直接求取宇宙背景輻射能量光譜

Abstract

大約在宇宙大霹靂爆炸後的40萬年, 電子和質子結合成中性的氫原子。由於光子很不容易和中性氫原子發生作用, 光子因此可以自由移動不受阻礙, 這樣原本黑暗的宇宙開使透明。這些可以自由移動的光子形成了我們現在所說的宇宙背景輻射。因此當我們詳細研究這些早期的宇宙光子時, 我們就越能瞭解我們宇宙早期的狀況。而宇宙背景輻射的能量光譜(CMB Power Spectrum) 正好可以提供我們一個很好的研究根據：其中包含可以了解了宇宙的組成和早期演化的歷史, 還有像是造成 背景輻射裡存在些微擾動和不均勻的成因也可以透過能量光譜來找到答案。能量光譜有三個比較明顯峰值, 這些峰值的所在位置和峰值的強度大小都隱含了宇宙演化過程的物理機制, 因此如何更精確的測量出這些峰值的大小和位置, 對於宇宙學家瞭解宇宙的早期演化格外重要。傳統上量測宇宙背景輻射能量光譜都必須先處理本銀河系所發出的輻射污染, 所用的方法通常是用模板去遮蓋背景輻射被銀河污染的部份,或是利用各不同譜段互相結合以降低輻射污染, 不過這樣的處理方式會破壞原本球諧分析的正交性,也會讓整個處理程序非常的複雜和冗長。因此我們提出令一種求取宇宙背景輻射能量光譜的簡單新方法, 他不需要處理複查的銀河輻射問題。在直接求取宇宙背景輻射能量光譜前, 首先, 我們介紹了小區塊近似法(flat-sky approximation) 和 cross power spectrum (XPS), 在小區塊近似法裡我們證實了他的精確性是可以靠的, 而 XPS 則有可以保留兩組不同資料裡的相關訊號但卻削減雜訊的功能. 有了這兩樣工具, 再搭配上傅立葉分析, 我們可以把 XPS 應用在點源上, 求取 WMAP DA 的窗函數。有了 WMAP DA窗函數求取成功的實例, 而由於WMAP的頻率全天球圖是由DA組合而成, 我們可以因此用同樣方法更進一步找出原本不存在的 WMAP 頻率譜段窗函數, 我們也是全球第一個找出頻率譜段窗函數的團隊。在求取宇宙背景輻射能量光譜前, 我們還必須先處理三個部份, 分別是銀河輻射的問題, 儀器雜訊還有求得 WMAP 頻率譜段窗函數。銀河輻射的問題我們透過選取天球上低變異的區塊來解決, 雜訊的部份則是再度透過 XPS的應用, 我們把 XPS 作用在 W和V 波段的全天球上同區塊, 因此可以保留CMB原本的訊號但卻可以削減雜訊。最後一步就是將原先求出的 WMAP 頻率窗函數和削減雜訊後求出的宇宙背景輻射的能量光譜做 deconvolution, 結果發現我們的方法可以清楚求出第一和第二個宇宙背景輻射能量光譜的峰值, 而第三個峰值也是可見的。

Roughly 400,000 years after the Big Bang, electrons and protons combined to form neutral hydrogen, an event usually known as recombination. At that time, cosmic microwave background photons interact very weakly with neutral hydrogen and therefore CMB photons started to move through the early universe, which makes our universe visible. Thus, by studying the detailed physical properties of the radiation, we can learn about conditions in the universe at very early times. The CMB angular power spectrum is a useful tool that makes it possible for us to study the composition and history of our early universe, as well as the processes that seeded the fluctuations. The physics behind the angular power spectrum manifest itself in the location and height of these acoustic peaks and hence its precise measurement is one of the crucial tasks in CMB studies. Traditionally estimating CMB angular power spectrum needs to use Galactic foreground templates or ILC method to avoid foreground emission, which would thus break the orthogonality in the spherical harmonic analysis and also makes the process complex. We thus propose another method without masking foreground contamination emission. First we introduce flat-sky approximation and cross power spectrum (XPS). For flat-sky approximation, we find its scaling relation precise and XPS has the ability to eliminate the uncorrelated signal while preserve the correlated one. Thus based on flat-sky approximation and XPS, we can estimate the window function of WMAP differential assemblies maps from bright point sources by calculating XPS of two square patches of sky where there is a bright point source in the center. We demonstrate that retrieving window function of WMAP Difference Assembly maps from bright extragalactic point sources is useful and we further apply it to extract the unknown window function of WMAP frequency band maps. We are also the first team to extract window functions of the WMAP frequency band maps. In order to reach CMB angular power spectrum, we need to deal with three parts independently, which are foreground contamination, noise and the window functions. The foreground contamination is mainly composed of synchrotron, free-free, and dust emission, which can be solved by choosing low-variance patches. The instrument noise can be eliminated by calculating the XPS from the same patches of the V and W band . It is then deconvolved by the window function of the V and W frequency band map. Our simple method can yields the CMB power spectrum a clear 2nd Doppler peak and the 3rd peak is visible. The first part of our thesis, 'Cross-Power Spectrum and Its Application on Window Functions in the WMAP Data', will be published in the Astrophysical Journal in August 20, 2011, V737 -2 and the second part, 'Direct measurement of the angular power spectrum of cosmic microwave background temperature anisotropies in the WMAP Data', is about to be submitted.