Jets from Spinning Black Holes in Active Galactic Nuclei

Jets from Spinning Black Holes in Active Galactic Nuclei Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn vorgelegt von Ioana Dut¸an aus Bukarest, Rumänien Bonn, im Oktober 2010 Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Promotionskommission: 1. Erstgutachter und Betreuer: Prof. Dr. Peter L. Biermann, Max Planck Institute for Radio Astronomy, Bonn 2. Zweitgutachter: Prof. Dr. Uli Klein, Argelander Institute for Astronomy, Bonn 3. Fachnahes Mitglied: PD Dr. Jörg Pretz, Institute of Physics, Bonn 4. Fachangrenzendes Mitglied: Prof. Dr. Jens Franke, Mathematical Institute of the University of Bonn Tag der Promotion: 31 Januar 2011 Diese Dissertation ist auf dem Hochschulschriftenserver der ULB Bonn http : //hss.ulb.uni bonn.de/diss−online − elektronisch publiziert. Das Erscheinungsjahr ist 2011. To my parents. iii iv . Acknowledgments This thesis could not have been completed without the generosity and assistance of a large number of people to whom I would like to express my gratitude. I am grateful to Peter L. Biermann, my thesis adviser, for the possibility he gave me to work on a subject I like and for his support that he made available in a number of ways. In particular, I would like to thank him for comprehensive and stimulating discussions, valuable suggestions and comments on this thesis and on my other manuscripts. I am also grateful to the second referee, Uli Klein, for reviewing this thesis. I also thank Jörg Pretz and Jens Franke, who kindly agreed to join the examination committee. I would like to thank my thesis committee (Peter L. Biermann, Uli Klein, Anton J. Zensus, and Frank Bertoldi) for offering suggestions to solve several problems encountered in my research. This work was supported by the International Max Planck Research School (IM- PRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne, being performed at the Max Planck Institute for Radio Astronomy, Bonn, in the Theory group. I am also grateful to Gerd Weigelt, the director of the Infrared Astronomy Department, for providing me with financial support during the final stage of this work. Furthermore, I would like to thank Ken-Ichi Nishikawa, Yosuke Mizuno, and Shinji Koide, my collaborators on General Relativistic Magnetohydrodynamic Simulations of Jet Formation, for providing me with their simulation code and for their scientific support and encouragement. The simulations were performed on a machine at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, USA, through a research project whose principal investigator is Ken-Ichi Nishikawa. The results of this collaboration are presented in Chapter 4. I would like to thank Laurent¸iu Caramete, my office mate, for providing me with a complete sample of active galactic nuclei, which is a part of the work for his PhD thesis. This has made it possible for me to extend the application of the model for Ultra-high- energy Cosmic Rays developed in Chapter 3 to observational data. I also thank him for his friendship, patience, and help in ways too numerous to mention. I thank Alex Curut¸iu for his expertise whenever I was stuck with a problem in my programs, as well as for his friendship. I also thank Alan Roy, Iván Aguido, and Manuel Peruchio (from the VLBI group) for insights into observational research of active galactic nuclei. I am grateful to Michelle Fekety for proofreading this thesis and my other manuscripts, as well as for her friendship and kind assistance in dealing with bureaucratic pro- cedures and many hassles. It is a pleasure to thank my colleagues and friends for a lot of help, for numerous discussions either related to science or just about life itself, and for creating a friendly atmosphere in which I could enjoy the work at this thesis. Beside those already mentioned, I thank Hyunjoo Kim, Laura Gómez, Sˆınziana Pˇaduroiu, Leonardo Castañeda, and Traian Popescu, with whom I spent a longer time in Bonn. There are Petru Ghenuche and Valeriu Tudose, abroad, who were there when I needed most. I would also like to thank my best friend back in Romania, Melania Chiciuc, for her never-ending support. I also acknowledge my Master’s thesis co-adviser at the University of Bucharest, Mircea Rusu, for his influence on my studies and more. It is quite difficult to catch in a few v vi Acknowledgments words his qualities as a professor, and as a person in general. It was a real privilege for me to have him as a mentor. At the end, I would like to thank my father especially for encouraging me in keeping my way and trying harder. I also thank my mother, in memoriam. Many of her words have been guiding me through life. Contents Abstract ........................................ ix Acronyms ....................................... xi Most Used Mathematical Symbols ....................... xii Preface ......................................... xiii 1 Introduction to Kerr Black Holes 1 1.1 Introduction.................................... 1 1.2 Kerrsolution ................................... 4 1.3 Kerr black holes in Boyer-Lindquist coordinates . .......... 5 1.4 OrbitsintheKerrmetric ........................... 8 1.5 Stretched horizon – membrane paradigm . ..... 10 2 Magnetic Connection Model for Launching Relativistic Jets from Kerr Black Holes 11 2.1 Introduction.................................... 12 2.2 Basicassumptions ................................ 17 2.3 Massflowrateintothejets .. .. .. .. .. .. .. .. 21 2.4 Angular momentum and energy conservation laws . ...... 24 2.5 Launchingpowerofthejets . 25 2.6 Rate of the disk angular momentum removed by the jets . ...... 32 2.7 Efficiencyofjetlaunching . 33 2.8 Spin evolution of the black hole . 34 2.9 Relevance to the observational data . ...... 36 2.9.1 Maximum lifetime of the AGN from the black hole spin-down power 36 2.9.2 On the relation between the spin-down power of a black hole and the particle maximum energy in the jets . 38 2.9.3 On the relation between the spin-down power of a black hole and the observed radio flux-density from flat-spectrum core source . ..... 39 2.10 Summaryandconclusions . 40 3 Ultra-High-Energy Cosmic Ray Contribution from the Spin-Down Power of Black Holes 45 3.1 Introduction.................................... 45 3.2 Modeldescription................................ 52 3.2.1 Modelconditions............................. 52 3.2.2 Magnetic field scaling along a steady jet . 52 3.2.3 Electron and proton number densities . 54 3.2.4 Particle energy distribution . 55 vii viii Contents 3.2.5 Self-absorbed synchrotron emission of the jets . ........ 56 3.3 Luminosity and flux of the ultra-high-energy cosmic rays ........... 61 3.4 Maximum particle energy of ultra-high-energy cosmic rays.......... 62 3.4.1 Spatiallimit ............................... 62 3.4.2 Synchrotronlosslimit . 63 3.5 ApplicationtoM87andCenA . 63 3.6 Predictions for nearby galaxies as ultra-high-energy cosmic ray sources . 65 3.7 Summaryandconclusions . 66 4 General Relativistic Magnetohydrodynamics Simulation of Jet Formation from Kerr Black Holes 69 4.1 Introduction.................................... 70 4.2 General relativistic magnetohydrodynamics equations in conservation form 75 4.2.1 3+1 decomposition of the space-time (in the Eulerean formulation) . 75 4.2.2 3+1 decomposition of the energy-momentum tensor . ..... 79 4.2.3 Perfectfluidapproximation . 80 4.2.4 Evolution of the electromagnetic fields . ..... 80 4.2.5 ConservationEquations . 82 4.3 General relativistic magnetohydrodynamics simulation code (Koide et al.) . 85 4.3.1 Metricandcoordinates ......................... 85 4.3.2 General relativistic magnetohydrodynamics equations in zero angular momentumobserver’sframe. 86 4.3.3 Descriptionofthecode ......................... 88 4.4 Simulation of jet formation from a Kerr black hole . ........ 94 4.4.1 Initialconditions . .. .. .. .. .. .. .. .. 94 4.4.2 Numericalresults............................. 95 4.4.3 Comparison with the RAISHIN simulation code (Mizuno et al.) . 108 4.4.4 Comparisonwithotherwork . 110 4.5 Summaryandconclusions . 111 Outlook ........................................ 113 References ....................................... 115 Appendix 1 ...................................... 127 Appendix 2 ...................................... 129 List of Publications ................................. 133 Abstract Relativistic jets are highly collimated plasma outflows that can be present in extra- galactic radio sources, which are associated with active galactic nuclei (AGN). Observations give strong support for the idea that a supermassive black hole (BH), surrounded by an accretion disk, is harbored in the center of an AGN. The jet power can be generally provided by the accretion disk, by the BH rotation, or both. Such powerful jets can also be sites of the origin of ultra-high-energy cosmic rays (UHECRs). In this work, we study the jet formation from rapidly-spinning BHs in the framework of General Relativity and General Relativistic Magnetohydrodynamics, as well as the acceleration of UHECRs in AGN jets. Magnetic connection model for launching relativistic jets from a Kerr black hole: Despite intense efforts to understand the processes responsible for formation of the AGN jets, we still face the problem of exactly how to explain them. Here, we present a model for launching relativistic jets in

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