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.

P. Ar ́evalo, E. Churazov, I. Zhuravleva, C. Hern ́andez-Monteagudo, and
M. Revnivtsev. A Mexican hat with holes: calculating low-resolution power
spectra from data with gaps. , 426(3):1793–1807, November 2012. doi: 10.1111/j.1365-2966.2012.21789.x.

Christopher J. Bambic and Christopher S. Reynolds. Efficient Production of Sound
Waves by AGN Jets in the Intracluster Medium. , 886(2):78, December 2019.
doi: 10.3847/1538-4357/ab4daf.

Ricarda S. Beckmann, Yohan Dubois, Alisson Pellisier, Valeria Olivares, Fiorella L.Polles, Oliver Hahn, Pierre Guillard, and Matthew D. Lehnert. Cosmic rays and thermal instability in self-regulating cooling flows of massive galaxy clusters.
arXiv e-prints, art. arXiv:2204.03629, April 2022.

H. Boehringer, W. Voges, A. C. Fabian, A. C. Edge, and D. M. Neumann. AROSAT HRI study of the interaction of the X-ray emitting gas and radio lobesof NGC 1275. , 264:L25–L28, October 1993. doi: 10.1093/mnras/264.1.L25.

E. Churazov, A. Vikhlinin, I. Zhuravleva, A. Schekochihin, I. Parrish, R. Sunyaev, W. Forman, H. B ̈ohringer, and S. Randall. X-ray surface brightness and gas density fluctuations in the Coma cluster. , 421(2):1123–1135, April 2012. doi: 10.1111/j.1365-2966.2011.20372.x.

S. Cielo, A. Babul, V. Antonuccio-Delogu, J. Silk, and M. Volonteri. Feedback from reorienting AGN jets. I. Jet-ICM coupling, cavity properties and global energetics. , 617:A58, September 2018. doi: 10.1051/0004-6361/201832582.

Xiaodong Duan and Fulai Guo. On the Energy Coupling Efficiency of AGN Out-bursts in Galaxy Clusters. , 896(2):114, June 2020. doi: 10.3847/1538-4357/ab93b3.

A. Dubey, L. B. Reid, and R. Fisher. Introduction to FLASH 3.0, with application to supersonic turbulence. Physica Scripta Volume T, 132:014046, December 2008. doi: 10.1088/0031-8949/2008/T132/014046.

K. Ehlert, R. Weinberger, C. Pfrommer, R. Pakmor, and V. Springel. Simulations of the dynamics of magnetized jets and cosmic rays in galaxy clusters. , 481(3): 2878–2900, December 2018. doi: 10.1093/mnras/sty2397.

A. C. Fabian. Cooling Flows in Clusters of Galaxies. , 32:277–318, January 1994. doi: 10.1146/annurev.aa.32.090194.001425.

A. C. Fabian and P. E. J. Nulsen. Subsonic accretion of cooling gas in clusters of galaxies. , 180:479–484, August 1977. doi: 10.1093/mnras/180.3.479.

B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J. W. Truran, and H. Tufo. FLASH: An Adaptive MeshHydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes. , 131(1):273–334, November 2000. doi: 10.1086/317361.

M. Gaspari, C. Melioli, F. Brighenti, and A. D’Ercole. The dance of heating and cooling in galaxy clusters: three-dimensional simulations of self-regulated active galactic nuclei outflows. , 411(1):349–372, February 2011. doi: 10.1111/j.1365-2966.2010.17688.x.

Fulai Guo. The Shape of X-Ray Cavities in Galaxy Clusters: Probing Jet Properties and Viscosity. , 803(1):48, April 2015. doi: 10.1088/0004-637X/803/1/48.

Fulai Guo. On the Importance of Very Light Internally Subsonic AGN Jets in Radio-mode AGN Feedback. , 826(1):17, July 2016. doi: 10.3847/0004-637X/826/1/17.

Fulai Guo. Probing the Physics of Mechanical AGN Feedback with Radial Elongations of X-Ray Cavities. , 903(1):3, November 2020. doi: 10.3847/1538-4357/abb777.

Fulai Guo and William G. Mathews. Cosmic-ray-dominated AGN Jets and the Formation of X-ray Cavities in Galaxy Clusters. , 728(2):121, February 2011. doi: 10.1088/0004-637X/728/2/121.

Fulai Guo and S. Peng Oh. Feedback heating by cosmic rays in clusters of galaxies., 384(1):251–266, February 2008. doi: 10.1111/j.1365-2966.2007.12692.x.

Fulai Guo, S. Peng Oh, and M. Ruszkowski. A Global Stability Analysis of Clusters of Galaxies with Conduction and AGN Feedback Heating., 688(2):859–874, December 2008. doi: 10.1086/592320.

Fulai Guo, Xiaodong Duan, and Ye-Fei Yuan. Reversing cooling flows with AGN jets: shock waves, rarefaction waves and trailing outflows. , 473(1):1332–1345, January 2018. doi: 10.1093/mnras/stx2404.

Matthew Kingsland, H. Y. Karen Yang, Christopher S. Reynolds, and John A. Zuhone. Effects of Anisotropic Viscosity on the Evolution of Active Galactic Nuclei Bubbles in Galaxy Clusters., 883(1):L23, September 2019. doi: 10. 3847/2041-8213/ab40be.

A. Leccardi and S. Molendi. Radial temperature profiles for a large sample of galaxy clusters observed with XMM-Newton., 486(2):359–373, August 2008. doi: 10.1051/0004-6361:200809538.

M. McDonald, M. Gaspari, B. R. McNamara, and G. R. Tremblay. Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies., 858(1): 45, May 2018. doi: 10.3847/1538-4357/aabace.

B. R. McNamara and P. E. J. Nulsen. Heating Hot Atmospheres with Active Galactic Nuclei., 45(1):117–175, September 2007. doi: 10.1146/annurev.astro. 45.051806.110625.

B. R. McNamara and P. E. J. Nulsen. Mechanical feedback from active galactic nuclei in galaxies, groups and clusters. New Journal of Physics, 14(5):055023, May 2012. doi: 10.1088/1367-2630/14/5/055023.

E. K. Panagoulia, A. C. Fabian, J. S. Sanders, and J. Hlavacek-Larrondo. A volume-limited sample of X-ray galaxy groups and clusters - II. X-ray cavity dynamics., 444(2):1236–1259, October 2014. doi: 10.1093/mnras/stu1499.

J. R. Peterson and A. C. Fabian. X-ray spectroscopy of cooling clusters., 427(1): 1–39, April 2006. doi: 10.1016/j.physrep.2005.12.007.

Deovrat Prasad, Prateek Sharma, and Arif Babul. Cool Core Cycles: Cold Gas and AGN Jet Feedback in Cluster Cores., 811(2):108, October 2015. doi: 10.1088/0004-637X/811/2/108.

Deovrat Prasad, Prateek Sharma, and Arif Babul. AGN jet-driven stochastic cold accretion in cluster cores. , 471(2):1531–1542, October 2017. doi: 10.1093/mnras/stx1698.

Mateusz Ruszkowski, H. Y. Karen Yang, and Christopher S. Reynolds. Cosmic-Ray Feedback Heating of the Intracluster Medium., 844(1):13, July 2017. doi:10.3847/1538-4357/aa79f8.

Alastair J. R. Sanderson, Trevor J. Ponman, and Ewan O’Sullivan. A statistically selected Chandra sample of 20 galaxy clusters - I. Temperature and cooling time profiles., 372(4):1496–1508, November 2006. doi: 10.1111/j.1365-2966. 2006.10956.x.

Debora Sijacki, Volker Springel, Tiziana Di Matteo, and Lars Hernquist. A unified model for AGN feedback in cosmological simulations of structure formation., 380(3):877–900, September 2007. doi: 10.1111/j.1365-2966.2007.12153.x.

Kung-Yi Su, Philip F. Hopkins, Greg L. Bryan, Rachel S. Somerville, Christopher C. Hayward, Daniel Angl ́es-Alc ́azar, Claude-Andr ́e Faucher-Gigu`ere, Sarah Wellons, Jonathan Stern, Bryan A. Terrazas, T. K. Chan, Matthew E. Orr, Cameron Hummels, Robert Feldmann, and Duˇsan Kereˇs. Which AGN jets quench star formation in massive galaxies? , 507(1):175–204, October 2021. doi: 10.1093/mnras/stab2021.

Ralph S. Sutherland and M. A. Dopita. Cooling Functions for Low-Density Astrophysical Plasmas., 88:253, September 1993. doi: 10.1086/191823.

Shutaro Ueda, Keiichi Umetsu, FanLam Ng, Yuto Ichinohe, Tetsu Kitayama, and Sandor M. Molnar. Systematic Perturbations of the Thermodynamic Properties in Cool Cores of HIFLUGCS Galaxy Clusters. , 922(1):81, November 2021. doi: 10.3847/1538-4357/ac1f16.

C. Wang, M. Ruszkowski, C. Pfrommer, S. Peng Oh, and H. Y. K. Yang. Non-Kolmogorov turbulence in multiphase intracluster medium driven by cold gas precipitation and AGN jets., 504(1):898–909, June 2021. doi: 10.1093/mnras/stab966.

Chaoran Wang, Mateusz Ruszkowski, and H. Y. Karen Yang. Chaotic cold accretion in giant elliptical galaxies heated by AGN cosmic rays., 493(3):4065–4076, April 2020. doi: 10.1093/mnras/staa550.

Shiang-Chih Wang and H. Y. Karen Yang. Production efficiencies of sound waves in the intracluster medium driven by AGN jets., 512(4):5100–5109, June 2022. doi: 10.1093/mnras/stac788.

H. Y. Karen Yang and Christopher S. Reynolds. How AGN Jets Heat the Intracluster Medium—Insights from Hydrodynamic Simulations., 829(2):90, October 2016a. doi: 10.3847/0004-637X/829/2/90.

H. Y. Karen Yang and Christopher S. Reynolds. Interplay Among Cooling, AGN Feedback, and Anisotropic Conduction in the Cool Cores of Galaxy Clusters., 818(2):181, February 2016b. doi: 10.3847/0004-637X/818/2/181.

H. Y. Karen Yang, Massimo Gaspari, and Carl Marlow. The Impact of Radio AGN Bubble Composition on the Dynamics and Thermal Balance of the Intracluster Medium., 871(1):6, January 2019. doi: 10.3847/1538-4357/aaf4bd.

Nadia L. Zakamska and Ramesh Narayan. Models of Galaxy Clusters with Thermal Conduction. , 582(1):162–169, January 2003. doi: 10.1086/344641.

I. Zhuravleva, E. Churazov, A. Kravtsov, and R. Sunyaev. Constraints on the ICM velocity power spectrum from the X-ray lines width and shift., 422(3): 2712–2724, May 2012. doi: 10.1111/j.1365-2966.2012.20844.x.

I. Zhuravleva, E. Churazov, P. Ar ́evalo, A. A. Schekochihin, W. R. Forman, S. W. Allen, A. Simionescu, R. Sunyaev, A. Vikhlinin, and N. Werner. The nature and energetics of AGN-driven perturbations in the hot gas in the Perseus Cluster., 458(3):2902–2915, May 2016. doi: 10.1093/mnras/stw520.

Irina Zhuravleva, Steven W. Allen, Adam Mantz, and Norbert Werner. Gas Perturbations in the Cool Cores of Galaxy Clusters: Effective Equation of State, Velocity Power Spectra, and Turbulent Heating., 865(1):53, September 2018. doi: 10.3847/1538-4357/aadae3.

J. A. ZuHone, M. Markevitch, and R. E. Johnson. Stirring Up the Pot: Can Cooling Flows in Galaxy Clusters be Quenched by Gas Sloshing? , 717(2): 908–928, July 2010. doi: 10.1088/0004-637X/717/2/908.

John A. ZuHone and Eric. J. Hallman. pyXSIM: Synthetic X-ray observations generator, August 2016.