引力波天文學(xué)與理論模型引力波理論建模課件

數(shù)值相對(duì)論與引力波建模的一些新進(jìn)展ZhoujianCao(曹周鍵)DepartmentofAstronomy,BNU2018-5-23第二屆引力波天體物理學(xué)術(shù)研討會(huì)數(shù)值相對(duì)論與引力波建模的一些新進(jìn)展ZhoujianCaoContentCurrentstateofGWtheoreticalmodelFiniteelementmethodtoNRTheoreticalmodeltoeccentricbinarysystemSummaryandprospectContentCurrentstateofGWthe引力波探測(cè)數(shù)據(jù)是典型的強(qiáng)噪聲、弱信號(hào)匹配濾波方法是引力波數(shù)據(jù)處理的理想方法引力波理論模型可以在既定硬件靈敏度的基礎(chǔ)上很好地提高引力波探測(cè)的能力GW151226?13,5sigma引力波理論模型是波源參數(shù)反演的基礎(chǔ)雙黑洞?雙中子星?星體質(zhì)量、自旋？……引力波天文學(xué)與理論模型引力波探測(cè)數(shù)據(jù)是典型的強(qiáng)噪聲、弱信號(hào)GW151226引力波理引力波理論建模針對(duì)實(shí)際的波源天體，求解愛(ài)因斯坦方程沒(méi)有對(duì)稱性，解析解基本沒(méi)有希望在極端條件下，近似方法失效數(shù)值計(jì)算成為主要依賴的方法(數(shù)值相對(duì)論NR)

引力波理論建模針對(duì)實(shí)際的波源天體，求解愛(ài)因斯坦方程CurrentproblemsfacedbyNRCurrentproblemsfacedbyNRCurrentNRcodesCurrentNRcodesPDEformusedbyAMSS-NCKUPDEformusedbyAMSS-NCKUPDEformforFEPDEformforFEFEnumericalschemeCao,Fu,Ji,andXia,2018FEnumericalschemeCao,Fu,Ji引力波天文學(xué)與理論模型引力波理論建模課件Shockforms,butreallystable!ConsistenttoPDEpropertyofnon-linearlydegenerateMoreflexiblethanPSShockforms,butreallystableConvergencebehaviorbetterthanFD,4thvs2ndMoreaccuratethanFD,2ordersbetterConvergencebehaviorbetterthComputationcostofNR10orbits,256CPUs,7daysGW150914:4orbitsGW151226:28orbits3daysx250000=2055years(256CPUs)GW150914ComputationcostofNR10orbit引力波天文學(xué)與理論模型引力波理論建模課件StateofartforEOBNRTotalmass:0<M<∞Massratio:1<q<20GW150914(1.24),LVT151012(1.77),GW151226(1.89),GW170104(1.61),GW170608(1.71),GW170814(1.21)Spin:-1<s<0.9GW150914(<0.24),LVT151012(<0.3),GW151226(<0.35),GW170104(<0.42),GW170608(<0.3),GW170814(<0.18)Precessionsimplified(BCV)GW150914,LVT151012&GW151226assumenoprecession,GW170104,GW170608&GW170814gainlittleconstrainonprecessione=0AllannouncedBBHGWeventsassumedStateofartforEOBNRTotalmaLSC,ApJ818,L22(2016)LSC,ApJ818,L22(2016)BinaryBlackHolewitheccentricorbitPlausiblesourceforLIGOManysourcesforLISABinaryBlackHolewitheccentrSEOBNREmodelAssumesmalleccentricityexpansion(c)parteffectivelymorethan4PNElippartabout2PNCao&Han,PRD96,044028(2017)SEOBNREmodelAssumesmallecceNotlikeadiabaticapproximatedmodel,consistentcheckfore=0caseNotlikeadiabaticapproximateCompareto‘standardanswer’NRm1:m2=1:1e=0.02Compareto‘standardanswer’Nm1:m2=1:5e=0.02m1:m2=1:5m1:m2=1:1e=0.2m1:m2=1:1m1:m2=1:1000e=0.3a=0.9a=0.5a=-0.5a=-0.9m1:m2=1:1000a=0.9a=0.5aax-modelforeccentricBBHadiabaticapproximationmodelax-modelforeccentricBBHadiam1:m2=1:1e=0.3Moreaccuratethanadiabaticmodelforlaterinspiralandmergerm1:m2=1:1Moreaccuratethan初步發(fā)展有限元數(shù)值相對(duì)論算法，希望實(shí)現(xiàn)大質(zhì)量比雙星系統(tǒng)和中子星雙星系統(tǒng)準(zhǔn)確建模描述橢圓軌道雙黑洞系統(tǒng)的引力波理論模型SEOBNRE準(zhǔn)確可靠，可直接被LIGO數(shù)據(jù)處理使用SEOBNRE模型可作為大質(zhì)量比雙黑洞系統(tǒng)理論模型的研究起點(diǎn)，發(fā)展未來(lái)空間引力波探測(cè)項(xiàng)目，如LISA，太極，天琴等，所需的雙黑洞并合系統(tǒng)的理論模板Summary初步發(fā)展有限元數(shù)值相對(duì)論算法，希望實(shí)現(xiàn)大質(zhì)量比雙星系統(tǒng)和中子數(shù)值相對(duì)論與引力波建模的一些新進(jìn)展ZhoujianCao(曹周鍵)DepartmentofAstronomy,BNU2018-5-23第二屆引力波天體物理學(xué)術(shù)研討會(huì)數(shù)值相對(duì)論與引力波建模的一些新進(jìn)展ZhoujianCaoContentCurrentstateofGWtheoreticalmodelFiniteelementmethodtoNRTheoreticalmodeltoeccentricbinarysystemSummaryandprospectContentCurrentstateofGWthe引力波探測(cè)數(shù)據(jù)是典型的強(qiáng)噪聲、弱信號(hào)匹配濾波方法是引力波數(shù)據(jù)處理的理想方法引力波理論模型可以在既定硬件靈敏度的基礎(chǔ)上很好地提高引力波探測(cè)的能力GW151226?13,5sigma引力波理論模型是波源參數(shù)反演的基礎(chǔ)雙黑洞?雙中子星?星體質(zhì)量、自旋？……引力波天文學(xué)與理論模型引力波探測(cè)數(shù)據(jù)是典型的強(qiáng)噪聲、弱信號(hào)GW151226引力波理引力波理論建模針對(duì)實(shí)際的波源天體，求解愛(ài)因斯坦方程沒(méi)有對(duì)稱性，解析解基本沒(méi)有希望在極端條件下，近似方法失效數(shù)值計(jì)算成為主要依賴的方法(數(shù)值相對(duì)論NR)

引力波理論建模針對(duì)實(shí)際的波源天體，求解愛(ài)因斯坦方程CurrentproblemsfacedbyNRCurrentproblemsfacedbyNRCurrentNRcodesCurrentNRcodesPDEformusedbyAMSS-NCKUPDEformusedbyAMSS-NCKUPDEformforFEPDEformforFEFEnumericalschemeCao,Fu,Ji,andXia,2018FEnumericalschemeCao,Fu,Ji引力波天文學(xué)與理論模型引力波理論建模課件Shockforms,butreallystable!ConsistenttoPDEpropertyofnon-linearlydegenerateMoreflexiblethanPSShockforms,butreallystableConvergencebehaviorbetterthanFD,4thvs2ndMoreaccuratethanFD,2ordersbetterConvergencebehaviorbetterthComputationcostofNR10orbits,256CPUs,7daysGW150914:4orbitsGW151226:28orbits3daysx250000=2055years(256CPUs)GW150914ComputationcostofNR10orbit引力波天文學(xué)與理論模型引力波理論建模課件StateofartforEOBNRTotalmass:0<M<∞Massratio:1<q<20GW150914(1.24),LVT151012(1.77),GW151226(1.89),GW170104(1.61),GW170608(1.71),GW170814(1.21)Spin:-1<s<0.9GW150914(<0.24),LVT151012(<0.3),GW151226(<0.35),GW170104(<0.42),GW170608(<0.3),GW170814(<0.18)Precessionsimplified(BCV)GW150914,LVT151012&GW151226assumenoprecession,GW170104,GW170608&GW170814gainlittleconstrainonprecessione=0AllannouncedBBHGWeventsassumedStateofartforEOBNRTotalmaLSC,ApJ818,L22(2016)LSC,ApJ818,L22(2016)BinaryBlackHolewitheccentricorbitPlausiblesourceforLIGOManysourcesforLISABinaryBlackHolewitheccentrSEOBNREmodelAssumesmalleccentricityexpansion(c)parteffectivelymorethan4PNElippartabout2PNCao&Han,PRD96,044028(2017)SEOBNREmodelAssumesmallecceNotlikeadiabaticapproximatedmodel,consistentcheckfore=0caseNotlikeadiabaticapproximateCompareto‘standardanswer’NRm1:m2=1:1e=0.02Compareto‘standardanswer’Nm1:m2=1:5e=0.02m1:m2=1:5m1:m2=1:1e=0.2m1:m2=1:1m1:m2=1:1000e=0.3a=0.9a=0.5a=-0.5a=-0.9m1:m2=1:1000a=0.9a=0.5aax-modelforeccentricBBHadiabaticapproximationmodelax-modelforeccentricBBHadiam1:m2=1:1e=0.3Moreaccura