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重叠引力波信号对参数估计的影响：宇宙学背景的研究

Impacts of overlapping gravitational-wave signals on the parameter estimation: Toward the search for cosmological backgrounds

Yoshiaki Himemoto, Atsushi Nishizawa, Atsushi Taruya

备注：
13 pages, 9 figures, presentation and several figures improved, updated to match version published in PRD
发表信息：
Phys. Rev. D 104, 044010 (2021)
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摘要：

第三代引力波探测器，如爱因斯坦望远镜和宇宙探测器，将探测到一束引力波（GW）信号，这些信号源自双星中子星（BNS）和双星黑洞（BBH）系统的合并，直到更高的红移，$z\sim 5-10$。存在这样的潜在问题，即以高统计显著性检测到的GW信号中的一些最终彼此重叠，并且这种重叠系统的参数估计可能不同于从单个事件预期的参数估计。此外，肯定存在重叠系统，其中重叠事件之一具有低信噪比$\lesssim 4$，因此不能被清楚地检测到。这些系统可能会被错误地识别为单个GW事件，并且二元GW的估计参数可能会有偏差。我们估计这些重叠事件的发生率。我们发现，重叠事件的数量是$\sim 200$每天的BNS和BBH每小时几个。然后，我们研究了这些重叠的GW的参数估计的基础上的Fisher矩阵分析的统计影响。我们的发现是，重叠信号对双星系统的参数既不会产生大的统计误差，也不会产生严重的系统偏差，除非两个重叠GW的合并时间和红移啁啾质量非常接近，即，$|\mathcal{M}_{z1}-\mathcal{M}_{z2}|\lesssim10^{-4} \,(10^{-1})\,M_\odot$和$|t_{\rm c1}-t_{\rm c2}|\lesssim10^{-2}\,(10^{-1})$用于BS（BBH）。这种紧密重叠的事件的发生率被证明是远远小于第三代探测器每年一次。

英文摘要：

Third-generation gravitational wave detectors, such as the Einstein Telescope and Cosmic Explorer, will detect a bunch of gravitational-wave (GW) signals originating from the coalescence of binary neutron star (BNS) and binary black hole (BBH) systems out to the higher redshifts, $z\sim 5-10$. There is a potential concern that some of the GW signals detected at a high statistical significance eventually overlap with each other, and the parameter estimation of such an overlapping system can differ from the one expected from a single event. Also, there are certainly overlapping systems in which one of the overlapping events has a low signal-to-noise ratio $\lesssim 4$, and is thus unable to be clearly detected. Those system will potentially be misidentified with a single GW event, and the estimated parameters of binary GWs can be biased. We estimate the occurrence rate of those overlapping events. We find that the numbers of overlapping events are $\sim 200$ per day for BNSs and a few per hour for BBHs. Then we study the statistical impacts of these overlapping GWs on a parameter estimation based on the Fisher matrix analysis. Our finding is that the overlapping signals produce neither large statistical errors nor serious systematic biases on the parameters of binary systems, unless the coalescence time and the redshifted chirp masses of the two overlapping GWs are very close to each other, i.e., $|\mathcal{M}_{z1}-\mathcal{M}_{z2}|\lesssim10^{-4} \,(10^{-1})\,M_\odot$ and $|t_{\rm c1}-t_{\rm c2}|\lesssim10^{-2}\,(10^{-1})$\,s for BNSs (BBHs). The occurrence rate of such a closely overlapping event is shown to be much smaller than one per year with the third-generation detectors.

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