來自活躍星系核噴流（active galactic nuclei jets）的回饋，被認為是最能有效抑制冷核星系團中冷卻流形成的機制之一。然而，噴流回饋的詳細機制仍有待釐清。在這篇論文中，我們旨在瞭解宇宙射線（cosmic-ray, CR）主導的噴流所提供的回饋，以及其與新發現的奇異電波圈（odd radio circles, ORCs）之間的潛在聯繫。

本論文的主要內容可以分為兩個部分。在第一部分（Chapter 2），我們通過使用三維宇宙射線磁流體力學（CR-MHD）模擬程式FLASH，研究宇宙射線質子（cosmic-ray protons, CRp）和宇宙射線電子（cosmic-ray electrons, CRe）主導的噴流與噴流產生的泡泡（bubbles）的演化和反饋效應。我們研究了它們的能量、動力學和加熱能力的演化，並計算了它們的X射線功率與無線電光度之間的關係（P_cav-L_R）。我們發現，即使宇宙射線電子泡泡明顯受到更強的同步輻射與逆康普頓冷卻，兩種泡泡的演化依然非常相似。這是因為隨著宇宙射線電子失去能量，泡泡會在約三千萬年內迅速變成由熱能主導。此時，它們的總能量將停止隨著宇宙射線能量的減少而下降，使得兩種泡泡走向相似的演化路徑。兩種泡泡對星系團內介質（ICM）的加熱能力也相當，通過局部熱不穩定形成的冷氣體在兩種情況下都被有效抑制。兩種泡泡在P_{cav-L_R平面上遵循不同的演化軌跡，但其數值與星系團中泡泡的觀測範圍大致相同。我們也討論了可能可以用於區別泡泡能量組成的觀測方法。

在第二部分（Chapter 3），我們研究了新發現的奇異電波圈是「平行視線方向的活躍星系核噴流產生的泡泡」的可能性。我們使用FLASH進行三維CR-MHD模擬，並預測了在強子輻射機制下，活躍星系核噴流產生的泡泡的無線電形態。我們發現，功率強且持續時間長的宇宙射線主導噴流，可以在低質量（M_vir ~ 8e12 - 8e13 M_sun）星系團中創造與觀測到的奇異電波圈大小相似（約三十至六十萬秒差距）的無線電天體。噴流能量相同時，持續時間更長（因此功率較低）的噴流往往會創造更大的泡泡，因為高功率噴流會產生強烈的震波，帶走大部分的噴流能量。奇異電波圈邊緣較亮的特徵，可以自然的以強子輻射機制解釋。我們因此認為宇宙射線主導的活躍星系核噴流是奇異電波圈的可能起源。

Jet feedback from active galactic nuclei (AGNs) is one of the most promising mechanisms for suppressing cooling flows in cool-core clusters. Despite its importance, the detail mechanisms underlying jet-mode feedback remain poorly understood. In this thesis, we aim to understand AGN feedback provided by cosmic-ray (CR) dominated jets, and its potential connection to the newly discovered odd radio circles (ORCs).

The main content of this thesis can be divided into two parts. In the first part (Chapter 2), we investigate the the evolution and feedback effects of cosmic-ray proton (CRp) and cosmic-ray electron (CRe) dominated jets by conducting three-dimensional (3D) cosmic-ray (CR) magnetohydrodynamic (MHD) simulations of AGN jet-inflated bubbles in the intracluster medium using the FLASH code. We present the evolution of their energies, dynamics and heating, and model their expected cavity-power versus radio-luminosity relation (P_cav-L_R).
We find that bubbles inflated by CRe dominated jets follow a very similar dynamical evolution to CRp dominated bubbles even though CRe within bubbles suffer significantly stronger synchrotron and inverse-Compton cooling. This is because, as CRe lose their energy, the jet-inflated bubbles quickly become thermally dominated within ~30 Myr. Their total energy stops decreasing with CR energy and evolves similarly to CRp dominated bubbles.
The ability of CRe and CRp dominated bubbles to heat the intracluster medium is also comparable; the cold gas formed via local thermal instabilities is well suppressed in both cases. The CRp and CRe bubbles follow different evolutionary trajectories on the P_cav-L_R plane, but the values are broadly consistent with observed ranges for bubbles in galaxy clusters. We also discuss observational techniques that have potential for constraining the composition of AGN jets and bubbles.

In the second part (Chapter 3), we investigate the possibility that the newly discovered ORCs may be end-on AGN jet-inflated bubbles.
We carry out 3D CR-MHD simulations using the FLASH code and predict the radio morphology of the AGN jet-inflated bubbles considering hadronic emission mechanisms. We find that powerful and long-duration CR-dominated jets can create radio objects with similar sizes (roughly 300-600 kpc) to the observed ORCs in low-mass (M_vir ~ 8e12 - 8e13 M_sun) clusters. For the same input jet energy, longer-duration (thus lower-power) jets tend to create larger bubbles since high-power jets tend to generate strong shocks that carry away a significant portion of the jet energy. The edge-brightening feature of the ORCs is naturally reproduced in the hadronic scenario. We conclude that CR-dominated AGN jets could be a plausible origin of the ORCs.

Abstract (Chinese) I
Acknowledgements (Chinese) III
Abstract VI
Acknowledgements VIII
Contents XIII
List of Figures XV
List of Tables XIX
1 Introduction 1
2 Evolution and Feedback of AGN Jets of Different Cosmic-ray Composition 4
2.1 Introduction 4
2.2 Methods 7
2.2.1 Cosmic-ray physics 8
2.2.2 Simulation setup 12
2.3 Results 14
2.3.1 Bubble evolution 14
2.3.2 Energy evolution 15
2.3.3 Cold gas evolution and CR heating 17
2.3.4 Observable properties in radio 21
2.4 Discussion 24
2.5 Conclusions 28
3 Odd Radio Circles as End-on Cosmic-ray Dominated AGN Jet inflated Bubbles 32
3.1 Introduction 32
3.2 Methods 34
3.2.1 3D-CRMHD formalism and simulation technique 34
3.2.2 Setup of the cluster environment 35
3.3.3 Mock observations 36
3.3 Results 37
3.3.1 Benchmark cases 37
3.3.2 Parameter search 40
3.4 Discussion 45
3.4.1 Key mechanisms for reproducing ORC features 45
3.4.2 Is the energy injection reasonable? 46
3.5 Conclusions 47
4 Summary 49
Bibliography 52

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