Department of Physics and MIT Kavli Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Department of Physics, University of Massachusetts, Dartmouth, Massachusetts 02747, USA.
Phys Rev Lett. 2019 Oct 18;123(16):161101. doi: 10.1103/PhysRevLett.123.161101.
The coalescence of two black holes generates gravitational waves that carry detailed information about the properties of those black holes and their binary configuration. The final coalescence cycles are in the form of a ringdown: a superposition of quasinormal modes of the merged remnant black hole. Each mode has an oscillation frequency and decay time that in general relativity is determined by the remnant's mass and spin. Measuring the frequency and decay time of multiple modes makes it possible to measure the remnant's mass and spin, and to test the waves against the predictions of gravity theories. In this Letter, we show that the relative amplitudes of these modes encode information about a binary's geometry. Focusing on the large mass-ratio limit, which provides a simple-to-use tool for effectively exploring parameter space, we demonstrate how a binary's geometry is encoded in the relative amplitudes of these modes, and how to parametrize the modes in this limit. Although more work is needed to assess how well this carries over to less extreme mass ratios, our results indicate that measuring multiple ringdown modes from coalescence may aid in measuring important source properties, such as the misalignment of its members' spins and orbit.
两个黑洞的并合会产生引力波，这些引力波携带着关于这些黑洞及其双星配置的详细信息。最终的并合循环以“衰减”的形式出现：合并后的残余黑洞的拟正则模式的叠加。每个模式都有一个振荡频率和衰减时间，在广义相对论中，这些频率和衰减时间由残余物的质量和自旋决定。测量多个模式的频率和衰减时间，可以测量残余物的质量和自旋，并根据引力理论的预测来检验这些波。在这封信中，我们表明这些模式的相对振幅编码了关于双星几何形状的信息。我们专注于大质量比极限，它为有效地探索参数空间提供了一个简单易用的工具，我们演示了双星的几何形状是如何编码在这些模式的相对振幅中的，以及如何在这个极限下参数化这些模式。尽管还需要做更多的工作来评估这种方法在更小的质量比下的效果如何，但我们的结果表明，从并合中测量多个衰减模式可能有助于测量重要的源性质，例如其成员的自旋和轨道的不对准。
