标题： 双正交调和函数在引力辐射分解中的应用 II：极端质量和可比较质量比黑洞双星的应用 显示英文标题

标题： Bi-orthogonal harmonics for the decomposition of gravitational radiation II: applications for extreme and comparable mass-ratio black hole binaries

摘要： 物理系统正常模的估计是物理学中的一个基本问题。 扰动克尔黑洞的准正则模及其相关的椭球谐函数是关键例子，在引力波理论和数据分析中有广泛的应用。 最近，已经证明\textit{伴随}椭球谐函数及相关椭球多极矩可用于估计任意源的辐射模。 在本文中，我们研究相对于球面谐函数，椭球多极矩是否能更好地近似双黑洞时空的底层模。 我们首先简要介绍伴随椭球谐函数。 然后详细描述一种简单的椭球谐函数分解方法，以及其推广形式，该形式可以同时估计前向和后向旋转的多极矩。 提供了对可比较质量和极端质量比双黑洞合并的数值波形的示例应用。 我们讨论了在 inspiral、合并和 ringdown 阶段相关椭球矩的形态。 最后，我们讨论了在引力波理论和信号建模中的潜在应用。 显示英文摘要

摘要： The estimation of a physical system's normal modes is a fundamental problem in physics. The quasi-normal modes of perturbed Kerr black holes, with their related spheroidal harmonics, are key examples, and have diverse applications in gravitational wave theory and data analysis. Recently, it has been shown that \textit{adjoint}-spheroidal harmonics and the related spheroidal multipole moments may be used to estimate the radiative modes of arbitrary sources. In this paper, we investigate whether spheroidal multipole moments, relative to their spherical harmonic counterparts, better approximate the underlying modes of binary black hole spacetimes. We begin with a brief introduction to adjoint-spheroidal harmonics. We then detail a rudimentary kind of spheroidal harmonic decomposition, as well as its generalization which simultaneously estimates pro- and retrograde moments. Example applications to numerical waveforms from comparable and extreme mass-ratio binary black hole coalescences are provided. We discuss the morphology of related spheroidal moments during inspiral, merger, and ringdown. We conclude by discussing potential applications in gravitational wave theory and signal modeling.