Improving the Accuracy, Robustness, and Computational Efficiency of the Spinning, Precessing Effective-One-Body Numerical-Relativity (SEOBNRv3/SEOBNRv4P) Codes

该奖项支持相对论和相对论天体物理学的研究，并阐述了美国国家科学基金会“宇宙之窗”宏伟构想的优先领域。为了探测和表征高级LIGO观测到的引力波信号，需要建立理论模型来预测信号的详细行为作为源参数的函数。这些模型必须为爱因斯坦方程的精确解提供准确的近似，但也必须是快速和可靠的可计算的，以便它们可以用于预测数亿个参数位置的信号，以便描述单个事件的特征。为此，该项目将在准确和高效的波形模型方面创造一个新的最先进的水平，从而帮助确保未来的高级LIGO观测不受所使用的波形模型的限制。除了科学上的好处外，这项工作还将对一名研究生进行分析相对论和引力波数据分析最佳做法方面的培训，从而帮助培训下一代引力波天文学家。最后，这项提议将通过开发一种关于引力波天体物理的新演示文稿来促进整个西弗吉尼亚州的有影响力的教育和推广，为现有的空间公共外联小组(SPOT)计划做出贡献。进动旋转有效一体数值相对论(SEOBNRv3和SEOBNRv4P目前正在开发中)引力波形模型是仅有的两个能够促进对黑洞双星事件的完整参数估计(PE)的模型之一(连同IMRPhenomP)。然而，尽管与数值相对论波形相比，SEOBNR码具有很高的效率和可靠性，但原始的SEOBNR码仍然太慢，不能直接用于基于标准马尔可夫链蒙特卡罗(MCMC)的PE。为了解决这个问题，PI的团队之前开发了SEOBNR近似的优化版本，这使得使用SEOBNRv3_OPT以更快的速度对候选事件执行PE成为可能。此外，SEOBNRv3_opt的发展揭示了SEOBNRv3近似物中偶尔的病理行为。虽然每10,000到100,000个案例中只有一个发生，但这种频率仍然是PE的主要障碍，这需要生成10^8个波形实现。因此，迫切需要开发一种既比SEOBNRv3_opt更有效，又更健壮的近似式。该项目将创造一种新的最先进的近似方法，它比目前存在的任何方法都更准确、更坚固。这将需要，首先，基于SEOBNRv3_OPT创建新的近似式，但用PI开发的向后一体(BOB)合并-振铃模型替换振铃附件，该模型在NR探测的整个参数空间范围内产生与NR结果一样准确的合并-振铃波形。由于Bob可以扩展到比光环更早的时间，它可以避免SEOBNRv3对准确的光环位置的极端敏感性，从而极大地提高模型的稳健性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports research in relativity and relativistic astrophysics and it addresses the priority areas of NSF's "Windows on the Universe" Big Idea. In order to detect and characterize the gravitational-wave signals observed by Advanced LIGO, theoretical models that predict the detailed behavior of the signal as a function of the source parameters are required. These models must provide an accurate approximation to the exact solution of Einstein's equations, but must also be rapidly and robustly calculable, so that they can be used to predict the signal at hundreds of millions of parameter locations in order to characterize a single event. To that end, this project will create a new state-of-the-art in accurate and efficient waveform models, thus helping to ensure that future Advanced LIGO observations are not limited by the waveform models being used. In addition to the scientific benefits, this work will result in the training of a graduate student in the best practices of analytical relativity and gravitational-wave data analysis, thereby helping to train the next generation of gravitational-wave astronomers. Finally, this proposal will help facilitate impactful education and outreach throughout the state of West Virginia, by contributing to the existing Space Public Outreach Team (SPOT) program through the development of a new presentation on gravitational-wave astrophysics.The Precessing Spinning Effective-One-Body Numerical-Relativity (SEOBNRv3, and SEOBNRv4P currently under development) gravitational waveform model is one of only two models (along with IMRPhenomP) capable of facilitating complete parameter estimation (PE) of black-hole binary events. However, despite their great efficiency and reliability when compared to numerical relativity waveforms, the original SEOBNR codes were still far too slow to be directly useful for standard Markov-Chain Monte Carlo (MCMC)-based PE. To address this issue, the PI's team previously developed optimized versions of the SEOBNR approximants, which make it possible, using SEOBNRv3_opt, to perform PE on a candidate event at a much faster rate. In addition, the development of SEOBNRv3_opt uncovered occasional pathological behavior in the underlying SEOBNRv3 approximant. While only occurring in one out of every ~10,000 to 100,000 cases, this frequency nonetheless presents a major obstacle to PE, which requires the generation of 10^8 waveform realizations. Therefore, there is an urgent need to develop an approximant that is both significantly more efficient than SEOBNRv3_opt, and also substantially more robust. This project will create a new state-of-the-art approximant that is both more accurate and more robust than any currently in existence. This will require, first, the creation of a new approximant based on SEOBNRv3_opt, but replacing the ringdown attachment with the Backwards One-Body (BOB) merger-ringdown model developed by the PI, which produces merger-ringdown waveforms as accurate as NR results across the entire range of parameter space probed by NR. Because BOB can be extended to earlier times than the light ring, it can avoid the extreme sensitivity of SEOBNRv3 to the exact light ring location, thereby dramatically improving the robustness of the model.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.