估算GW190521中亚主导准简正模式的误报率
Estimating False Alarm Rates of Sub-Dominant Quasi-normal Modes in GW190521
AI总结：
本研究通过模拟信号分析量化GW190521中亚主导(3,3,0)铃宕模式的误报率，验证了该模式探测的可靠性，支持GW190521信号含可观测亚主导准简正模式的结论，为黑洞克尔性质检验提供依据。
摘要：
引力波天文学的一个主要目标是通过观测检验黑洞的克尔（Kerr）性质。这类检验中假设最少且效力最强的方法是对多模铃宕（ringdown）模式的观测，也称为黑洞光谱学。针对引力波并合事件GW190521，我们此前曾宣称探测到了残留黑洞发出的两种铃宕模式。本文为该事件中多铃宕模式的探测提供了进一步证据。我们分析了旨在复现GW190521铃宕特性的模拟引力波信号的恢复情况，量化了即便模拟信号中不存在亚主导的$(\u2113,m,n)=(3,3,0)$铃宕模式，我们的探测统计量仍报告存在该模式强证据的频率。我们发现这种情况的发生概率仅约为0.02，这与针对GW190521得到的贝叶斯因子为$t_{\rm ref} + 6\text{ms}$（1σ不确定度）的结果一致。我们还量化了对GW190521的不可知论分析（该分析未假设铃宕模式之间存在关联），发现每250个不含$(3,3,0)$模式的模拟信号中，仅有1个能产生与GW190521同等显著的结果。反过来，我们验证了当模拟信号确实存在可观测的$(3,3,0)$模式时，它们始终会产生强证据和显著的不可知论分析结果。我们还发现，对于带有$(3,3,0)$模式的类GW190521信号，对$(3,3,0)$模式偏离的约束与我们此前对GW190521分析得到的结果一致。我们的结果支持了此前的结论，即GW190521的引力波信号包含可观测的亚主导$(\u2113,m,n)=(3,3,0)$模式。
英文摘要：
A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell,m,n)=(3,3,0)$ ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability $\sim 0.02$, which is consistent with a Bayes factor of $t_{\rm ref} + 6\,\mathrm{ms}$ (1$σ$ uncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a $(3,3,0)$ mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$ mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the $(3,3,0)$ mode on GW190521-like signals with a $(3,3,0)$ mode are consistent with what was obtained from our previous analysis of GW190521. Our results support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell,m,n)=(3,3,0)$ mode.
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