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系統識別號 U0026-2001202010424300
論文名稱(中文) 重力波數據分析:偏心軌道緻密雙星系統的參數估算和波源定位
論文名稱(英文) Data Analysis of Gravitational Wave: Parameter Estimation and Source Localization of Eccentric Compact Binary Coalescence
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 108
學期 1
出版年 109
研究生(中文) 潘星伯
研究生(英文) Hsing-Po Pan
學號 L28011075
學位類別 博士
語文別 英文
論文頁數 69頁
口試委員 指導教授-游輝樟
口試委員-許祖斌
口試委員-楊緒濃
口試委員-曹慶堂
口試委員-林俊鈺
中文關鍵字 重力波分析  參數估算  波源定位  費雪訊息矩陣  探測器網路  緻密雙星併合系統  離心率 
英文關鍵字 Gravitational wave analysis  Parameter estimation  Source localization  Fisher Information Matrix  Detector network  Compact binary coalescence  Eccentricity 
學科別分類
中文摘要 在重力波天文學裡,重力波的參數估算和波源定位是相當重要的問題。當緻密雙星合併所產生的重力波進入第二世代和第三世代地面探測器的靈敏帶時,其軌道離心率將可能無法忽略。因此,針對波源的軌道離心率影響跟提高定位的精確度是相當有趣的議題。在本論文中,吾人以強化後圓形軌道模型來探討此效應。我們藉由費雪資訊矩陣方法,以計算波源定位和參數估算的精確度,並探討五種探測器網路的結果。

如同預期,當一個網路使用較多探測器,能使波源定位和參數估算的精確度有效提升。同時,在大質量(總質量約大於40倍太陽質量)雙星系統,增加模型的軌道離心率亦能明顯提升估算的精確度。然而,在小質量(總質量約小於40倍太陽質量)雙星系統,針對波源定位和慢參數的估算,軌道離心率則無法有效提升精確度。而在總質量更小(約小於5倍太陽質量)的雙星系統,模型的軌道離心率甚至會使波源定位的精確度變差。此現象主要來自於由軌道離心率造成的高階諧波模,其頻率是否在探測器更加靈敏的頻率帶上所致。在總質量為100倍太陽質量的雙黑洞系統,當初始軌道離心率從0增加到0.4時,其波源定位的精確度改善因子約為2。而在總質量為22倍太陽質量的雙黑洞系統和總質量為2.74倍太陽質量的雙中子星系統,則改善因子小於1.1,甚至在某些方向雙星系統,改善因子會小於1。
英文摘要 The problem of gravitational wave parameter estimation and source localization is crucial in gravitational-wave astronomy. Gravitational waves emitted by compact binary coalescences in the sensitivity band of second-generation and third-generation ground-based detectors could have non-negligible eccentricities.
Thus it is an interesting topic to study how the eccentricity of a binary source affects and improves the accuracy of its localization. In this thesis, we continue to investigate this effect with the enhanced postcircular waveform model. Using the Fisher information matrix method, we determine the accuracy of source localization and parameter estimation with five ground-based detector networks.

As expected, the accuracy of source localization and parameter estimation is improved considerably with more detectors in a network. We find that the accuracy also increases significantly by increasing the eccentricity for the large total mass (larger than about 40 solar masses) binaries with all five networks. For the small total mass (smaller than about 40 solar masses) binaries, this effect for the slow parameters and sky localization is negligible. For the smaller total mass (smaller than about 5 solar masses) binaries, the accuracy of localization could be even worse at some orientations with increasing eccentricity. This phenomenon comes mainly from how well the frequency of the higher harmonic modes induced by increasing eccentricity coincides with the sensitive bandwidth of the detectors. For the case of the black hole binary with total 100 solar masses, the improvement factor is about 2 in general when the initial eccentricity grows from 0 to 0.4. For the cases of the black hole binary with total 22 solar masses and the neutron star binary with total 2.74 solar masses, the improvement factor is less than 1.1, and it may be less than 1 at some orientations.
論文目次 Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Eccentric Waveform Model 4
2.1. Enhanced Post Circular (EPC) Model . . . . . . . . . . . . . . . . . . . . 4
2.2. EPC Model for Detector Network . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3. Methodology . . . . . . . . . . . . . . . . . . . . 18
3.1. Gravitational-Wave Detector Networks . . . . . . . . . . . . . . . . . . . . 18
3.2. Fisher Information Matrix (FIM) Formalism . . . . . . . . . . . . . . . . . 20
Chapter 4. Result and Discussion . . . . . . . . . . . . . . . . . . . . 22
4.1. Big BBH case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2. GW151226-like BBH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3. GW170817-like BNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Chapter 5. Conclusions . . . . . . . . . . . . . . . . . . . . 59
Bibliography . . . . . . . . . . . . . . . . . . . . 61
Appendix A. List of Coefficients $C_{+, imes}^{(ell)}$ and $S_{+, imes}^{(ell)}$ . . . . . . . . . . . . . . . . . . . . 67
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