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Dissertation Submitted to the Combined Faculties of the Natural Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg. Germany for the degree of Doctor of Natural Sciences Put forward by Iwona Mochol born in Bielsko-Biała, Poland Oral examination: 7th November 2012 Nonlinear waves in Poynting-flux dominated outflows Referees: Prof. John G. Kirk Prof. Matthias Bartelmann Abstract Rotating, compact objects power some of the most spectacular phenomena in astrophysics, e.g., gamma-ray bursts, active galactic nuclei and pulsar winds. The energy is carried by Poynting flux, and the system is usually modelled using relativistic magnetohydrodynamics (MHD). How- ever, in the relatively low density medium expected around some of these objects, the MHD approximation breaks down, allowing new, large-amplitude waves to propagate. We discuss the role of these waves in two astrophysical contexts: In blazar jets, we show that a magnetic shear, launched together with a plasma from the black hole magnetosphere, begins to accelerate particles at a large distance from its source. The resulting non-thermal emission can, nevertheless, be modulated on very short timescales, which can explain the rapid variability of the TeV gamma-ray flux observed from some blazars. In pulsar winds, we analyze the radial propagation of superluminal modes, including their damp- ing by radiation reaction and by interaction with an external photon field. We discuss their effect on the structure of the pulsar wind termination shock, presenting new solutions in which the non-linear wave is asymptotically matched to the constant pressure surroundings. The obser- vational implications of these solutions are discussed for both isolated pulsars, and pulsars in binary systems. Zusammenfassung Rotierende kompakte Objekte treiben einige der spektakulärsten Prozesse in der Astrophysik an, beispielsweise Gammastrahlenblitze, aktive Galaxienkerne oder Pulsarwinde. Der Energieaus- tausch wird durch elektromagnetische Felder („Poynting flux“) vermittelt und über relativistische Magnetohydrodynamik modelliert. Diese Beschreibung ist jedoch ungeeignet für ein Medium mit relativ geringer Dichte, welches um solche Objekte erwartet wird und in dem sich Wellen mit grosser Amplitude ausbreiten können. Die Rolle dieser Wellen wird in zwei astrophysikalischen Zusammenhängen diskutiert: Erstens wird gezeigt, dass magnetische Scherwellen in Blazar Jets, welche zusammen mit Plasma aus der Magnetosphäre eines Schwarzen Loches erzeugt werden, in grossem Abstand zur Quelle Teilchen zu beschleunigen beginnen. Nichtsdestotrotz kann die resultierende nicht-thermische Emission auf sehr kurzen Zeitskalen moduliert werden, was die schnelle Änderung des TeV Gam- mastrahlenflusses erklärt, welche bei einigen Blazaren beobachtet wird. Zweitens wird die radiale Ausbreitung von superluminalen Moden in Pulsarwinden analysiert, inklusive der Strahlungsdämpfung und Abschwächung durch Wechselwirkung mit einem externen Photonfeld. Der Effekt der Wellen auf die Struktur des Terminationshocks eines Pulsarwindes wird diskutiert und neue Lösungen präsentiert, in denen die nichtlineare Welle an die Umgebung mit konstanten Druck asymptotisch angepasst wird. Die Implikationen für Beobachtungen dieser Lösungen werden sowohl für isolierte Pulsare, als auch für Pulsare in binären Systemen diskutiert. To my parents, and Gosia Contents I 1 1 Introduction 3 1.1 Blazars.......................................... 4 1.2 Pulsars.......................................... 6 1.3 Structureofthethesis .............................. ... 8 2 Beyond MHD: nonlinear waves in plasmas 11 2.1 Motion of a particle in an electromagnetic wave . .... 11 2.2 Large-amplitude waves in cold pair plasmas . .. 13 2.2.1 Specialframes ................................. 15 2.2.2 Subluminal mode: magnetic shear . 15 2.2.3 Superluminal mode: linearized theory . 16 2.2.4 Superluminal nonlinear waves . 17 2.3 Radiationprocesses................................. .. 20 2.3.1 Radiationreaction ............................... 20 2.3.2 Inverse Compton scattering on an external photon field . .... 21 II 23 3 Rotating black holes and jet launching 25 3.1 Kerrblackholes..................................... 26 3.1.1 Themetric ................................... 26 3.1.2 Spacetime splitting and physics in ZAMO’s frame . 27 3.1.3 Energy extraction from Kerr black holes – the Penrose process ...... 32 3.2 Wald’s solution and the vacuum magnetosphere . ..... 33 3.3 Particle acceleration and cascade pair production . ....... 36 3.4 Force-free magnetosphere and Blandford-Znajek mechanism ............ 38 3.4.1 TheBlandford-Znajekmechanism . 38 3.4.2 Blandford-ZnajekasaPenroseprocess . .... 40 3.4.3 Vacuum of a curved spacetime as an electromagnetically active medium . 41 3.4.4 EfficiencyoftheBlandford-Znajekprocess . .... 42 3.5 Astrophysicaljets................................. ... 43 3.5.1 Central engine – accreting black hole . 43 3.5.2 Diskjets..................................... 44 3.5.3 Collimation and acceleration . 46 3.5.4 Extreme TeV variability in blazars . 47 4 Subluminal waves in blazar jets 51 4.1 Parameters ....................................... 51 4.2 Themodel........................................ 53 i 4.3 Multiple-scale perturbation calculation . .... 53 4.3.1 Lowest order solution: nonlinear waves . 55 4.3.2 First order solution . 56 4.3.3 Radial evolution of a magnetic shear . 59 4.4 Application to blazar variability . 60 4.5 Summaryandconclusions .............................. 62 III 63 5 Pulsar winds 65 5.1 Launchingfromthemagnetosphere . .... 65 5.2 Thestripedwind .................................... 70 5.2.1 Structure .................................... 70 5.2.2 Parameters ................................... 73 5.2.3 MHDshocksofpulsarwinds ......................... 76 5.2.4 σ-problem.................................... 77 5.3 Relativistically strong waves in pulsar winds . ... 79 5.3.1 Propagation condition . 80 5.3.2 Conversion ................................... 81 6 Superluminal waves in pulsar winds 85 6.1 Radialpropagation.................................. 86 6.2 Matchingtotheexternalpressure. ...... 87 6.2.1 Conservation of γ′ .............................. 88 h i 6.2.2 Matching of a circularly polarized wave . 90 6.2.3 Matching of a linearly polarized wave . 91 6.2.4 Externalpressure................................ 92 6.3 EMprecursorsofpulsarwindshocks . .... 92 6.3.1 Damping due to radiation reaction . 94 6.3.2 Application to binaries . 97 6.3.3 Implications for lightcurves . 101 6.3.4 Parametric instabilities . 102 6.4 Summaryandconclusions .............................. 105 Summary 107 Bibliography 109 Acknowledgments 121 ii List of Figures 1.1 CollimatedjetsfromCygnusA . 4 1.2 Edge-darkenedjetsfrom3C31. ..... 5 1.3 Crabnebula....................................... 7 3.1 SketchofKerrspacetime............................. ... 26 3.2 Spacetime slicing . 29 3.3 Rotating black hole in an asymptotically uniform magnetic field (Wald’s field) . 35 3.4 Trajectories of charged particles in the Wald field . ..... 36 3.5 LightsurfacesinKerrgeometry. ... 40 3.6 Ergosphericjet .................................... 41 3.7 Blackholebattery ................................... 42 3.8 Formation of a low density funnel in the accretion flow . ..... 45 3.9 Sketchofatwo-compositejet . .... 45 4.1 Radial evolution of a magnetic shear in a blazar jet . ..... 60 5.1 Goldreich-Julian space charge . ... 66 5.2 Sketchofapulsarmagnetosphere . ..... 69 5.3 Corrugated current sheet in a pulsar wind of an oblique rotator . ......... 71 5.4 Sketchofasupernovaremnant . .... 76 5.5 Lorentz factor of a strong wave vs conversion radius . ........ 83 6.1 Radial evolution of the wave Lorentz factor for different conversion radii . 87 6.2 Sketch of the model in which an MHD wind converts to an EM precursor .... 88 6.3 Radial evolution of a strong wave matched to the external medium........ 93 6.4 Radial evolution of a strong wave undergoing radiation damping . ....... 95 6.5 Damping length of a strong wave as a function of the external pressure, charac- terized by the distance at which it would balance the ram pressure of an MHD wind........................................... 97 6.6 Shock regime switching in the binary PSR B1259-63 . .... 99 6.7 Shock properties vs orbital separation in binary PSR B1259-63 . ......... 100 iii iv Part I 1 Chapter 1 Introduction The mechanism underlying the most energetic phenomena in the Universe is thought to be the extraction of the rotational energy of a central, compact object by a relativistic outflowing wind. The energy transfer is mediated by the electromagnetic fields that are launched together with a plasma, and, presumably, are responsible for the outflow collimation and acceleration of the particles that radiate nonthermal photons. Theoretical and numerical investigations suggest that such an outflowing wind is rather dense close to the central object, since the magnetospheres around rapidly spinning neutron stars or black holes are prone to avalanche pair production processes. The electromagnetic cascades are started by primary particles, ripped out of the stellar surface or supplied by the accretion flow around a black hole, and are sustained by the radiation these particles emit when accelerating in the curved, extremely strong magnetic fields in the magnetosphere. Even though the created plasma has a density high enough to screen out any electric field component along the magnetic field lines, the particles are thought to contribute
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