Jets from spinning black holes in active galactic nuclei [Elektronische Ressource] / vorgelegt von Ioana Duţan

Ioana Dutan

Sujets

• Astronomie

Informations

• Publié par: rheinische_friedrich-wilhelms-universitat_bonn
• Publié le: 01 janvier 2010
• Nombre de lectures: 22
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Jets from Spinning Black Holes
in Active Galactic Nuclei
Dissertation
zur
Erlangung des Doktorgrades (Dr. rer. nat.)
der
Mathematisch-Naturwissenschaftlichen Fakult¨at
der
Rheinischen Friedrich-Wilhelms-Universita¨t Bonn
vorgelegt von
Ioana Dut¸an
aus
Bukarest, Rum¨anien
Bonn, im Oktober 2010Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakult¨at
der Rheinischen Friedrich-Wilhelms-Universita¨t 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. Jo¨rg 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.
iiiiv
.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.
IamgratefultoPeterL.Biermann,mythesisadviser,forthepossibilityhegaveme
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 Jo¨rg Pretz and Jens Franke, who kindly agreed to join the examination committee.
Iwouldlike to thankmythesiscommittee (Peter L.Biermann, UliKlein, 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,IwouldliketothankKen-IchiNishikawa, YosukeMizuno,andShinji
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 Lauren¸tiu 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 Curu¸tiu for his expertise whenever I was stuck with a problem in my
programs, as well as for his friendship.
I also thank Alan Roy, Iva´n 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 manu-
scripts, 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 Go´mez, Sˆınziana Paˇduroiu, Leonardo Castan˜eda, 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
vvi 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 Kerr solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Kerr black holes in Boyer-Lindquist coordinates . . . . . . . . . . . . . . . . 5
1.4 Orbits in the Kerr metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Basic assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Mass flow rate into the jets . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Angular momentum and energy conservation laws . . . . . . . . . . . . . . 24
2.5 Launching power of the jets . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Rate of the disk angular momentum removed by the jets . . . . . . . . . . 32
2.7 Efficiency of jet launching . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Ultra-High-Energy Cosmic Ray Contribution from the Spin-Down Power
of Black Holes 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.1 Model conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
viiviii 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 Spatial limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4.2 Synchrotron loss limit . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.5 Application to M87 and Cen A . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.6 Predictions for nearby galaxies as ultra-high-energy cosmic ray sources . . . 65
3.7 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4 GeneralRelativisticMagnetohydrodynamics SimulationofJetFormation
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 Perfect fluid approximation . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.4 Evolution of the electromagnetic fields . . . . . . . . . . . . . . . . . 80
4.2.5 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3 General relativistic magnetohydrodynamics simulation code (Koide et al.) . 85
4.3.1 Metric and coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3.2 General relativistic magnetohydrodynamicsequations in zero angular
momentum observer’s frame . . . . . . . . .