Gravitational Wave Data Analysis Of Massive Black Hole Binaries For TianQin

The detection of the high-frequency gravitational wave（GW）from stellar-mass black hole binary coalescence GW150914 made by the ground-based observatory LIGO（Laser In-terferometer Gravitational-Wave Observatory）marking that GW has become a new method to study the universe.This event opens a new era of GW astronomy.The detection of GW in m Hz band needs to be carried out in space due to seismic noise and gravity gradient noise.There are abundant GW sources in the low-frequency band including Galactic White Dwarf Binaries,Stellar-mass Black Hole Binaries,Extreme Mass Ratio Inspirals,Massive Black Hole Binaries（MBHBs）and source in the universe that may not yet be known.However,the laser frequency noise will be 7-8 orders of magnitude higher than the amplitude of GW signal due to unequal arm length of space-based detectors.Time Delay Interferom-etry（TDI）that synthesizes virtual interferometers from time-delayed one-way frequency measurements has been proposed to suppress the laser frequency noise to the level that is comparable or below the secondary noises.The data processed using TDI is called scientific data.Tian Qin is a space mission proposed by China,aimed at detecting GW at low frequen-cies（0.1m Hz-1 Hz）.It is formed by three identical drag-free spacecraft in an equilateral triangular constellation orbiting around the Earth.MBHB is one of the most promising source for space-based detectors.Scientific data analysis of MBHBs can lay the foundation for future massive black holes GW astronomy.This thesis will focus on GW data analysis of MBHBs for Tian Qin.The second chapter calculates analytical expression of approximated orbit,detector response and sensitivity curve of Tian Qin.The guiding center of the constellation and the spacecraft trace nearly circular Keplerian orbit around the Sun and the Earth,respectively.The antenna pattern functions can be obtained by contract of detector tensor and polarization tensor.It allows us to simulate Tian Qin detector signal for any GW source which serves as the foundation for GW data analysis.The sensitivity curve of Tian Qin shows that scientific research can be enriched because it is more sensitive than LISA in higher frequency band.The third chapter illustrates the principle of TDI first.The sensitivity curves of different TDI combinations for static and moving constellations are obtained.We found that the first generation TDI can be applied to Tian Qin’s approximated orbit which requires the eccentricity of spacecraft orbit e₁<0.001.This requirement provides guidance for selection of highly stable orbit.On the other hand,Principal Component Analysis（PCA）combines eigenvectors that independent of laser frequency noise to cancel the laser frequency noise.We compare covariance matrix between static and moving constellations.We proved that PCA and the second generation TDI are equivalent.We completed the Tian Qin science data simulation and data analysis pipeline for MBHBs which is based on the F-Statistic method and the PSO algorithm.This part is included in the fourth chapter.The fifth chapter introduces the joint detection of MBHBs by LISA and Tian Qin.The results of data analysis showed that joint detection of space-based detectors can significantly improve the parameters estimation of MBHBs.For high signal-to-noise-ratio（SNR）case with LISA SNR of 277 and with Tian Qin SNR of 124,the sky localization uncertainty of joint detection is less than 1 deg²which is improved about3 orders of magnitude than LISA only.Tian Qin with SNR of 3.9 in joint detection can still improve the source localization by about 2 times than LISA only（with SNR of 37）with the localization uncertainty of 353 deg².This means that sources that cannot be detected by a single detector can also contribute to the source localization in joint detection.