基于双中子星引力波标准汽笛法测量的哈勃参量对于宇宙学参数的限制能力的预言
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摘要
展示了一种新的测量哈勃参数(H(z))的方法的应用,并用定义品质因子的方式对其所得H(z)进行了评估.这种测量H(z)的方法基于对双中子星系统的引力波汽笛法的分析,其中利用了光度距离(dL)的各向异性.引力波的成功探测预示着引力波标准汽笛法潜在的可能性.在此之前对其相应效果进行预言和研究是十分必要的.把这种方法应用在几个比较主流的引力波探测项目上,并进行Fisher Matrix的计算,包括advanced LIGO(aLIGO)、Einstein telescope(ET)、DECIGO等.结果显示,aLIGO和ET测得的H(z)精度都比较差,而DECIGO测得的H(z)显示出良好的精度.利用DECOIGO得到的H(z)的相对误差信息,对H(z)进行模拟,然后用贝叶斯定理对宇宙学参量进行预言,最后利用画contour图和计算品质因子(FoM)方法评估出其限制宇宙学参量的能力.对于DECIGO 3a观测的引力波标准汽笛法,其相应H(z)数据的品质因子为170.82.如果进行10a期的观测,其相应H (z)数据的品质因子更是高达569.42.显示出引力波标准汽笛法的极大前景和潜力.
In this paper,we present a new method measuring Hubble parameter(H(z)),making use of the anisotropy of luminosity distance(dL),based on analysis of gravitational wave(GW)standard sirens of neutron star(NS)binary system.The method has never been put into practice due to inability to detect GW and corresponding electromagnetic counterpart.Last year the LIGO team detected GW of a binary neutron star system,and corresponding electromagnetic counterpart.This success announced potential possibility of GW standard sirens.Before actual detection,it is meaningful to do some investigation.We apply this new method to several GW detecting projects,including Advanced LIGO(aLIGO),Einstein Telescope(ET),DECIGO,and evaluate constraint ability on cosmological parameters of their H(z).We mainly use Fisher Matrix and Bayes theorem to do the calculation and analysis.We plot‘contour figure'of mock data and define‘Figure of Merit'(FoM)to evaluate constraint ability.It turns out that H(z)by aLIGO and ET is of poor accuracy,while H(z)by DECIGO shows good accuracy.We simulate H(z)data by python code at every 0.1 redshift span using error information of H(z)by DECIGO,and put mock data into forecasting of cosmological parameters.Compared with 38 actual observed H(z)data(OHD),mock data show a higher value of Figure of Merit(FoM,reciprocal of area enclosed by 2σconfidence region).For a 3-year-observation by standard sirens of DECIGO,FoM value is as high as 170.82.If a 10-year-observation is launched,FoM could reach 569.42.For comparison,FoM of 38 actual observed H(z)data(OHD)is 9.3.We also investigate undulant universe.These improvements indicate that the new method has great potential in further cosmological constraints.
In this paper,we present a new method measuring Hubble parameter(H(z)),making use of the anisotropy of luminosity distance(dL),based on analysis of gravitational wave(GW)standard sirens of neutron star(NS)binary system.The method has never been put into practice due to inability to detect GW and corresponding electromagnetic counterpart.Last year the LIGO team detected GW of a binary neutron star system,and corresponding electromagnetic counterpart.This success announced potential possibility of GW standard sirens.Before actual detection,it is meaningful to do some investigation.We apply this new method to several GW detecting projects,including Advanced LIGO(aLIGO),Einstein Telescope(ET),DECIGO,and evaluate constraint ability on cosmological parameters of their H(z).We mainly use Fisher Matrix and Bayes theorem to do the calculation and analysis.We plot‘contour figure'of mock data and define‘Figure of Merit'(FoM)to evaluate constraint ability.It turns out that H(z)by aLIGO and ET is of poor accuracy,while H(z)by DECIGO shows good accuracy.We simulate H(z)data by python code at every 0.1 redshift span using error information of H(z)by DECIGO,and put mock data into forecasting of cosmological parameters.Compared with 38 actual observed H(z)data(OHD),mock data show a higher value of Figure of Merit(FoM,reciprocal of area enclosed by 2σconfidence region).For a 3-year-observation by standard sirens of DECIGO,FoM value is as high as 170.82.If a 10-year-observation is launched,FoM could reach 569.42.For comparison,FoM of 38 actual observed H(z)data(OHD)is 9.3.We also investigate undulant universe.These improvements indicate that the new method has great potential in further cosmological constraints.
引文
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[8]NISHIZAWA A,TARUYA A,SAITO S.Tracing the redshift evolution of Hubble parameter with gravitationalwave standard sirens[J].Physical Review D,2011,83(8):084045
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[14]GORDON C,LAND K,SLOSAR A.Cosmological constraints from type ia supernovae peculiar velocity measurements[J].Physical Review Letters,2007,99(8):081301
[15]CUTLER C,HARMS J.Big bang observer and the neutron-star-binary subtraction problem[J].Physical Review D,2006,73(4):042001
[16]HILBERT S,GAIR J R,KING L J.Reducing distance errors for standard candles and standard sirens with weak-lensing shear and flexion maps[J].Monthly Notices of the Royal Astronomical Society,2011,412:1023
[17]SHAPIRO C,BACON D J,HENDRY M,et al.Delensing gravitational wave standard sirens with shear and flexion maps[J].Monthly Notices of the Royal Astronomical Society,2010,404:858
[18]YUAN S,ZHANG T J.Breaking through the high redshift bottleneck of observational hubble parameter data:the sandage-loeb signal scheme[J].Journal of Cosmology and Astroparticle Physics,2015,2:25
[19]ALBRECHT A,BERNSTEIN G,CAHN R,et al.Report of the dark energy task force[J].Office of Scientific Technical Information Technical Reports,2006,31(3):540
[20]RIESS A G,MACRI L,CASERTANO S,et al.Aredetermination of the Hubble constant with the Hubble space telescope from a differential distance ladder[J].The Astrophysical Journal,2009,699:539
[21]METZGER B D,BERGER E.What is the most promising electromagnetic counterpart of a neutron star binary merger?[J].The Astrophysical Journal,2012,746:48
[22]CANNON K,CARIOU R,CHAPMAN A.Toward early-warning detection of gravitational waves from compact binary coalescence[J].The Astrophysical Journal,2012,748:136
[23]FAIRHURST S.Source localization with an advanced gravitational wave detector network[J].Classical and Quantum Gravity,2011,28(10):105021
[24]COWPERTHWAITE P S,BERGER E.A comprehensive study of detectability and contamination in deep rapid optical searches for gravitational wave counterparts[J].The Astrophysical Journal,2015,814:25
[25]SINGER L P,PRICE L R,FARR B,et al.The first two years of electromagnetic follow-up with advanced ligo and virgo[J].The Astrophysical Journal,2014,795:105
[26]CHU Q,HOWELL E J,ROWLINSON A,et al.Capturing the electromagnetic counterparts of binary neutron star mergers through low-latency gravitational wave triggers[J].Monthly Notices of the Royal Astronomical Society,2016,459:121
[27]LAZIO J W,KIMBALL A,BARGER A J,et al.Radio astronomy in LSST era[J].Publications of the Astronomical Society of the Pacific,2014,126:196
[28]SCHUTZ B F.Networks of gravitational wave detectors and three figures of merit[J].Classical and Quantum Gravity,2011,28(12):125023
[2]MA C,ZHANG T J.Power of observational Hubble parameter data:a figure of merit exploration[J].The Astrophysical Journal,2011,730:74
[3]STERN D,JIMENEZ R,VERDE L,et al.Cosmic chronometers:constraining the equation of state of dark energy-I:H(z)measurements[J].Journal of Cosmology and Astroparticle Physics,2010,2:008
[4]GAZTANAGA E,CABRE A,HUI L.Clustering of luminous red galaxies-IV:baryon acoustic peak in the line-of-sight direction and a direct measurement of H(z)[J].Monthly Notices of the Royal Astronomical Society,2009,399:1663
[5]SCHUTZ B F.Determining the Hubble constant from gravitational wave observations[J].Nature,1986,323:310
[6]ABBOTT B P,ABBOTT R,ABBOTT T D,et al.Observation of gravitational waves from a binary black hole merger[J].Physical Review Letters,2016,116(6):061102
[7]BONVIN C,DURRER R,KUNZ M.Dipole of the luminosity distance:a direct measure of H(z)[J].Physical Review Letters,2006,96(19):191302
[8]NISHIZAWA A,TARUYA A,SAITO S.Tracing the redshift evolution of Hubble parameter with gravitationalwave standard sirens[J].Physical Review D,2011,83(8):084045
[9]SASAKI M.The magnitude-redshift relation in a perturbed Friedmann universe[J].Monthly Notices of the Royal Astronomical Society,1987,228:653
[10]KAWAMURA S,NAKAMURA T,ANDO M,et al.The Japanese space gravitational wave antenna-mdash DECIGO[J].Classical and Quantum Gravity,2006,23:S125
[11]KEPPEL D,AJITH P.Constraining the mass of the graviton using coalescing black-hole binaries[J].Physical Review D,2010,82(12):122001
[12]CUTLER C,THORNE K S.An overview of gravitational-wave sources[J].Proceedings of General Relativity Gravitation XVI,2002,6(12):1761
[13]HIRATA C M,HOLZ D E,CUTLEr C.Reducing the weak lensing noise for the gravitational wave Hubble diagram using the non-Gaussianity of the magnification distribution[J].Physical Review D,2010,81(12):124046
[14]GORDON C,LAND K,SLOSAR A.Cosmological constraints from type ia supernovae peculiar velocity measurements[J].Physical Review Letters,2007,99(8):081301
[15]CUTLER C,HARMS J.Big bang observer and the neutron-star-binary subtraction problem[J].Physical Review D,2006,73(4):042001
[16]HILBERT S,GAIR J R,KING L J.Reducing distance errors for standard candles and standard sirens with weak-lensing shear and flexion maps[J].Monthly Notices of the Royal Astronomical Society,2011,412:1023
[17]SHAPIRO C,BACON D J,HENDRY M,et al.Delensing gravitational wave standard sirens with shear and flexion maps[J].Monthly Notices of the Royal Astronomical Society,2010,404:858
[18]YUAN S,ZHANG T J.Breaking through the high redshift bottleneck of observational hubble parameter data:the sandage-loeb signal scheme[J].Journal of Cosmology and Astroparticle Physics,2015,2:25
[19]ALBRECHT A,BERNSTEIN G,CAHN R,et al.Report of the dark energy task force[J].Office of Scientific Technical Information Technical Reports,2006,31(3):540
[20]RIESS A G,MACRI L,CASERTANO S,et al.Aredetermination of the Hubble constant with the Hubble space telescope from a differential distance ladder[J].The Astrophysical Journal,2009,699:539
[21]METZGER B D,BERGER E.What is the most promising electromagnetic counterpart of a neutron star binary merger?[J].The Astrophysical Journal,2012,746:48
[22]CANNON K,CARIOU R,CHAPMAN A.Toward early-warning detection of gravitational waves from compact binary coalescence[J].The Astrophysical Journal,2012,748:136
[23]FAIRHURST S.Source localization with an advanced gravitational wave detector network[J].Classical and Quantum Gravity,2011,28(10):105021
[24]COWPERTHWAITE P S,BERGER E.A comprehensive study of detectability and contamination in deep rapid optical searches for gravitational wave counterparts[J].The Astrophysical Journal,2015,814:25
[25]SINGER L P,PRICE L R,FARR B,et al.The first two years of electromagnetic follow-up with advanced ligo and virgo[J].The Astrophysical Journal,2014,795:105
[26]CHU Q,HOWELL E J,ROWLINSON A,et al.Capturing the electromagnetic counterparts of binary neutron star mergers through low-latency gravitational wave triggers[J].Monthly Notices of the Royal Astronomical Society,2016,459:121
[27]LAZIO J W,KIMBALL A,BARGER A J,et al.Radio astronomy in LSST era[J].Publications of the Astronomical Society of the Pacific,2014,126:196
[28]SCHUTZ B F.Networks of gravitational wave detectors and three figures of merit[J].Classical and Quantum Gravity,2011,28(12):125023