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研究生： 黃祥瑜
Huang, Hsiang-Yu
論文名稱： 藉由重力場效校準器改進用於校正的不準度之誤差計算方法
Improvement of error estimation method for calibration uncertainty with gravity field calibrator
指導教授： 張嘉泓
Chang, Chia-Hung
王子敬
Wong, Tsz-King
口試委員： 王子敬
Wong, Tsz-King
張嘉泓
Chang, Chia-Hung
井上優貴
Inoue, Yuki
口試日期： 2021/06/22
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 138
英文關鍵詞： KAGRA, calibration, gravity field calibrator, photon calibrator, maximum likelihood, higher order harmonics, demodulation, gravitational wave
DOI URL： http://doi.org/10.6345/NTNU202101277
論文種類： 學術論文
相關次數： 點閱：123  下載：4 
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    • Calibration and detector characterization play important role in gravitational waves signal reconstruction from interferometer response. KAGRA, a newly gravitational wave detector in Japan, joined the third observation(O3), and also have joint observation with GEO600, called O3GK. In calibration, we use photon calibrator(PCAL) in KAGRA during the observation. PCAL push mirror by radiation pressure to characterize interferometer response. We plan to use gravity field calibrator(GCAL), a dynamic gravitational field generator in our calibration in near future. GCAL actuate the interferometer mirror by rotating multipole masses.
    In this thesis, we proposed maximum likelihood method to crosscheck the error estimation independently. We characterize the operation of PCAL used in KAGRA in O3GK by signal demodulation to verify the stability of PCAL. For GCAL, we estimate the systematic error of two component, radius and mass in GCAL geometry by Monte Carlo simulation. In the end of this thesis, we proposed a new method with combination of above two calibration instruments. By estimating of the ratio of higher order harmonics in GCAL to PCAL calibration signal in specific frequency, we can reduce the systematic error of GCAL and error of calibration measurement. We also derive new formula for estimation of time-dependent correction factor(TDCFs) with GCAL for future application. However, the KAGRA Collaboration does not yet have consensus views on the results presented in this thesis.

    1 Introduction 1 2 Gravitational Wave Science 3 2.1 Gravitational wave theory 3 2.1.1 Einstein Field Equation 3 2.1.1.1 Christoffel Symbol and Ricci Tensor 4 2.1.1.2 Trace-reversed of hμν 6 2.1.1.3 Gauge transformation 6 2.1.1.4 Lorentz gauge 7 2.1.2 Gravitational waves 7 2.2 Source of Gravitational waves 9 2.2.1 Compact Binary Coalescence(CBC) 9 2.2.1.1 Binary black hole merger 11 2.2.1.2 Binary neutron star merger 11 2.2.1.3 Neutron star-black hole merger 14 2.2.2 Continuous Waves(CW) 14 2.2.3 Burst 14 2.2.4 Stochastic gravitational waves 14 2.3 Event catalog and parameter estimation 15 2.4 Unsolved Problem 16 2.4.1 Mass Gap between NS and BH 16 2.4.2 Hubble tension problem 17 2.4.3 Test of Gravity 18 2.4.4 Second Peak of BNS 19 3 Gravitational Waves Detector 20 3.1 Gravitational Wave Interferometer 20 3.1.1 Michelson Interferometer 20 3.1.2 Fabry-Perot Michelson Interferometer 22 3.2 Kamioka Gravitational Waves Detector 23 3.2.1 Overview of KAGRA 23 3.2.2 Design and Current sensitivity 24 3.2.3 Global observation network 25 3.3 Other GW Detectors in the worldwide 26 3.3.1 LIGO 26 3.3.2 Virgo 28 3.3.3 GEO600 28 3.4 Future GW project 29 3.4.1 LIGO-India 29 3.4.2 Einstein Telescope 29 3.4.3 Cosmic Explorer 31 3.4.4 LISA 31 3.4.5 DECIGO 33 4 Calibration 35 4.1 Overview of Calibration 35 4.2 Calibration Instruments 36 4.2.1 Photon Calibrator 37 4.2.2 Gravity field Calibrator 38 4.3 DARM Model 38 4.4 Calibration measurement 39 4.5 Reconstruction pipeline 40 4.5.1 C00 40 4.5.2 C10 40 4.5.3 C20 41 4.6 Motivation of the thesis 41 5 Error estimation of transfer functions in sensing function 42 5.1 Error estimation by maximum likelihood method 42 5.2 Time-dependent factor analysis 64 5.3 Conclusion 68 6 PCAL signal demodulation 69 6.1 Principle 69 6.2 Data quality state vector 70 6.3 Result 71 6.4 Conclusion 83 7 Uncertainty estimation of GCAL geometry 85 7.1 Principle 85 7.2 Setup and Input parameter 86 7.3 Result 86 7.4 Conclusion 91 8 Development of GCAL Analysis 92 8.1 Higher order harmonics method 92 8.1.1 Principle 92 8.1.2 The case align the axis of the test mass 93 8.1.3 Input parameters 95 8.1.4 Result 96 8.1.5 The case off-axis of the test mass 99 8.1.6 Input parameters 102 8.1.7 Result 103 8.2 Time-dependent factor with GCAL 106 8.3 Conclusion 107 9 Discussion 108 10 Conclusion 112 11 Future work 113 11.1 Improvement of Higher order harmonics method 113 11.2 Astronomical Calibration 113 Bibliography 114 Appendix 126

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