臺灣博碩士論文加值系統

這篇論文包含兩個部分：利用MAXIPOL及WMAP觀測資料估計宇宙微波背景(CMB)的頻譜，以及透過SZ效應來研究星系團的性質。在第一個部分，我們結合MAXIPOL的CMB偏振資料以及WMAP的CMB溫度資料來估算CMB頻譜，過程中使用馬可夫鏈蒙地卡羅(MCMC)法進行最大概率分析，並使用大量的模擬資料來驗證此自建的分析程式。我們也討論了詳細的概率分布函數計算以及重要的數值相關問題。我們的分析結果和已知的文獻結果相符合，而觀測資料的品質改善將是改進此處結果的關鍵因素。第二個部分我們介紹AMiBA實驗計畫，並進一步探討多頻率分析對星系團性質估算的改善。我們首先探討AMiBA計畫的幾個不同面向，包括觀測方法、資料處理、以及資料品質的控制。接著將AMiBA及其它計畫的星系團SZ效應觀測資料結合，以進行多頻率的分析，我們的結果為星系團A2163及A2390的中心康普頓參數及運動速率提供了較準確的估計。我們也探討了本論文成果的未來前景。

This dissertation contains two parts : estimation of Cosmic Microwave Background (CMB) power spectrum with
data from Maxipol and WMAP experiments, and investigation of cluster property through
the Sunyaev-Zel’dovich effect. In the first part, we cross correlate the CMB polarization maps from
Maxipol and the temperature map from WMAP to estimate the CMB power spectrum,
using Markov Chain Monte Carlo (MCMC) method to deliver the maximum-likelihood analysis.
Simulations are heavily invoked to justify our analysis pipeline. Detailed calculation of likelihood function
and some numerical issues are discussed. We show that our results are consistent with
previous results, and the key for improvement is the data quality.
In part II we describe the decade project AMiBA, with particular address on how a multi-frequency analysis
can provide better constraint on the properties of galaxy clusters.
We first describe the project in several aspects, including the observation strategy, data reduction, and data quality control.
Data of the Sunyaev-Zel’dovich effect from AMiBA and several other experiments are then combined
to deliver the multi-frequency analysis, yielding better estimation for the central Compton parameter and peculiar velocity
for clusters A2163 and A2390.
The future of the work presented here is also addressed.

Acknowledgement I
Contents II
Figures V
Tables IX
abstract X
I CMB power spectrum measured by MAXIPOL
and WMAP 1
1 Introduction 2
1.1 Cosmology with inflation and CMB . . . . . . . . . . . . . . . 2
1.2 MAXIPOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 WMAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 CMB angular power spectrum 4
2.1 CMB temperature and polarization . . . . . . . . . . . . . . . 4
2.2 CMB Likelihood function . . . . . . . . . . . . . . . . . . . . . 6
2.3 Covariance matrix . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Full-sky formula . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Flat-sky approximation . . . . . . . . . . . . . . . . . . 11

3 Bayesian approach 13
3.1 Theoretical basics . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Determination of credible region . . . . . . . . . . . . . . . . . 14
4 Likelihood function analysis 16
4.1 Markov Chain Monte Carlo (MCMC) . . . . . . . . . . . . . . 16
4.1.1 Metropolis-Hastings algorithm . . . . . . . . . . . . . . 17
4.1.2 Practical implementation of Markov chain . . . . . . . 17
4.1.3 convergence test . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Alternative analysis methods . . . . . . . . . . . . . . . . . . . 18
4.2.1 Frequentist analysis . . . . . . . . . . . . . . . . . . . . 19
4.2.2 Newton-Raphson technique and grid search . . . . . . 19
5 Test of Likelihood analysis 20
5.1 Test of Covariance matrix . . . . . . . . . . . . . . . . . . . . 20
5.2 Simulation of Maps . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.1 Flat-Sky approximation . . . . . . . . . . . . . . . . . 21
5.2.2 Full-Sky Maps . . . . . . . . . . . . . . . . . . . . . . . 26
6 Results and conclusion 38
6.1 Results from Maxipol, WMAP maps . . . . . . . . . . . . . . 38
6.2 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . 41

II Sunyaev-Zeldovich effect with AMiBA experiment
47
7 Introduction 48
8 AMiBA experiment 50
8.1 Configuration and resolution . . . . . . . . . . . . . . . . . . . 50
8.2 Observing strategy . . . . . . . . . . . . . . . . . . . . . . . . 50
8.3 calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
III
8.4 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 51
8.5 SZ targets : A2163, A2390 . . . . . . . . . . . . . . . . . . . . 52
9 On-site observations and Data analysis 54
9.1 Calibration for observation . . . . . . . . . . . . . . . . . . . . 54
9.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10 Related SZ experiments 58
10.1 SuZIE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
10.2 APEX-SZ and LABOCA . . . . . . . . . . . . . . . . . . . . . 58
10.3 BIMA/OVRO . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11 SZ spectrum modelling 60
12 Possible contaminations 63
12.1 Point sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
12.2 Galactic emission and CMB anisotropy . . . . . . . . . . . . . 63
13 Multi-frequency Analysis 65
13.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
13.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
13.3 Conclusion and Future work . . . . . . . . . . . . . . . . . . . 67
A 71
A.1 Relativistic correction of Sunyaev-Zel’dolvich effect . . . . . . 71

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