利用最大熵方法製作隨機重力波背景全天圖

隨著世界上第一個重力波的直接觀測證據出現，不僅驗證了廣義相對論對於重力波歷經百年的預測，更開啟了對於天文、宇宙學觀測來說一扇新的大門。在整個宇宙中因為有非常多不同的重力波來源，產生了重力波的隨機背景。隨機重力波背景可以透過收集來自早期宇宙或是本銀河系內所產生的重力波的方式構成，且有很多理論預測隨機重力波背景很有可能是異向性的。但是，目前的隨機重力波背景製圖過程雖然日趨成熟，但仍有些許問題仍處於研究階段。例如：最後的背景圖中會有負值的出現，相較於實際觀測仍須再做處理，而且在製圖過程中的本徵值的數量多寡，僅透過模擬的方式來給出一個相對數量，並沒有一個嚴謹的科學公式來解釋。在此我們想透過最大熵方法的特性來嘗試解決上述的問題，且在過去四十年餘，最大熵方法在天文觀測中的製圖過程被廣泛使用，並且由於熵的特性，在應對一些連續分佈的天體時有不錯的成效，最終提供一個完整的製圖方法來應對未來即將加入觀測的地面重力波探測器。

關鍵字

隨機重力波背景；最大熵方法

並列摘要

The first direct evidence of gravitational wave has not only verifying the prediction lasting for nearly a century but also opening a new door to probe the universe. There are lots of resolved and unresolved sources in the universe, and stochastic gravitational wave background(SGWB) is one of the most interesting ones. SGWB can be generated by collecting all the sources from different stages in the evolution of the universe, and it is likely to be anisotropy because it might be dominated by the local universe. However, although the map making process of SGWB continues to mature, there are some problems being not resolved yet. For instance, there are some negative values in the final result, which is unrealistic. There is no a rigorous formula to decide the number of the eigenmode, only by simulation instead. In this thesis we want to use Maximum Entropy Method(MEM) to resolve these problems. In addition, MEM has been widely used in astronomy for the past forty years, and due to the properties of the entropy, this method achieves good results while considering continuous distribution. Finally we will develop a complete map making process to consider the upcoming ground based detectors in the future.