/6/065104

    2017 doi

  111. [119]

    I., Guyer , R

    Cheng , B., Epstein , R. I., Guyer , R. A., & Young , A. C. 1996, , 382, 518, 10.1038/382518a0

    1996 doi

  112. [120]

    Q., & Wang , F

    Cheng , Y., Zhang , G. Q., & Wang , F. Y. 2020, , 491, 1498, 10.1093/mnras/stz3085

    2020 doi

  113. [121]

    2022, GRB Coordinates Network, 32648, 1

    de Ugarte Postigo , A., Izzo , L., Pugliese , G., et al. 2022, GRB Coordinates Network, 32648, 1

    2022

  114. [122]

    2022, GRB Coordinates Network, 32668, 1

    Frederiks , D., Lysenko , A., Ridnaia , A., et al. 2022, GRB Coordinates Network, 32668, 1

    2022

  115. [123]

    2023, , 131, 251001, 10.1103/PhysRevLett.131.251001

    Galanti , G., Nava , L., Roncadelli , M., Tavecchio , F., & Bonnoli , G. 2023, , 131, 251001, 10.1103/PhysRevLett.131.251001

    2023 doi

  116. [124]

    2024, , 968, 40, 10.3847/1538-4357/ad4a55

    Gao , C.-Y., & Wei , J.-J. 2024, , 968, 40, 10.3847/1538-4357/ad4a55

    2024 doi

  117. [125]

    2023, , 956, L38, 10.3847/2041-8213/acfed1

    Gao , D.-Y., & Zou , Y.-C. 2023, , 956, L38, 10.3847/2041-8213/acfed1

    2023 doi

  118. [126]

    2024, , 961, L6, 10.3847/2041-8213/ad167d

    ---. 2024, , 961, L6, 10.3847/2041-8213/ad167d

    2024 doi

  119. [127]

    2024, , 2024, 026, 10.1088/1475-7516/2024/01/026

    Gao , L.-Q., Bi , X.-J., Li , J., Yao , R.-M., & Yin , P.-F. 2024, , 2024, 026, 10.1088/1475-7516/2024/01/026

    2024 doi

  120. [128]

    H. E. S. S. Collaboration , Abdalla , H., Aharonian , F., et al. 2021, Science, 372, 1081, 10.1126/science.abe8560

    2021 doi

  121. [129]

    2022, GRB Coordinates Network, 32677, 1

    Huang , Y., Hu , S., Chen , S., et al. 2022, GRB Coordinates Network, 32677, 1

    2022

  122. [130]

    A., Williams , M., & Swift Team

    Kennea , J. A., Williams , M., & Swift Team . 2022, GRB Coordinates Network, 32635, 1

    2022

  123. [131]

    2024, Science Bulletin, 69, 449, 10.1016/j.scib.2023.12.040

    LHAASO Collaboration . 2024, Science Bulletin, 69, 449, 10.1016/j.scib.2023.12.040

    2024 doi

  124. [132]

    2023, Science, 380, 1390, 10.1126/science.adg9328

    LHAASO Collaboration , Cao , Z., Aharonian , F., et al. 2023, Science, 380, 1390, 10.1126/science.adg9328

    2023 doi

  125. [133]

    2023, , 2023, 061, 10.1088/1475-7516/2023/10/061

    Li , H., & Ma , B.-Q. 2023, , 2023, 061, 10.1088/1475-7516/2023/10/061

    2023 doi

  126. [134]

    2023, , 955, L34, 10.3847/2041-8213/acf12c

    Li , X.-J., & Yang , Y.-P. 2023, , 955, L34, 10.3847/2041-8213/acf12c

    2023 doi

  127. [135]

    2023, , 265, 56, 10.3847/1538-4365/acc398

    Li , X.-J., Zhang , W.-L., Yi , S.-X., Yang , Y.-P., & Li , J.-L. 2023, , 265, 56, 10.3847/1538-4365/acc398

    2023 doi

  128. [136]

    2021, Frontiers of Physics, 16, 14501, 10.1007/s11467-020-0989-x

    Lyu , F., Li , Y.-P., Hou , S.-J., et al. 2021, Frontiers of Physics, 16, 14501, 10.1007/s11467-020-0989-x

    2021 doi

  129. [137]

    2024, , 965, 72, 10.3847/1538-4357/ad26f4

    Maccary , R., Guidorzi , C., Amati , L., et al. 2024, , 965, 72, 10.3847/1538-4357/ad26f4

    2024 doi

  130. [138]

    A., Ansoldi , S., et al

    MAGIC Collaboration , Acciari , V. A., Ansoldi , S., et al. 2019 a , , 575, 455, 10.1038/s41586-019-1750-x

    2019 doi

  131. [139]

    2019 b , , 575, 459, 10.1038/s41586-019-1754-6

    ---. 2019 b , , 575, 459, 10.1038/s41586-019-1754-6

    2019 doi

  132. [140]

    2023 a , , 518, 3959, 10.1093/mnras/stac3308

    Peng , F.-K., Wang , F.-Y., Shu , X.-W., & Hou , S.-J. 2023 a , , 518, 3959, 10.1093/mnras/stac3308

    2023 doi

  133. [141]

    2023 b , , 959, 109, 10.3847/1538-4357/acfcb2

    Peng , F.-K., Wei , J.-J., & Wang , H.-Q. 2023 b , , 959, 109, 10.3847/1538-4357/acfcb2

    2023 doi

  134. [142]

    Rees , M. J. 1984, , 22, 471, 10.1146/annurev.aa.22.090184.002351

    1984

  135. [143]

    I., S \'a nchez-Col \'o n , G., & Rajpoot , S

    Sahu , S., Medina-Carrillo , B., P \'a ez-S \'a nchez , D. I., S \'a nchez-Col \'o n , G., & Rajpoot , S. 2024, , 533, L64, 10.1093/mnrasl/slae063

    2024 doi

  136. [144]

    A., Belfiore , A., et al

    Sidoli , L., Postnov , K. A., Belfiore , A., et al. 2019, , 487, 420, 10.1093/mnras/stz1283

    2019 doi

  137. [145]

    Tsallis , C., Mendes , R., & Plastino , A. R. 1998, Physica A Statistical Mechanics and its Applications, 261, 534, 10.1016/S0378-4371(98)00437-3

    1998 doi

  138. [146]

    2022, GRB Coordinates Network, 32636, 1

    Veres , P., Burns , E., Bissaldi , E., et al. 2022, GRB Coordinates Network, 32636, 1

    2022

  139. [148]

    2017, , 470, 1101, 10.1093/mnras/stx1292

    ---. 2017, , 470, 1101, 10.1093/mnras/stx1292

    2017 doi

  140. [149]

    Y., Wu , Q., & Dai , Z

    Wang , F. Y., Wu , Q., & Dai , Z. G. 2023 a , , 949, L33, 10.3847/2041-8213/acd5d2

    2023 doi

  141. [150]

    Y., & Yu , H

    Wang , F. Y., & Yu , H. 2017, , 2017, 023, 10.1088/1475-7516/2017/03/023

    2017 doi

  142. [151]

    2023 b , Science China Physics, Mechanics, and Astronomy, 66, 289511, 10.1007/s11433-023-2128-9

    Wang , K., Ma , Z.-P., Liu , R.-Y., et al. 2023 b , Science China Physics, Mechanics, and Astronomy, 66, 289511, 10.1007/s11433-023-2128-9

    2023 doi

  143. [152]

    2023 c , arXiv e-prints, arXiv:2310.11821, 10.48550/arXiv.2310.11821

    Wang , K., Tang , Q.-W., Zhang , Y.-Q., et al. 2023 c , arXiv e-prints, arXiv:2310.11821, 10.48550/arXiv.2310.11821

    2023 doi arXiv

  144. [153]

    2024, , 975, 188, 10.3847/1538-4357/ad7de5

    Wang , P., Song , L.-M., Xiong , S.-L., et al. 2024, , 975, 188, 10.3847/1538-4357/ad7de5

    2024 doi

  145. [154]

    2023, Physical Review Research, 5, 013019, 10.1103/PhysRevResearch.5.013019

    Wei , J.-J. 2023, Physical Review Research, 5, 013019, 10.1103/PhysRevResearch.5.013019

    2023 doi

  146. [155]

    2021, , 920, 153, 10.3847/1538-4357/ac2604

    Wei , J.-J., Wu , X.-F., Dai , Z.-G., et al. 2021, , 920, 153, 10.3847/1538-4357/ac2604

    2021 doi

  147. [156]

    Wheatland , M. S. 2000, , 536, L109, 10.1086/312739

    2000 doi

  148. [157]

    2003, , 214, 361, 10.1023/A:1024222511574

    ---. 2003, , 214, 361, 10.1023/A:1024222511574

    2003 doi

  149. [158]

    S., Sturrock , P

    Wheatland , M. S., Sturrock , P. A., & McTiernan , J. M. 1998, , 509, 448, 10.1086/306492

    1998 doi

  150. [159]

    Wu , Q., & Wang , F. Y. 2024, Chinese Physics Letters, 41, 119801, 10.1088/0256-307X/41/11/119801

    2024 doi

  151. [160]

    2018, , 864, 164, 10.3847/1538-4357/aadd01

    Yan , D., Yang , S., Zhang , P., et al. 2018, , 864, 164, 10.3847/1538-4357/aadd01

    2018 doi

  152. [163]

    2023, Research in Astronomy and Astrophysics, 23, 115013, 10.1088/1674-4527/acf979

    Zhang , W.-L., Li , X.-J., Yang , Y.-P., et al. 2023, Research in Astronomy and Astrophysics, 23, 115013, 10.1088/1674-4527/acf979

    2023 doi

  153. [164]

    2022, Research in Astronomy and Astrophysics, 22, 065012, 10.1088/1674-4527/ac6aac

    Zhang , W.-L., Yi , S.-X., Yang , Y.-P., & Qin , Y. 2022, Research in Astronomy and Astrophysics, 22, 065012, 10.1088/1674-4527/ac6aac

    2022 doi

  154. [165]

    2024, , 972, L25, 10.3847/2041-8213/ad6df8

    Zhang , Y.-Q., Lin , H., Xiong , S.-L., et al. 2024, , 972, L25, 10.3847/2041-8213/ad6df8

    2024 doi

  155. [166]

    doi:10.1051/0004-6361:20020722

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

    2002 doi

  156. [167]

    doi:10.1093/mnrasl/slz056

    Amati, L., D'Agostino, R., Luongo, O., et al.\ 2019, , 486, L46. doi:10.1093/mnrasl/slz056

    2019 doi

  157. [168]

    doi:10.1093/mnras/stu523

    Anderson, L., Aubourg, \'E ., Bailey, S., et al.\ 2014, , 441, 24. doi:10.1093/mnras/stu523

    2014 doi

  158. [169]

    doi:10.1086/172995

    Band, D., Matteson, J., Ford, L., et al.\ 1993, , 413, 281. doi:10.1086/172995

    1993 doi

  159. [170]

    V., Reinsch, K., et al.\ 1999, , 352, L26

    Beuermann, K., Hessman, F. V., Reinsch, K., et al.\ 1999, , 352, L26

    1999

  160. [171]

    doi:10.3847/1538-4357/aadcf8

    Bi, X., Mao, J., Liu, C., et al.\ 2018, , 866, 97. doi:10.3847/1538-4357/aadcf8

    2018 doi

  161. [172]

    S., Frail, D

    Bloom, J. S., Frail, D. A., & Sari, R.\ 2001, , 121, 2879. doi:10.1086/321093

    2001 doi

  162. [173]

    J., et al.\ 2006, , 442, 1008

    Campana, S., Mangano, V., Blustin, A. J., et al.\ 2006, , 442, 1008. doi:10.1038/nature04892

    2006 doi

  163. [174]

    doi:10.1093/mnras/stab3559

    Cao, S., Khadka, N., & Ratra, B.\ 2022, , 510, 2928. doi:10.1093/mnras/stab3559

    2022 doi

  164. [175]

    & Izzo, L.\ 2008, , 490, 31

    Capozziello, S. & Izzo, L.\ 2008, , 490, 31. doi:10.1051/0004-6361:200810337

    2008 doi

  165. [176]

    F., Dainotti, M

    Cardone, V. F., Dainotti, M. G., Capozziello, S., et al.\ 2010, , 408, 1181. doi:10.1111/j.1365-2966.2010.17197.x

    2010

  166. [177]

    B., Frail, D

    Cenko, S. B., Frail, D. A., Harrison, F. A., et al.\ 2011, , 732, 29. doi:10.1088/0004-637X/732/1/29

    2011 doi

  167. [178]

    & Frail, D

    Chandra, P. & Frail, D. A.\ 2012, , 746, 156. doi:10.1088/0004-637X/746/2/156

    2012 doi

  168. [179]

    J., Urata, Y., Huang, K., et al.\ 2020, , 891, L15

    Chen, W. J., Urata, Y., Huang, K., et al.\ 2020, , 891, L15. doi:10.3847/2041-8213/ab76d4

    2020 doi

  169. [180]

    J., Peacock, J

    Cole, S., Percival, W. J., Peacock, J. A., et al.\ 2005, , 362, 505. doi:10.1111/j.1365-2966.2005.09318.x

    2005

  170. [181]

    D'Agostini, G.\ 2005, physics/0511182

    2005 arXiv

  171. [182]

    G., Liang, E

    Dai, Z. G., Liang, E. W., & Xu, D.\ 2004, , 612, L101. doi:10.1086/424694

    2004 doi

  172. [183]

    G.\ 2004, , 606, 1000

    Dai, Z. G.\ 2004, , 606, 1000. doi:10.1086/383019

    2004 doi

  173. [184]

    Dai, Z. G. & Lu, T.\ 1998a, , 81, 4301. doi:10.1103/PhysRevLett.81.4301

    doi

  174. [185]

    Dai, Z. G. & Lu, T.\ 1998b, , 333, L87

  175. [187]

    G., Willingale, R., Capozziello, S., et al.\ 2010, , 722, L215

    Dainotti, M. G., Willingale, R., Capozziello, S., et al.\ 2010, , 722, L215. doi:10.1088/2041-8205/722/2/L215

    2010 doi

  176. [188]

    doi:10.3847/1538-4357/acaefd

    Deng, C., Huang, Y.-F., & Xu, F.\ 2023, , 943, 126. doi:10.3847/1538-4357/acaefd

    2023 doi

  177. [189]

    doi:10.1051/0004-6361/201628909

    Demianski, M., Piedipalumbo, E., Sawant, D., et al.\ 2017, , 598, A112. doi:10.1051/0004-6361/201628909

    2017 doi

  178. [190]

    doi:10.3847/1538-4357/abd6bd

    Du, M., Yi, S.-X., Liu, T., et al.\ 2021, , 908, 242. doi:10.3847/1538-4357/abd6bd

    2021 doi

  179. [191]

    & Petrosian, V.\ 1992, , 399, 345

    Efron, B. & Petrosian, V.\ 1992, , 399, 345. doi:10.1086/171931

    1992 doi

  180. [192]

    doi:10.1038/340126a0

    Eichler, D., Livio, M., Piran, T., et al.\ 1989, , 340, 126. doi:10.1038/340126a0

    1989 doi

  181. [193]

    J., Zehavi, I., Hogg, D

    Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al.\ 2005, , 633, 560. doi:10.1086/466512

    2005 doi

  182. [194]

    Fan, Y. Z. & Wei, D. M.\ 2005, , 364, L42. doi:10.1111/j.1745-3933.2005.00102.x

    2005

  183. [195]

    A., Kulkarni, S

    Frail, D. A., Kulkarni, S. R., Sari, R., et al.\ 2001, , 562, L55. doi:10.1086/338119

    2001 doi

  184. [196]

    J., Vreeswijk, P

    Galama, T. J., Vreeswijk, P. M., van Paradijs, J., et al.\ 1998, , 395, 670. doi:10.1038/27150

    1998 doi

  185. [197]

    & Piro, L.\ 2006, , 455, 413

    Galli, A. & Piro, L.\ 2006, , 455, 413. doi:10.1051/0004-6361:20054448

    2006 doi

  186. [198]

    P., Wang, F

    Hu, J. P., Wang, F. Y., & Dai, Z. G.\ 2021, , 507, 730. doi:10.1093/mnras/stab2180

    2021 doi

  187. [199]

    D., Hu, J

    Jia, X. D., Hu, J. P., Yang, J., et al.\ 2022, , 516, 2575. doi:10.1093/mnras/stac2356

    2022 doi

  188. [200]

    doi:10.1111/j.1745-3933.2008.00508.x

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

    2008

  189. [201]

    & Zhang, B.\ 2015, , 561, 1

    Kumar, P. & Zhang, B.\ 2015, , 561, 1. doi:10.1016/j.physrep.2014.09.008

    2015 doi

  190. [202]

    R., Schroeder, G., et al.\ 2022, , 935, L11

    Laskar, T., Escorial, A. R., Schroeder, G., et al.\ 2022, , 935, L11. doi:10.3847/2041-8213/ac8421

    2022 doi

  191. [203]

    doi:10.1088/0004-637X/765/2/125

    Lei, W.-H., Zhang, B., & Liang, E.-W.\ 2013, , 765, 125. doi:10.1088/0004-637X/765/2/125

    2013 doi

  192. [204]

    doi:10.1093/mnras/stac3730

    Levine, D., Dainotti, M., Fraija, N., et al.\ 2023, , 519, 4670. doi:10.1093/mnras/stac3730

    2023 doi

  193. [205]

    J., et al.\ 2022, , 925, 15

    Levine, D., Dainotti, M., Zvonarek, K. J., et al.\ 2022, , 925, 15. doi:10.3847/1538-4357/ac4221

    2022 doi

  194. [206]

    doi:10.1088/0004-637X/758/1/27

    Li, L., Liang, E.-W., Tang, Q.-W., et al.\ 2012, , 758, 27. doi:10.1088/0004-637X/758/1/27

    2012 doi

  195. [207]

    doi:10.1086/521870

    Liang, E.-W., Zhang, B.-B., & Zhang, B.\ 2007, , 670, 565. doi:10.1086/521870

    2007 doi

  196. [208]

    & Zhang, B.\ 2005, , 633, 611

    Liang, E. & Zhang, B.\ 2005, , 633, 611. doi:10.1086/491594

    2005 doi

  197. [209]

    K., Liu, Y., et al.\ 2008, , 685, 354

    Liang, N., Xiao, W. K., Liu, Y., et al.\ 2008, , 685, 354. doi:10.1086/590903

    2008 doi

  198. [210]

    doi:10.3847/1538-4357/aca08a

    Liang, N., Li, Z., Xie, X., et al.\ 2022, , 941, 84. doi:10.3847/1538-4357/aca08a

    2022 doi

  199. [211]

    doi:10.1093/mnras/stv2471

    Lin, H.-N., Li, X., & Chang, Z.\ 2016, , 455, 2131. doi:10.1093/mnras/stv2471

    2016 doi

  200. [212]

    doi:10.3847/1538-4357/aa9e4f

    Liu, T., Song, C.-Y., Zhang, B., et al.\ 2018, , 852, 20. doi:10.3847/1538-4357/aa9e4f

    2018 doi

  201. [213]

    doi:10.3847/1538-4357/aa92c4

    Liu, T., Lin, C.-Y., Song, C.-Y., et al.\ 2017, , 850, 30. doi:10.3847/1538-4357/aa92c4

    2017 doi

  202. [214]

    doi:10.1093/mnras/sty2176

    L \"u , H.-J., Zou, L., Lan, L., et al.\ 2018, , 480, 4402. doi:10.1093/mnras/sty2176

    2018 doi

  203. [215]

    & Zhang, B.\ 2014, , 785, 74

    L \"u , H.-J. & Zhang, B.\ 2014, , 785, 74. doi:10.1088/0004-637X/785/1/74

    2014 doi

  204. [216]

    MacFadyen, A. I. & Woosley, S. E.\ 1999, , 524, 262. doi:10.1086/307790

    1999 doi

  205. [217]

    & Rees, M

    Meszaros, P. & Rees, M. J.\ 1993, , 405, 278. doi:10.1086/172360

    1993 doi

  206. [218]

    Minaev, P. Y. & Pozanenko, A. S.\ 2020, , 492, 1919. doi:10.1093/mnras/stz3611

    2020 doi

  207. [219]

    & Rees, M

    M \'e sz \'a ros, P. & Rees, M. J.\ 1997, , 476, 232. doi:10.1086/303625

    1997 doi

  208. [220]

    doi:10.1088/0034-4885/69/8/R01

    M \'e sz \'a ros, P.\ 2006, Reports on Progress in Physics, 69, 2259. doi:10.1088/0034-4885/69/8/R01

    2006 doi

  209. [221]

    doi:10.1086/184740

    Paczynski, B.\ 1986, , 308, L43. doi:10.1086/184740

    1986 doi

  210. [222]

    Paczynski, B.\ 1991, , 41, 257

    1991

  211. [223]

    & Kumar, P.\ 2002, , 571, 779

    Panaitescu, A. & Kumar, P.\ 2002, , 571, 779. doi:10.1086/340094

    2002 doi

  212. [224]

    doi:10.1086/307221

    Perlmutter, S., Aldering, G., Goldhaber, G., et al.\ 1999, , 517, 565. doi:10.1086/307221

    1999 doi

  213. [225]

    M.\ 1993, , 413, L105

    Phillips, M. M.\ 1993, , 413, L105. doi:10.1086/186970

    1993 doi

  214. [226]

    doi:10.1103/RevModPhys.76.1143

    Piran, T.\ 2004, Reviews of Modern Physics, 76, 1143. doi:10.1103/RevModPhys.76.1143

    2004 doi

  215. [227]

    doi:10.1051/0004-6361/201833910

    Planck Collaboration, Aghanim, N., Akrami, Y., et al.\ 2020, , 641, A6. doi:10.1051/0004-6361/201833910

    2020 doi

  216. [228]

    Planck Collaboration, Ade, P. A. R., Aghanim, N., et al.\ 2016, , 594, A13. doi:10.1051/0004-6361/201525830

    2016 doi

  217. [229]

    E., & Fryer, C.\ 1999, , 518, 356

    Popham, R., Woosley, S. E., & Fryer, C.\ 1999, , 518, 356. doi:10.1086/307259

    1999 doi

  218. [230]

    doi:10.1088/0004-637X/763/1/15

    Qin, Y., Liang, E.-W., Liang, Y.-F., et al.\ 2013, , 763, 15. doi:10.1088/0004-637X/763/1/15

    2013 doi

  219. [231]

    A., et al.\ 2015, , 813, 92

    Rea, N., Gull \'o n, M., Pons, J. A., et al.\ 2015, , 813, 92. doi:10.1088/0004-637X/813/2/92

    2015 doi

  220. [232]

    G., Filippenko, A

    Riess, A. G., Filippenko, A. V., Challis, P., et al.\ 1998, , 116, 1009. doi:10.1086/300499

    1998 doi

  221. [233]

    B.\ 2003, , 345, 1077

    Rosswog, S., Ramirez-Ruiz, E., & Davies, M. B.\ 2003, , 345, 1077. doi:10.1046/j.1365-2966.2003.07032.x

    2003

  222. [234]

    T., Metzger, B

    Rowlinson, A., O'Brien, P. T., Metzger, B. D., et al.\ 2013, , 430, 1061. doi:10.1093/mnras/sts683

    2013 doi

  223. [235]

    doi:10.1086/311269

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

    1998 doi

  224. [236]

    E.\ 2007, , 660, 16

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

    2007 doi

  225. [237]

    M., Jones, D

    Scolnic, D. M., Jones, D. O., Rest, A., et al.\ 2018, , 859, 101. doi:10.3847/1538-4357/aab9bb

    2018 doi

  226. [238]

    doi:10.3847/1538-4357/aad08a

    Si, S.-K., Qi, Y.-Q., Xue, F.-X., et al.\ 2018, , 863, 50. doi:10.3847/1538-4357/aad08a

    2018 doi

  227. [239]

    M., Ciolfi, R., & Rezzolla, L.\ 2014, , 785, L6

    Siegel, D. M., Ciolfi, R., & Rezzolla, L.\ 2014, , 785, L6. doi:10.1088/2041-8205/785/1/L6

    2014 doi

  228. [240]

    N., Verde, L., Peiris, H

    Spergel, D. N., Verde, L., Peiris, H. V., et al.\ 2003, , 148, 175. doi:10.1086/377226

    2003 doi

  229. [241]

    Z., Matheson, T., Garnavich, P

    Stanek, K. Z., Matheson, T., Garnavich, P. M., et al.\ 2003, , 591, L17. doi:10.1086/376976

    2003 doi

  230. [242]

    doi:10.3847/1538-4365/ab4711

    Tang, C.-H., Huang, Y.-F., Geng, J.-J., et al.\ 2019, , 245, 1. doi:10.3847/1538-4365/ab4711

    2019 doi

  231. [243]

    doi:10.1093/mnras/270.3.480

    Thompson, C.\ 1994, , 270, 480. doi:10.1093/mnras/270.3.480

    1994 doi

  232. [244]

    doi:10.1038/s41550-022-01832-7

    Urata, Y., Toma, K., Covino, S., et al.\ 2023, Nature Astronomy, 7, 80. doi:10.1038/s41550-022-01832-7

    2023 doi

  233. [245]

    Wang, F. Y. & Dai, Z. G.\ 2013, Nature Physics, 9, 465. doi:10.1038/nphys2670

    2013 doi

  234. [246]

    Y., Dai, Z

    Wang, F. Y., Dai, Z. G., & Liang, E. W.\ 2015, , 67, 1. doi:10.1016/j.newar.2015.03.001

    2015 doi

  235. [247]

    Y., Hu, J

    Wang, F. Y., Hu, J. P., Zhang, G. Q., et al.\ 2022, , 924, 97. doi:10.3847/1538-4357/ac3755

    2022 doi

  236. [248]

    doi:10.1111/j.1365-2966.2011.18961.x

    Wang, F.-Y., Qi, S., & Dai, Z.-G.\ 2011, , 415, 3423. doi:10.1111/j.1365-2966.2011.18961.x

    2011

  237. [249]

    doi:10.3847/1538-4357/ab0a86

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

    2020 doi

  238. [250]

    S., Wang, F

    Wang, J. S., Wang, F. Y., Cheng, K. S., et al.\ 2016, , 585, A68. doi:10.1051/0004-6361/201526485

    2016 doi

  239. [251]

    & Dai, M.\ 2016, , 94, 083521

    Wang, Y. & Dai, M.\ 2016, , 94, 083521. doi:10.1103/PhysRevD.94.083521

    2016 doi

  240. [252]

    doi:10.3847/1538-4357/aabc13

    Wang, X.-G., Zhang, B., Liang, E.-W., et al.\ 2018, , 859, 160. doi:10.3847/1538-4357/aabc13

    2018 doi

  241. [253]

    E.\ 1993, , 405, 273

    Woosley, S. E.\ 1993, , 405, 273. doi:10.1086/172359

    1993 doi

  242. [254]

    doi:10.1088/0004-637X/776/2/98

    Xu, D., de Ugarte Postigo, A., Leloudas, G., et al.\ 2013, , 776, 98. doi:10.1088/0004-637X/776/2/98

    2013 doi

  243. [255]

    & Huang, Y

    Xu, M. & Huang, Y. F.\ 2012, , 538, A134. doi:10.1051/0004-6361/201117754

    2012 doi

  244. [256]

    doi:10.3847/1538-4357/ac158a

    Xu, F., Tang, C.-H., Geng, J.-J., et al.\ 2021, , 920, 135. doi:10.3847/1538-4357/ac158a

    2021 doi

  245. [257]

    doi:10.1088/0004-637X/776/2/120

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

    2013 doi

  246. [258]

    doi:10.3847/1538-4357/ab8a53

    Yi, S.-X., Wu, X.-F., Zou, Y.-C., et al.\ 2020, , 895, 94. doi:10.3847/1538-4357/ab8a53

    2020 doi

  247. [259]

    Y., et al.\ 2017, , 844, 79

    Yi, S.-X., Yu, H., Wang, F. Y., et al.\ 2017, , 844, 79. doi:10.3847/1538-4357/aa7b7b

    2017 doi

  248. [260]

    doi:10.3847/0067-0049/224/2/20

    Yi, S.-X., Xi, S.-Q., Yu, H., et al.\ 2016, , 224, 20. doi:10.3847/0067-0049/224/2/20

    2016 doi

  249. [261]

    doi:10.1086/421285

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

    2004 doi

  250. [262]

    doi:10.3847/1538-4357/aab0a2

    Yu, H., Ratra, B., & Wang, F.-Y.\ 2018, , 856, 3. doi:10.3847/1538-4357/aab0a2

    2018 doi

  251. [263]

    doi:10.1088/1009-9271/7/1/01

    Zhang, B.\ 2007, , 7, 1. doi:10.1088/1009-9271/7/1/01

    2007 doi

  252. [264]

    & M \'e sz \'a ros, P.\ 2001, , 552, L35

    Zhang, B. & M \'e sz \'a ros, P.\ 2001, , 552, L35. doi:10.1086/320255

    2001 doi

  253. [265]

    doi:10.3847/1538-4357/ab38c4

    Zhao, L., Zhang, B., Gao, H., et al.\ 2019, , 883, 97. doi:10.3847/1538-4357/ab38c4

    2019 doi

  254. [266]

    doi:10.3847/1538-4357/aba43a

    Zhao, W., Zhang, J.-C., Zhang, Q.-X., et al.\ 2020, , 900, 112. doi:10.3847/1538-4357/aba43a

    2020 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.