透镜效应还是运气？引力波强引力透镜效应的误报概率
Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves
AI总结：
本文研究引力波强透镜事件识别中的误报问题，发现基于啁啾质量、天空位置和并合相位的简单重叠判据在现实透镜率下误报将主导真实透镜事件，需设计更严格的识别判据，未来探测器有望实现决定性探测。
摘要：
引力波（GWs）的强引力透镜效应已被预测将在即将到来的观测运行中变得可探测。然而，确定地区分透镜成对源与随机关联是一个具有挑战性的问题。我们研究了未透镜事件由于参数重叠而在多大程度上模拟透镜事件，这种重叠源于随机巧合与参数估计误差的共同作用。我们构建了一个包含透镜和未透镜事件的模拟目录。我们发现，基于啁啾质量、天空位置和并合相位的巧合重叠，每对事件的误报概率（FAP）分别约为9%、1%和10%。将三者结合后，每对事件的总误报概率约为10的负4次方。随着引力波目录中事件数量N的增加，随机事件对的数量以约N的平方增长。与此同时，透镜事件的数量将随N线性增长，这意味着当N足够高时，误报将始终主导真实的透镜事件。这一问题可以通过对透镜候选体设置更高的阈值来弥补（例如，选择更高的信噪比（SNR）阈值），这将带来更好的参数估计，从而降低每对事件的误报概率——但代价是透镜样本的规模急剧减小（约按SNR的三次方分之一缩减）。我们表明，在当前探测器设计灵敏度下，采用我们简单的重叠判据，即使选择信噪比最高的事件对，对于现实的透镜率（约小于等于10的负3次方），误报仍将占主导地位。这些结果凸显了设计超越简单波形和天空位置重叠的替代识别判据的必要性。未来的引力波探测器Cosmic Explorer和Einstein Telescope可能在参数估计方面提供足够的改进，从而实现对引力波强透镜效应的决定性探测。
英文摘要：
Strong gravitational lensing of gravitational waves (GWs) has been forecasted to become detectable in the upcoming observing runs. However, definitively distinguishing pairs of lensed sources from random associations is a challenging problem. We investigate the degree to which unlensed events mimic lensed ones because of the overlap of parameters due to a combination of random coincidence and errors in parameter estimation. We construct a mock catalog of lensed and unlensed events. We find that the false alarm probability (FAP) based on coincidental overlaps of the chirp mass, sky location, and coalescence phase are approximately $9\%$, $1\%$, and $10\%$ per pair, respectively. Combining all three, the overall FAP per pair is $\sim10^{-4}$. As the number of events, $N$, in the GW catalogs increases, the number of random pairs of events increases as $\sim N^2$. Meanwhile, the number of lensed events will increase linearly with $N$, implying that for sufficiently high $N$, the false alarms will always dominate over the true lensing events. This issue can be compensated for by placing higher thresholds on the lensing candidates (e.g., selecting a higher signal-to-noise ratio (SNR) threshold), which will lead to better parameter estimation and, thus, lower FAP per pair -- at the cost of dramatically decreasing the size of the lensing sample (by $\sim 1/\mbox{SNR}^3$). We show that with our simple overlap criteria for current detectors at design sensitivity, the false alarms will dominate for realistic lensing rates ($\lesssim10^{-3}$) even when selecting the highest SNR pairs. These results highlight the necessity to design alternative identification criteria beyond simple waveform and sky location overlap. Future GW detectors Cosmic Explorer and Einstein Telescope may provide sufficient improvement in parameter estimation, allowing for the conclusive detection of strong lensing of GWs.
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