High-overtone fits to numerical relativity ringdowns: Beyond the dismissed n=8 special tone
High-overtone fits to numerical relativity ringdowns: Beyond the dismissed
n=8
special tone
复制标题
高泛音适合数值相对论振铃：超越被忽略的 n=8 特殊音调
作者：
X. J. Forteza;P. Mourier
在广义相对论中，起源于未带电黑洞合并的残余物是克尔黑洞。这种最终状态是通过发射一列被称为黑洞环行的晚期辐射来达到的。在围绕终态的线性微扰理论中，振铃形态是由一组可计数的无限衰减正弦波--准正交模--描述的，其复频率完全由最终黑洞的质量和自转决定。最近的结果表明，如果使用Nmax=7个泛音(基模以外)的准正交模模型，则数值相对论的振铃波形可以从应变的峰值开始得到完整的描述。在这项工作中，我们将这种分析扩展到Nmax≥7到Nmax=16个泛音的模型，通过探索通过拟合来自SXS星表的非进动双星黑洞模拟获得的最终质量和自旋的参数偏差。为此，我们计算了(L=m=2，n=8，9)余弦和反旋转泛音的自旋重量−_2Kerr准正规模频率和角分离常数，它们在低自旋时都接近于Schwarzschild代数特殊模。我们提供了这些模式所获得的值的表格，这与以前的结果是一致的。从系统变量-Nmax分析中，我们发现Nmax∼6泛音平均足以模拟从应变峰值开始的振铃，尽管大约21%的研究情况需要至少Nmax∼12泛音才能在最终状态参数上达到类似的精度。考虑来自较早或较晚时间点的波形，我们发现在每种情况下都可以达到非常相似的最大精度，发生在不同数量的泛音Nmax处。我们还给出了基于引力波应变的外推和分辨率不确定性的SXS波形的新的误差估计，该误差超过了由最终质量和自旋的准局部测量所获得的误差。最后，我们观察到基模和第一泛音以外的音调的最适合幅度上的实质性不稳定，然而，这并不显著地影响质量和自旋估计。
In general relativity, the remnant object originating from an uncharged black hole merger is a Kerr black hole. This final state is reached through the emission of a late train of radiation known as the black hole ringdown. In linear perturbation theory around the final state, the ringdown morphology is described by a countably infinite set of damped sinusoids — the quasinormal modes — whose complex frequencies are solely determined by the final black hole’s mass and spin. Recent results advocate that ringdown waveforms from numerical relativity can be fully described from the peak of the strain onwards if quasinormal mode models with Nmax = 7 overtones (beyond the fundamental mode) are used. In this work we extend this analysis to models with Nmax ≥ 7 up to Nmax = 16 overtones by exploring the parameter bias on the final mass and spin obtained by fitting the nonprecessing binary black hole simulations from the SXS catalog. To this aim, we have computed the spin weight −2 Kerr quasinormal mode frequencies and angular separation constants for the (l = m = 2, n = 8, 9) coand counter-rotating overtones, which all approach a Schwarzschild algebraically special mode at low spins. We provide tables of the values obtained for these modes, which are in agreement with previous results. From the systematic variable-Nmax analysis, we find that Nmax ∼ 6 overtones are on average sufficient to model the ringdown from the peak of the strain, although about 21% of the cases studied require at least Nmax ∼ 12 overtones to reach a comparable accuracy on the final state parameters. Considering the waveforms from an earlier or later point in time, we find that a very similar maximum accuracy can be reached in each case, occurring at a different number of overtones Nmax. We also provide new error estimates for the SXS waveforms based on the extrapolation and the resolution uncertainties of the gravitational wave strain, which dominate over the errors obtained from the quasilocal measures of the final mass and spin. Finally, we observe substantial instabilities on the best-fit amplitudes of the tones beyond the fundamental mode and the first overtone, that, nevertheless, do not impact significantly the mass and spin estimates.