发表机构
Institute of High Energy Physics, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Beijing Academy Science and Technology Branch（中国科学院高能物理研究所; 中国科学院大学; 北京科学院技术分院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用分层贝叶斯推断框架分析Fermi/GBM星表中的I型伽马射线暴，重建内禀事件率，并约束至z=5，局部率密度与引力波测量一致。
AI 中文摘要
I型伽马射线暴（GRB）的内禀事件率作为红移的函数，为双中子星（BNS）并合群体提供了探针。然而，上述推断因仪器选择效应、大多数GRB缺乏红移测量以及喷流几何的不确定性而变得复杂。在本工作中，我们将分层贝叶斯推断框架应用于{\it Fermi}/GBM I型GRB星表，以重建潜在的事件率群体。该框架考虑了选择效应，并对单个GRB红移和喷流结构的有限信息后验进行了边缘化。群体模型使用了参数化的光度函数、喷流结构参数分布、Madau-Dickinson恒星形成率以及BNS并合的延迟时间分布。模型中超参数的后验分布将使用GPU加速的MCMC算法进行推断。内禀事件率密度作为红移的函数被约束至$z=5$，局部率密度为\\(R_0 = 22.6^{+15.0}_{-10.6}\\,{\rm Gpc^{-3}\\,yr^{-1}}\\)，这与最新的引力波测量结果一致。
英文摘要
The intrinsic event-rate of Type I gamma-ray bursts (GRBs) as a function of redshift, provides a probe for binary neutron star (BNS) mergers population. However, the above-mentioned inference is complicated by instrumental selection effects, the lack of redshift measurements for the majority of GRBs, and uncertainties in jet geometry. In this work, we applied a hierarchical Bayesian inference framework to the {\it Fermi}/GBM Type I GRB catalogue to reconstruct the underlying event-rate population. This framework accounts for the selection effects and marginalizes over the limited-information posteriors of individual GRB redshifts and jet structures. The population model uses parameterized luminosity function, distribution of jet structure parameters, the Madau-Dickinson star-formation rate and a delay-time distribution of BNS mergers. The posterior distribution of the hyperparameters in the model are to be inferred, using a GPU-accelerated MCMC algorithm. The intrinsic event rate density as function of redshift is constrained up to $z=5$, which a local rate density of \(R_0 = 22.6^{+15.0}_{-10.6}\,{\rm Gpc^{-3}\,yr^{-1}},\), which is consistent with the latest gravitational-wave measurements.
Comments31 pages, 8 tables, 9 figures; Accepted for publication in The Astrophysical Journal
