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UMT Landau States and Astrophysical Jets By Herve Guy A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science In Physics Carleton University Ottawa, Ontario © 2009, Herve Guy Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-68620-1 Our file Notre reference ISBN: 978-0-494-68620-1 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lntemet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non­ support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 14-1 Canada f Abstract Since the beginning of the twentieth century, astrophysical jets have been observed at all scales and with a wide range of parameters, in terms of jet sources, sizes, speeds and emit­ ted wavelengths. Several models that explained the origin of astrophysical jets have been created over time with varying degrees of success! Surprisingly, none of them have used Landau states to explain the origin of the astrophysical jets, which are always formed in the vicinity of a bizarre object, such as a black hole or a neutron star. Among the exotic properties shared by these, one in particular is that they often have an extremely strong magnetic field, which is precisely the environment where the Landau states are present. The purpose of this work is then to examine the role that Landau States could play in explaining the origin of astrophysical jets. After having determined how Landau states behave in uniform varying magnetic fields, two models will be proposed: 1) a Quasi-Realistic Astrophysical Jet Model that will try to explain how an astrophysical jet could be formed in the atmosphere of a neutron star, and 2) a Quasi-Realistic Jet Propulsion Mechanism that will try to explain how photons could be emitted when the density in the Landau states changes in the vicinity of a neutron stars surface and propelled via the astrophysical jets formed in the atmosphere of the neutron star. Please note: The original title page for this thesis has been removed due to formatting problems. All information has been transferred to the Carleton University standard title page template for theses. 11 Acknowledgements I would like to thank all the people who have helped and inspired me during my mas­ ter's study. I especially want to thank my advisor, Prof. Peter J. Watson, for his guidance during my research and study at Carleton University. He taught me my first course when I initi­ ated this crazy adventure. Once successfully completed, he was so generous in sharing me his thoughts about the potential role that Landau States could play in explaining the origin of astrophysical jets. In this regard, he showed me all roads that allowed me to complete this project. His perpetual energy and enthusiasm in research had always motivated me. In addition, he was always accessible and willing to help his students with their research. The generous support from my employer CANARIE Inc. is greatly appreciated. In retrospect, I am amazed by the confidence of managers and colleagues. Without their great patience and support, my ambition to study at part-time would hardly be realized. My deepest gratitude goes to my wonderful spouse, my two adorable sons, as well as my family, for their unflagging love and support throughout my life; this dissertation would have been simply impossible without them. Contents Abstract i Acknowledgements ii Table of Contents iii List of Tables vi List of Figures vii 1 Introduction 1 1.1 Jet phenomena 1 1.2 Purpose of this thesis 5 1.3 Structure of this document 6 1 Surveys of Exotic Objects 8 2 SS 433 9 2.1 Overall picture of the SS 433 system 9 2.2 The five-parameter kinematic model of the jet in SS 433 14 2.3 SS 433: A neutron star or black hole candidate? 15 CONTENTS iv 3 Neutron Stars and their Magnetic Fields 20 3.1 Overall picture of the neutron star 20 3.2 Extremely strong magnetic fields 23 3.3 Magnetic dipole model for rotating neutron stars 24 II Survey of the Landau States 29 4 Landau States in Constant Magnetic Fields 30 4.1 Non-Relativistic Solutions 30 4.2 Relativistic Solutions 39 5 Landau States in Varying Magnetic Fields 51 5.1 Magnetic Dipole 51 5.2 Non-Relativistic Solutions 55 5.3 Relativistic Solutions 59 III Toward the Jet Model via Landau States 64 6 The effective force in a varying magnetic field 65 6.1 From a classical approach to a quantized result 65 6.2 Motion of the charged particle given by the new force F (Bz (z), n) 68 7 The Quasi-Realistic Jet Model - preliminary version 70 7.1 The current density conservation principle 71 7.2 The 1-D kinematics of radial constant-acceleration 71 7.3 The quasi-realistic jet model in spherical coordinates - first version 74 CONTENTS v 8 The Quasi-Realistic Jet Propulsion Mechanism 85 8.1 Degeneracy of Landau Levels 85 8.2 The Landau-Fermi decay mechanism 90 8.3 First Quasi-Realistic Jet Propulsion Mechanism 97 9 The Quasi-Realistic Jet Model - final version 100 9.1 The quasi-realistic jet model in spherical coordinates - final version .... 100 9.2 Jet Model via the Landau States and SS 433 105 IV Conclusion 110 10 Conclusion 111 10.1 Results Ill 10.2 Suggestions for Further Research 112 V Bibliography 114 Bibliography 115 List of Tables 2.1 The five-parameter kinematic model of the jet in SS 433 15 8.1 Estimated Fermi energy with respect to the electron density from the neu­ 6 tron star's upper atmosphere to the bottom boundaries; for Tsf»3x 10 K and kBTs » 259 eV 94 9.1 Ep and related pairs of ni that give some identical initial current densities 105 List of Figures 1.1 Multifrequency images of M87 jet structure with arcsecond resolution in­ struments. [4] 2 1.2 (left) Visible [22] and (right) X-ray observation [1] of the Quasar 3C 273 with a jet 3 1.3 Artist's rendition of SS 433 and its Relativistic Jet [42] 4 1.4 SS 433: Optical and X-ray spectrums [23] 5 2.1 Location of SS 433 in constellation Aquila [39] 10 2.2 X-ray brightness distribution of the supernova remnant W 50 with its central object SS 433 [5] 11 2.3 The semidetached binary SS 433 showing the accretion disk around the primary /compact star. [6] 12 2.4 The X-ray lobes of SS 433 (W 50) [23] 14 2.5 The precession geometry of SS 433 [23] 16 3.1 Rotating dipole model [35] 26 3.2 Plot of period derivative P versus the period P for the presently known rotation pulsars. (Green) lines of constant Bs found in (3.11) and (violet) lines of constant characteristic age of pulsars are illustrated as well [19]. 27 LIST OF FIGURES viii 3.3 Resulting magnetic fields of a neutron star [2] 28 4.1 Classical Helical Motion of a positive charge in an uniform, constant mag­ netic field that points in the z direction [26] 37 4.2 Effect of varying the number of nodes n in the Schrodinger equation, when the Landau Gauge is applied 38 5.1 Magnetic dipole moment created by a loop of wire (area S, current I) [27]. 52 7.1 Evidence of the conserved current density when the particle is accelerated radially at a constant rate 73 7.2 The particle velocity v(r,9,riL) versus r for 9 = 0° to 5° and for nL = 0 (lowest red curve), TIL = 1 (blue curve), and ni — 2 (highest red curve); when m = q = h = JJL. = fid = ra = 1 77 7.3 The particle velocity v(r, 9, TIL) versus 9 for r = 1 to 8, UL = 0 (lowest red- to-blue series of curves), TIL = 1 (middle red-to-blue series of curves), TIL = 2 (highest red-to-violet series of curves); when m = q = h = Lt = Hd = rx = 1.