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研究生:譚雪瑩
研究生(外文):Sut-Ieng Tam
論文名稱:利用弱重力透鏡效應探測星系團暗物質暈的橢圓率
論文名稱(外文):Testing LCDM Predictions for the Dark-Matter Halo Asphericity Using Cluster Weak Lensing
指導教授:闕志鴻梅津敬一
指導教授(外文):Tzi-Hong ChiuehKeiichi Umetsu
口試委員:林彥廷
口試委員(外文):Yen-Ting Lin
口試日期:2016-07-22
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理學研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:88
中文關鍵詞:宇宙學星系團弱重力透鏡
外文關鍵詞:cosmologygalaxy clusterweak gravitataional lensing
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Cosmological N-body simulations of Λ cold dark matter (ΛCDM) predicted the shape of DM halos to be triaxial, reflecting the collisionless nature of DM, and to be elongated in the preferential infall direction of materials. The predicted halo ellipticity is about 0.4(Jing & Suto (2002) [16]). Here we test this well-defined pre- dictions of the standard ΛCDM paradigm using wide-field weak shear lensing data of Umetsu et al.(2016) [41] obtained for a sample of 16 galaxy clusters targeted in the CLASH survey. We examine the mean halo ellipticity (projected halo aspheric- ity) in our cluster sample by measuring the quadrupole weak-lensing signal for each cluster, following the method of Clampitt & Jain(2015) [7]. First we assume the DM halos align with the BCGs. Our best-fit value for the ellipticity of an ensemble of CLASH clusters in this measurement is 0.26±0.07 corresponding to axis-ratio of 0.73±0.07. We also use the position angle of X-ray gas, assuming the dark matter halos align with the X-ray gas halo. In this measurement, we get the mean ellip- ticity is 0.29 ± 0.09 corresponding to axis-ratio of 0.71±0.10. The different between there two measurement is not significant but this give us a hint that the DM halo may be more likely align with X-ray gas. We will also discuss the estimates of the misalignment between central galaxies and halos from simulations and apply this correction to our result.

Contents
Abstract i
List of Figures vii
List of Tables xiv
Chapter 1 Introduction 1
Chapter 2 Cosmological Background 5
2.1 FRW Model................................ 5
2.2 Friedmann’s Equation .......................... 6
2.3 Cosmological Distance .......................... 7
Chapter 3 Weak Gravitational Lensing 10
3.1 Introduction................................ 10
3.2 GravitationalLensingTheory ...................... 11
3.2.1 Lens Equation........................... 12
3.2.2 Lensing Jacobian Matrix..................... 15
3.2.3 Lensing Covergence and Shear.................. 17
3.2.4 Magnification Effect ....................... 18
3.3 Weak Gravitational Lensing ....................... 18
3.3.1 Weak Lensing Distortion Observables . . . . . . . . . . . . . . 19
3.3.2 Mass Reconstruction ....................... 20
3.4 Quadrupole Weak Lensing Signal .................... 21
3.4.1 Elliptical Clusters Lensing Effect ................ 21
3.4.2 Using Multipole Expansion.................... 22
3.5 Elliptical NFW Model .......................... 27
3.5.1 Spherical NFW Model ...................... 27
3.5.2 Elliptical NFW Model ...................... 29
3.5.3 Notation.............................. 31
Chapter 4 Methodology 32
4.1 Quadrupole Signal Measurement..................... 32
4.1.1 Measurement with Cartesian Components . . . . . . . . . . . 33
4.1.2 Measurement with Tangential Components . . . . . . . . . . . 34
4.2 Stacked Measurement........................... 34
4.3 Error Estimation ............................. 35
4.4 Simulation Test.............................. 37
4.5 MCMC Fitting .............................. 38
4.6 Systematic Tests ............................. 40
4.6.1 Measurement Based on eNFWmodel.............. 40
4.6.2 Comparison Between Two Models................ 41
Chapter 5 Applications to the Superlens Cluster A1689 45
5.1 ClusterA1689............................... 45
5.2 Results and Constraints on Halo Ellipticity. . . . . . . . . . . . . . . 46
5.3 Discussion................................. 51
Chapter 6 Applications to the CLASH Lensing Data 52
6.1 Data:CLASH Samples.......................... 53
6.2 Sample Selection ............................. 54
6.3 Measurement with CLASH sample ................... 58
6.3.1 Measured Quadrupole Signal................... 58
6.3.2 Constraints on halo ellipticity .................. 61
6.4 Measurement with X-ray Position Angle ................ 66
Chapter 7 Discussion and Conclusion 72
7.1 Comparison Between Different Measurements . . . . . . . . . . . . . 72
7.2 Comparison Between Measurement with BCG and X-ray PA . . . . . 73
7.3 MisalignmentCorrection......................... 74
7.4 Comparison with Earlier Studies and ΛCDM Predicition . . . . . . . 78
7.5 Conclusion................................. 80
Acknowledgments 82
Bibliography 83


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