26引力波天文学与理论模型引力波理论建模

数值相对论与引力波建模的一些新进展ZhoujianCao(曹周键)DepartmentofAstronomy,BNU2018-5-23第二届引力波天体物理学术研讨会Content•CurrentstateofGWtheoreticalmodel•FiniteelementmethodtoNR•Theoreticalmodeltoeccentricbinarysystem•Summaryandprospect引力波探测数据是典型的强噪声、弱信号匹配滤波方法是引力波数据处理的理想方法引力波理论模型可以在既定硬件灵敏度的基础上很好地提高引力波探测的能力GW151226?13,5sigma引力波理论模型是波源参数反演的基础双黑洞?双中子星?星体质量、自旋？……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数值计算成为主要依赖的方法(数值相对论NR)CurrentproblemsfacedbyNRCurrentNRcodesPDEformusedbyAMSS-NCKUjjiijjijjkjkijijkjkjijjijjkjkijijiijkkkkijkjikjkikijTFijjiijijkkkkijkjikijijiiijijiiiiiiAKAAtAAAAAAKRDDetAAtKKAADDtKKt~32~~~31~)~6~32~~(2~2~~~32~2)~~2~()(~~~32~2~2~)31~~()(61)(4)(2PDEformforFEFEnumericalschemeCao,Fu,Ji,andXia,2018Shockforms,butreallystable!ConsistenttoPDEpropertyofnon-linearlydegenerateMoreflexiblethanPSConvergencebehaviorbetterthanFD,4thvs2ndMoreaccuratethanFD,2ordersbetterComputationcostofNR•10orbits,256CPUs,7days•GW150914:4orbitsGW151226:28orbits3daysx250000=2055years(256CPUs)GW150914StateofartforEOBNR•Totalmass:0M∞•Massratio:1q20GW150914(1.24),LVT151012(1.77),GW151226(1.89),GW170104(1.61),GW170608(1.71),GW170814(1.21)•Spin:-1s0.9GW150914(0.24),LVT151012(0.3),GW151226(0.35),GW170104(0.42),GW170608(0.3),GW170814(0.18)•Precessionsimplified(BCV)GW150914,LVT151012&GW151226assumenoprecession,GW170104,GW170608&GW170814gainlittleconstrainonprecession•e=0AllannouncedBBHGWeventsassumedLSC,ApJ818,L22(2016)BinaryBlackHolewitheccentricorbitPlausiblesourceforLIGOManysourcesforLISASEOBNREmodelAssumesmalleccentricityexpansion(c)parteffectivelymorethan4PNElippartabout2PNCao&Han,PRD96,044028(2017)Notlikeadiabaticapproximatedmodel,consistentcheckfore=0caseCompareto‘standardanswer’NRm1:m2=1:1e=0.02m1:m2=1:5e=0.02m1:m2=1:1e=0.2m1:m2=1:1000e=0.3a=0.9a=0.5a=-0.5a=-0.9ax-modelforeccentricBBHadiabaticapproximationmodelm1:m2=1:1e=0.3Moreaccuratethanadiabaticmodelforlaterinspiralandmerger•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准确可靠，可直接被LIGO数据处理使用•SEOBNRE模型可作为大质量比双黑洞系统理论模型的研究起点，发展未来空间引力波探测项目，如LISA，太极，天琴等，所需的双黑洞并合系统的理论模板Summary