标题： 短伽马射线暴的表观率和宇宙率 显示英文标题

标题： The apparent and cosmic rates of short gamma-ray bursts

摘要： 短伽马射线暴（sGRB），GRB~170817A，通常被认为是一个罕见事件。 然而，其推导出的事件率，$\mathcal{O}(100s)\ \text{Gpc}^{-3}\ \text{yr}^{-1}$，比高红移样本的宇宙sGRB率估计值高出一个数量级。 这种差异可以通过与相对论喷流结构相关的几何效应来解释。 我们首先说明采用探测器通量阈值点估计而不是效率函数，可能导致率估计的大幅变化。 模拟费米-GBM sGRB探测效率后，我们表明对于一个通用的结构化喷流轮廓，可以建模与红移相关的几何偏差。 假设不同的喷流轮廓，我们表明GRB~170817A的几何缩放率与宇宙无束流校正的短$\gamma$射线暴（sGRBs）率估计是一致的，并且几何效应可以提升$\mathcal{O}(100s)$Mpc范围内的观测率。 我们发现GRB~170817A的明显速率为$303_{-300}^{+1580}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ ，经过几何校正后分别为$6.15_{-6.06}^{+31.2}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ 和$3.34_{-3.29}^{+16.7}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ ，这是两种不同的喷流轮廓，与2017年之前的各向同性sGRB速率估计一致。 我们的研究显示了喷流结构如何影响速率估算，并可能允许测试结构化的喷流轮廓。 我们最后展示了一种通过红移对最大结构化喷流观测角度进行建模的方法，可以将未校正的宇宙束流速率转化为双中子星合并速率的代表性估计。 我们建议这个框架可用于证明与合并速率的对称性，或得出sGRB成功喷流比例的估计。 显示英文摘要

摘要： The short gamma-ray burst (sGRB), GRB~170817A, is often considered a rare event. However, its inferred event rate, $\mathcal{O}(100s)\ \text{Gpc}^{-3}\ \text{yr}^{-1}$, exceeds cosmic sGRB rate estimates from high-redshift samples by an order of magnitude. This discrepancy can be explained by geometric effects related to the structure of the relativistic jet. We first illustrate how adopting a detector flux threshold point estimate rather than an efficiency function, can lead to a large variation in rate estimates. Simulating the Fermi-GBM sGRB detection efficiency, we then show that for a given a universal structured jet profile, one can model a geometric bias with redshift. Assuming different jet profiles, we show a geometrically scaled rate of GRB~170817A is consistent with the cosmic beaming uncorrected rate estimates of short $\gamma$-ray bursts (sGRBs) and that geometry can boost observational rates within $\mathcal{O}(100s)$\,Mpc. We find an apparent GRB~170817A rate of $303_{-300}^{+1580}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ which when corrected for geometry yields $6.15_{-6.06}^{+31.2}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ and $3.34_{-3.29}^{+16.7}$ $\mathrm{Gpc}^{-3}\, \mathrm{yr}^{-1} $ for two different jet profiles, consistent with pre-2017 estimates of the isotropic sGRB rate. Our study shows how jet structure can impact rate estimations and could allow one to test structured jet profiles. We finally show that modelling the maximum structured jet viewing angle with redshift can transform a cosmic beaming uncorrected rate to a representative estimate of the binary neutron star merger rate. We suggest this framework can be used to demonstrate parity with merger rates or to yield estimates of the successful jet fraction of sGRBs.