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 (ℓ,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 ∼0.02, which is consistent with a Bayes factor of 56±1 (1σ 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 (ℓ,m,n)=(3,3,0) mode.

中文翻译：

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估计 GW190521 中次显性准正态模态的误报率


引力波天文学的一个主要目标是通过观测来测试黑洞的克尔性质。最强的此类测试（具有最少的额外假设）由对多种振铃模式的观测提供，也称为黑洞光谱。对于引力波合并事件GW190521，我们之前声称检测到了残余黑洞发射的两种振铃模式。在本文中，我们为从该事件中检测多种振铃模式提供了进一步的证据。我们分析了模拟引力波信号的恢复情况，旨在复制GW190521的振铃特性。我们量化了我们的检测统计量报告次显性 （l，m，n）=（3,3,0） 振铃模式的有力证据的频率，即使模拟信号中不存在这种模式。我们发现这仅在 ∼0.02 的概率下发生，这与 GW190521 的贝叶斯因子 56±1（1σ 不确定性）一致。我们还量化了对 GW190521 的不可知分析，其中假设振铃模式之间没有关系，并发现 250 个没有 （3,3,0） 模式的模拟信号中只有 1 个产生与 GW190521 一样显著的结果。相反，我们验证了当仿真信号确实具有可观察 （3,3,0） 模式时，它们始终产生强有力的证据和显着的不可知结果。我们还发现，在具有 （3,3,0） 模式的类 GW190521 信号上对 （3,3,0） 模式偏差的约束与我们之前对 GW190521 的分析一致。我们的结果支持了我们之前的结论，即来自 GW190521 的引力波信号包含一个可观测的次主导 （l，m，n）=（3,3,0） 模式。