We study the luminosity function of long gamma-ray bursts (LGRBs) using the peak flux obtained from three LGRB samples with known redshifts: (a) a sample of 251 LGRBs from the Swift/BAT satellite/instrument; (b) a sample of 37 LGRBs from the Fermi/GBM telescope; (c) a sample of 152 GRBs from the Konus-Wind instrument. For the Swift/BAT and Fermi/GBM samples, we use data available on the Swift Burst Analyser websites ( http://www.swift.ac.uk/burst_analyser ; (Evans at al. in Astron. Astrophys. 519:102, 2010)) and ( http://swift.gsfc.nasa.gov/archive/grb/table/ ) and on the Fermi website ( https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html ; (Gruber et al. in Astrophys. J. Suppl. Ser. 211(1):12, 2014; von Kienlin et al. in Astrophys. J. Suppl. Ser. 211(1):13, 2014; Bhat et al. in Astrophys. J. Suppl. Ser. 223(2):28, 2016)) to calculate the luminosity at the peak of the flux by using a cut-off power-law spectrum (CPL). For the Konus-Wind sample, we use the Yonetoku correlation relationship (Yonetoku et al. in Publ. Astron. Soc. Jpn. 62:1495, 2010) to determine the isotropic luminosity from the energy at the peak of the flux measured in the source frame (Minaev and Pozanenko in Mon. Not. R. Astron. Soc. 492(2):1919, 2019). With these three samples (totalling 439 GRBs), we use the Monte Carlo method to synthesize 10,000 “artificial” GRBs similar to each real GRB by considering that each physical quantity observed obeys a normal distribution, where the tabulated value and uncertainty represent the mean and the $3\sigma$ error. The results obtained for the luminosity function from our data samples are consistent with those published in previous works.

中文翻译：

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从 Swift/BAT、Fermi/GBM 和 Konus-Wind 数据合成的 GRB 光度函数

我们使用从三个已知红移的 LGRB 样本获得的峰值通量研究了长伽马射线暴 (LGRB) 的光度函数：(a) 来自 Swift/BAT 卫星/仪器的 251 个 LGRB 样本；(b) 来自费米/GBM 望远镜的 37 个 LGRB 样本；(c) 来自 Konus-Wind 仪器的 152 个 GRB 样本。对于 Swift/BAT 和 Fermi/GBM 样本，我们使用 Swift Burst Analyzer 网站 (http://www.swift.ac.uk/burst_analysisr; (Evans 等人在 Astron. Astrophys. 519:102, 2010)) 和 ( http://swift.gsfc.nasa.gov/archive/grb/table/ ) 和 Fermi 网站 ( https://heasarc.gsfc.nasa.gov/W3Browse/fermi/fermigbrst.html ; （Gruber 等人在 Astrophys. J. Suppl. Ser. 211(1):12, 2014 中；von Kienlin 等人在 Astrophys. J. Suppl. Ser. 211(1):13, 2014 中；Bhat 等人。在天体物理学. J. Suppl. Ser. 223(2):28, 2016)) 使用截止幂律谱 (CPL) 计算通量峰值处的光度。对于 Konus-Wind 样本，我们使用 Yonetoku 相关关系（Yonetoku et al. in Publ. Astron. Soc. Jpn. 62:1495, 2010）根据在源框架（Minaev 和 Pozanenko 在 Mon. Not. R. Astron. Soc. 492(2):1919, 2019）。对于这三个样本（总共 439 个 GRB），考虑到每个观测到的物理量都服从正态分布，我们使用蒙特卡罗方法合成了 10,000 个类似于每个真实 GRB 的“人造”GRB，其中列表值和不确定性代表平均值和$3\sigma$ 错误。从我们的数据样本中获得的光度函数的结果与先前作品中发表的结果一致。