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，并解决了NSF“宇宙之窗”大构想的优先领域。为了探测和表征高级LIGO观测到的引力波信号，需要理论模型来预测信号作为源参数函数的详细行为。这些模型必须提供一个精确的近似于爱因斯坦方程的精确解，但也必须是快速和可靠的可计算的，以便它们可以用来预测数亿个参数位置的信号，以表征单个事件。为此，该项目将在精确和高效的波形模型上创造一种新的最先进的技术，从而有助于确保未来的高级LIGO观测不受正在使用的波形模型的限制。除了科学上的好处，这项工作还将培养一名研究生，掌握分析相对论和引力波数据分析的最佳实践，从而有助于培养下一代引力波天文学家。最后，该提案将通过开发引力波天体物理学的新演示文稿，为现有的空间公共推广小组（SPOT）计划做出贡献，从而有助于促进西弗吉尼亚州的有效教育和推广。进动自旋有效单体数值相对论（SEOBNRv3和目前正在开发的SEOBNRv4P）引力波形模型是仅有的两个能够促进黑洞双事件完全参数估计（PE）的模型之一（以及IMRPhenomP）。然而，尽管与数值相关波形相比，SEOBNR编码具有很高的效率和可靠性，但原始SEOBNR编码仍然太慢，无法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的团队之前开发了优化版本的SEOBNR近似值，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的发展揭示了潜在的SEOBNRv3近似物中偶尔的病理行为。虽然每10,000到100,000例中只发生一次，但该频率仍然是PE的主要障碍，PE需要生成10^8的波形实现。因此，迫切需要开发一种既比SEOBNRv3_opt更有效，又比SEOBNRv3_opt更健壮的近似。该项目将创建一个新的最先进的近似值，比目前存在的任何近似值都更准确，更健壮。这将需要，首先，创建一个基于SEOBNRv3_opt的新近似，但用PI开发的向后一体（BOB）合并-衰荡模型取代衰荡附件，该模型在NR探测的整个参数空间范围内产生与NR结果一样精确的合并-衰荡波形。由于BOB可以扩展到比光环更早的时间，它可以避免SEOBNRv3对精确光环位置的极端灵敏度。从而极大地提高了模型的鲁棒性。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.