The detection of GW170817 in gravitational waves and gamma rays revealed that short gamma-ray bursts are associated with the merger of neutron-stars. Gamma rays are thought to result from the formation of collimated jets, but the details of this process continue to elude us. One fundamental observable is the emission profile of the jet as a function of viewing angle. We present two methods to measure the effective angular width, $\theta_B$, of short gamma-ray burst (sGRB) jets using gravitational wave and gamma-ray data, assuming all sGRBs have the same angular dependence for their luminosities. The first is a counting experiment, where we combine the known detection thresholds of the LIGO/Virgo and Fermi Gamma Ray Burst Monitor detectors to infer parameters of systems that are detected in gravitational waves. This method requires minimal knowledge about each event, beyond whether or not they were detected in gamma-rays. The second method uses additional information from the gravitational-wave and electromagnetic data to estimate parameters of the source, and thereby improve constraints on jet properties. Applying our methods to GW170817, we find only weak constraints on the sGRB luminosity profile, with statistical uncertainty dominating differences between models. We also analyze simulated events from future observing runs, and find that with 5 and 100 BNS detections, the counting method constrains the relative uncertainty in $\theta_B$ to within 51% and 12%, respectively. Incorporating gravitational-wave parameter estimation would further tighten these constraints to 43% and 9.6%. In the limit of many detections, incorporating parameter estimation achieves only marginal improvements; we conclude that the majority of the information about jet structure comes from the relative sensitivities of gravitational-wave and gamma-ray detectors as encoded in simple counting experiments.

中文翻译：

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依靠短伽马射线暴：喷射几何的引力波约束

在引力波和伽马射线中探测到 GW170817 表明，短伽马射线爆发与中子星的合并有关。伽马射线被认为是由准直射流的形成引起的，但这个过程的细节仍然不为我们所知。一个基本的观察结果是作为视角函数的射流的发射剖面。我们提出了两种方法来使用引力波和伽马射线数据测量短伽马射线暴 (sGRB) 射流的有效角宽度 $\theta_B$，假设所有 sGRB 的光度都具有相同的角度依赖性。第一个是计数实验，我们结合 LIGO/Virgo 和费米伽玛射线暴监视器探测器的已知探测阈值来推断在引力波中探测到的系统参数。除了是否在伽马射线中检测到它们之外，这种方法需要对每个事件的了解最少。第二种方法使用来自引力波和电磁数据的附加信息来估计源的参数，从而改进对射流特性的约束。将我们的方法应用于 GW170817，我们发现仅对 sGRB 光度剖面的弱约束，统计不确定性主导了模型之间的差异。我们还分析了来自未来观测运行的模拟事件，发现通过 5 和 100 个 BNS 检测，计数方法将 $\theta_B$ 的相对不确定性分别限制在 51% 和 12% 以内。结合引力波参数估计将进一步将这些限制收紧至 43% 和 9.6%。在许多检测的限度内，结合参数估计只能实现边际改进；我们得出的结论是，关于喷流结构的大部分信息来自引力波和伽马射线探测器的相对灵敏度，如简单计数实验中编码的那样。