[论文解读] Relative binning for complete gravitational-wave parameter estimation with higher-order modes and precession, and applications to lensing and third-generation detectors

Harsh Narola, Justin Janquart+3 more|arXiv (Cornell University)|Aug 23, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy被引用 3

一句话总结

本文提出了一种相对分箱方法，用于引力波天文学中快速且精确的贝叶斯参数估计，能够高效分析具有进动和高阶模态的信号——这对当前及未来的探测器至关重要。该方法相较于标准技术实现了最高达10倍的速度提升，尤其在低质量双星系统中表现显著，同时保持后验概率的准确性，并可扩展至强引力透镜信号的联合推断。

ABSTRACT

Once a gravitational wave signal is detected, the measurement of its source parameters is important to achieve various scientific goals. This is done through Bayesian inference, where the analysis cost increases with the model complexity and the signal duration. For typical binary black hole signals with precession and higher-order modes, one has 15 model parameters. With standard methods, such analyses require at least a few days. For strong gravitational wave lensing, where multiple images of the same signal are produced, the joint analysis of two data streams requires 19 parameters, further increasing the complexity and run time. Moreover, for third generation detectors, due to the lowered minimum sensitive frequency, the signal duration increases, leading to even longer analysis times. With the increased detection rate, such analyses can then become intractable. In this work, we present a fast and precise parameter estimation method relying on relative binning and capable of including higher-order modes and precession. We also extend the method to perform joint Bayesian inference for lensed gravitational wave signals. Then, we compare its accuracy and speed to those of state-of-the-art parameter estimation routines by analyzing a set of simulated signals for the current and third generation of interferometers. Additionally, for the first time, we analyze some real events known to contain higher-order modes with relative binning. For binary black hole systems with a total mass larger than $50\, M_{\odot}$, our method is about 2.5 times faster than current techniques. This speed-up increases for lower masses, with the analysis time being reduced by a factor of 10 on average. In all cases, the recovered posterior probability distributions for the parameters match those found with traditional techniques.

研究动机与目标

• 解决复杂引力波信号（含进动和高阶模态）的贝叶斯参数估计日益增长的计算负担。
• 减少需要对19个参数进行联合推断的透镜信号的分析时间。
• 实现对第三代探测器（如爱因斯坦望远镜、宇宙探索者）的可扩展参数估计，其信号持续时间可能长达一天。
• 开发一种在高维参数空间中显著降低运行时间的同时保持高精度的方法。
• 支持未来观测运行中预期检测率上升的实时或准实时分析。

提出的方法

• 使用相对分箱通过在粗略频率网格上近似波形比值（相对于基准波形）来加速似然评估。
• 使用插值后的比值计算数据与波形之间的内积，从而减少每次MCMC步骤中完整波形评估的次数。
• 将该方法扩展至波形模型中包含进动和高阶球谐模态（h^L_{l,m}）的情况。
• 将该技术应用于强引力透镜引力波信号的联合参数估计，将两个数据流与四个透镜参数关联。
• 使用基准波形（即注入信号或最大似然估计）以实现高效的相对分箱近似。
• 使用LALSimulation生成波形，并通过Numba加速的Python实现系数计算（C_{l,m}），未来可进一步优化。

Figure 1: Ratio (vertical axis) of the real part of the proposal to the fiducial waveform for the plus polarization as a function of frequency (horizontal axis). The top panel is for the IMRPhenomD waveform model with only the dominant mode and without precession, while the bottom panel is for the I

实验结果

研究问题

• RQ1 相对分箱方法能否在几乎不损失精度的前提下，扩展至包含引力波参数估计中的进动和高阶模态？
• RQ2 对于总质量超过50 M⊙的信号，相对分箱方法在速度和精度方面相较于标准方法表现如何？
• RQ3 该方法能否有效应用于强引力透镜引力波信号的联合推断，其参数多达19个？
• RQ4 基准波形的选择对相对分箱框架的性能和收敛性有何影响？
• RQ5 考虑到低质量信号是计算最昂贵的分析对象，该方法在质量减小时的可扩展性如何？

主要发现

• 对于总质量 >50 M⊙ 的双黑洞系统，相对分箱方法的速度约为标准参数估计技术的2.5倍。
• 对于低质量系统，速度提升平均达到10倍，显著缩短了最计算密集型信号的分析时间。
• 使用相对分箱恢复的后验概率分布与传统方法在统计不确定性范围内一致，证实了其准确性。
• 该方法成功实现了强引力透镜信号的联合贝叶斯推断，扩展了其在多图像引力波事件中的适用性。
• 重加权分析表明，相对分箱获得的后验样本与标准似然评估结果一致，验证了该方法的保真度。
• 该框架可扩展至未来探测器，并可通过将C_{l,m}系数计算直接集成到LALSimulation中进一步加速。

Figure 2: The top (bottom) panel shows the ratio of $h^{L}$ (C) for the fiducial waveform to the proposal waveform for each mode as a function of frequency. The source and the fiducial parameters used to generate the plot are identical to the ones used in Fig. 1 .