引力波天文学与理论模型引力波理论建模

1、数值相对论与引力波建模的一些新进展,Zhoujian Cao (曹周键) Department of Astronomy, BNU 2018-5-23 第二届引力波天体物理学术研讨会,Content,Current state of GW theoretical model Finite element method to NR Theoretical model to eccentric binary system Summary and prospect,引力波天文学与理论模型,引力波理论建模,针对实际的波源天体，求解爱因斯坦方程 没有对称性，解析解基本没有希望 在极端条件下，近似方法失效

2、 数值计算成为主要依赖的方法(数值相对论NR),Current problems faced by NR,Current NR codes,PDE form used by AMSS-NCKU,PDE form for FE,FE numerical scheme,Cao, Fu, Ji, and Xia, 2018,Shock forms, but really stable!,Consistent to PDE property of non-linearly degenerate More flexible than PS,Convergence behavior better than

3、 FD, 4th vs 2nd More accurate than FD, 2 orders better,Computation cost of NR,10 orbits, 256 CPUs, 7days GW150914: 4 orbits GW151226: 28 orbits 3days x 250000 = 2055 years (256CPUs),GW150914,State of art for EOBNR,Total mass: 0M Mass ratio: 1q20 GW150914 (1.24), LVT151012 (1.77), GW151226 (1.89), GW

4、170104 (1.61), GW170608 (1.71), GW170814 (1.21) Spin: -1s0.9 GW150914 (0.24), LVT151012 (0.3), GW151226 (0.35), GW170104 (0.42), GW170608 (0.3), GW170814 (0.18) Precession simplified (BCV) GW150914, LVT151012 & GW151226 assume no precession, GW170104, GW170608 & GW170814 gain little constrain on pre

5、cession e = 0 All announced BBH GW events assumed,LSC, ApJ 818, L22 (2016),Binary Black Hole with eccentric orbit,Plausible source for LIGO Many sources for LISA,SEOBNRE model,Assume small eccentricity expansion (c) part effectively more than 4 PN Elip part about 2PN,Cao & Han, PRD 96, 044028 (2017)

6、,Not like adiabatic approximated model, consistent check for e=0 case,Compare to standard answer NR,m1:m2 = 1:1 e = 0.02,m1:m2 = 1:5 e = 0.02,m1:m2 = 1:1 e = 0.2,m1:m2 = 1:1000 e = 0.3,a = 0.9,a = 0.5,a =-0.5,a =-0.9,ax-model for eccentric BBH,adiabatic approximation model,m1:m2 = 1:1 e = 0.3,More accurate than adiabatic model for later inspiral and merger,初步发展有限元数值相对论算法，希望实现大质量比双星系统和中子星双星系统准确建模 描述椭圆轨道双黑洞系统的引力波理论模型SEOBNRE准