标题： 利用$\mathcal{F}$-统计量的引力波回响分析 显示英文标题

标题： Gravitational wave ringdown analysis using the $\mathcal{F}$-statistic

摘要： 在两个黑洞合并的最后阶段之后，环振荡信号在提供强场引力动力学信息方面发挥了重要作用。 我们引入了一种基于$\mathcal{F}$统计量的新时间域（TD）方法，用于环振荡分析。 与传统TD技术不同的是，这种方法的参数空间始终保持不变，无论包含多少模式。 通过重新配置似然函数并对所有模式的振幅和参考相位等外在参数进行解析最大化，实现了这一特性。 因此，在假设爱因斯坦望远镜检测到环振荡信号的情况下，与传统TD方法相比，参数估计计算时间最多缩短了五个数量级。 此外，我们还证明，由于不同过调模式之间的振荡频率和阻尼时间接近，传统TD方法在包含多个过调模式时变得困难。 令人鼓舞的是，我们的新TD技术有效解决了这个问题。 这种新TD方法的适用范围广泛，为当前和未来的引力波探测器相关的黑洞光谱学研究提供了灵活性。 显示英文摘要

摘要： After the final stage of the merger of two black holes, the ringdown signal takes an important role on providing information about the gravitational dynamics in strong field. We introduce a novel time-domain (TD) approach, predicated on the $\mathcal{F}$-statistic, for ringdown analysis. This method diverges from traditional TD techniques in that its parameter space remains constant irrespective of the number of modes incorporated. This feature is achieved by reconfiguring the likelihood and analytically maximizing over the extrinsic parameters that encompass the amplitudes and reference phases of all modes. Consequently, when performing the ringdown analysis under the assumption that the ringdown signal is detected by the Einstein Telescope, parameter estimation computation time is shortened by at most five orders of magnitude compared to the traditional TD method. We further establish that traditional TD methods become difficult when including multiple overtone modes due to close oscillation frequencies and damping times across different overtone modes. Encouragingly, this issue is effectively addressed by our new TD technique. The accessibility of this new TD method extends to a broad spectrum of research and offers flexibility for various topics within black hole spectroscopy applicable to both current and future gravitational wave detectors.