数值相对论和引力波源建模

Numerical relativity is an ideal and powerful tool for the study of strong gravitational wave sources without any symmetry. Since the amplitude of gravitational wave is very small, gravitational wave model is very important for both signal detection and parameter estimate. The gravitational wave source model is the accurate wave form for sources with specific parameters. Binary black hole systems are the most promising and most important sources for almost all of the gravitational wave detection projects in the world. Mass ratio and spin are two important parameters of binary black hole systems. After the breakthrough of numerical relativity in 2005, ones have got accurate wave form for almost equal mass and small spinning binary black holes. But current numerical methods can not simulate binary black hole with relatively large mass ratio and large spin. This makes people fail to construct the gravitational wave source model for binary black holes with large mass ratio and/or large spin. In this project we propose to develop novel numerical methods to deal with these binary black hole systems. Then combine the numerical simulation of these systems with suitable analytical methods to construct gravitational wave source model for them. Our results will definitely give theoretical supports to gravitational wave detection.

数值相对论是研究无对称性、动态强引力场的有效方法和引力波源建模的有力手段。由于引力波很弱，引力波源模型对引力波信号探测和参数估计都非常重要。引力波源模型也就是波源在不同参数时分别对应的准确引力波形。双黑洞系统是各大引力波探测项目主要和重要的引力波源。质量比和黑洞自旋是双黑洞系统非常重要的两个参数。2005年，数值相对论计算稳定性问题得到突破后，人们通过数值研究，对近等质量、小自旋双黑洞系统所辐射引力波的波形给出了比较准确的描述。但由于目前的数值计算方法不能很好地模拟较大质量比和大自旋的双黑洞系统，现在还没有准确的引力波源模型描述大质量比和大自旋双黑洞系统。本项目将研究和发展新颖的数值计算方法，模拟较大质量比、大自旋的双黑洞系统；建立这类双黑洞系统的引力波源模型，为引力波探测提供理论支持。

发展和建成了数值相对论软件AMSSNCKU并获得计算机软件著作权，帮助建立了双黑洞并合系统引力波理论模型--有效单体数值相对论模型(EOBNR)。EOBNR模型是目前LIGO数据处理主要依赖的引力波理论模型之一。发展了EOBNR模型描述引力波记忆效应，拓展EOBNR模型到SEOBNRE模型来描述椭圆轨道双星并合系统。为相关引力波探测提供了理论基础。发展了数值相对论计算方法，特别是改进BSSN方程形式，发展提出Z4c方程形式，对计算的准确性有大幅度的提升；提出了新颖的类光演化方法；设计了初步的有限元数值相对论算法并大规模科学计算实现，为发展下一代数值相对论软件积累基础。