AI 中文总结
本研究提出模块化数值框架GWMemoryLab，探究双黑洞并合阶段Christodoulou引力波记忆的探测器依赖性，发现最优总质量与探测器低频截止频率近似反比关系，为该记忆的可探测性提供了见解。
AI 中文摘要
非线性引力波记忆，又称Christodoulou记忆效应，是广义相对论预言的、由引力波自相互作用产生的永久位移。本研究提出GWMemoryLab，这是一个模块化数值框架，用于在后牛顿近似下研究无自旋双黑洞系统并合阶段的主导阶Christodoulou记忆。该框架包含双黑洞动力学、后牛顿并合演化、振荡波形生成、引力波能流及非线性记忆累积等模块。分析对比与收敛测试验证了其数值稳定性。我们研究了累积记忆对双黑洞质量比、总质量及探测器低频截止频率的依赖性。模拟结果显示，对于给定探测器带宽，存在一个最优总质量，可最大化可观测的并合记忆；在所探索的参数空间内，最优质量与探测器低频截止频率呈近似反比关系。该行为源于双黑洞趋近最内稳定圆轨道时，引力波光度增加与并合时长缩短之间的竞争。这些结果为非线性引力波记忆的可探测性提供了见解，并证明了GWMemoryLab在系统参数研究中的实用性。
英文摘要
The nonlinear gravitational-wave memory, or Christodoulou memory effect, is a permanent displacement produced by the self-interaction of gravitational waves predicted by General Relativity. In this work, we present GWMemoryLab, a modular numerical framework for investigating leading-order Christodoulou memory during the inspiral of non-spinning binary black hole systems within the post-Newtonian approximation. The framework implements modules for binary dynamics, post-Newtonian inspiral evolution, oscillatory waveform generation, gravitational-wave energy flux, and nonlinear memory accumulation. Analytical comparisons and convergence tests demonstrate numerical stability. We investigate the dependence of accumulated memory on binary mass ratio, total mass, and detector low-frequency cutoff. The simulations reveal an optimal total mass that maximizes the observable inspiral memory for a given detector bandwidth. Within the explored parameter space, the optimal mass follows an approximately inverse dependence on the detector low-frequency cutoff. This behaviour arises from the competition between increasing gravitational-wave luminosity and decreasing inspiral duration as the binary approaches the innermost stable circular orbit. These results provide insight into the detectability of nonlinear gravitational-wave memory and demonstrate the utility of GWMemoryLab for systematic parameter studies.
