活躍星系核噴流（AGN）的反饋被視為抑制在冷核（CC）星團中冷卻流的一個重要的機制，但是活躍星系核噴流及泡泡中的確切能量組成仍然無法被精確的了解。我們採用了Sunyaev-Zel'dovich（SZ）效應來測試在能量以宇宙射線為主的泡泡中是否能看到宇宙射線的存在。能以這樣的方式來測試是因為宇宙射線電子在thermal SZ（tSZ）效應中並不明顯，因此會產生與通常在冷核星團中低密度的X射線泡泡相近的"SZ空洞"或是"SZ泡泡"。值得注意的是，近期已經能偵測到所謂的SZ泡泡，確定可以使用tSZ效應來了解泡泡中是否具有宇宙射線電子，因此我們該深入研究SZ泡泡的性質。

我們使用FLASH code來模擬三維流體力學的活躍星系核噴流，這個星團是以Perseus做為參考，並且能量以宇宙射線為主。我們使用氣體及宇宙射線的分布來對視線上星團的tSZ訊號做積分得到tSZ的地圖及地圖上的SZ泡泡，確認tSZ能作為一個約束活躍星系核泡泡中能量組成的潛在工具。此外，我們從星團中心開始往外分析tSZ訊號的增加/減少，並且調整視角來了解結果是否會有所不同。

在tSZ的地圖上，泡泡可能在視角及泡泡的年齡上具出現簡併的狀況，這會讓我們在分辨這些泡泡時困難重重。我們試圖透過kinetic SZ（kSZ）效應來利用速度及其方向來分辨這些泡泡。然而我們發現kSZ效應產生的訊號對於tSZ效應產生的訊號（KTR）大約差了兩個數量級，因此無法利用這個方法來進行分辨。

我們另外模擬出不同功率及噴射時間的活躍星系核噴流，藉此觀察tSZ及kSZ效應的變化趨勢及KTR數值的大小。我們發現在較高功率及較長噴射時間的泡泡會具有較高的KTR數值（最大值5%），使其更有可能被探測到。

Feedback from active galactic nucleus (AGN) jets is considered a significant mechanism in the suppression of cooling flows within cool-core (CC) clusters. However, the precise energy composition of AGN jets and bubbles remains uncertain. To address this, we employ the Sunyaev-Zel'dovich (SZ) effect as a means to test the presence of cosmic-ray (CR) dominated bubbles. This approach is rising due to the faintness of CR electrons in thermal SZ (tSZ) maps, appearing as ``SZ cavities'' or ``SZ bubbles'', similar to the low-density X-ray cavities and bubbles commonly observed in CC clusters. Remarkably, recently there has been detection of these SZ bubbles, confirming the viability of utilizing the tSZ effect to assess the content of CR electrons. Therefore, it is timely to study the properties of the SZ bubbles in more detail.

We employ the FLASH code to conduct three-dimensional hydrodynamic simulations of AGN jet feedback in a Perseus-like cluster, with a dominant composition of CRs. Using the gas and CR distributions obtained in these simulations, we compute the tSZ signals of the cluster along the line-of-sight (LOS) and generate tSZ maps, confirming that the SZ effect is a potent tool for constraining the composition of CRs within AGN bubbles. Furthermore, we analyzed the decrements/increments of tSZ signals as a function of radius from the cluster center, as well as how the results change with different viewing angles.

The bubbles found in the simulated tSZ maps exhibit a degeneracy between the LOS and the age of the bubbles, making it challenging to distinguish between these factors. In order to address this degeneracy and improve observability, we employed the kinetic SZ (kSZ) effect by incorporating velocity calculations as a distinguishing factor. However, our findings indicate that the kinetic-to-thermal ratios (KTRs), which is the ratio between the kSZ signal to the tSZ signal, are too low to be detected.

We have conducted a parameter study of the duration and power of the jets in order to observe the trends regarding tSZ, kSZ, and the values of KTR. Our findings indicate that bubbles with higher power and longer duration exhibit elevated KTR values, with a maximum value of 5%, thereby increasing the likelihood of their detectability.

Abstract (Chinese)-----------------------------------------I
Acknowledgements (Chinese)---------------------------------II
Abstract---------------------------------------------------III
Acknowledgements-------------------------------------------V
Contents---------------------------------------------------VI
List of Figures--------------------------------------------VIII
List of Tables---------------------------------------------XII
1 Introduction---------------------------------------------1
2 Methodology----------------------------------------------4
2.1 FLASH code and simulation setup------------------------4
2.2 Thermal SZ effect and analysis-------------------------6
2.2.1 Thermal SZ effect------------------------------------6
2.2.2 Analysis---------------------------------------------10
2.3 Kinetic SZ effect and analysis-------------------------12
2.3.1 Kinetic SZ effect------------------------------------12
2.3.2 Analysis---------------------------------------------13
3 Results--------------------------------------------------15
3.1 Thermal SZ effect--------------------------------------15
3.2 Kinetic SZ effect and the kinetic-to-thermal ratio-----18
3.2.1 kSZ--------------------------------------------------18
3.2.2 Maps of the kinetic-to-thermal ratio (KTR)-----------20
4 Discussion-----------------------------------------------25
4.1 Jet parameter adjustments------------------------------25
4.2 Kinetic-to-thermal ratios------------------------------27
5 Conclusions----------------------------------------------35
Bibliography-----------------------------------------------38

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