GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

Lin Lan; He Gao; An Li; Shuo Xiao; Shunke Ai; Zong-Kai Peng; Long Li; Chen-Yu Wang; Nan Xu; Shijie Lin; Wei-Hua Lei; Bing Zhang; Yan-Qiu Zhang; Chao Zheng; Jia-Cong Liu; Wang-Chen Xue; Chen-Wei Wang; Wen-Jun Tan; Shao-Lin Xiong

doi:10.3847/2041-8213/accf93

GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

Lan, Lin; Gao, He; Li, An; Xiao, Shuo; Ai, Shunke; Peng, Zong-Kai; Li, Long; Wang, Chen-Yu; Xu, Nan; Lin, Shijie; Lei, Wei-Hua; Zhang, Bing; Zhang, Yan-Qiu; Zheng, Chao; Liu, Jia-Cong; Xue, Wang-Chen; Wang, Chen-Wei; Tan, Wen-Jun; Xiong, Shao-Lin 2023-05-01 00:00:00 The gamma-ray burst GRB 221009A, known as the “brightest of all time,” is the closest energetic burst detected so far, with an energy of E ∼ 10 erg. This study aims to assess its compatibility with known GRB energy and γ,iso luminosity distributions. Our analysis indicates that the energy/luminosity function of GRBs is consistent across various redshift intervals, and that the inclusion of GRB 221009A does not signiﬁcantly impact the function at low redshifts. Additionally, our evaluation of the best-ﬁtting result of the entire GRB sample suggests that the expected number of GRBs with energy greater than 10 erg at a low redshift is 0.2, so that the emergence of GRB 221009A is consistent with expected energy/luminosity functions within ∼2σ Poisson ﬂuctuation error, still adhering to the principles of small number statistics. Furthermore, we ﬁnd that GRB 221009A and other energetic bursts, deﬁned as E  10 erg, exhibit no signiﬁcant differences in terms of distributions of T , minimum timescale, Amati γ,iso 90 relation, E –E relation, L –Γ relation, E –Γ relation, L –E –Γ relation, and host galaxy γ,iso X,iso γ,iso 0 γ,iso 0 γ,iso p,i 0 properties, compared to normal long GRBs. This suggests that energetic GRBs (including GRB 221009A) and other long GRBs likely have similar progenitor systems and undergo similar energy dissipation and radiation processes. The generation of energetic GRBs may be due to more extreme central engine properties or, more likely, a rarer viewing conﬁguration of a quasi-universal structured jet. Uniﬁed Astronomy Thesaurus concepts: Gamma-ray bursts (629) Supporting material: machine-readable table 1. Introduction Burst Monitor (GBM) at 13:16:59 UT on 2022 October 9, with a −5 −2 ﬂuence of (2.12± 0.05) × 10 erg cm in 10–1000 keV within As one of the most violent explosions in the universe, a duration of T = 327 s (Lesage et al. 2022). Around the similar gamma-ray bursts (GRBs) are detected in a wide redshift range time, it triggered Insight-HXMT (Tan et al. 2022) and had been (from z = 0.0085 to z = 9.4) and a wide energy distribution detected by HEBS (Liu et al. 2022). Later, it was registered by the 46 54 (E ranging from ∼10 erg to 10 erg; Zhang 2018, for a γ,iso Swift Burst Alert Telescope (BAT) at 14:10:17 UT (Dichiara review). The distribution of E generally follows a simple γ,iso et al. 2022). Multiple ground- and space-based follow-up power-law distribution with a cutoff above (1–3) × 10 erg observations were performed, from radio to very-high-energy (Atteia et al. 2017). The cutoff feature, which should not be due γ-ray (Perley 2022;Kuin&Dichiara 2022; Pillera et al. 2022; to a selection effect because of their high brightness, may be Gotz et al. 2022; de Ugarte Postigo et al. 2022; Huang et al. 2022; related to some intrinsic limit of generating apparently Iwakirietal. 2022; Leung et al. 2022;O’Connor et al. 2023; energetic GRBs. In this paper, we deﬁne “energetic GRBs” Laskar et al. 2022; Tan et al. 2022). Most interestingly, the Large as GRBs with the isotropic-equivalent energy E  10 erg. γ,iso High Altitude Air Shower Observatory (LHAASO) reported more Most recently, the “brightest-of-all-time” gamma-ray burst, than 5000 very-high-energy photons within the ﬁrst ∼2000 s after GRB 221009A, was detected by many space-borne and ground- the burst trigger with energies above 500 GeV all the way to 18 based telescopes in all wavelength. The burst was located at TeV, making them the most energetic photons ever observed from redshift z= 0.151, and had an isotropic radiation energy of aGRB (Huang et al. 2022). Various physical models and ∼10 erg, making it the most energetic GRB among energetic radiation mechanisms have been proposed to explain the observed GRBs (An et al. 2023).It ﬁrst triggered the Fermi/Gamma-ray 18 TeV photon (Baktash et al. 2022;Brdar &Li 2023; Carenza & Marsh 2022; Finke & Razzaque 2023; Galanti et al. 2022; Original content from this work may be used under the terms González et al. 2023;Li & Ma 2023; Ren et al. 2023;Sahuet al. of the Creative Commons Attribution 4.0 licence. Any further 2023; Smirnov & Trautner 2022; Troitsky 2022; Xia et al. 2022; distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Zhang et al. 2023;Zhaoetal. 2023; Zheng et al. 2023). 1 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. With a geometric extrapolation of the total ﬂuence and peak 3. Energy Distribution Function ﬂux distributions, Burns et al. (2023) argue that GRB 221009A For the purpose of this work, we ﬁrst divide the collected appears to be a once-in-10,000 yr event. Given that the most sample into several subsamples with different redshift bins: prominent characteristic of GRB 221009A is its exceedingly [0 ∼ 0.5], [0 ∼ 1], [1 ∼ 2], [2 ∼ 3], [3 ∼ 4], [4 ∼ 9.4], [0 ∼ 9.4]. high total isotropic energy, our objective is to ascertain the For each subsample, we ﬁt the distribution function of E with iso predictability and low probability of its occurrence through a three models of the energy function: a simple power-law comprehensive examination of the energy/luminosity func- function (PL), a broken power-law function (BPL), and a tions of GRBs. In particular, we intend to investigate the power-law with a high-energy cutoff feature (CPL), whose following questions: expressions are as follows: 1. Is there an obvious difference between the energy/ -a f()EA = E,1( ) iso 0 iso luminosity distributions of high- and low-redshift ener- getic burst samples? -a ⎧ iso 2. Due to the addition of GRB 221009A, does the energy ⎛ ⎞ ⎜⎟ ;EE  iso b distribution for the low-redshift sample still follow a ⎝ ⎠ f()EA = (2) iso 0 cutoff power-law function? -b iso ⎛ ⎞ 3. Normalized to the existing sample size, what is the ⎜⎟;, EE > ⎪ iso b expected number of GRBs with energy greater than 10 ⎝ ⎠ erg at low redshifts? 4. Are GRB 221009A and other energetic GRBs system- atically different from other GRBs in terms of statistics of -a E E iso iso ⎛ ⎞ ⎛ ⎞ various properties, including the prompt emission, after- f()EA = ⎜⎟ exp⎜⎟, (3) iso 0 E E cc glow, and host galaxy properties? ⎝ ⎠ ⎝ ⎠ where A is a normalization factor, α and β are the power-law 2. GRB Sample Selection indices, and E and E are the break energy and cutoff energy b c for the BPL and CPL model, respectively. For different models, For this work, we extensively search for the sample of the Markov Chain Monte Carlo method through the emcee GRBs with measured redshift (both spectroscopic and package (Foreman-Mackey et al. 2013) is employed to obtain photometric) peak energy E ,aswellasisotropic-equivalent the best-ﬁtting parameters and their uncertainties. All ﬁtting energy E from published papers or the Gamma-ray γ,iso Coordinates Network Circulars if no published paper is results for different subsamples are presented in Figures 2–3 available. We eventually ﬁnd 355 GRBs in total registered and Table 2. In order to justify which model is best ﬁtted to the from 1997 February up to 2022 November, covering the distribution of E for a given subsample, we compared the iso redshift range from 0.0098 (GRB 170817A) to 9.4 (GRB goodness of the ﬁts by invoking the Bayesian information 090429B). For each burst in our sample, we collect their criteria (BIC; Schwarz 1978). BIC is a criterion to evaluate the temporal and spectral properties from previous statistical best-ﬁtted model among a ﬁnite set of models, and the model investigations (Amati et al. 2008; Zhang et al. 2009; Qin & with the lowest BIC is preferred. The deﬁnition of BIC can be Chen 2013; Li et al. 2016; Zhang et al. 2018; Zou et al. 2018; written as BIC=-2lnL+ k·( ln n), where k is the number of Minaev & Pozanenko 2020; Jia et al. 2022). In Table 1, we list model parameters, n is the number of data points, and L is the their prompt emission duration T , spectral peak energy in the maximum value of the likelihood function of the estimated rest frame E = E (1 + z) and isotropic-equivalent energy E . p,i p iso For GRB 221009A, the value of E and E are calculated model. (1) if 0 < ΔBIC < 2, the evidence against the model iso p based on the observational data from HXMT and HEBS (An with higher BIC is not worth more than a bare mention; (2) if et al. 2023), which made an unprecedentedly accurate 2 < ΔBIC < 6, the evidence against the model with higher BIC measurement of the prompt emission during the ﬁrst ∼1800 s, is positive; (3) if 6 < ΔBIC < 10, the evidence against the including its precursor emission, main emission, ﬂaring model with higher BIC is strong; (4) if 10 < ΔBIC, the emission and early afterglow. A record-breaking isotropic- evidence against the model with higher BIC is very strong. equivalent energy E = (1.5 ± 0.2) × 10 erg was measured iso Before discussing the ﬁtting results, we would like to based on the HEBS unsaturated data. The peak energy illustrate two things in advance: ﬁrst, due to the sensitivity of E = 1247.4 ± 91.2 keV for the time-integrated spectral of full 52 the γ-ray detectors, only sources with E > 10 erg can be iso burst in prompt emission. detected at high redshifts (see Figure 1). To fairly compare the The bursts in the sample are mainly observed by the Konus- ﬁtting results, for all the samples at different redshift, we only Wind, Swift, and Fermi satellites, including 36 s GRBs and 319 52 adopt GRBs with E > 10 erg. Second, GRBs in our iso lGRBs, with 12 bursts being characterized by an extended collected sample are detected by different detectors, e.g., emission (EE) component. Among the sample, 31 are energetic Konus-Wind, Swift, Fermi, CGRO/BATSE, and HETE-2, 14 54 GRBs with E  10 erg. Figure 1 shows the distribution γ,iso which may cause concern about systematic uncertainty when of redshift and E for our sample. iso we put them together to study the energy distribution. Because of this, we perform all analyses twice, one for the total samples and one for pure Konus-Wind samples (the majority of our collected sample are detected by Konus-Wind).We ﬁnd that https://gcn.gsfc.nasa.gov/gcn3_archive.html the results of the two analysis are consistent, which proves that We take GRB 130427A as an energetic GRB, although its isotropic energy there is no clear systematic error caused by the difference in is 9.51 × 10 erg, since it has similar characteristics to GRB 221009A in temporal and spectral properties from the prompt emission to afterglow. detection sensitivity for different instruments. 2 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Table 1 The Sample of Gamma-Ray Bursts GRB z T E Type Detector References p,i 90 iso (s)(10 erg)(keV) 970228 0.695 56.0 1.65 ± 0.12 195 ± 64 L SAX (1), (2), (4) 970508 0.835 14.0 0.61 ± 0.13 145 ± 43 L SAX (1), (2), (5) 970828 0.9578 146.59 30.38 ± 3.57 586 ± 117 L GRO (1), (2), (6) 971214 3.42 6.0 22.06 ± 2.76 685 ± 133 L SAX (1), (2), (7) 980326 1.0 312.0 0.482 ± 0.09 35.5 ± 18 L SAX (2), (3) LL L L L L L L 220117A 4.961 49.81 12.6 ± 3.1 387 ± 102 L SWI/KW (309), (310) 220521A 5.6 14.0 3.56 ± 0.26 244 ± 46 L FER (311), (312) 220527A 0.857 21.3 12.2 ± 0.65 286 ± 18 L KW (313), (314) 220627A 3.084 138.0 230.0 ± 30.0 1020 ± 225 L FER/KW (315), (316) 221009A 0.151 600.0 1500 ± 200 1436 ± 105 L FER/KW/HXMT/GECAM (317), (318), (319), (320) Notes. Column (1): GRB name. Column (2): redshift. Column (3): value of T . Column (4): isotropic γ-ray energy in rest-frame 1–10 keV. Column (5): peak energy in spectral parameter. Column (6): the classiﬁcation of the burst: ‘L’—regular long GRBs, ‘S+EE’—short GRBs with an extended emission, ‘S’—regular short GRBs. Column (7): the experiment, used for the calculation of T , E , and E values (GRO = CGRO/BATSE, SAX = BeppoSAX, HET = HETE-2, 90 p iso KW = Konus-Wind, SWI = Swift, FER = Fermi). Column (8): the reference of redshift, T , E , and E for our sample. 90 p iso References: (1) Jia et al. (2022); (2) Li et al. (2016); (3) Minaev & Pozanenko (2020); (4) Djorgovski et al. (1999); (5) Galama et al. (1997); (6) Djorgovski et al. (2001); (7) Kulkarni et al. (1998); (8) Tinney et al. (1998); (9) Djorgovski et al. (2003); (10) Djorgovski et al. (1998); (11) Kulkarni et al. (1999); (12) Bloom et al. (2003); (13) Vreeswijk et al. (2001); (14) Le Floc’h et al. (2002); (15) Castro-Tirado et al. (2001); (16) Vreeswijk et al. (1999); (17) Andersen et al. (2000); (18) Piro et al. (2002); (19) Jensen et al. (2001); (20) Price et al. (2002a); (21) Castro et al. 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(2007b); (92) Leibler & Berger (2010); (93) Rowlinson et al. (2010); (94) Greiner et al. (2009);(95) Berger et al. (2008b); (96) Zou et al. (2018); (97) Berger et al. (2008a); (98) D’Elia et al. (2008); (99) Berger & Rauch (2008); (100) Kuin et al. (2009); (101) Cucchiara et al. (2008); (102) de Ugarte Postigo et al. (2009c); (103) Cenko et al. (2011c); (104) Chornock et al. (2009a); (105) Tanvir et al. (2009); (106) Chornock et al. (2009b); (107) Rau et al. (2009); (108) de Ugarte Postigo et al. (2009b); (109) Cenko et al. (2009); (110); Perley et al. 2013; (111) Wiersema et al. (2009); (112) de Ugarte Postigo et al. (2009a); (113) Cucchiara et al. (2009c); (114) Rau et al. (2010); (115) Cucchiara et al. (2009b); (116) Xu et al. (2009); (117) Cucchiara et al. (2009a); (118) Chornock et al. (2009c); (119) Chornock & Berger (2009); (120) Perley et al. (2009a); (121) Fong et al. (2011); (122) Perley et al. (2012); (123) Cucchiara & Fox (2010a); (124) Cucchiara & Fox (2010b); (125) Fong et al. (2013); (126) Flores et al. (2010); (127) Tanvir et al. (2010b); (128) Tanvir et al. (2010a); (129) Chornock & Berger (2011a); (130) Chornock & Berger (2011b); (131) Sparre et al. (2011); (132) Levan et al. (2014); (133) Cenko et al. (2011a); (134) Milne & Cenko (2011); (135) Cenko et al. (2011b); (136) Rufﬁni et al. (2011); (137) de Ugarte Postigo et al. (2011a); (138) de Ugarte Postigo et al. (2011b); (139) Piranomonte et al. (2011); (140) Tanvir et al. (2011); (141) Wiersema et al. (2011); (142) Selsing et al. (2018); (143) Tello et al. (2012); (144) Tanvir et al. (2012b); (145) Xu et al. (2012); (146) Greiner et al. (2012); (147) Cucchiara et al. (2012); (148) Tanvir & Ball (2012); (149) Berger et al. (2013); (150) Thoene et al. (2012); (151) Hartoog et al. (2012); (152) Knust et al. (2012); (153) Tanvir et al. (2012a); (154) Cucchiara & Fumagalli (2013); (155) Tanvir et al. (2013a); (156) de Ugarte Postigo et al. (2013a); (157) Tanvir et al. (2013b); (158) Schmidl et al. (2013); (159) Sanchez-Ramirez et al. (2013); (160) Cucchiara et al. (2013); (161) Chornock et al. (2013); (162) Smette et al. (2013);(163) Tanvir et al. (2013c); (164) Kelly et al. (2013); (165) Cucchiara & Perley (2013); (166) de Ugarte Postigo et al. (2013c); (167) Zhang et al. (2018); (168) Rau et al. (2013); (169) Xu et al. (2013); (170) de Ugarte Postigo et al. (2013b); (171) Hartoog et al. (2013); (172) Malesani et al. (2014b); (173) Cenko et al. (2015); (174) Jeong et al. (2014); (175) Tanvir et al. (2014a); (176) Tanvir et al. (2014b); (177) Malesani et al. (2014a); (178) de Ugarte Postigo et al. (2014b); (179) Chornock et al. (2014b); (180) Chornock et al. (2014c); (181) Cano et al. (2015); (182) Kasliwal et al. (2014); (183) Hartoog et al. (2014); (184) Bhalerao et al. (2014); (185) D’Avanzo et al. (2014); (186) Castro- Tirado et al. (2014a); (187) de Ugarte Postigo et al. (2014a); (188) Gorosabel et al. (2014a); (189) Cucchiara et al. (2014); (190) Castro-Tirado et al. (2014b); (191) de Ugarte Postigo et al. (2014d); (192) Xu et al. (2014a); (193) Xu et al. (2014b); (194) Chornock et al. (2014a); (195) de Ugarte Postigo et al. (2014c); (196) Perley et al. (2014);(197) Gorosabel et al. (2014b); (198) Levan et al. (2015); (199) Chornock & Fong (2015); (200) Kruehler et al. (2015); (201) de Ugarte Postigo et al. (2015c); (202) de Ugarte Postigo et al. (2015b); (203) Perley & Cenko (2015); (204) Pugliese et al. (2015); (205) de Ugarte Postigo & Tomasella (2015); (206) Malesani et al. (2015); (207) Castro-Tirado et al. (2015); (208) de Ugarte Postigo et al. (2015e); (209) Tanvir et al. (2015b); (210) de Ugarte Postigo et al. (2015a); (211) D’Elia et al. (2015); (212) de Ugarte Postigo et al. (2015d); (213) Perley et al. (2015); (214) Tanvir et al. (2015a); (215) Bolmer et al. (2015); (216) de Ugarte Postigo et al. (2016a); (217) Xu et al. (2016a); (218) Selsing et al. (2016b); (219) Tanvir et al. (2016c); (220) Malesani et al. (2016b); (221) O’Connor et al. (2021); (222) Xu et al. (2016c); (223) Castro-Tirado et al. (2016); (224) Xu et al. (2016b); (225) Levan et al. (2016); (226) Selsing et al. (2016a); (227) de Ugarte Postigo et al. (2016b); (228) Tanvir et al. (2016a); (229) Malesani et al. (2016a); (230) Cano et al. (2016); (231) Tanvir et al. (2016b); (232) Xu et al. (2017); (233) de Ugarte Postigo et al. (2017b); (234) Kruehler et al. (2017); (235) Izzo et al. (2017a); (236) Izzo et al. (2017b); (237) de Ugarte Postigo et al. (2017c); (238) de Ugarte Postigo et al. (2017e); (239) de Ugarte Postigo et al. (2017d); (240) de Ugarte Postigo et al. (2017f); (241) Izzo et al. (2017c); (242) de Ugarte Postigo et al. (2017a); (243) Tanvir et al. (2018); (244) Heintz et al. (2018); (245) Izzo et al. (2018a); (246) Izzo et al. (2018b); (247) Vreeswijk et al. (2018); (248) Rossi et al. (2018); (249) D’Avanzo et al. (2018); (250) Fynbo et al. (2018); (251) Perley et al. (2018); (252) Izzo et al. (2018c); (253) Schady et al. (2019); (254) Castro-Tirado et al. (2019); (255) Gupta et al. (2022); (256) Poolakkil et al. (2019); (257) Rossi et al. (2019); (258) Chand et al. (2020); (259) Valeev et al. (2019); (260) Bissaldi et al. (2019); (261) Malesani et al. (2019); (262) Ukwatta & Swift-BAT Team (2020); (263) Vielfaure & Stargate Collaboration (2020); (264) Fong et al. (2021); (265) Pookalil et al. (2020); (266) Yao et al. (2021); 3 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. (267) Bissaldi et al. (2020); (268) de Ugarte Postigo et al. (2021a); (269) Lesage et al. (2020a); (270) Oates et al. (2020); (271) Ror et al. (2023); (272) de Ugarte Postigo et al. (2020a); (273) Malacaria et al. (2020); (274) Kann et al. (2020); (275) Lesage et al. (2020b); (276) Vielfaure et al. (2020a); (277) Svinkin et al. (2020); (278) Xu et al. (2020); (279) Vielfaure et al. (2020b); (280) Yuan et al. (2022); (281) de Ugarte Postigo et al. (2020b); (282) Ho et al. (2022); (283) Xu et al. (2021b); (284) Frederiks et al. (2021b); (285) de Ugarte Postigo et al. (2021b); (286) Markwardt et al. (2021); (287) de Ugarte Postigo et al. (2021d); (288) Veres et al. (2021); (289) Zhu et al. (2021b); (290) de Ugarte Postigo et al. (2021c); (291) Oganesyan et al. (2021); (292) de Ugarte Postigo et al. (2021e); (293) Frederiks et al. (2021c); (294) Xu et al. (2021a); (295) Wood & Fermi GBM Team (2021); (296) Thoene et al. (2021); (297) Lesage & Meegan (2021);(298) Kann et al. (2021); (299) Frederiks et al. (2021d); (300) Zhu et al. (2021a); (301) Frederiks et al. (2021a); (302) Tanvir et al. (2021); (303) Lü et al. (2022); (304) Zhu et al. (2022); (305) Tsvetkova et al. (2022); (306) Fynbo et al. (2022a); (307) Veres et al. (2022); (308) Castro-Tirado et al. (2022); (309) Frederiks et al. (2022c); (310) Palmerio et al. (2022); (311) Poolakkil et al. (2022); (312) Fynbo et al. (2022b); (313) Lysenko et al. (2022); (314) Xu et al. (2022); (315) Frederiks et al. (2022b); (316) Izzo et al. (2022); (317) Lesage et al. (2022); (318) Frederiks et al. (2022a); (319) de Ugarte Postigo et al. (2022); (320) An et al. (2023); (321) Cucchiara et al. (2011). (This table is available in its entirety in machine-readable form.) Figure 1. The isotropic gamma-ray energy E for our collected GRBs as a function of the redshift z. The blue circles, orange circles, blue stars, red stars, and green γ,iso circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic GRBs, respectively. The red horizontal dotted line represent E γ, = 10 erg. The histograms on top and right represent the E and z distribution for all GRBs, and the blue and red vertical lines represent GRB 130427A and iso γ,iso GRB 221009A location, respectively. We ﬁrst focus on the low-redshift subsample with In order to exclude the inﬂuence of the sample size, we also 0 < z < 0.5. We ﬁnd that when GRB 221009A is not analyzed the subsample with 0 < z < 1. In this case, we ﬁnd introduced, the best-ﬁtting model of the energy function in that when GRB 221009A is not introduced, the best-ﬁtting this redshift interval is PL, although the other two models are model of energy distribution is CPL. The BIC difference not signiﬁcantly excluded from the BIC analysis results (see between PL and CPL is around 3, and the BIC difference Figure 2). The BIC difference between PL and CPL is less than between PL and BPL is around 2. With the addition of GRB 3, and the BIC difference between PL and BPL is larger than 2 221009A, the best-ﬁt model of the energy function is also CPL. but smaller than 6. With the addition of GRB 221009A The BIC difference between CPL and PL is less than 2, and the (currently the highest energy source in this redshift bin), the BIC difference between PL and BPL is only around 2. In general, the energy distribution of low-redshift GRBs best-ﬁt model of the energy function is still PL. Again, the BIC difference between PL and CPL is only around 3, and the BIC does not show an obvious cutoff at the high-energy end, which may be due to the small sample size, especially the small difference between PL and BPL is larger than 2 but smaller than 6. number of high-energy sources. With the expansion of the 4 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 2. Cumulative distribution of GRB isotropic energy for total samples (left panels) and pure Konus-Wind samples (right panels) in the low-redshift bins. The blue circles show the observed distribution, and the red solid lines, red dashed lines, and blue solid lines represent the best-ﬁtting CPL model, BPL model, and PL model, respectively. 5 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 3. Similar to Figure 2, but for high-redshift bins. 6 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 4. The likelihood distribution of α and E in the CPL model, from the total samples (left panel) and pure Konus-Wind samples (right panel) in different redshift bins. Table 2 The Best-ﬁtting Results of Energy Function for Pure Konus-Wind and Total Sample GRBs in Different Redshift Bins BPL CPL Redshift Interval PL 54 54 Konus-Wind GRBs αα β E (10 erg) α E (10 erg) b c +0.08 +0.08 +1.21 +1.55 +0.10 +2.87 [0.0 ∼ 0.5] 0.38 0.36 1.06 2.70 0.31 5.83 -0.07 -0.07 -0.72 -1.58 -0.10 -3.15 +0.05 +0.09 +0.32 +0.90 +0.06 +1.98 [0.0 ∼ 1.0] 0.53 0.41 0.94 0.38 0.42 2.77 -0.04 -0.15 -0.24 -0.27 -0.08 -1.51 +0.03 +0.05 +0.60 +0.27 +0.06 +0.52 [1.0 ∼ 2.0] 0.39 0.22 1.22 0.49 0.17 1.26 -0.03 -0.07 -0.37 -0.26 -0.06 -0.34 +0.03 +0.06 +0.66 +0.25 +0.06 +0.27 [2.0 ∼ 3.0] 0.44 0.17 1.50 0.45 0.09 0.87 -0.03 -0.07 -0.41 -0.19 -0.07 -0.23 +0.05 +0.09 +0.56 +0.31 +0.09 +1.12 [3.0 ∼ 4.0] 0.32 0.13 1.08 0.50 0.11 1.77 -0.11 -0.25 -0.10 -0.74 -0.05 -0.40 +0.07 +0.09 +0.59 +0.29 +0.08 +1.65 [4.0 ∼ 9.4] 0.23 0.17 0.62 0.60 0.13 3.47 -0.06 -0.09 -0.33 -0.35 -0.09 -1.59 +0.02 +0.04 +0.24 +0.23 +0.03 +0.30 [0.0 ∼ 9.4] 0.52 0.22 1.23 0.45 0.18 1.41 -0.01 -0.05 -0.19 -0.18 -0.04 -0.26 Total sample GRBs +0.08 +0.05 +0.72 +1.37 +0.08 +2.96 [0.0 ∼ 0.5] 0.40 0.38 0.86 2.89 0.33 5.62 -0.07 -0.06 -0.58 -1.32 -0.09 -3.16 +0.04 +0.05 +0.32 +0.64 +0.05 +1.22 [0.0 ∼ 1.0] 0.54 0.49 0.95 0.97 0.44 3.19 -0.03 -0.05 -0.27 -0.48 -0.05 -1.38 +0.02 +0.04 +0.53 +0.22 +0.05 +0.48 [1.0 ∼ 2.0] 0.47 0.30 1.21 0.43 0.26 1.24 -0.02 -0.06 -0.32 -0.22 -0.05 -0.34 +0.03 +0.05 +0.63 +0.16 +0.06 +0.22 [2.0 ∼ 3.0] 0.52 0.25 1.74 0.45 0.16 0.73 -0.03 -0.05 -0.43 -0.15 -0.06 -0.17 +0.04 +0.08 +0.51 +0.29 +0.07 +0.80 [3.0 ∼ 4.0] 0.45 0.27 1.14 0.36 0.25 1.40 -0.04 -0.09 -0.33 -0.17 -0.09 -0.56 +0.05 +0.07 +0.50 +0.37 +0.06 +2.23 [4.0 ∼ 9.4] 0.39 0.30 0.81 0.46 0.31 3.38 -0.04 -0.11 -0.27 -0.33 -0.07 -1.68 +0.01 +0.03 +0.15 +0.10 +0.03 +0.29 [0.0 ∼ 9.4] 0.57 0.29 1.19 0.37 0.27 1.28 -0.01 -0.04 -0.14 -0.13 -0.03 -0.24 sample, from 0 < z < 0.5 to 0 < z < 1, the CPL model does subsample with 3 < z < 4, the best-ﬁtting model is the CPL, change from inferior to slightly better than the PL model. The but the BIC difference between PL/BPL and CPL is smaller addition of GRB 201009A has no signiﬁcant inﬂuence on the than 6. For the subsample with z > 4, the best-ﬁtting model is above conclusions. PL, but the BIC difference between CPL/BPL and PL is also For comparison, we have made similar analyses on other smaller than 6. subsamples with high redshift. We ﬁnd that for subsamples In Figures 4–5, we plot the best-ﬁt parameter contours for with sufﬁcient sample size (e.g., 1 < z < 2 and 2 < z < 3), the CPL and BPL models at different redshift for total samples and best-ﬁtting model of the energy function is the CPL model, pure Konus-Wind samples. We ﬁnd that the best-ﬁtting although the BIC difference between the BPL model and the parameters for different redshift samples are in good agreement with each other, supporting the hypothesis that the energy CPL model is larger than 2 but smaller than 6. In these cases, the PL model is signiﬁcantly excluded (the BIC difference function of GRBs does not evolve with redshift. Under such a hypothesis, we compare the distribution of E for the total between the PL model and the CPL model is much more than iso 10). For subsamples with higher redshift, the sample size sample (0 < z < 9.4) with PL/BPL/CPL models. We ﬁnd that the best-ﬁtting model for the total sample is the CPL model, decreases again, and the goodness of ﬁt of the three models for +0.03 +0.30 energy distribution becomes indistinguishable again. For the with a = 0.18 and E = 1.41 . The results are -0.04 c,54 -0.26 7 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 5. The likehood distribution of α, β and E in the BPL model, from the total samples (left panel) and pure Konus-Wind samples (right panel) in different redshift bins. Table 3 The Best-ﬁtting Results of Luminosity Function for Total Sample GRBs in Different Redshift Bins BPL CPL Redshift interval PL 54 −1 54 −1 αα β L (10 erg s ) α L (10 erg s ) b c +0.10 +0.08 +0.70 +0.07 +0.07 +0.35 [0.0 ∼ 0.5] 0.52 0.51 0.93 0.10 0.47 0.45 -0.09 -0.09 -0.72 -0.06 -0.09 -0.28 +0.05 +0.05 +0.59 +0.05 +0.06 +0.34 [0.0 ∼ 1.0] 0.60 0.59 1.11 0.12 0.56 0.48 -0.05 -0.05 -0.61 -0.05 -0.06 -0.28 +0.03 +0.07 +0.57 +0.07 +0.06 +0.29 [1.0 ∼ 2.0] 0.48 0.40 0.89 0.03 0.39 0.21 -0.03 -0.11 -0.22 -0.02 -0.06 -0.09 +0.03 +0.06 +0.40 +0.01 +0.07 +0.03 [2.0 ∼ 3.0] 0.45 0.25 1.21 0.03 0.19 0.08 -0.03 -0.07 -0.31 -0.01 -0.07 -0.02 +0.05 +0.08 +0.42 +0.03 +0.09 +0.05 [3.0 ∼ 4.0] 0.48 0.31 1.36 0.04 0.23 0.09 -0.04 -0.10 -0.41 -0.02 -0.10 -0.03 +0.05 +0.08 +0.55 +0.03 +0.07 +0.05 [4.0 ∼ 9.4] 0.34 0.22 1.03 0.04 0.16 0.12 -0.04 -0.09 -0.39 -0.02 -0.08 -0.04 +0.02 +0.05 +0.11 +0.01 +0.03 +0.03 [0.0 ∼ 9.4] 0.46 0.26 0.75 0.01 0.30 0.11 -0.02 -0.07 -0.08 -0.01 -0.03 -0.02 consistent with the previous results from Atteia et al. (2017).In addition of GRB 201009A has no signiﬁcant inﬂuence on the this case, the PL model is signiﬁcantly excluded, since the BIC above conclusions. All best-ﬁtting parameters are collected in difference between the PL model and the CPL model is larger Table 3. Our results are generally consistent with previous than 100. However, it is worth to noting that the BIC difference studies. For instance, our best-ﬁtting results of the BPL model +0.05 +0.11 between BPL and CPL is smaller than 3, indicating that there is to the entire sample areab== 0.26 , 0.75 and -0.07 -0.08 +0.01 no clear evidence to distinguish between these two models. L = 0.01 . our low-luminosity power-law index and the b,54 -0.01 With our collected sample, we also studied the luminosity break luminosity is well consistent with Wanderman & Piran +0.2 +0.02 function of GRBs. In Figure 6, we plot the best-ﬁtting results (2010)(a== 0.2 , L 0.03 ) and Sun et al. (2015) b,54 -0.1 -0.02 of the luminosity function for PL, BPL, and CPL models in (α = 0.3, L = 0.01), while our high-luminosity power-law b,54 +0.3 different redshift bins. Similar to the results of the energy index is smaller than Wanderman & Piran (2010)(b = 1.4 ) -0.6 function, the luminosity distribution of low-redshift GRBs and Sun et al. (2015)(β = 1.3), which may be because we (z < 1) does not show a clear cutoff feature, which may be also invoke more energetic GRBs in our sample. due to the small sample size, especially the small number of Overall, based on the results of different subsamples, it is high-luminosity sources. For samples with sufﬁcient size more likely that the energy/luminosity function of GRBs (subsamples with z > 1 and the total sample), the luminosity always follows the CPL or BPL model, namely, there is always function also follows the CPL or BPL model. Again, the a cutoff or break at the high-energy end. This conclusion is consistent with results from previous studies both on 15 luminosity function (Liang et al. 2007; Virgili et al. 2009; To construct the luminosity function, we use the average luminosity (E /T ) instead of peak luminosity. It is found that the results from two Wanderman & Piran 2010; Sun et al. 2015) and energy iso 90 approaches have good agreement for the low-luminosity power-law index and function (Atteia et al. 2017; Lan et al. 2022). the break luminosity, but a discrepancy for the high-luminosity power-law The weak advantage of PL model performance in low- and index (Wanderman & Piran 2010). Therefore, the utilization of the average luminosity will not signiﬁcantly impact our discussion here. high-redshift samples is likely due to the limited sample size. 8 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 6. Cumulative distribution of GRB isotropic luminosity for total samples in the different redshift bins. The blue circles show the observed distribution, and the red solid lines, red dashed lines, and blue solid lines represent the best-ﬁtting CPL model, BPL model, and PL model, respectively. 9 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 7. Comparison between the normalized best-ﬁtting CPL model of the total-redshift bin (0 < z < 9.4) and the best-ﬁtting CPL model of the low-redshift bin (0 < z < 0.5) for total samples (left panel) and pure Konus-Wind samples (right panel). The blue dashed lines and red solid lines represent the best-ﬁtting CPL model for total-redshift bin and low-redshift bin. There is no clear evidence that more energetic GRBs are easily energetic GRB sample, we employ the Bayesian blocks generated at low redshift. To further prove this, we normalize algorithm and deﬁne the 1/2 shortest signiﬁcant structures of the best-ﬁtting CPL function of the total sample to compare blocks as the duration of minimum time interval (Vianello with the distribution of E at 0 < z < 0.5 (see Figure 1 and 7). et al. 2018; Xiao et al. 2022c). The median minimum timescale iso If the best-ﬁtting result of the total sample can represent the of the energetic GRB sample is about 2.32 s at 10–1000 keV, intrinsic distribution of the GRB energy function, we ﬁnd that which is well consistent with typical lGRBs. The minimum the occurrence of GRB 221009A is consistent with the timescale upper limit of GRB 221009A is 0.4 s at expectation within 1.84σ Poisson ﬂuctuation error. 10–1000 keV, which is no signiﬁcant difference compared to typical lGRBs and other energetic GRBs. We also adopt the continuous wavelet transform method (Vianello et al. 2018) 4. Statistic Investigation and the results are consistent. The result is shown in Figure 9. With our collected sample, it is of great interest to investigate whether GRB 221009A and other energetic GRBs are system- atically different from other GRBs in terms of statistics of 4.3. Amati Relation various properties. Here we focus on the following aspects: T Some empirical correlations among GRB observational distribution, minimum variability timescale distribution, Amati parameters have been discovered in the literature. The most relation, spectral-lag distribution, X-ray and optical afterglow famous one is the Amati relations (Amati et al. 2002), which is properties, the relation between the E and E , initial γ,iso X,iso a correlation between the GRB isotropic energy E and the γ,iso Lorentz factor distribution, and host galaxy properties. rest-frame peak energy E = (1 + z)E . Amati et al. (2002) p,i p discovered that higher-energy lGRBs have a harder spectrum 4.1. T Distribution than that of lower-energy lGRBs, and the sGRBs also follow the same trend between E and E but form distinct tracks Phenomenologically, GRBs fall into two classes: the long- p,i γ,iso (Zhang et al. 2009). Here we plot the Amati diagram for both duration, soft-spectrum class (duration <2 s; lGRBs) and the the lGRB and sGRB populations (see Figure 10) with our short-duration, hard-spectrum class (duration >2 s; sGRBs), collected sample. We ﬁnd that most-energetic GRBs are well based on the bimodal distribution of GRBs in the duration- located in the same trend as normal lGRBs, although their E hardness diagram (Kouveliotou et al. 1993). In Figure 8,we γ,iso are higher than those of most observed lGRBs. GRB 221009A show the GRBs in our sample in the duration T versus slightly deviates from the Amati relation toward higher intrinsic peak energy E diagram. We ﬁnd that all the p,i isotropic energy (see An et al. 2023 for more details). energetic GRBs fall into the distribution of lGRBs, and the distributions in T and E are not signiﬁcantly different with 90 p,i respect to the other lGRBs in our sample. Among the energetic 4.4. Spectral-lag Distribution bursts, GRB 221009A is distributed at the relatively large side of T and the center of E . 90 p,i The redshift distribution of energetic GRBs in our sample ranges from 0.151 to 6.318. For each GRB, the ﬁxed rest-frame energy bands are selected to be 100–150 keV and 4.2. Minimum Variability Timescale Distribution 200–250 keV, corresponding to the observed energy of The minimum timescale (Dt ) on which a GRB exhibits min [200–250]/(1+z) keV and [100–150]/(1+z) keV, which is signiﬁcant ﬂux variations is believed to provide an upper limit the same as in Ukwatta et al. (2012). The purpose of the above as to the size of the radiation zone, the lower limit of the selection of energy bands is to make full use of the data and Lorentz factor and potentially shedding light on the nature of ensure sufﬁcient energy difference between these two bands. emission mechanism (Schmidt 1978). For typical lGRBs and sGRBs, the average minimum timescales in the rest frame (i.e., GBM detectors have reached saturation for the extremely bright GRB Dt /(1+z)) are 45 and 10 ms, respectively (Golkhou et al. min 221009A in main emission phase, and we can only get the upper limit of the 2015). In order to calculate the minimum timescale for the minimum variability timescale in main emission. 10 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 8. lGRB/sGRB classiﬁcation diagram in the T − E domain. The blue circles, orange circles, blue star, red star, and green circles represent the sGRBs, 90 p lGRBs, GRB 130427A, GRB 221009A, and other energetic GRBs, respectively. The red vertical dotted line represent T = 2 s. The histograms of top and right represent the T and E distribution for all GRBs, and the blue and red vertical lines represent GRB 130427A and GRB 221009A location, respectively. 90 p Based on the high-time-resolution initial light curves of where b and b are the estimated background counts of light x y Swift/BAT or Fermi/GBM, we utilize the Li-CCF method (see curves x (Δt) and y (Δt), respectively. We can obtain a value m m Li et al. 2004 and Xiao et al. 2021, 2022a, 2022b for details) to k of k that maximizes MCCF(k = k , Δt); then the max max calculate the spectral lags for energetic GRBs in our sample, relative time lag between two light curves y (i; Δt) and which is deﬁned as x (i; Δt) on Δt is Dt td ()D=tk t.6( ) max MCCF() kt ,D= Dt m=1 We implement a Monte Carlo simulation of the observed light ui();;DD tus () i t /s, (4) mm+k u u curves based on Poisson probability distribution to obtain the uncertainty of spectral lag. It has long been found that there is an anticorrelation where the combination starts from the mth bin of the initial between spectral lag and peak luminosity exists for lGRBs light curves, the phase factor m = 1, 2,L, M , and u (Δt) and Δt m (Norris et al. 2000; Hakkila et al. 2008) namely short-lag and υ (Δt) are the background-subtracted series of x (Δt) and m m variable bursts having greater luminosities than long-lag and y (Δt). By rebinning the initial series, we obtain the light smooth bursts (Norris 2002; Hakkila et al. 2007; Ukwatta et al. curves with an optimized time bin Δt = M δt (from 1 to Δt 2012; Shao et al. 2017). Here we found that the energetic 100 ms for sGRBs, from 1 ms to 1 s for lGRBs), respectively, sources systematically deviate from this relationship, and their average spectral lag is smaller than that of normal lGRBs (see ui();; D= t x () i Dt -b () i;Dt, mm x Figure 11). We adopt two unsaturated emission episodes (T + 180 s ∼T + 210 s, T + 280 s ∼ T + 350 s) in the main u () it;; D=y() i Dt -b () it;D, 0 0 0 0 m y burst to calculate the spectral lag for GRB 221009A. We ﬁnd s=D ui();,t u å m that the spectral lags of the two unsaturated emission episodes in 200–250 keV compared to that in 100–150 keV at rest frame su=D() it;, (5) u å m are 292 ± 15 and 276 ± 36 ms, respectively. In order to 11 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 9. The diagram in theTt -D domain. The samples of sGRBs (blue circles) and lGRBs (orange circles) are from Golkhou et al. (2015). The red arrow and 90 min green circles represent GRB 221009A and other energetic GRBs, respectively. The red vertical dotted line represent T = 2s. Figure 10. E and E correlation diagram with known redshift data (Zhang et al. 2009; Qin & Chen 2013; Zou et al. 2018; Minaev & Pozanenko 2020; Jia p,i γ,iso et al. 2022). The orange and blue solid lines represent the best-ﬁt correlations for lGRBs and sGRBs, respectively. The blue circles, orange circles, blue star, red star, and green circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic lGRBs, respectively. 12 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 11. The correlation between spectral lag and peak luminosity in the rest frame. The GRB sample is collected from the previous statistical investigations (Li et al. 2004; Gehrels et al. 2006; Ukwatta et al. 2012; Goldstein et al. 2017; Xiao et al. 2022a; Lü et al. 2022). The GRB 221009A for spectral lag of the two unsaturated main emission episodes (T + 180 s ∼T + 210 s, T + 280 s ∼T + 350 s) and other energetic GRBs are highlighted by red star, blue star, and green circles, 0 0 0 0 respectively. The blue shaded region represents the common intrinsic spectral lags (3σ) calculated from 46 sGRBs with redshift measurements (Xiao et al. 2022a). estimate the peak luminosity of these two unsaturated emission Here N(E) is the observed time-dependent X-ray photon episodes, a time-resolved spectral ﬁtting was performed by a spectrum, which could be best ﬁtted by a power-law model Band spectrum, and the peak energy ﬂux of these two episodes (spectral parameters could be obtained from the Swift archive). −5 −2 −1 are (4.31 ± 0.03) × 10 erg cm s and (1.32 ± 0.01) × To calculate D (z), the concordance cosmology parameters −4 −2 −1 10 erg cm s in the 10 keV–1000 keV energy range, −1 −1 H = 67.4 km s Mpc , Ω = 0.315, and Ω = 0.685 have 0 M Λ respectively. As shown in Figure 11, the two unsaturated main been adopted according to the Planck results (Planck emission episodes of GRB 221009A are located in the long- Collaboration et al. 2020). In the left panel of Figure 12,we burst region for the anticorrelation between spectral lag and plot the X-ray luminosity curves for GRB 221009A and other peak luminosity. energetic GRBs. We ﬁnd that most energetic GRBs show simple power-law decay characteristics in the late phase with 4.5. X-Ray and Optical Afterglow Properties decay slopes systemically steeper compared to the so-called In order to compare whether GRB 221009A and other “normal decay slope” (with a typical slope approximately energetic GRBs are systematically different from other GRBs −1.2; Zhang et al. 2006). The distribution of decay slope is in X-ray and optical afterglow, here, we collected the X-ray and shown in the right panel of Figure 12, where the decay slope of optical afterglow for GRB 221009A and other energetic GRBs. GRB 221009A is located at the center. The XRT light curve is obtained by using the public data from For optical afterglow, we extensively search for the optical the Swift archive. For each energetic GRB, we derived the data from published papers or from the Gamma-ray Coordi- X-ray luminosity, which is calculated by L = 4kD p F , X X nates Network (GCN) Circulars if no published paper is where F is observed X-ray ﬂux, D is the GRB luminosity X L available. We found 358 GRBs in total with optical observa- distance, and the k-correction factor corrects the XRT-band tions being reported from 1997 February to 2020 December, (0.3–10 keV) ﬂux to a wide band in the burst rest frame including 308 GRBs having well-sampled optical light curves, (0.1–1000 keV in this analysis), i.e., which contain at least three data points, excluding upper limits. In Figure 13, we show the optical light curves (in absolute 10 1+z EN() E dE magnitude) for energetic GRBs and other GRBs. We ﬁnd that 0.1 1+z k = .7 () the optical afterglow is systematically brighter than other EN() E dE ò GRBs. Because of this, the optical afterglow observation of 0.3 energetic GRBs generally starts earlier. Many of these bursts have been detected the reverse shock radiation and/or the onset https://www.swift.ac.uk/xrt_curves/ bump of the forward shock radiation (unfortunately, the optical 13 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 12. Left panel: the X-ray luminosity light curves of energetic GRBs in our sample. The blue circles and red circles represent the GRB 130427A and GRB 221009A, respectively. The gray background circles show that other energetic GRBs. Right panel: the distribution of decay slope in X-ray late phase for energetic GRBs in our sample, and the red vertical line represent GRB 221009A location. Figure 13. Galactic extinction corrected R band afterglow light curves. The gray background lines show that we collected optical data, and the green lines show the optical afterglow of energetic GRBs in our sample. The blue star line and red star line represent the GRB 130427A and GRB 221009A, respectively. observation of GRB 221009A stars relatively late, because energetic afterglow emission (Zou et al. 2019). Here it is of Swift/BAT triggered is ∼0.88 hr later than Fermi/GBM). interest to investigate the relation between the energies released Considering that the host galaxy properties of energetic GRBs in the γ-ray band (E ) and in the X-ray band (E ). E γ,iso X,iso X,iso have no obvious distinctiveness (see Section 4.8 for details), can be calculated by E =+ 41 kD p S ()z , where S is X,iso L X X the brighter optical afterglow should not be attributed to the observed X-ray ﬂuence and k is the correction factor that impact of the circumburst environment but should be due to corrects the XRT-band (0.3–10 keV) ﬂux to a wide band in the higher kinetic energy. This infers that the radiation efﬁciency of burst rest frame (0.1–1000 keV). As shown in Figure 14, there these energetic GRBs should not be special compared with is indeed a strong correlation between E and E . γ,iso X,iso other normal long bursts. Pearsons correlation coefﬁcient is r = 0.92 and chance −4 probability p < 10 . Our linear ﬁt with the least square regression algorithm gives 4.6. Energy Relation between the E and E γ,iso X,iso It has been proposed that the energy partition between the log E erg=+ () 8.25 1.12 () 0.86 0.02 g,iso prompt emission and afterglow may be quasi-universal, i.e., a ´ log E erg. () 8 X,iso GRB with more energetic prompt emission can power a more 14 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 14. The correlation between E and E . The red solid line and dashed lines are the best ﬁt and the 95% conﬁdence level of the ﬁts, respectively. The blue X,iso γ,iso circles, orange circles, blue star, red star, and green circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic lGRBs, respectively. Our result strengthens that the energy partition between the and the deceleration radius prompt emission and afterglow is quasi-universal. We ﬁnd that Rc=G21 t ()+z dec peak dec all energetic GRBs, including GRB 221009A, also satisfy this =´ 2.25 10 cmGtz () 1+ . (10) correlation very well. peak,2 0,2 −3 Here we take n =1cm and η = 0.2. 4.7. Initial Lorentz Factor Distribution Using the method above, we can constrain Γ for the It is well known that GRBs are powered by relativistic energetic GRBs with enough observational data. For GRB outﬂows. The initial Lorentz factor Γ during the GRB prompt 221009A, the onset timescale is earlier than the very ﬁrst emission phase is very important to understand the physics of optical detection at ∼3000 s. One can take the ﬁrst optical GRBs. Here, the collected optical afterglow data allows us to observation time of the normal decay phase as the upper limit estimate the Γ for our sample. Using the peak time t of the of the peak time and thus derive the lower limit Γ > 72 for 0 peak onset of early afterglow as the deceleration time of the external GRB 221009A. forward shock, one can constrain the Γ (Sari & Piran 1999).If Liang et al. (2010) proposed a correlation between the the peak time is not detected due to without timely observations isotropic energy of prompt emission E and the initial γ,iso or pollution of other emission components (e.g., reverse shock Lorentz factor Γ . Later, Lü et al. (2012) proposed a correlation emission), one can take the ﬁrst optical observation time of the between the average isotropic luminosity of prompt emission normal decay phase as the upper limit of the peak time and thus L and the initial Lorentz factor Γ . Here we plot the γ,iso 0 derive the lower limit of Γ . In the so-called “thin” shell case, L − Γ and E − Γ diagram in Figure 15.We ﬁnd that γ,iso 0 γ,iso 0 the deceleration timescaletRc~G() 2 corresponds to dec dec energetic GRBs with onset features well satisfy the correlation, dec the quantity t /(1 + z), where R is the deceleration radius, peak dec and some energetic GRBs without onset features systematically c is the speed of light, and Γ is the ﬁreball Lorentz factor at dec deviate from this relationship (including GRB 221009A), t . We apply the standard afterglow model with a constant- dec which is mainly due to the lack of peak time observation. density medium (i.e., the interstellar medium) to derive the Liang et al. (2015) found another tight L − γ,iso 45.62- 0.35 1 initial Lorentz factor, which is twice that of the Lorentz factor L = 10 erg s E − Γ correlation, i.e., p,i 0 g,iso 1.320.19 at the deceleration timescale (Sari & Piran 1999) 1.340.14 (E keV) G . This relation combines the GRB pi , jet luminosity, the initial Lorentz factor, and the prompt emission spectrum. It signiﬁcantly reduces the intrinsic scatters 31Ez () + ⎡ g,iso ⎤ -18 G= 2  193() nh of the L − E (Liang et al. 2004; Amati 2006) and ⎢ 5 3 ⎥ γ,iso p,i 32ph nm c t peak ⎣ ⎦ L − Γ (Liang et al. 2010; Lü et al. 2012) relations. Here we γ,iso 0 also plot the L − E − Γ diagram in Figure 16.We ﬁnd γ,iso p,i 0 g,, iso52 ⎛ ⎞ ´ ,9 () that the GRB 221009A and other energetic GRBs follow well ⎜⎟ dec,2 this relation and tend to locate at the high-luminosity end. ⎝ ⎠ 15 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 15. The L , E , and Γ relation reported by Lü et al. (2012) and Liang et al. (2010). The orange circles data from Lü et al. (2012; top panel) and Liang γ,iso γ,iso 0 et al. (2015; bottom panel), and the GRB 130427A, GRB 221009A, and other energetic GRBs are marked with different colors and shapes in the plot. The orange solid line marks the relation. 4.8. Host Galaxy Properties to keep enough mass and angular momentum when a massive star collapses, the metallicity should not be too large (Li et al. The properties of the host galaxy can provide important 2016). On the other hand, sGRBs are believed to be formed information for the study of the properties of the progenitors of from compact star mergers and have been conﬁrmed by GRBs. For instance, the association of some lGRBs with type GW170817/GRB 170817A (Abbott et al. 2017, 2017). There- Ic supernovae (SNe) veriﬁes that lGRBs likely originate from fore, sGRBs’ host galaxies have more widely distributed the collapse of massive stars. Therefore, the host galaxies of parameters (Li et al. 2016, and reference therein): sGRBs were lGRBs are generally dwarf galaxies with actively star-forming detected in both early- and late-type galaxies; no metallicity rates, and lGRBs generally occur in regions with a high star limitation is required for sGRBs; some sGRBs are expected to formation rate (SFR) in galaxies (Savaglio et al. 2009). In order 16 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 16. Luminosity calculated with the L –E –Γ relation reported by Liang et al. (2015) as a function of the observed luminosity for GRB 130427A, GRB γ,iso p,z 0 221009A, and other energetic GRBs as marked in the plot. The orange circles data from Liang et al. (2015), and the black solid and dashed lines mark the relation and its 3σ dispersion. be associated with the old stellar populations and no recent star models. If we extend the redshift range from z < 0.5 to z < 1, formation is required; some sGRBs are expected to have a large the best-ﬁtting model of the energy function becomes a CPL offset from the original birth location in the host galaxy, since (regardless of whether GRB 221009A is introduced or not), the explosion of SNe that formed the compact binary systems and again the results of the BIC analysis do not support that the would have given the system two kicks. CPL model is clearly better than the other two models. For the Here we compare the energetic GRBs with other GRBs in high-redshift samples, we ﬁnd that both the CPL and BPL terms of four important host galaxy properties, including the models could well ﬁt the observational data, but the PL model stellar mass, the SFR, the metallicity, and the offset. The data could be excluded with high signiﬁcance as long as the sample are mainly taken from Li et al. (2016). Although there are few size is large enough. Nevertheless, we ﬁnd that the best-ﬁtting samples with good host galaxy measurements, it can be clearly parameters for different redshift samples are in good agreement seen from Figure 17 that there is no systematic difference with each other. Based on our ﬁnding, we suggest that the between the energetic GRBs and other normal lGRBs, energy function of GRBs does not evolve with redshift, and indicating that the energetic GRBs are likely not from special always follows the CPL or BPL model, namely, there is always progenitor systems. a cutoff or break in the high-energy end. Assuming that the best-ﬁtting result of the total sample can represent the intrinsic distribution of the GRB energy function, we ﬁnd that the 5. Conclusion and Discussion occurrence of GRB 221009A is consistent with the expectation GRB 221009A is the closest and most-energetic GRB (with within 1.84σ Poisson ﬂuctuation error. E ∼ 10 erg) detected so far. Its emergence further γ,iso On the other hand, with the collected sample, we have strengthens our interest in the study of energetic GRBs. In investigated whether GRB 221009A and other energetic GRBs this work, we extensively collect a good sample of GRBs with are systematically different from other normal GRBs in terms well-measured redshifts and spectral parameters. The sample of various statistical properties, including the prompt emission, covers the redshift range from 0.0098 to 8.23, and the isotropic 46 55 afterglow, and host galaxy properties. We ﬁnd that the γ-ray energy range from 4.7 × 10 to ∼10 erg. energetic GRBs, including GRB 221009A, do not show With the collected sample, we have studied the GRB energy signiﬁcant peculiarity compared with other normal lGRBs in functions and luminosity functions at different redshifts in the following aspects: T distribution, minimum timescale detail. We ﬁnd that for the low-redshift subsample with 90 distribution, Amati relation, E –E relation, L –Γ 0 < z < 0.5, even though the best-ﬁtting model of the energy γ,iso X,iso γ,iso 0 relation, E –Γ relation, L –E –Γ relation, and the function is a PL (regardless of whether GRB 221009A is γ,iso 0 γ,iso p,i 0 distributions of host galaxy properties, including stellar mass, introduced or not), the results of the BIC analysis do not support that PL model is clearly better than CPL and BPL SFR, metallicity and offset. 17 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 17. Distribution of host galaxy properties of GRBs. The blue and orange circles represent sGRBs and lGRBs respectively. The green circles are energetic GRBs. The red stars mark GRB 221009A and the data are from Levan et al. (2023). The red dashed lines mark the position of 10 erg. There are some characteristics of energetic GRBs that differ the accretion process of the central engine. However, a more somewhat from normal GRBs. However, they are all under- natural understanding would be that they are related to a special standable. For example, the average spectral lag of energetic viewing angle of a quasi-universal structured jet, as has been GRBs is smaller than that of normal lGRBs, but this is proposed to account for the luminosity function of the entire consistent with the luminosity–spectral lag correlation (Norris lGRB population (Rossi et al. 2002; Zhang & Mészáros 2002). et al. 2000; Gehrels et al. 2006). Their optical afterglows are Within this picture, the structured jet has a nearly uniform systematically brighter than other GRBs, but this is expected if narrow core surrounded by a wing with a decreasing energy per the GRB efﬁciency does not signiﬁcantly depend on energy unit solid angle with increasing viewing angle. Depending on (Lloyd-Ronning & Zhang 2004; Wang et al. 2015)). Finally, the shape of the structured jet in the wing (e.g., power law or most-energetic GRBs show a simple power-law decay light Gaussian; Zhang & Mészáros 2002), the slope of the energy curve with decay slopes systemically steeper compared to the function/luminosity function could be different. When the line so-called “normal decay slope” (with a typical slope approxi- of sight enters the core, the luminosity would show a cutoff. mately −1.2; Zhang et al. 2006). This may be related to a The narrowness of the core ensures the rareness of energetic structured jet viewed at the central core, which can explain their GRBs. GRB 221009A, with the record-breaking E ∼ 10 γ,iso high isotropic energy (Mészáros et al. 1998; Dai & Gou 2001). erg, suggests that central core can be very narrow. This is The facts that GRB 221009A and other energetic GRBs consistent with the LHAASO results (Cao et al. 2023). The follow the same energy function and luminosity function as structured jet wing can also help to interpret the relatively steep normal lGRBs and that their statistical properties are consistent afterglow decay index in the X-ray band; see also Sato et al. with normal lGRBs suggest that there is nothing special for (2023). these bursts except their apparent brightness (E ). This γ,iso suggests that they likely share the similar progenitor systems This work is supported by the National Natural Science and experience similar energy dissipation processes and Foundation of China (Projects:12021003, U2038107, radiation mechanisms as normal lGRBs. U1931203), and the National SKA Program of China (grant The large apparent energies may be related to the properties No. 2022SKA0130101). of the central engine, such as the black hole mass and spin, or 18 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. ORCID iDs Cenko, S. B., Prochaska, J. X., Cucchiara, A., Perley, D. 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Publisher: IOP Publishing
Copyright: © 2023. The Author(s). Published by the American Astronomical Society.
ISSN: 2041-8205
eISSN: 2041-8213
DOI: 10.3847/2041-8213/accf93
Publisher site: See Article on Publisher Site

Abstract

The gamma-ray burst GRB 221009A, known as the “brightest of all time,” is the closest energetic burst detected so far, with an energy of E ∼ 10 erg. This study aims to assess its compatibility with known GRB energy and γ,iso luminosity distributions. Our analysis indicates that the energy/luminosity function of GRBs is consistent across various redshift intervals, and that the inclusion of GRB 221009A does not signiﬁcantly impact the function at low redshifts. Additionally, our evaluation of the best-ﬁtting result of the entire GRB sample suggests that the expected number of GRBs with energy greater than 10 erg at a low redshift is 0.2, so that the emergence of GRB 221009A is consistent with expected energy/luminosity functions within ∼2σ Poisson ﬂuctuation error, still adhering to the principles of small number statistics. Furthermore, we ﬁnd that GRB 221009A and other energetic bursts, deﬁned as E  10 erg, exhibit no signiﬁcant differences in terms of distributions of T , minimum timescale, Amati γ,iso 90 relation, E –E relation, L –Γ relation, E –Γ relation, L –E –Γ relation, and host galaxy γ,iso X,iso γ,iso 0 γ,iso 0 γ,iso p,i 0 properties, compared to normal long GRBs. This suggests that energetic GRBs (including GRB 221009A) and other long GRBs likely have similar progenitor systems and undergo similar energy dissipation and radiation processes. The generation of energetic GRBs may be due to more extreme central engine properties or, more likely, a rarer viewing conﬁguration of a quasi-universal structured jet. Uniﬁed Astronomy Thesaurus concepts: Gamma-ray bursts (629) Supporting material: machine-readable table 1. Introduction Burst Monitor (GBM) at 13:16:59 UT on 2022 October 9, with a −5 −2 ﬂuence of (2.12± 0.05) × 10 erg cm in 10–1000 keV within As one of the most violent explosions in the universe, a duration of T = 327 s (Lesage et al. 2022). Around the similar gamma-ray bursts (GRBs) are detected in a wide redshift range time, it triggered Insight-HXMT (Tan et al. 2022) and had been (from z = 0.0085 to z = 9.4) and a wide energy distribution detected by HEBS (Liu et al. 2022). Later, it was registered by the 46 54 (E ranging from ∼10 erg to 10 erg; Zhang 2018, for a γ,iso Swift Burst Alert Telescope (BAT) at 14:10:17 UT (Dichiara review). The distribution of E generally follows a simple γ,iso et al. 2022). Multiple ground- and space-based follow-up power-law distribution with a cutoff above (1–3) × 10 erg observations were performed, from radio to very-high-energy (Atteia et al. 2017). The cutoff feature, which should not be due γ-ray (Perley 2022;Kuin&Dichiara 2022; Pillera et al. 2022; to a selection effect because of their high brightness, may be Gotz et al. 2022; de Ugarte Postigo et al. 2022; Huang et al. 2022; related to some intrinsic limit of generating apparently Iwakirietal. 2022; Leung et al. 2022;O’Connor et al. 2023; energetic GRBs. In this paper, we deﬁne “energetic GRBs” Laskar et al. 2022; Tan et al. 2022). Most interestingly, the Large as GRBs with the isotropic-equivalent energy E  10 erg. γ,iso High Altitude Air Shower Observatory (LHAASO) reported more Most recently, the “brightest-of-all-time” gamma-ray burst, than 5000 very-high-energy photons within the ﬁrst ∼2000 s after GRB 221009A, was detected by many space-borne and ground- the burst trigger with energies above 500 GeV all the way to 18 based telescopes in all wavelength. The burst was located at TeV, making them the most energetic photons ever observed from redshift z= 0.151, and had an isotropic radiation energy of aGRB (Huang et al. 2022). Various physical models and ∼10 erg, making it the most energetic GRB among energetic radiation mechanisms have been proposed to explain the observed GRBs (An et al. 2023).It ﬁrst triggered the Fermi/Gamma-ray 18 TeV photon (Baktash et al. 2022;Brdar &Li 2023; Carenza & Marsh 2022; Finke & Razzaque 2023; Galanti et al. 2022; Original content from this work may be used under the terms González et al. 2023;Li & Ma 2023; Ren et al. 2023;Sahuet al. of the Creative Commons Attribution 4.0 licence. Any further 2023; Smirnov & Trautner 2022; Troitsky 2022; Xia et al. 2022; distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Zhang et al. 2023;Zhaoetal. 2023; Zheng et al. 2023). 1 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. With a geometric extrapolation of the total ﬂuence and peak 3. Energy Distribution Function ﬂux distributions, Burns et al. (2023) argue that GRB 221009A For the purpose of this work, we ﬁrst divide the collected appears to be a once-in-10,000 yr event. Given that the most sample into several subsamples with different redshift bins: prominent characteristic of GRB 221009A is its exceedingly [0 ∼ 0.5], [0 ∼ 1], [1 ∼ 2], [2 ∼ 3], [3 ∼ 4], [4 ∼ 9.4], [0 ∼ 9.4]. high total isotropic energy, our objective is to ascertain the For each subsample, we ﬁt the distribution function of E with iso predictability and low probability of its occurrence through a three models of the energy function: a simple power-law comprehensive examination of the energy/luminosity func- function (PL), a broken power-law function (BPL), and a tions of GRBs. In particular, we intend to investigate the power-law with a high-energy cutoff feature (CPL), whose following questions: expressions are as follows: 1. Is there an obvious difference between the energy/ -a f()EA = E,1( ) iso 0 iso luminosity distributions of high- and low-redshift ener- getic burst samples? -a ⎧ iso 2. Due to the addition of GRB 221009A, does the energy ⎛ ⎞ ⎜⎟ ;EE  iso b distribution for the low-redshift sample still follow a ⎝ ⎠ f()EA = (2) iso 0 cutoff power-law function? -b iso ⎛ ⎞ 3. Normalized to the existing sample size, what is the ⎜⎟;, EE > ⎪ iso b expected number of GRBs with energy greater than 10 ⎝ ⎠ erg at low redshifts? 4. Are GRB 221009A and other energetic GRBs system- atically different from other GRBs in terms of statistics of -a E E iso iso ⎛ ⎞ ⎛ ⎞ various properties, including the prompt emission, after- f()EA = ⎜⎟ exp⎜⎟, (3) iso 0 E E cc glow, and host galaxy properties? ⎝ ⎠ ⎝ ⎠ where A is a normalization factor, α and β are the power-law 2. GRB Sample Selection indices, and E and E are the break energy and cutoff energy b c for the BPL and CPL model, respectively. For different models, For this work, we extensively search for the sample of the Markov Chain Monte Carlo method through the emcee GRBs with measured redshift (both spectroscopic and package (Foreman-Mackey et al. 2013) is employed to obtain photometric) peak energy E ,aswellasisotropic-equivalent the best-ﬁtting parameters and their uncertainties. All ﬁtting energy E from published papers or the Gamma-ray γ,iso Coordinates Network Circulars if no published paper is results for different subsamples are presented in Figures 2–3 available. We eventually ﬁnd 355 GRBs in total registered and Table 2. In order to justify which model is best ﬁtted to the from 1997 February up to 2022 November, covering the distribution of E for a given subsample, we compared the iso redshift range from 0.0098 (GRB 170817A) to 9.4 (GRB goodness of the ﬁts by invoking the Bayesian information 090429B). For each burst in our sample, we collect their criteria (BIC; Schwarz 1978). BIC is a criterion to evaluate the temporal and spectral properties from previous statistical best-ﬁtted model among a ﬁnite set of models, and the model investigations (Amati et al. 2008; Zhang et al. 2009; Qin & with the lowest BIC is preferred. The deﬁnition of BIC can be Chen 2013; Li et al. 2016; Zhang et al. 2018; Zou et al. 2018; written as BIC=-2lnL+ k·( ln n), where k is the number of Minaev & Pozanenko 2020; Jia et al. 2022). In Table 1, we list model parameters, n is the number of data points, and L is the their prompt emission duration T , spectral peak energy in the maximum value of the likelihood function of the estimated rest frame E = E (1 + z) and isotropic-equivalent energy E . p,i p iso For GRB 221009A, the value of E and E are calculated model. (1) if 0 < ΔBIC < 2, the evidence against the model iso p based on the observational data from HXMT and HEBS (An with higher BIC is not worth more than a bare mention; (2) if et al. 2023), which made an unprecedentedly accurate 2 < ΔBIC < 6, the evidence against the model with higher BIC measurement of the prompt emission during the ﬁrst ∼1800 s, is positive; (3) if 6 < ΔBIC < 10, the evidence against the including its precursor emission, main emission, ﬂaring model with higher BIC is strong; (4) if 10 < ΔBIC, the emission and early afterglow. A record-breaking isotropic- evidence against the model with higher BIC is very strong. equivalent energy E = (1.5 ± 0.2) × 10 erg was measured iso Before discussing the ﬁtting results, we would like to based on the HEBS unsaturated data. The peak energy illustrate two things in advance: ﬁrst, due to the sensitivity of E = 1247.4 ± 91.2 keV for the time-integrated spectral of full 52 the γ-ray detectors, only sources with E > 10 erg can be iso burst in prompt emission. detected at high redshifts (see Figure 1). To fairly compare the The bursts in the sample are mainly observed by the Konus- ﬁtting results, for all the samples at different redshift, we only Wind, Swift, and Fermi satellites, including 36 s GRBs and 319 52 adopt GRBs with E > 10 erg. Second, GRBs in our iso lGRBs, with 12 bursts being characterized by an extended collected sample are detected by different detectors, e.g., emission (EE) component. Among the sample, 31 are energetic Konus-Wind, Swift, Fermi, CGRO/BATSE, and HETE-2, 14 54 GRBs with E  10 erg. Figure 1 shows the distribution γ,iso which may cause concern about systematic uncertainty when of redshift and E for our sample. iso we put them together to study the energy distribution. Because of this, we perform all analyses twice, one for the total samples and one for pure Konus-Wind samples (the majority of our collected sample are detected by Konus-Wind).We ﬁnd that https://gcn.gsfc.nasa.gov/gcn3_archive.html the results of the two analysis are consistent, which proves that We take GRB 130427A as an energetic GRB, although its isotropic energy there is no clear systematic error caused by the difference in is 9.51 × 10 erg, since it has similar characteristics to GRB 221009A in temporal and spectral properties from the prompt emission to afterglow. detection sensitivity for different instruments. 2 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Table 1 The Sample of Gamma-Ray Bursts GRB z T E Type Detector References p,i 90 iso (s)(10 erg)(keV) 970228 0.695 56.0 1.65 ± 0.12 195 ± 64 L SAX (1), (2), (4) 970508 0.835 14.0 0.61 ± 0.13 145 ± 43 L SAX (1), (2), (5) 970828 0.9578 146.59 30.38 ± 3.57 586 ± 117 L GRO (1), (2), (6) 971214 3.42 6.0 22.06 ± 2.76 685 ± 133 L SAX (1), (2), (7) 980326 1.0 312.0 0.482 ± 0.09 35.5 ± 18 L SAX (2), (3) LL L L L L L L 220117A 4.961 49.81 12.6 ± 3.1 387 ± 102 L SWI/KW (309), (310) 220521A 5.6 14.0 3.56 ± 0.26 244 ± 46 L FER (311), (312) 220527A 0.857 21.3 12.2 ± 0.65 286 ± 18 L KW (313), (314) 220627A 3.084 138.0 230.0 ± 30.0 1020 ± 225 L FER/KW (315), (316) 221009A 0.151 600.0 1500 ± 200 1436 ± 105 L FER/KW/HXMT/GECAM (317), (318), (319), (320) Notes. Column (1): GRB name. Column (2): redshift. Column (3): value of T . Column (4): isotropic γ-ray energy in rest-frame 1–10 keV. Column (5): peak energy in spectral parameter. Column (6): the classiﬁcation of the burst: ‘L’—regular long GRBs, ‘S+EE’—short GRBs with an extended emission, ‘S’—regular short GRBs. Column (7): the experiment, used for the calculation of T , E , and E values (GRO = CGRO/BATSE, SAX = BeppoSAX, HET = HETE-2, 90 p iso KW = Konus-Wind, SWI = Swift, FER = Fermi). Column (8): the reference of redshift, T , E , and E for our sample. 90 p iso References: (1) Jia et al. (2022); (2) Li et al. (2016); (3) Minaev & Pozanenko (2020); (4) Djorgovski et al. (1999); (5) Galama et al. (1997); (6) Djorgovski et al. (2001); (7) Kulkarni et al. (1998); (8) Tinney et al. (1998); (9) Djorgovski et al. (2003); (10) Djorgovski et al. (1998); (11) Kulkarni et al. (1999); (12) Bloom et al. (2003); (13) Vreeswijk et al. (2001); (14) Le Floc’h et al. (2002); (15) Castro-Tirado et al. (2001); (16) Vreeswijk et al. (1999); (17) Andersen et al. (2000); (18) Piro et al. (2002); (19) Jensen et al. (2001); (20) Price et al. (2002a); (21) Castro et al. (2003); (22) Mirabal et al. (2002); (23) Price et al. (2002b); (24) Greiner et al. (2003); (25) Holland et al. (2002); (26) Hjorth et al. (2003a); (27) Berger et al. (2007a); (28) Masetti et al. (2003); (29) Barth et al. (2003); (30) Jakobsson et al. (2005); (31) Soderberg et al. (2004); (32) Møller et al. (2002); (33) Vreeswijk et al. (2003); (34) Klose et al. (2004); (35) Vreeswijk et al. (2004); (36) Maiorano et al. (2006); (37) Hjorth et al. (2003b); (38) Jakobsson et al. (2004); (39) Rau et al. (2005); (40) Prochaska et al. (2004); (41) Stratta et al. (2007); (42) Wiersema et al. (2008); (43) Soderberg et al. (2006a); (44) Berger et al. (2005a); (45) Pellizza et al. (2006); (46) Berger & Mulchaey (2005); (47) Watson et al. (2006); (48) Krühler et al. (2015); (49) Berger et al. (2006); (50) Prochaska et al. (2005); (51) Berger & Becker (2005); (52) Fox et al. (2005); (53) Berger et al. (2005b); (54) Qin & Chen (2013); (55) Gladders et al. (2006); (56) Jakobsson et al. (2006a); (57) Prochaska et al. (2007); (58) Kawai et al. (2006); (59) Fynbo et al. (2009); (60) Jakobsson et al. (2016b); (61) Volnova et al. (2014); (62) Quimby et al. (2005); (63) Soderberg et al. (2006b); (64) de Ugarte Postigo et al. (2006); (65) Mirabal et al. (2006); (66) Chary et al. (2007); (67) Vreeswijk et al. (2007); (68) Bloom et al. (2006); (69) Price (2006); (70) Cenko et al. (2006a); (71) Berger & Gladders (2006); (72) Ferrero et al. (2009); (73) Fox et al. (2008); (74) Gal-Yam et al. (2006); (75) Berger (2009); (76) Rol et al. (2006); (77) Ruiz-Velasco et al. (2007); (78) Berger (2007); (79) Osip et al. (2006); (80) Perley et al. (2008b); (81) Berger (2006a); (82) Cenko et al. (2006b); (83) Perley et al. (2009b); (84) Berger (2006b); (85) Cenko et al. (2008); (86) Jakobsson et al. (2007); (87) Cucchiara et al. (2007); (88) Perley et al. (2008a); (89) Perley et al. (2008c); (90) Cenko et al. (2007); (91) Berger et al. (2007b); (92) Leibler & Berger (2010); (93) Rowlinson et al. (2010); (94) Greiner et al. (2009);(95) Berger et al. (2008b); (96) Zou et al. (2018); (97) Berger et al. (2008a); (98) D’Elia et al. (2008); (99) Berger & Rauch (2008); (100) Kuin et al. (2009); (101) Cucchiara et al. (2008); (102) de Ugarte Postigo et al. (2009c); (103) Cenko et al. (2011c); (104) Chornock et al. (2009a); (105) Tanvir et al. (2009); (106) Chornock et al. (2009b); (107) Rau et al. (2009); (108) de Ugarte Postigo et al. (2009b); (109) Cenko et al. (2009); (110); Perley et al. 2013; (111) Wiersema et al. (2009); (112) de Ugarte Postigo et al. (2009a); (113) Cucchiara et al. (2009c); (114) Rau et al. (2010); (115) Cucchiara et al. (2009b); (116) Xu et al. (2009); (117) Cucchiara et al. (2009a); (118) Chornock et al. (2009c); (119) Chornock & Berger (2009); (120) Perley et al. (2009a); (121) Fong et al. (2011); (122) Perley et al. (2012); (123) Cucchiara & Fox (2010a); (124) Cucchiara & Fox (2010b); (125) Fong et al. (2013); (126) Flores et al. (2010); (127) Tanvir et al. (2010b); (128) Tanvir et al. (2010a); (129) Chornock & Berger (2011a); (130) Chornock & Berger (2011b); (131) Sparre et al. (2011); (132) Levan et al. (2014); (133) Cenko et al. (2011a); (134) Milne & Cenko (2011); (135) Cenko et al. (2011b); (136) Rufﬁni et al. (2011); (137) de Ugarte Postigo et al. (2011a); (138) de Ugarte Postigo et al. (2011b); (139) Piranomonte et al. (2011); (140) Tanvir et al. (2011); (141) Wiersema et al. (2011); (142) Selsing et al. (2018); (143) Tello et al. (2012); (144) Tanvir et al. (2012b); (145) Xu et al. (2012); (146) Greiner et al. (2012); (147) Cucchiara et al. (2012); (148) Tanvir & Ball (2012); (149) Berger et al. (2013); (150) Thoene et al. (2012); (151) Hartoog et al. (2012); (152) Knust et al. (2012); (153) Tanvir et al. (2012a); (154) Cucchiara & Fumagalli (2013); (155) Tanvir et al. (2013a); (156) de Ugarte Postigo et al. (2013a); (157) Tanvir et al. (2013b); (158) Schmidl et al. (2013); (159) Sanchez-Ramirez et al. (2013); (160) Cucchiara et al. (2013); (161) Chornock et al. (2013); (162) Smette et al. (2013);(163) Tanvir et al. (2013c); (164) Kelly et al. (2013); (165) Cucchiara & Perley (2013); (166) de Ugarte Postigo et al. (2013c); (167) Zhang et al. (2018); (168) Rau et al. (2013); (169) Xu et al. (2013); (170) de Ugarte Postigo et al. (2013b); (171) Hartoog et al. (2013); (172) Malesani et al. (2014b); (173) Cenko et al. (2015); (174) Jeong et al. (2014); (175) Tanvir et al. (2014a); (176) Tanvir et al. (2014b); (177) Malesani et al. (2014a); (178) de Ugarte Postigo et al. (2014b); (179) Chornock et al. (2014b); (180) Chornock et al. (2014c); (181) Cano et al. (2015); (182) Kasliwal et al. (2014); (183) Hartoog et al. (2014); (184) Bhalerao et al. (2014); (185) D’Avanzo et al. (2014); (186) Castro- Tirado et al. (2014a); (187) de Ugarte Postigo et al. (2014a); (188) Gorosabel et al. (2014a); (189) Cucchiara et al. (2014); (190) Castro-Tirado et al. (2014b); (191) de Ugarte Postigo et al. (2014d); (192) Xu et al. (2014a); (193) Xu et al. (2014b); (194) Chornock et al. (2014a); (195) de Ugarte Postigo et al. (2014c); (196) Perley et al. (2014);(197) Gorosabel et al. (2014b); (198) Levan et al. (2015); (199) Chornock & Fong (2015); (200) Kruehler et al. (2015); (201) de Ugarte Postigo et al. (2015c); (202) de Ugarte Postigo et al. (2015b); (203) Perley & Cenko (2015); (204) Pugliese et al. (2015); (205) de Ugarte Postigo & Tomasella (2015); (206) Malesani et al. (2015); (207) Castro-Tirado et al. (2015); (208) de Ugarte Postigo et al. (2015e); (209) Tanvir et al. (2015b); (210) de Ugarte Postigo et al. (2015a); (211) D’Elia et al. (2015); (212) de Ugarte Postigo et al. (2015d); (213) Perley et al. (2015); (214) Tanvir et al. (2015a); (215) Bolmer et al. (2015); (216) de Ugarte Postigo et al. (2016a); (217) Xu et al. (2016a); (218) Selsing et al. (2016b); (219) Tanvir et al. (2016c); (220) Malesani et al. (2016b); (221) O’Connor et al. (2021); (222) Xu et al. (2016c); (223) Castro-Tirado et al. (2016); (224) Xu et al. (2016b); (225) Levan et al. (2016); (226) Selsing et al. (2016a); (227) de Ugarte Postigo et al. (2016b); (228) Tanvir et al. (2016a); (229) Malesani et al. (2016a); (230) Cano et al. (2016); (231) Tanvir et al. (2016b); (232) Xu et al. (2017); (233) de Ugarte Postigo et al. (2017b); (234) Kruehler et al. (2017); (235) Izzo et al. (2017a); (236) Izzo et al. (2017b); (237) de Ugarte Postigo et al. (2017c); (238) de Ugarte Postigo et al. (2017e); (239) de Ugarte Postigo et al. (2017d); (240) de Ugarte Postigo et al. (2017f); (241) Izzo et al. (2017c); (242) de Ugarte Postigo et al. (2017a); (243) Tanvir et al. (2018); (244) Heintz et al. (2018); (245) Izzo et al. (2018a); (246) Izzo et al. (2018b); (247) Vreeswijk et al. (2018); (248) Rossi et al. (2018); (249) D’Avanzo et al. (2018); (250) Fynbo et al. (2018); (251) Perley et al. (2018); (252) Izzo et al. (2018c); (253) Schady et al. (2019); (254) Castro-Tirado et al. (2019); (255) Gupta et al. (2022); (256) Poolakkil et al. (2019); (257) Rossi et al. (2019); (258) Chand et al. (2020); (259) Valeev et al. (2019); (260) Bissaldi et al. (2019); (261) Malesani et al. (2019); (262) Ukwatta & Swift-BAT Team (2020); (263) Vielfaure & Stargate Collaboration (2020); (264) Fong et al. (2021); (265) Pookalil et al. (2020); (266) Yao et al. (2021); 3 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. (267) Bissaldi et al. (2020); (268) de Ugarte Postigo et al. (2021a); (269) Lesage et al. (2020a); (270) Oates et al. (2020); (271) Ror et al. (2023); (272) de Ugarte Postigo et al. (2020a); (273) Malacaria et al. (2020); (274) Kann et al. (2020); (275) Lesage et al. (2020b); (276) Vielfaure et al. (2020a); (277) Svinkin et al. (2020); (278) Xu et al. (2020); (279) Vielfaure et al. (2020b); (280) Yuan et al. (2022); (281) de Ugarte Postigo et al. (2020b); (282) Ho et al. (2022); (283) Xu et al. (2021b); (284) Frederiks et al. (2021b); (285) de Ugarte Postigo et al. (2021b); (286) Markwardt et al. (2021); (287) de Ugarte Postigo et al. (2021d); (288) Veres et al. (2021); (289) Zhu et al. (2021b); (290) de Ugarte Postigo et al. (2021c); (291) Oganesyan et al. (2021); (292) de Ugarte Postigo et al. (2021e); (293) Frederiks et al. (2021c); (294) Xu et al. (2021a); (295) Wood & Fermi GBM Team (2021); (296) Thoene et al. (2021); (297) Lesage & Meegan (2021);(298) Kann et al. (2021); (299) Frederiks et al. (2021d); (300) Zhu et al. (2021a); (301) Frederiks et al. (2021a); (302) Tanvir et al. (2021); (303) Lü et al. (2022); (304) Zhu et al. (2022); (305) Tsvetkova et al. (2022); (306) Fynbo et al. (2022a); (307) Veres et al. (2022); (308) Castro-Tirado et al. (2022); (309) Frederiks et al. (2022c); (310) Palmerio et al. (2022); (311) Poolakkil et al. (2022); (312) Fynbo et al. (2022b); (313) Lysenko et al. (2022); (314) Xu et al. (2022); (315) Frederiks et al. (2022b); (316) Izzo et al. (2022); (317) Lesage et al. (2022); (318) Frederiks et al. (2022a); (319) de Ugarte Postigo et al. (2022); (320) An et al. (2023); (321) Cucchiara et al. (2011). (This table is available in its entirety in machine-readable form.) Figure 1. The isotropic gamma-ray energy E for our collected GRBs as a function of the redshift z. The blue circles, orange circles, blue stars, red stars, and green γ,iso circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic GRBs, respectively. The red horizontal dotted line represent E γ, = 10 erg. The histograms on top and right represent the E and z distribution for all GRBs, and the blue and red vertical lines represent GRB 130427A and iso γ,iso GRB 221009A location, respectively. We ﬁrst focus on the low-redshift subsample with In order to exclude the inﬂuence of the sample size, we also 0 < z < 0.5. We ﬁnd that when GRB 221009A is not analyzed the subsample with 0 < z < 1. In this case, we ﬁnd introduced, the best-ﬁtting model of the energy function in that when GRB 221009A is not introduced, the best-ﬁtting this redshift interval is PL, although the other two models are model of energy distribution is CPL. The BIC difference not signiﬁcantly excluded from the BIC analysis results (see between PL and CPL is around 3, and the BIC difference Figure 2). The BIC difference between PL and CPL is less than between PL and BPL is around 2. With the addition of GRB 3, and the BIC difference between PL and BPL is larger than 2 221009A, the best-ﬁt model of the energy function is also CPL. but smaller than 6. With the addition of GRB 221009A The BIC difference between CPL and PL is less than 2, and the (currently the highest energy source in this redshift bin), the BIC difference between PL and BPL is only around 2. In general, the energy distribution of low-redshift GRBs best-ﬁt model of the energy function is still PL. Again, the BIC difference between PL and CPL is only around 3, and the BIC does not show an obvious cutoff at the high-energy end, which may be due to the small sample size, especially the small difference between PL and BPL is larger than 2 but smaller than 6. number of high-energy sources. With the expansion of the 4 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 2. Cumulative distribution of GRB isotropic energy for total samples (left panels) and pure Konus-Wind samples (right panels) in the low-redshift bins. The blue circles show the observed distribution, and the red solid lines, red dashed lines, and blue solid lines represent the best-ﬁtting CPL model, BPL model, and PL model, respectively. 5 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 3. Similar to Figure 2, but for high-redshift bins. 6 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 4. The likelihood distribution of α and E in the CPL model, from the total samples (left panel) and pure Konus-Wind samples (right panel) in different redshift bins. Table 2 The Best-ﬁtting Results of Energy Function for Pure Konus-Wind and Total Sample GRBs in Different Redshift Bins BPL CPL Redshift Interval PL 54 54 Konus-Wind GRBs αα β E (10 erg) α E (10 erg) b c +0.08 +0.08 +1.21 +1.55 +0.10 +2.87 [0.0 ∼ 0.5] 0.38 0.36 1.06 2.70 0.31 5.83 -0.07 -0.07 -0.72 -1.58 -0.10 -3.15 +0.05 +0.09 +0.32 +0.90 +0.06 +1.98 [0.0 ∼ 1.0] 0.53 0.41 0.94 0.38 0.42 2.77 -0.04 -0.15 -0.24 -0.27 -0.08 -1.51 +0.03 +0.05 +0.60 +0.27 +0.06 +0.52 [1.0 ∼ 2.0] 0.39 0.22 1.22 0.49 0.17 1.26 -0.03 -0.07 -0.37 -0.26 -0.06 -0.34 +0.03 +0.06 +0.66 +0.25 +0.06 +0.27 [2.0 ∼ 3.0] 0.44 0.17 1.50 0.45 0.09 0.87 -0.03 -0.07 -0.41 -0.19 -0.07 -0.23 +0.05 +0.09 +0.56 +0.31 +0.09 +1.12 [3.0 ∼ 4.0] 0.32 0.13 1.08 0.50 0.11 1.77 -0.11 -0.25 -0.10 -0.74 -0.05 -0.40 +0.07 +0.09 +0.59 +0.29 +0.08 +1.65 [4.0 ∼ 9.4] 0.23 0.17 0.62 0.60 0.13 3.47 -0.06 -0.09 -0.33 -0.35 -0.09 -1.59 +0.02 +0.04 +0.24 +0.23 +0.03 +0.30 [0.0 ∼ 9.4] 0.52 0.22 1.23 0.45 0.18 1.41 -0.01 -0.05 -0.19 -0.18 -0.04 -0.26 Total sample GRBs +0.08 +0.05 +0.72 +1.37 +0.08 +2.96 [0.0 ∼ 0.5] 0.40 0.38 0.86 2.89 0.33 5.62 -0.07 -0.06 -0.58 -1.32 -0.09 -3.16 +0.04 +0.05 +0.32 +0.64 +0.05 +1.22 [0.0 ∼ 1.0] 0.54 0.49 0.95 0.97 0.44 3.19 -0.03 -0.05 -0.27 -0.48 -0.05 -1.38 +0.02 +0.04 +0.53 +0.22 +0.05 +0.48 [1.0 ∼ 2.0] 0.47 0.30 1.21 0.43 0.26 1.24 -0.02 -0.06 -0.32 -0.22 -0.05 -0.34 +0.03 +0.05 +0.63 +0.16 +0.06 +0.22 [2.0 ∼ 3.0] 0.52 0.25 1.74 0.45 0.16 0.73 -0.03 -0.05 -0.43 -0.15 -0.06 -0.17 +0.04 +0.08 +0.51 +0.29 +0.07 +0.80 [3.0 ∼ 4.0] 0.45 0.27 1.14 0.36 0.25 1.40 -0.04 -0.09 -0.33 -0.17 -0.09 -0.56 +0.05 +0.07 +0.50 +0.37 +0.06 +2.23 [4.0 ∼ 9.4] 0.39 0.30 0.81 0.46 0.31 3.38 -0.04 -0.11 -0.27 -0.33 -0.07 -1.68 +0.01 +0.03 +0.15 +0.10 +0.03 +0.29 [0.0 ∼ 9.4] 0.57 0.29 1.19 0.37 0.27 1.28 -0.01 -0.04 -0.14 -0.13 -0.03 -0.24 sample, from 0 < z < 0.5 to 0 < z < 1, the CPL model does subsample with 3 < z < 4, the best-ﬁtting model is the CPL, change from inferior to slightly better than the PL model. The but the BIC difference between PL/BPL and CPL is smaller addition of GRB 201009A has no signiﬁcant inﬂuence on the than 6. For the subsample with z > 4, the best-ﬁtting model is above conclusions. PL, but the BIC difference between CPL/BPL and PL is also For comparison, we have made similar analyses on other smaller than 6. subsamples with high redshift. We ﬁnd that for subsamples In Figures 4–5, we plot the best-ﬁt parameter contours for with sufﬁcient sample size (e.g., 1 < z < 2 and 2 < z < 3), the CPL and BPL models at different redshift for total samples and best-ﬁtting model of the energy function is the CPL model, pure Konus-Wind samples. We ﬁnd that the best-ﬁtting although the BIC difference between the BPL model and the parameters for different redshift samples are in good agreement with each other, supporting the hypothesis that the energy CPL model is larger than 2 but smaller than 6. In these cases, the PL model is signiﬁcantly excluded (the BIC difference function of GRBs does not evolve with redshift. Under such a hypothesis, we compare the distribution of E for the total between the PL model and the CPL model is much more than iso 10). For subsamples with higher redshift, the sample size sample (0 < z < 9.4) with PL/BPL/CPL models. We ﬁnd that the best-ﬁtting model for the total sample is the CPL model, decreases again, and the goodness of ﬁt of the three models for +0.03 +0.30 energy distribution becomes indistinguishable again. For the with a = 0.18 and E = 1.41 . The results are -0.04 c,54 -0.26 7 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 5. The likehood distribution of α, β and E in the BPL model, from the total samples (left panel) and pure Konus-Wind samples (right panel) in different redshift bins. Table 3 The Best-ﬁtting Results of Luminosity Function for Total Sample GRBs in Different Redshift Bins BPL CPL Redshift interval PL 54 −1 54 −1 αα β L (10 erg s ) α L (10 erg s ) b c +0.10 +0.08 +0.70 +0.07 +0.07 +0.35 [0.0 ∼ 0.5] 0.52 0.51 0.93 0.10 0.47 0.45 -0.09 -0.09 -0.72 -0.06 -0.09 -0.28 +0.05 +0.05 +0.59 +0.05 +0.06 +0.34 [0.0 ∼ 1.0] 0.60 0.59 1.11 0.12 0.56 0.48 -0.05 -0.05 -0.61 -0.05 -0.06 -0.28 +0.03 +0.07 +0.57 +0.07 +0.06 +0.29 [1.0 ∼ 2.0] 0.48 0.40 0.89 0.03 0.39 0.21 -0.03 -0.11 -0.22 -0.02 -0.06 -0.09 +0.03 +0.06 +0.40 +0.01 +0.07 +0.03 [2.0 ∼ 3.0] 0.45 0.25 1.21 0.03 0.19 0.08 -0.03 -0.07 -0.31 -0.01 -0.07 -0.02 +0.05 +0.08 +0.42 +0.03 +0.09 +0.05 [3.0 ∼ 4.0] 0.48 0.31 1.36 0.04 0.23 0.09 -0.04 -0.10 -0.41 -0.02 -0.10 -0.03 +0.05 +0.08 +0.55 +0.03 +0.07 +0.05 [4.0 ∼ 9.4] 0.34 0.22 1.03 0.04 0.16 0.12 -0.04 -0.09 -0.39 -0.02 -0.08 -0.04 +0.02 +0.05 +0.11 +0.01 +0.03 +0.03 [0.0 ∼ 9.4] 0.46 0.26 0.75 0.01 0.30 0.11 -0.02 -0.07 -0.08 -0.01 -0.03 -0.02 consistent with the previous results from Atteia et al. (2017).In addition of GRB 201009A has no signiﬁcant inﬂuence on the this case, the PL model is signiﬁcantly excluded, since the BIC above conclusions. All best-ﬁtting parameters are collected in difference between the PL model and the CPL model is larger Table 3. Our results are generally consistent with previous than 100. However, it is worth to noting that the BIC difference studies. For instance, our best-ﬁtting results of the BPL model +0.05 +0.11 between BPL and CPL is smaller than 3, indicating that there is to the entire sample areab== 0.26 , 0.75 and -0.07 -0.08 +0.01 no clear evidence to distinguish between these two models. L = 0.01 . our low-luminosity power-law index and the b,54 -0.01 With our collected sample, we also studied the luminosity break luminosity is well consistent with Wanderman & Piran +0.2 +0.02 function of GRBs. In Figure 6, we plot the best-ﬁtting results (2010)(a== 0.2 , L 0.03 ) and Sun et al. (2015) b,54 -0.1 -0.02 of the luminosity function for PL, BPL, and CPL models in (α = 0.3, L = 0.01), while our high-luminosity power-law b,54 +0.3 different redshift bins. Similar to the results of the energy index is smaller than Wanderman & Piran (2010)(b = 1.4 ) -0.6 function, the luminosity distribution of low-redshift GRBs and Sun et al. (2015)(β = 1.3), which may be because we (z < 1) does not show a clear cutoff feature, which may be also invoke more energetic GRBs in our sample. due to the small sample size, especially the small number of Overall, based on the results of different subsamples, it is high-luminosity sources. For samples with sufﬁcient size more likely that the energy/luminosity function of GRBs (subsamples with z > 1 and the total sample), the luminosity always follows the CPL or BPL model, namely, there is always function also follows the CPL or BPL model. Again, the a cutoff or break at the high-energy end. This conclusion is consistent with results from previous studies both on 15 luminosity function (Liang et al. 2007; Virgili et al. 2009; To construct the luminosity function, we use the average luminosity (E /T ) instead of peak luminosity. It is found that the results from two Wanderman & Piran 2010; Sun et al. 2015) and energy iso 90 approaches have good agreement for the low-luminosity power-law index and function (Atteia et al. 2017; Lan et al. 2022). the break luminosity, but a discrepancy for the high-luminosity power-law The weak advantage of PL model performance in low- and index (Wanderman & Piran 2010). Therefore, the utilization of the average luminosity will not signiﬁcantly impact our discussion here. high-redshift samples is likely due to the limited sample size. 8 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 6. Cumulative distribution of GRB isotropic luminosity for total samples in the different redshift bins. The blue circles show the observed distribution, and the red solid lines, red dashed lines, and blue solid lines represent the best-ﬁtting CPL model, BPL model, and PL model, respectively. 9 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 7. Comparison between the normalized best-ﬁtting CPL model of the total-redshift bin (0 < z < 9.4) and the best-ﬁtting CPL model of the low-redshift bin (0 < z < 0.5) for total samples (left panel) and pure Konus-Wind samples (right panel). The blue dashed lines and red solid lines represent the best-ﬁtting CPL model for total-redshift bin and low-redshift bin. There is no clear evidence that more energetic GRBs are easily energetic GRB sample, we employ the Bayesian blocks generated at low redshift. To further prove this, we normalize algorithm and deﬁne the 1/2 shortest signiﬁcant structures of the best-ﬁtting CPL function of the total sample to compare blocks as the duration of minimum time interval (Vianello with the distribution of E at 0 < z < 0.5 (see Figure 1 and 7). et al. 2018; Xiao et al. 2022c). The median minimum timescale iso If the best-ﬁtting result of the total sample can represent the of the energetic GRB sample is about 2.32 s at 10–1000 keV, intrinsic distribution of the GRB energy function, we ﬁnd that which is well consistent with typical lGRBs. The minimum the occurrence of GRB 221009A is consistent with the timescale upper limit of GRB 221009A is 0.4 s at expectation within 1.84σ Poisson ﬂuctuation error. 10–1000 keV, which is no signiﬁcant difference compared to typical lGRBs and other energetic GRBs. We also adopt the continuous wavelet transform method (Vianello et al. 2018) 4. Statistic Investigation and the results are consistent. The result is shown in Figure 9. With our collected sample, it is of great interest to investigate whether GRB 221009A and other energetic GRBs are system- atically different from other GRBs in terms of statistics of 4.3. Amati Relation various properties. Here we focus on the following aspects: T Some empirical correlations among GRB observational distribution, minimum variability timescale distribution, Amati parameters have been discovered in the literature. The most relation, spectral-lag distribution, X-ray and optical afterglow famous one is the Amati relations (Amati et al. 2002), which is properties, the relation between the E and E , initial γ,iso X,iso a correlation between the GRB isotropic energy E and the γ,iso Lorentz factor distribution, and host galaxy properties. rest-frame peak energy E = (1 + z)E . Amati et al. (2002) p,i p discovered that higher-energy lGRBs have a harder spectrum 4.1. T Distribution than that of lower-energy lGRBs, and the sGRBs also follow the same trend between E and E but form distinct tracks Phenomenologically, GRBs fall into two classes: the long- p,i γ,iso (Zhang et al. 2009). Here we plot the Amati diagram for both duration, soft-spectrum class (duration <2 s; lGRBs) and the the lGRB and sGRB populations (see Figure 10) with our short-duration, hard-spectrum class (duration >2 s; sGRBs), collected sample. We ﬁnd that most-energetic GRBs are well based on the bimodal distribution of GRBs in the duration- located in the same trend as normal lGRBs, although their E hardness diagram (Kouveliotou et al. 1993). In Figure 8,we γ,iso are higher than those of most observed lGRBs. GRB 221009A show the GRBs in our sample in the duration T versus slightly deviates from the Amati relation toward higher intrinsic peak energy E diagram. We ﬁnd that all the p,i isotropic energy (see An et al. 2023 for more details). energetic GRBs fall into the distribution of lGRBs, and the distributions in T and E are not signiﬁcantly different with 90 p,i respect to the other lGRBs in our sample. Among the energetic 4.4. Spectral-lag Distribution bursts, GRB 221009A is distributed at the relatively large side of T and the center of E . 90 p,i The redshift distribution of energetic GRBs in our sample ranges from 0.151 to 6.318. For each GRB, the ﬁxed rest-frame energy bands are selected to be 100–150 keV and 4.2. Minimum Variability Timescale Distribution 200–250 keV, corresponding to the observed energy of The minimum timescale (Dt ) on which a GRB exhibits min [200–250]/(1+z) keV and [100–150]/(1+z) keV, which is signiﬁcant ﬂux variations is believed to provide an upper limit the same as in Ukwatta et al. (2012). The purpose of the above as to the size of the radiation zone, the lower limit of the selection of energy bands is to make full use of the data and Lorentz factor and potentially shedding light on the nature of ensure sufﬁcient energy difference between these two bands. emission mechanism (Schmidt 1978). For typical lGRBs and sGRBs, the average minimum timescales in the rest frame (i.e., GBM detectors have reached saturation for the extremely bright GRB Dt /(1+z)) are 45 and 10 ms, respectively (Golkhou et al. min 221009A in main emission phase, and we can only get the upper limit of the 2015). In order to calculate the minimum timescale for the minimum variability timescale in main emission. 10 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 8. lGRB/sGRB classiﬁcation diagram in the T − E domain. The blue circles, orange circles, blue star, red star, and green circles represent the sGRBs, 90 p lGRBs, GRB 130427A, GRB 221009A, and other energetic GRBs, respectively. The red vertical dotted line represent T = 2 s. The histograms of top and right represent the T and E distribution for all GRBs, and the blue and red vertical lines represent GRB 130427A and GRB 221009A location, respectively. 90 p Based on the high-time-resolution initial light curves of where b and b are the estimated background counts of light x y Swift/BAT or Fermi/GBM, we utilize the Li-CCF method (see curves x (Δt) and y (Δt), respectively. We can obtain a value m m Li et al. 2004 and Xiao et al. 2021, 2022a, 2022b for details) to k of k that maximizes MCCF(k = k , Δt); then the max max calculate the spectral lags for energetic GRBs in our sample, relative time lag between two light curves y (i; Δt) and which is deﬁned as x (i; Δt) on Δt is Dt td ()D=tk t.6( ) max MCCF() kt ,D= Dt m=1 We implement a Monte Carlo simulation of the observed light ui();;DD tus () i t /s, (4) mm+k u u curves based on Poisson probability distribution to obtain the uncertainty of spectral lag. It has long been found that there is an anticorrelation where the combination starts from the mth bin of the initial between spectral lag and peak luminosity exists for lGRBs light curves, the phase factor m = 1, 2,L, M , and u (Δt) and Δt m (Norris et al. 2000; Hakkila et al. 2008) namely short-lag and υ (Δt) are the background-subtracted series of x (Δt) and m m variable bursts having greater luminosities than long-lag and y (Δt). By rebinning the initial series, we obtain the light smooth bursts (Norris 2002; Hakkila et al. 2007; Ukwatta et al. curves with an optimized time bin Δt = M δt (from 1 to Δt 2012; Shao et al. 2017). Here we found that the energetic 100 ms for sGRBs, from 1 ms to 1 s for lGRBs), respectively, sources systematically deviate from this relationship, and their average spectral lag is smaller than that of normal lGRBs (see ui();; D= t x () i Dt -b () i;Dt, mm x Figure 11). We adopt two unsaturated emission episodes (T + 180 s ∼T + 210 s, T + 280 s ∼ T + 350 s) in the main u () it;; D=y() i Dt -b () it;D, 0 0 0 0 m y burst to calculate the spectral lag for GRB 221009A. We ﬁnd s=D ui();,t u å m that the spectral lags of the two unsaturated emission episodes in 200–250 keV compared to that in 100–150 keV at rest frame su=D() it;, (5) u å m are 292 ± 15 and 276 ± 36 ms, respectively. In order to 11 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 9. The diagram in theTt -D domain. The samples of sGRBs (blue circles) and lGRBs (orange circles) are from Golkhou et al. (2015). The red arrow and 90 min green circles represent GRB 221009A and other energetic GRBs, respectively. The red vertical dotted line represent T = 2s. Figure 10. E and E correlation diagram with known redshift data (Zhang et al. 2009; Qin & Chen 2013; Zou et al. 2018; Minaev & Pozanenko 2020; Jia p,i γ,iso et al. 2022). The orange and blue solid lines represent the best-ﬁt correlations for lGRBs and sGRBs, respectively. The blue circles, orange circles, blue star, red star, and green circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic lGRBs, respectively. 12 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 11. The correlation between spectral lag and peak luminosity in the rest frame. The GRB sample is collected from the previous statistical investigations (Li et al. 2004; Gehrels et al. 2006; Ukwatta et al. 2012; Goldstein et al. 2017; Xiao et al. 2022a; Lü et al. 2022). The GRB 221009A for spectral lag of the two unsaturated main emission episodes (T + 180 s ∼T + 210 s, T + 280 s ∼T + 350 s) and other energetic GRBs are highlighted by red star, blue star, and green circles, 0 0 0 0 respectively. The blue shaded region represents the common intrinsic spectral lags (3σ) calculated from 46 sGRBs with redshift measurements (Xiao et al. 2022a). estimate the peak luminosity of these two unsaturated emission Here N(E) is the observed time-dependent X-ray photon episodes, a time-resolved spectral ﬁtting was performed by a spectrum, which could be best ﬁtted by a power-law model Band spectrum, and the peak energy ﬂux of these two episodes (spectral parameters could be obtained from the Swift archive). −5 −2 −1 are (4.31 ± 0.03) × 10 erg cm s and (1.32 ± 0.01) × To calculate D (z), the concordance cosmology parameters −4 −2 −1 10 erg cm s in the 10 keV–1000 keV energy range, −1 −1 H = 67.4 km s Mpc , Ω = 0.315, and Ω = 0.685 have 0 M Λ respectively. As shown in Figure 11, the two unsaturated main been adopted according to the Planck results (Planck emission episodes of GRB 221009A are located in the long- Collaboration et al. 2020). In the left panel of Figure 12,we burst region for the anticorrelation between spectral lag and plot the X-ray luminosity curves for GRB 221009A and other peak luminosity. energetic GRBs. We ﬁnd that most energetic GRBs show simple power-law decay characteristics in the late phase with 4.5. X-Ray and Optical Afterglow Properties decay slopes systemically steeper compared to the so-called In order to compare whether GRB 221009A and other “normal decay slope” (with a typical slope approximately energetic GRBs are systematically different from other GRBs −1.2; Zhang et al. 2006). The distribution of decay slope is in X-ray and optical afterglow, here, we collected the X-ray and shown in the right panel of Figure 12, where the decay slope of optical afterglow for GRB 221009A and other energetic GRBs. GRB 221009A is located at the center. The XRT light curve is obtained by using the public data from For optical afterglow, we extensively search for the optical the Swift archive. For each energetic GRB, we derived the data from published papers or from the Gamma-ray Coordi- X-ray luminosity, which is calculated by L = 4kD p F , X X nates Network (GCN) Circulars if no published paper is where F is observed X-ray ﬂux, D is the GRB luminosity X L available. We found 358 GRBs in total with optical observa- distance, and the k-correction factor corrects the XRT-band tions being reported from 1997 February to 2020 December, (0.3–10 keV) ﬂux to a wide band in the burst rest frame including 308 GRBs having well-sampled optical light curves, (0.1–1000 keV in this analysis), i.e., which contain at least three data points, excluding upper limits. In Figure 13, we show the optical light curves (in absolute 10 1+z EN() E dE magnitude) for energetic GRBs and other GRBs. We ﬁnd that 0.1 1+z k = .7 () the optical afterglow is systematically brighter than other EN() E dE ò GRBs. Because of this, the optical afterglow observation of 0.3 energetic GRBs generally starts earlier. Many of these bursts have been detected the reverse shock radiation and/or the onset https://www.swift.ac.uk/xrt_curves/ bump of the forward shock radiation (unfortunately, the optical 13 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 12. Left panel: the X-ray luminosity light curves of energetic GRBs in our sample. The blue circles and red circles represent the GRB 130427A and GRB 221009A, respectively. The gray background circles show that other energetic GRBs. Right panel: the distribution of decay slope in X-ray late phase for energetic GRBs in our sample, and the red vertical line represent GRB 221009A location. Figure 13. Galactic extinction corrected R band afterglow light curves. The gray background lines show that we collected optical data, and the green lines show the optical afterglow of energetic GRBs in our sample. The blue star line and red star line represent the GRB 130427A and GRB 221009A, respectively. observation of GRB 221009A stars relatively late, because energetic afterglow emission (Zou et al. 2019). Here it is of Swift/BAT triggered is ∼0.88 hr later than Fermi/GBM). interest to investigate the relation between the energies released Considering that the host galaxy properties of energetic GRBs in the γ-ray band (E ) and in the X-ray band (E ). E γ,iso X,iso X,iso have no obvious distinctiveness (see Section 4.8 for details), can be calculated by E =+ 41 kD p S ()z , where S is X,iso L X X the brighter optical afterglow should not be attributed to the observed X-ray ﬂuence and k is the correction factor that impact of the circumburst environment but should be due to corrects the XRT-band (0.3–10 keV) ﬂux to a wide band in the higher kinetic energy. This infers that the radiation efﬁciency of burst rest frame (0.1–1000 keV). As shown in Figure 14, there these energetic GRBs should not be special compared with is indeed a strong correlation between E and E . γ,iso X,iso other normal long bursts. Pearsons correlation coefﬁcient is r = 0.92 and chance −4 probability p < 10 . Our linear ﬁt with the least square regression algorithm gives 4.6. Energy Relation between the E and E γ,iso X,iso It has been proposed that the energy partition between the log E erg=+ () 8.25 1.12 () 0.86 0.02 g,iso prompt emission and afterglow may be quasi-universal, i.e., a ´ log E erg. () 8 X,iso GRB with more energetic prompt emission can power a more 14 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 14. The correlation between E and E . The red solid line and dashed lines are the best ﬁt and the 95% conﬁdence level of the ﬁts, respectively. The blue X,iso γ,iso circles, orange circles, blue star, red star, and green circles represent the sGRBs, lGRBs, GRB 130427A, GRB 221009A, and other energetic lGRBs, respectively. Our result strengthens that the energy partition between the and the deceleration radius prompt emission and afterglow is quasi-universal. We ﬁnd that Rc=G21 t ()+z dec peak dec all energetic GRBs, including GRB 221009A, also satisfy this =´ 2.25 10 cmGtz () 1+ . (10) correlation very well. peak,2 0,2 −3 Here we take n =1cm and η = 0.2. 4.7. Initial Lorentz Factor Distribution Using the method above, we can constrain Γ for the It is well known that GRBs are powered by relativistic energetic GRBs with enough observational data. For GRB outﬂows. The initial Lorentz factor Γ during the GRB prompt 221009A, the onset timescale is earlier than the very ﬁrst emission phase is very important to understand the physics of optical detection at ∼3000 s. One can take the ﬁrst optical GRBs. Here, the collected optical afterglow data allows us to observation time of the normal decay phase as the upper limit estimate the Γ for our sample. Using the peak time t of the of the peak time and thus derive the lower limit Γ > 72 for 0 peak onset of early afterglow as the deceleration time of the external GRB 221009A. forward shock, one can constrain the Γ (Sari & Piran 1999).If Liang et al. (2010) proposed a correlation between the the peak time is not detected due to without timely observations isotropic energy of prompt emission E and the initial γ,iso or pollution of other emission components (e.g., reverse shock Lorentz factor Γ . Later, Lü et al. (2012) proposed a correlation emission), one can take the ﬁrst optical observation time of the between the average isotropic luminosity of prompt emission normal decay phase as the upper limit of the peak time and thus L and the initial Lorentz factor Γ . Here we plot the γ,iso 0 derive the lower limit of Γ . In the so-called “thin” shell case, L − Γ and E − Γ diagram in Figure 15.We ﬁnd that γ,iso 0 γ,iso 0 the deceleration timescaletRc~G() 2 corresponds to dec dec energetic GRBs with onset features well satisfy the correlation, dec the quantity t /(1 + z), where R is the deceleration radius, peak dec and some energetic GRBs without onset features systematically c is the speed of light, and Γ is the ﬁreball Lorentz factor at dec deviate from this relationship (including GRB 221009A), t . We apply the standard afterglow model with a constant- dec which is mainly due to the lack of peak time observation. density medium (i.e., the interstellar medium) to derive the Liang et al. (2015) found another tight L − γ,iso 45.62- 0.35 1 initial Lorentz factor, which is twice that of the Lorentz factor L = 10 erg s E − Γ correlation, i.e., p,i 0 g,iso 1.320.19 at the deceleration timescale (Sari & Piran 1999) 1.340.14 (E keV) G . This relation combines the GRB pi , jet luminosity, the initial Lorentz factor, and the prompt emission spectrum. It signiﬁcantly reduces the intrinsic scatters 31Ez () + ⎡ g,iso ⎤ -18 G= 2  193() nh of the L − E (Liang et al. 2004; Amati 2006) and ⎢ 5 3 ⎥ γ,iso p,i 32ph nm c t peak ⎣ ⎦ L − Γ (Liang et al. 2010; Lü et al. 2012) relations. Here we γ,iso 0 also plot the L − E − Γ diagram in Figure 16.We ﬁnd γ,iso p,i 0 g,, iso52 ⎛ ⎞ ´ ,9 () that the GRB 221009A and other energetic GRBs follow well ⎜⎟ dec,2 this relation and tend to locate at the high-luminosity end. ⎝ ⎠ 15 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 15. The L , E , and Γ relation reported by Lü et al. (2012) and Liang et al. (2010). The orange circles data from Lü et al. (2012; top panel) and Liang γ,iso γ,iso 0 et al. (2015; bottom panel), and the GRB 130427A, GRB 221009A, and other energetic GRBs are marked with different colors and shapes in the plot. The orange solid line marks the relation. 4.8. Host Galaxy Properties to keep enough mass and angular momentum when a massive star collapses, the metallicity should not be too large (Li et al. The properties of the host galaxy can provide important 2016). On the other hand, sGRBs are believed to be formed information for the study of the properties of the progenitors of from compact star mergers and have been conﬁrmed by GRBs. For instance, the association of some lGRBs with type GW170817/GRB 170817A (Abbott et al. 2017, 2017). There- Ic supernovae (SNe) veriﬁes that lGRBs likely originate from fore, sGRBs’ host galaxies have more widely distributed the collapse of massive stars. Therefore, the host galaxies of parameters (Li et al. 2016, and reference therein): sGRBs were lGRBs are generally dwarf galaxies with actively star-forming detected in both early- and late-type galaxies; no metallicity rates, and lGRBs generally occur in regions with a high star limitation is required for sGRBs; some sGRBs are expected to formation rate (SFR) in galaxies (Savaglio et al. 2009). In order 16 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 16. Luminosity calculated with the L –E –Γ relation reported by Liang et al. (2015) as a function of the observed luminosity for GRB 130427A, GRB γ,iso p,z 0 221009A, and other energetic GRBs as marked in the plot. The orange circles data from Liang et al. (2015), and the black solid and dashed lines mark the relation and its 3σ dispersion. be associated with the old stellar populations and no recent star models. If we extend the redshift range from z < 0.5 to z < 1, formation is required; some sGRBs are expected to have a large the best-ﬁtting model of the energy function becomes a CPL offset from the original birth location in the host galaxy, since (regardless of whether GRB 221009A is introduced or not), the explosion of SNe that formed the compact binary systems and again the results of the BIC analysis do not support that the would have given the system two kicks. CPL model is clearly better than the other two models. For the Here we compare the energetic GRBs with other GRBs in high-redshift samples, we ﬁnd that both the CPL and BPL terms of four important host galaxy properties, including the models could well ﬁt the observational data, but the PL model stellar mass, the SFR, the metallicity, and the offset. The data could be excluded with high signiﬁcance as long as the sample are mainly taken from Li et al. (2016). Although there are few size is large enough. Nevertheless, we ﬁnd that the best-ﬁtting samples with good host galaxy measurements, it can be clearly parameters for different redshift samples are in good agreement seen from Figure 17 that there is no systematic difference with each other. Based on our ﬁnding, we suggest that the between the energetic GRBs and other normal lGRBs, energy function of GRBs does not evolve with redshift, and indicating that the energetic GRBs are likely not from special always follows the CPL or BPL model, namely, there is always progenitor systems. a cutoff or break in the high-energy end. Assuming that the best-ﬁtting result of the total sample can represent the intrinsic distribution of the GRB energy function, we ﬁnd that the 5. Conclusion and Discussion occurrence of GRB 221009A is consistent with the expectation GRB 221009A is the closest and most-energetic GRB (with within 1.84σ Poisson ﬂuctuation error. E ∼ 10 erg) detected so far. Its emergence further γ,iso On the other hand, with the collected sample, we have strengthens our interest in the study of energetic GRBs. In investigated whether GRB 221009A and other energetic GRBs this work, we extensively collect a good sample of GRBs with are systematically different from other normal GRBs in terms well-measured redshifts and spectral parameters. The sample of various statistical properties, including the prompt emission, covers the redshift range from 0.0098 to 8.23, and the isotropic 46 55 afterglow, and host galaxy properties. We ﬁnd that the γ-ray energy range from 4.7 × 10 to ∼10 erg. energetic GRBs, including GRB 221009A, do not show With the collected sample, we have studied the GRB energy signiﬁcant peculiarity compared with other normal lGRBs in functions and luminosity functions at different redshifts in the following aspects: T distribution, minimum timescale detail. We ﬁnd that for the low-redshift subsample with 90 distribution, Amati relation, E –E relation, L –Γ 0 < z < 0.5, even though the best-ﬁtting model of the energy γ,iso X,iso γ,iso 0 relation, E –Γ relation, L –E –Γ relation, and the function is a PL (regardless of whether GRB 221009A is γ,iso 0 γ,iso p,i 0 distributions of host galaxy properties, including stellar mass, introduced or not), the results of the BIC analysis do not support that PL model is clearly better than CPL and BPL SFR, metallicity and offset. 17 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. Figure 17. Distribution of host galaxy properties of GRBs. The blue and orange circles represent sGRBs and lGRBs respectively. The green circles are energetic GRBs. The red stars mark GRB 221009A and the data are from Levan et al. (2023). The red dashed lines mark the position of 10 erg. There are some characteristics of energetic GRBs that differ the accretion process of the central engine. However, a more somewhat from normal GRBs. However, they are all under- natural understanding would be that they are related to a special standable. For example, the average spectral lag of energetic viewing angle of a quasi-universal structured jet, as has been GRBs is smaller than that of normal lGRBs, but this is proposed to account for the luminosity function of the entire consistent with the luminosity–spectral lag correlation (Norris lGRB population (Rossi et al. 2002; Zhang & Mészáros 2002). et al. 2000; Gehrels et al. 2006). Their optical afterglows are Within this picture, the structured jet has a nearly uniform systematically brighter than other GRBs, but this is expected if narrow core surrounded by a wing with a decreasing energy per the GRB efﬁciency does not signiﬁcantly depend on energy unit solid angle with increasing viewing angle. Depending on (Lloyd-Ronning & Zhang 2004; Wang et al. 2015)). Finally, the shape of the structured jet in the wing (e.g., power law or most-energetic GRBs show a simple power-law decay light Gaussian; Zhang & Mészáros 2002), the slope of the energy curve with decay slopes systemically steeper compared to the function/luminosity function could be different. When the line so-called “normal decay slope” (with a typical slope approxi- of sight enters the core, the luminosity would show a cutoff. mately −1.2; Zhang et al. 2006). This may be related to a The narrowness of the core ensures the rareness of energetic structured jet viewed at the central core, which can explain their GRBs. GRB 221009A, with the record-breaking E ∼ 10 γ,iso high isotropic energy (Mészáros et al. 1998; Dai & Gou 2001). erg, suggests that central core can be very narrow. This is The facts that GRB 221009A and other energetic GRBs consistent with the LHAASO results (Cao et al. 2023). The follow the same energy function and luminosity function as structured jet wing can also help to interpret the relatively steep normal lGRBs and that their statistical properties are consistent afterglow decay index in the X-ray band; see also Sato et al. with normal lGRBs suggest that there is nothing special for (2023). these bursts except their apparent brightness (E ). This γ,iso suggests that they likely share the similar progenitor systems This work is supported by the National Natural Science and experience similar energy dissipation processes and Foundation of China (Projects:12021003, U2038107, radiation mechanisms as normal lGRBs. U1931203), and the National SKA Program of China (grant The large apparent energies may be related to the properties No. 2022SKA0130101). of the central engine, such as the black hole mass and spin, or 18 The Astrophysical Journal Letters, 949:L4 (22pp), 2023 May 20 Lan et al. ORCID iDs Cenko, S. B., Prochaska, J. X., Cucchiara, A., Perley, D. 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GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

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GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

GRB 221009A: An Ordinary Nearby GRB with Extraordinary Observational Properties

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