來自活躍星系核中強力的噴流被視為是最有可能的加熱機制，以阻止星系團核心發生崩潰性的冷卻；包含震波以及泡泡等，許多活躍星系核噴流產生的擾動都在星系團內介質的X射線影像上被發現。為了研究這些擾動的性質，我們使用交叉譜法分析Perseus星系團且具有不同能量組成的活躍星系核噴流，並利用三維度流體力學模型模擬該系統。具體來說，我們比較宇宙射線及動能為主的活躍星系核噴流在X射線影像上產生的擾動模式差異(絕熱,等溫或者等壓為主)。由單次噴發的噴流模擬中，我們發現:(1) 交叉譜法成功的分辨了擾動的模式(震波跟泡泡分別由絕熱及等溫的擾動所主導)；(2) 在150千秒差距內的分析中，整個系統的演化在前20萬年是由絕熱的擾動所主導，超過20萬年則是由等溫的擾動主導；(3)所有宇宙射線噴流產生的擾動振幅均為動能噴流所產生的數倍。對於自我調節的活躍星系核噴流模擬中，我們發現:(1) 自我調節的宇宙射線以及動能噴流所產生的擾動模式均為等壓所主導，這與觀測到在Perseus星系團內的擾動模式相吻合；(2) 整體來說，自我調節的動能噴流模擬處於準平衡的狀態，自我調節的宇宙射線噴流模擬則變化很大，後者的擾動性質取決於星系團內加熱以及冷卻效應之間的競爭。

Powerful jets from active galactic nuclei (AGN) are regarded as the most promising heating mechanism to prevent cooling catastrophe in cool-core clusters. A lot of AGN-driven perturbations including weak shocks and bubbles are found in X-ray images of the intracluster medium (ICM). In order to understand the properties of these perturbations, we apply the cross-spectrum method to analyze 3D hydrodynamic simulations of a Perseus-like cluster with different composition of AGN jets. Specifically, we compare the dominant modes (adiabatic, isothermal or isobaric) of X-ray perturbations generated by cosmic-ray (CR) versus kinetic-energy (KE) dominated jets. Using simulations of a single jet outburst, we find that: (1) the cross-spectrum method can successfully identify the modes of perturbations (shocks and bubbles are dominated by adiabatic and isothermal perturbations, respectively); (2) within 150 kpc, the evolution of perturbations is dominated by adiabatic shocks before 20 Myr and isothermal processes after 20 Myr; (3) the amplitude of perturbations for the CR jet is several times higher than those of the KE jet. For the self-regulated AGN feedback simulations, we find that: (1) the perturbations for both CR/KE jets are isobaric, consistent with the observed Perseus cluster; (2) overall, the self-regulated KE jet simulation is in a quasi-equilibrium state, but the self-regulated CR jet simulation is more variable and the properties of perturbations depend on the competition between heating and cooling within the cluster core.

Contents
Abstract (Chinese) I
Acknowledgements (Chinese) II
Abstract III
Contents IV
List of Figures VI
List of Tables IX
List of Algorithms 1
1 Introduction 1
2 Method 5
2.1 Simulation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 X-ray approximation vs pyXSIM . . . . . . . . . . . . . . . . . . . 9
2.2.1 X-ray approximation . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 The synthetic X-ray observations generator: pyXSIM . . . . 10
2.3 Cross-spectrum analysis . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Physics of the cross-spectrum method . . . . . . . . . . . . . 11
2.3.2 Mathematical formalism . . . . . . . . . . . . . . . . . . . . 13
IV
3 Results of the single-jet simulations 18
3.1 Identify the region of bubble/shock/rarefaction wave . . . . . . . . 18
3.2 Subregion analysis of KE/CR dominated jets . . . . . . . . . . . . . 21
3.3 Whole region analysis of KE/CR jets . . . . . . . . . . . . . . . . . 26
4 Perturbations in the Self-regulated simulations 28
4.1 The properties of perturbations in the self-regulated simulations . . 28
4.2 The nature of self-regulated jets simulation and two point correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Discussion 38
6 CONCLUSIONS 40
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