极端质量比旋进系统高精度重校准引力波建模（英文）
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摘要
针对空间引力波探测器的数据处理,需高精度高效率计算极端质量比旋进系统引力波,本文提出了一个完全重校准波形计算模型。该模型基于高精度Teukolsky方程数值求解的数据,对等效单体问题的因子化波形中所有与质量比无关的系数进行重校准,并利用重校准后的系数实现波形的高效计算(相同计算环境下效率是Teukolsky方程数值求解的1 400倍)。其精度高于已有的校准模型精度至少一个量级,可满足空间引力波探测器对于无轨道倾角准圆轨道EMRI波形的精度要求。文中还研究了致密天体的自旋以及旋进系统的质量比引起的相位偏移,发现在波形计算中自旋和质量比均不可忽略。利用该模型对极端质量比旋进系统的波形实现高精度、高效率计算对于今后的空间引力波探测器波形模版构建将发挥重大作用。
For the data analysis of space-based interferometers,calculating the gravitational waves of Extrememass-ratio-inspirals( EMRIs) in a highly accurate and efficient way is in high demand. In this paper,we present so-called "fully recalibrated waveform"for EMRIs with high accuracy. Based on the numerical data,by solving the Teukolsky equations,we recalibrate all of the mass-ratio independent coefficients of the factorized waveforms that are used in the effective-one-body( EOB) models. Due to these new coefficients with great efficiency( about 1 400 times more efficient than numerically solving the Teukolsky equations with the same computing environment),the precision of waveforms is improved enormously and is more accurate than other existing calibration models by at least one order in magnitude. For this reason,it meets the requirements of the space-based gravitational wave detection mission for the accuracy of EMRI waveform for uninclined,quasi-circular orbits. By investigating the dephasing value with our model,the spin of compact objects and the mass-ratio of the inspiralling system cannot be omitted in the waveform calculations. We believe our model will play an important role in the waveform-template construction of space-based GW detectors.
For the data analysis of space-based interferometers,calculating the gravitational waves of Extrememass-ratio-inspirals( EMRIs) in a highly accurate and efficient way is in high demand. In this paper,we present so-called "fully recalibrated waveform"for EMRIs with high accuracy. Based on the numerical data,by solving the Teukolsky equations,we recalibrate all of the mass-ratio independent coefficients of the factorized waveforms that are used in the effective-one-body( EOB) models. Due to these new coefficients with great efficiency( about 1 400 times more efficient than numerically solving the Teukolsky equations with the same computing environment),the precision of waveforms is improved enormously and is more accurate than other existing calibration models by at least one order in magnitude. For this reason,it meets the requirements of the space-based gravitational wave detection mission for the accuracy of EMRI waveform for uninclined,quasi-circular orbits. By investigating the dephasing value with our model,the spin of compact objects and the mass-ratio of the inspiralling system cannot be omitted in the waveform calculations. We believe our model will play an important role in the waveform-template construction of space-based GW detectors.
引文
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[27]PAN Y,BUONANNO A,FUJITA R,et al..Post-Newtonian factorized multipolar waveforms for spinning,nonprecessing black-hole binaries[J].Phys.Rev.,2011,83(6):064003.
[28]DAMOUR T,IYER B R,NAGAR A.Improved resummation of post-newtonian multipolar waveforms from circularized compact binaries[J].Phys.Rev.,2009,79(6):064004.
[29]DAMOUR T,NAGAR A.Faithful effective-one-body waveforms of small-mass-ratio coalescing black hole binaries[J].Phys.Rev.,2007,76(6):064028.
[30]TARACCHINI A,PAN Y,BUONANNO A,et al..Prototype effective-one-body model for nonprecessing spinning inspiralmerger-ringdown waveforms[J].Phys.Rev.,2012,86(2):024011.
[31]BABAK S,TARACCHINI A,BUONANNO A.Validating the effective-one-body model of spinning,precessing binary black holes against numerical relativity[J].Phys.Rev.,2017,95(2):024010.
[32]JARANOWSKI P,KRLAK A.Gravitational-wave data analysis.formalism and sample applications:the gaussian case[J].Living Reviews in Relativity,2005,8:3.
[33]MINO Y,SASAKI M,SHIBAT A M,et al..Chapter 1.Black Hole Perturbation[M].Prog.Theor.Phys.,1997,128:1-121.
[34]HAN W B.Fast evolution and waveform generator for extreme-mass-ratio inspirals in equatorial-circular orbits[J].Class.Quantum Grav.,2016,33(6):065009.
[35]HAN W B.Gravitational radiation from a spinning compact object around a supermassive Kerr black hole in circular orbit[J].Phys.Rev.,2010,82(8):084013.
[36]HAN W B,CAO Z J.Constructing effective one-body dynamics with numerical energy flux for intermediate-mass-ratio inspirals[J].Phys.Rev.,2011,84(4):044014.
[37]HAN W B.Gravitational waves from extreme-mass-ratio inspirals in equatorially eccentric orbits[J].Internation Journal of Madern Physics D,2014,23(7):1450064.
[2]OLTEAN M,SOPUERTA C F,SPALLICCI A D A M.A frequency-domain implementation of the particle-without-particle approach to EMRIs[J].J.Phys.:Conf.Ser.,2017,840:012056.
[3]KHAN F M,BERCZIK P,JUST A.Gravitational wave driven mergers and coalescence time of supermassive black holes[J].Astronomy&Astrophysics,2018,A71:615.
[4]GUO Z K,CAI R G,ZHANG Y ZH,et al..Taiji program:gravitational-wave sources[R].ar Xiv:2018,1807:09495.
[5]LUO J,CHEN L SH,DUAN H Z,et al..Tian Qin:a space-borne gravitational wave detector[J].Class.Quantum Grav.,2016,33(3):035010.
[6]FINN L S,THORNE K S.Gravitational waves from a compact star in a circular,inspiral orbit,in the equatorial plane of a massive,spinning black hole,as observed by LISA[J].Phys.Rev.,2000,62:124021.
[7]CUTLER C,THORNE K S.Proceedings of general relativity and gravitation XVI[C].BISHPO N T,Singapore,World Scientific,2002.
[8]AMARO-SEOANE P,GAIR J R,FREITAG M,et al..Astrophysics,detection and science applications of intermediate-and extreme mass-ratio inspirals[J].Class.Quantum Grav.,2007,24:R113-R169.
[9]GAIR J R,BARACK L,CREIGHTON T,et al..Event rate estimates for LISA extreme mass ratio capture sources[J].Class.Quantum Grav.,2004,21(20):S1595-S1606.
[10]HOPMAN C,ALEXANDER T.The effect of mass segregation on gravitational wave sources near massive black holes[J].Astrophys.J.Letters,2006,645(2):L133-L136.
[11]BARACK L,CARDOSO V,NISSANKE S,et al..Black holes,gravitational waves and fundamental physics:a roadmap[R].ar Xiv:2018,1806:05195.
[12]REGGE T,WHEELER J A.Stability of a schwarzschild singularity[J].Phys.Rev.,1957,108(4):1063-1069.
[13]TEUKOLSKY S A.Perturbations of a rotating black hole.I.fundamental equations for gravitational,electromagnetic,and neutrino-field perturbations[J].Astrophy.J.,1973,185:635-647.
[14]TEUKOLSKY S A,PRESS W H.Perturbations of a rotating black hole.III-Interaction of the hole with gravitational and electromagnetic radiation[J].Astrophy.J.,1974,193:443-461.
[15]GAIR J R,GLAMPEDAKIS K.Improved approximate inspirals of test bodies into Kerr black holes[J].Phys.Rev.,2006,73(6):064037.
[16]BABAK S,FANG H,GAIR J R,et al..“Kludge”gravitational waveforms for a test-body orbiting a Kerr black hole[J].Phys.Rev D,2007,75(2):024005.
[17]BIERI L,YUNES N,GARFINKLE D.Gravitational waves and their mathematics[J].AMS Notices,2017,64(7):693-708.
[18]GLAMPEDAKIS K,HUGHES S A,KENNEFICK D.Approximating the inspiral of test bodies into Kerr black holes[J].Phys.Rev.D,2002,66(6):064005.
[19]TARACCHINI A,BUONANNO A,PAN Y,et al..Effective-one-body model for black-hole binaries with generic mass ratios and spins[J].Phys.Rev.,2014,89(6):061502.
[20]PüRRER M.Frequency domain reduced order model of aligned-spin effective-one-body waveforms with generic mass ratios and spins[J].Phys.Rev.,2016,93(6):064041.
[21]ABBOTT B P,ABBOTT R,ABBOTT T D,et al..Binary black hole mergers in the first advanced LIGO observing run[J].Phys.Rev X,2016,6(4):041015.
[22]YUNES N,BUONANNO A,HUGHES S A,et al..Modeling extreme mass ratio inspirals within the effective-one-body approach[J].Phys.Rev.Lett.,2010,104(9):091102.
[23]YUNES N,BUONANNO A,HUGHES S A,et al..Extreme mass-ratio inspirals in the effective-one-body approach:Quasicircular,equatorial orbits around a spinning black hole[J].Phys.Rev.,2013,83(10):109904.
[24]CUTLER C,FINN L S,POISSON E,et al..Gravitational radiation from a particle in circular orbit around a black hole.II.numerical results for the nonrotating case[J].Phys.Rev.,1993,47(3):1511-1518.
[25]POISSON E.Gravitational radiation from a particle in circular orbit around a black hole.VI.accuracy of the post-Newtonian expansion[J].Phys.Rev.,1995,52(10):5719-5723.
[26]DAMOUR T,IYER B R,SATHYAPRAKASH B S.Improved filters for gravitational waves from inspiralling compact binaries[J].Phys.Rev.,1998,57(2):885-907.
[27]PAN Y,BUONANNO A,FUJITA R,et al..Post-Newtonian factorized multipolar waveforms for spinning,nonprecessing black-hole binaries[J].Phys.Rev.,2011,83(6):064003.
[28]DAMOUR T,IYER B R,NAGAR A.Improved resummation of post-newtonian multipolar waveforms from circularized compact binaries[J].Phys.Rev.,2009,79(6):064004.
[29]DAMOUR T,NAGAR A.Faithful effective-one-body waveforms of small-mass-ratio coalescing black hole binaries[J].Phys.Rev.,2007,76(6):064028.
[30]TARACCHINI A,PAN Y,BUONANNO A,et al..Prototype effective-one-body model for nonprecessing spinning inspiralmerger-ringdown waveforms[J].Phys.Rev.,2012,86(2):024011.
[31]BABAK S,TARACCHINI A,BUONANNO A.Validating the effective-one-body model of spinning,precessing binary black holes against numerical relativity[J].Phys.Rev.,2017,95(2):024010.
[32]JARANOWSKI P,KRLAK A.Gravitational-wave data analysis.formalism and sample applications:the gaussian case[J].Living Reviews in Relativity,2005,8:3.
[33]MINO Y,SASAKI M,SHIBAT A M,et al..Chapter 1.Black Hole Perturbation[M].Prog.Theor.Phys.,1997,128:1-121.
[34]HAN W B.Fast evolution and waveform generator for extreme-mass-ratio inspirals in equatorial-circular orbits[J].Class.Quantum Grav.,2016,33(6):065009.
[35]HAN W B.Gravitational radiation from a spinning compact object around a supermassive Kerr black hole in circular orbit[J].Phys.Rev.,2010,82(8):084013.
[36]HAN W B,CAO Z J.Constructing effective one-body dynamics with numerical energy flux for intermediate-mass-ratio inspirals[J].Phys.Rev.,2011,84(4):044014.
[37]HAN W B.Gravitational waves from extreme-mass-ratio inspirals in equatorially eccentric orbits[J].Internation Journal of Madern Physics D,2014,23(7):1450064.