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arXiv 2201.10657astro-ph.HEastro-ph.IM
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脉冲星定时阵列的引力波统计:使用有限数量脉冲星检查偏差

Gravitational Wave Statistics for Pulsar Timing Arrays: Examining Bias from Using a Finite Number of Pulsars

Aaron D. Johnson, Sarah J. Vigeland, Xavier Siemens, Stephen R. Taylor

摘要:

最近,许多不同的脉冲星定时阵列(PTA)合作报告了强有力的证据,在他们的数据集中的一个共同的随机过程。所报告的振幅与先前计算的上限处于紧张状态。在本文中,我们研究如何使用一个子集的一个集的一个样本偏差贝叶斯上限恢复。我们生成500个模拟PTA数据集的基础上NANOGrav 11年的数据集注入随机引力波背景(GWB)。然后,我们通过对单个脉冲星的似然性进行采样来计算上限,并通过PTA似然性的因子分解版本将它们组合起来,以使用不同数量的脉冲星来获得GWB振幅的上限。我们发现,它是可能的,以恢复上限(95\%可信区间)\textit{below}注入值,它是显着更有可能发生这种情况时,使用一个子集来计算的上限。当挑选样本以引起最大可能的偏差时,我们发现在10.6%(500个中的53个)的实现中,回收的95%贝叶斯上限低于注入值。此外,我们发现,如果我们选择一个子组的双极子,以获得一个较低的上限比使用全组的双极子时,从这500个实现获得的上限的分布被转移到较低的幅度值。

英文摘要:

Recently, many different pulsar timing array (PTA) collaborations have reported strong evidence for a common stochastic process in their data sets. The reported amplitudes are in tension with previously computed upper limits. In this paper, we investigate how using a subset of a set of pulsars biases Bayesian upper limit recovery. We generate 500 simulated PTA data sets based on the NANOGrav 11-year data set with an injected stochastic gravitational wave background (GWB). We then compute upper limits by sampling individual pulsar likelihoods, and combine them through a factorized version of the PTA likelihood to obtain upper limits on the GWB amplitude using different numbers of pulsars. We find that it is possible to recover an upper limit (95\% credible interval) \textit{below} the injected value, and that it is significantly more likely for this to occur when using a subset of pulsars to compute the upper limit. When picking pulsars to induce the maximum possible bias, we find that the 95\% Bayesian upper limit recovered is below the injected value in 10.6\% (53 of 500) of realizations. Further, we find that if we choose a subset of pulsars in order to obtain a lower upper limit than when using the full set of pulsars, the distribution of upper limits obtained from these 500 realizations is shifted to lower amplitude values.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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