Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves
Lensing or luck? False alarm probabilities for gravitational lensing of gravitational waves
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DOI：
10.1103/physrevd.107.063023
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发表时间：
2022-01
影响因子：
5
通讯作者：
Mesut Çalışkan;J. Ezquiaga;O. Hannuksela;D. Holz
中科院分区：
文献类型：
--
作者：
Mesut Çalışkan;J. Ezquiaga;O. Hannuksela;D. Holz
据预测，在即将到来的观测中，引力波（GWs）的强引力透镜效应将被探测到。然而，从随机关联中明确区分对透镜源是一个具有挑战性的问题。我们研究了由于随机巧合和参数估计误差的组合导致参数重叠而导致的非透镜事件模仿透镜事件的程度。我们构造一个有透镜事件和无透镜事件的模拟目录。我们发现基于啁啾质量、天空位置和聚并相位的巧合重叠的误报警概率（FAP）分别约为$9\%$、$1\%$和$10\%$ /对。结合这三者，每对的总体FAP为$\sim10^{-4}$。随着GW目录中事件数量$N$的增加，事件随机对的数量也随着$\sim N^2$的增加而增加。同时，透镜事件的数量将随着$N$线性增加，这意味着对于足够高的$N$，假警报将始终主导真实的透镜事件。这个问题可以通过在透镜候选者上设置更高的阈值来补偿（例如，选择更高的信噪比（SNR）阈值），这将导致更好的参数估计，从而降低每对的FAP——代价是大大减少透镜样本的大小（通过$\sim 1/\mbox{SNR}^3$）。我们表明，在设计灵敏度下，电流检测器的简单重叠标准，即使在选择最高信噪比对时，假警报也会在实际透镜率（$\lesssim10^{-3}$）中占主导地位。这些结果强调了设计替代识别标准的必要性，而不是简单的波形和天空位置重叠。未来的GW探测器宇宙探索者和爱因斯坦望远镜可能会在参数估计方面提供足够的改进，从而能够最终探测到GW的强透镜效应。
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.