On the Cosmological Propagation of High Energy Particles in Magnetic Fields Dissertation with the aim of achieving a doctoral degree at the Faculty of Mathematics, Informatics and Natural Sciences Department of Physics Universit¨atHamburg submitted by Rafael Alves Batista from Uberaba, Brazil Hamburg 2015 Day of oral defense: April 8th, 2015 Examiners of the oral doctoral defense: Prof. Dr. Dieter Horns Prof. Dr. Johannes Haller Prof. Dr. Andreas Ringwald The following evaluators recommend the admission of the dissertation: Prof. Dr. G¨unterSigl Prof. Dr. Robi Banerjee Acknowledgements During this journey many people have contributed to my personal and academic growth. These pages are dedicated to express my gratitude to all those individuals who, in some way, have directly or indirectly contributed to this work. I apologize for forgetting and omitting some names. First of all, I would like to express my gratitude to my supervisor G¨unterSigl for his guidance during these three years. Without him this work definitely would not have been possible. I would like to specially thank my mom, Helena Maria Alves, who has always supported me in all possible ways, alongside with my dad, Francisco Batista. They provided me with all the necessary conditions to trail this path. I thank Luciana Oliveira Fernandes who was always there to support and cheer me up during difficult times and the long nights when I was working and asking myself \will I ever get this done?". I also thank all my close friends for their support. I thank Dmitri Semikoz (APC, Paris) and Julien Devriendt and Min-Su Shin (University of Oxford) for their hospitality during multiple visits to their institutes. I am indebted to Dmitri Semikoz for his help and guidance in many parts of this work. I also gratefully acknowledge the cosmological simulations performed by Julien Devriendt and Min-Su Shin, which were the core of chapter 6, and thank them for productive discussions. I acknowledge the crucial contribution of the CRPropa developers team (Martin Erdmann, Carmelo Evoli, Karl-Heinz Kampert, Daniel Kuempel, Gero Mueller, Guenter Sigl, Arjen van Vliet, David Walz, Tobias Winchen) to this work. My special thanks to David Walz for many discussions and for promptly helping me solving some problems with the code. I thank Carmelo Evoli, Andrey Saveliev, Peter Schiffer and Arjen van Vliet for discussions, and Andrey for his contribution to the development of the gamma ray propagation code. I also thank my fellow colleagues from the Pierre Auger Collaboration for useful discussions. My life in Hamburg would not have been the same without the companionship of former and current members of the astroparticle theory group. Thank you all! I am also glad for having had such great friends office mates (Andrey Saveliev and Martin Vollmann). I cannot fail to mention two people who mentored me in the early stages of my career: my former advisor Ernesto Kemp, who supervised me for 5 years, and my former co-supervisor Rogerio de Almeida, who patiently guided my first steps in the field of cosmic rays. This work was possible thanks to the support of the Forschungs- und Wissenschaftsstiftung Hamburg through the program \Astroparticle Physics with Multiple Messengers". I also acknowledge the complemen- tary funding from the Helmholtz Alliance for Astroparticle Physics (HAP). iii Abstract In the present work the connection between high energy particles and cosmic magnetic fields is explored. Particularly, the focus lies on the propagation of ultra-high energy cosmic rays (UHECRs) and very-high energy gamma rays (VHEGRs) over cosmological distances, under the influence of cosmic magnetic fields. The first part of this work concerns the propagation of UHECRs in the magnetized cosmic web, which was studied both analytically and numerically. A parametrization for the suppression of the UHECR flux at energies ∼ 1018 eV due to diffusion in extragalactic magnetic fields was found, making it possible to set an 17 upper limit on the energy at which this magnetic horizon effect sets in, which is . 10 eV. To confront theoretical models with experimental data collected by large cosmic ray experiments such as the Pierre Auger Observatory, and at the same time to address the open questions regarding the origin and nature of UHECRs, the CRPropa code was developed. It allows the propagation of UHECRs and secondary gamma rays and neutrinos in the universe including all relevant energy loss and interaction processes as well as effects of galactic and extragalactic magnetic fields. The newest version, CRPropa 3, is discussed in details, including the novel feature of cosmological effects in three-dimensional simulations, which enables time dependent studies considering simultaneously magnetic field effects and the cosmological evolution of the universe. An interesting possibility is to use UHECRs to constrain properties of cosmic magnetic fields, and vice-versa. Numerical simulations of the propagation of UHECRs in the magnetized cosmic web, obtained through magnetohydrodynamical simulations of structure formation, were performed. It was studied the effects of different magnetic field seeds on the distribution of cosmic magnetic fields today, and their impact on the propagation of cosmic rays. Furthermore, the influence of uncertainties of the strength of intergalactic magnetic fields on the propagation of UHECRs was analyzed. It is shown that magnetic fields are crucial for the propagation of cosmic rays, and the lack of knowledge about their properties can spoil the possibilities of identifying individual sources of UHECRs. The prospects for UHECR astronomy are discussed in light of these results. The second part of this work concerns the propagation of VHEGRs in the universe. Gamma rays interact with pervasive photon fields creating electron-positron pairs which scatter background photons, in a process known as electromagnetic cascade. The electron-positron pairs can provide valuable information about the intervening magnetic fields, including the possibility of constraining the strength of these fields. A new Monte Carlo code for propagating VHEGRs in the universe was developed, based on the code structure of CRPropa. This code was applied to the study of pair halos from blazars under the assumption of different magnetic field configurations. The results suggest that the observation of pair halos can provide important clues on the strength of intergalactic magnetic fields, as well as the maximal energy attainable by VHEGR sources. v Zusammenfassung In der vorliegenden Dissertation wird die Beziehung zwischen hochenergetischen Teilchen und kosmis- chen Magnetfeldern erforscht. Insbesondere geht es dabei um die Ausbreitung der ultrahochenergetischen kosmischen Strahlung (UHECRs) und der sehr hochenergetischen Gammastrahlung (VHEGRs) in kosmichen Magnetfeldern. Der erste Teil dieser Arbeit betrifft die Ausbreitung der UHECRs im kosmischen Netz, die analytisch und numerisch untersucht wurde. Es wurde eine Parametrisierung der Unterdr¨uckungdes UHECR-Flusses bei Energien ∼ 1018 eV aufgrund der Diffusion in extragalaktischen Magnetfeldern gefunden, die es erm¨oglicht, eine Obergrenze f¨urdie Energie, bei der dieser Effekt des magnetischen Horizonts einsetzt, zu bestimmen, 17 n¨amlich . 10 eV. Um theoretische Modelle mit Daten von Großexperimenten zur kosmischen Strahlung wie dem Pierre Auger Observatorium zu vergleichen und um gleichzeitig die offenen Fragen in Bezug auf den Ursprung und die Natur der UHECRs zu beantworten, wurde die Software CRPropa entwickelt. Mit dieser ist es m¨oglich,die Ausbreitung von UHECRs sowie der sekund¨arenGammastrahlung und Neutrinos im Univer- sum zu simulieren, einschließlich aller relevanter Energieverlust- und Wechselwirkungsprozesse sowie der Auswirkungen der galaktischen und extragalaktischen Magnetfelder. Die neueste Version, CRPropa 3, wird detailliert diskutiert, darunter die neue M¨oglichkeit der Einbeziehung der kosmologischen Effekte bei dreidi- mensionalen Simulationen, welche zeitabh¨angigeStudien unter gleichzeitiger Beachtung von Magnetfeldern und der kosmologischen Entwicklung des Universums erm¨oglicht. Es ist eine interessante M¨oglichkeit, UHECRs zu benutzen, um Eigenschaften der kosmischen Mag- netfelder einzuschr¨anken und umgekehrt. Numerische Simulationen der Ausbreitung von UHECRs im mag- netisierten kosmischen Netz, welches durch magnetohydrodynamische Simulationen der Strukturbildung er- halten wurde, wurden durchgef¨uhrt. Die Effekte unterschiedlicher Saatmagnetfelder auf die heutige kos- mische Magnetfeldverteilung sowie ihre Auswirkung auf die Ausbreitung der kosmischen Strahlung wurden untersucht. Weiterhin wurde eine Analyse gemacht, um den Einfluss der Unsicherheiten der St¨arke inter- galaktischer Magnetfelder auf die Ausbreitung der UHECRs zu verstehen. Es wird gezeigt, dass Magnetfelder entscheidend f¨urdie Ausbreitung der kosmischen Strahlung sind und dass die mangelnde Kenntnis ihrer Eigen- schaften die Identifizierung der Quellen der UHECRs teilweise verhindern k¨onnen.Die Perspektiven f¨urdie UHECR-Astronomie werden angesichts diese Ergebnisse diskutiert. Der zweite Teil dieser Arbeit behandelt die Ausbreitung der VHEGRs im Universum. Die Wechsel- wirkung der Gammastrahlen mit den durchdringenden Photonenfeldern kann Elektron-Positron-Paare erzeu- gen, die wiederum die Hintergrundphotonen streuen. Dieser Prozess ist die sogenannte elektromagnetische Kaskade. Die Elektron-Positron-Paare k¨onnenwertvolle Informationen ¨uberdie den von ihnen durchquerten Raum durchziehenden Magnetfelder