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A Phenomenological Approach to the Study of the Cosmic Ray Galactic-Extragalactic Transition

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A Phenomenological Approach to the Study of the Cosmic Ray Galactic-Extragalactic Transition A phenomenological approach to the study of the cosmic ray Galactic-extragalactic transition C. De Donato November 21, 2008 Ai miei genitori “... fatti non foste a viver come bruti, ma per seguir virtute e canoscenza” Dante Alighieri Divina Commedia Inferno XXVI vv 118-120 Acknowledgments I would like to thank my tutor Dr. Battistoni and all the people of the Univer- sit`adegli Studi di Milano which, despite not taking part in the Auger project, demonstrated a lot of interest in my studies with stimulating discussions. I am grateful to the Pierre Auger Collaboration; I have benefited from the inter- action with several colleagues and from a very stimulating professional environ- ment. Special thanks are reserved to Prof. Gianni Navarra for his availability and the time he dedicated to my thesis work. I would like to thank also the Instituto de Ciencias Nucleares (UNAM), for its hospitality during my extended stays, and all the ICN group with whom I have spent a very productive and pleasant period of my PhD studies. A special mention is reserved to Dr. Gustavo Medina Tanco who guided and supported me along my PhD studies not only as a co-tutor but also as a friend. The knowledge and the passion he transmits in his work is a rare and spe- cial gift and I feel honored by the trust he put in my capabilities and work. The challenges he presented me every day made my work very stimulating and productive (and my night rests very short!), feeding my enthusiasm in my re- searches. Finally, but not less important, I want to thank all my family and friends, who always believed in me. There are not enough words to describe the importance of my parents, grandparents, brothers and sisters in my life. Their encourage- ment during my studies and their support in my professional choices have been fundamental. The values my parents have transmitted to me have been, and are still, decisive in my life and made me the person I am proud to be. I hope they will always perceive the love I feel for all of them. Special thanks are reserved to my best friends Rossella and Eleonora who always have been close to me anywhere I were. The experiences we lived and shared together made our friendship deep and unique; they will have a special place in my heart and life forever. i Abstract The cosmic ray (CR) energy spectrum extends for many orders of magnitude with a power law index 2.7. Along this range of energies, three spectral fea- tures are known: the first≈ knee at E 3 P eV , the second knee at E 0.5 EeV and the ankle, a depression extending≈ from the second knee to beyond≈ 10 EeV . The nature of the second knee and of the ankle is still uncertain; a possible interpretation of the two features is the transition between the Galactic and extragalactic components. At energies between 1017 1018 eV the Galactic supernova remnants (SNR) are expected to become inefficient− as particle accel- erators. This fact, combined with magnetic deconfinement, should lead to the end of the observation of a Galactic component of cosmic rays, although the picture could be confused by the existence of additional Galactic accelerators at higher energy. On the other hand, at energies above the second knee, extra- galactic particles are able to travel from the nearest extragalactic sources in less than a Hubble time. Since Galactic deconfinement at these energies would also allow them to penetrate the Galactic field, the spectrum may present above 1017.5 eV a growing extragalactic component that becomes dominant above 1019 eV . Therefore, the region encompassing the second knee and the ankle could be the transition region between the Galactic and extragalactic compo- nents. The energy region spanning from 1017 eV to . 1019 eV is critical for un- derstanding both, the Galactic and∼ the extragalactic cosmic ray fluxes. The detailed knowledge of the way in which this transition takes place, i.e. the exact spectral shapes of the involved components and the evolution of their composition as a function of energy, is essential in order to understand the origin and propagation of CRs, since important information can be deduced on the astrophysical sources, the conditions of propagation in the extragalactic space and the cosmological evolution of the sources of the most energetic CRs. The study of the transition region can provide important information able, in principle, to break the degeneracy between astrophysical models existing at the highest energies due to the low available statistics. The present PhD thesis deals with theoretical and phenomenological aspects of ultra-high energy cosmic ray physics, with specific emphasis on the numer- ical modeling of the transition between the diffusive and ballistic propagation regimes in the 1017 to 1019 eV energy range, i.e., the end of the Galactic con- finement and the mixing of the Galactic and extragalactic components of the cosmic ray flux. The Galactic spectrum from regular Supernova remnants was calculated using a numerical diffusive propagation code in a realistic realization of the interstellar medium, properly accounting for in-flight spallation and de- iii iv cay. The calculated diffusive Galactic spectrum is used to analyze the end of the Galactic cosmic ray spectrum and its mixing with the extragalactic cosmic ray flux by comparing alternative theoretical scenarios with data from the most relevant experiments in the relevant energy region. In particular, the transition region is analyzed combining the diffusive Galactic spectrum from SNRs with two different models of extragalactic spectrum, one in which only protons are injected at the sources and another one in which a mixed composition of nuclei is injected instead. In order to discriminate between possible astrophysical scenarios, the experi- mental parameter Xmax, a composition indicator, was inferred from the differ- ent theoretical extragalactic (EG) models for the several hadronic interaction models currently in use in the literature. A comparison of these results with experimental data was performed with special attention to Auger and HiRes re- sults. Spectral and composition data (in the form of Xmax) provided by HiRes and Auger experiments, which favor an EG mixed composition, were used to set constraints on the Galactic and extragalactic CR fluxes and on their change in composition as a function of energy. The conditions that must be met by the Galactic and extragalactic fluxes in or- der to reproduce simultaneously the total spectrum and elongation rate observed by either Auger or HiRes, were studied in detail. The present analysis favors a mixed extragalactic spectrum, combined with a Galactic spectrum enhanced by two additional high energy components of mixed composition, extending be- yond the maximum energies expected from regular supernova remnants. The evolution of composition inside each component and their relative compo- sition suggest two contributions, the main one consistent with acceleration in different populations of SNRs immersed in differing environments and a minor contribution from another acceleration mechanisms, without a rigidity cut-off, operating at the highest energies, possibly associated with inductors such as compact objects like pulsars and magnetars. The potential impact on the astrophysical analysis of the assumed hadronic in- teraction model was also assessed. As a by-product of the diffusive propagation of lower energy CR, the diffuse neutrino background produced by our Galaxy from the decay of pions origi- nated in p-p interactions between cosmic rays and the interstellar medium has been numerically calculated. Contents 1 UHECR physics 1 1.1 Thecosmicrayspectrum ...................... 1 1.2 Transitionmodels........................... 4 1.3 Sources ................................ 7 1.3.1 “Bottom-up”models: cosmicaccelerators . 9 1.3.2 “Top-down” models: alternative models . 12 1.3.3 Z-burstmodelsandothers. 13 1.4 InteractionwithCBR . .. .. .. .. .. .. .. .. .. 13 1.4.1 Protons ............................ 14 1.4.2 Nuclei ............................. 17 1.4.3 Photons............................ 18 1.5 Magneticfields ............................ 18 1.5.1 Galacticmagneticfield. 18 1.5.2 Extragalacticmagneticfield . 19 2 Detection of UHECRs 23 2.1 EAS .................................. 23 2.2 Detectiontechniques . 29 2.2.1 Surfacedetectors: GroundArrays . 30 2.2.2 Fluorescencedetectors . 32 2.2.3 Radiodetectors. .. .. .. .. .. .. .. .. .. 37 2.3 Experiments.............................. 37 2.3.1 VolcanoRanchArray . 37 2.3.2 HaverahParkArray . 39 2.3.3 YakutskArray ........................ 40 2.3.4 Akeno Giant Air-Shower Array (AGASA) . 42 2.3.5 Fly’sEyeDetector . 43 2.3.6 HiRes ............................. 45 2.3.7 KASCADEandKASCADE-Grande . 46 2.3.8 PierreAugerObservatory . 47 2.3.9 AMIGAandHEAT ..................... 49 2.3.10 TelescopeArray(TA)andTALE . 51 3 Results 53 3.1 Spectrum ............................... 53 3.1.1 Dipcalibration ........................ 57 3.1.2 SpectrumandEGastrophysicalmodels . 58 3.2 Composition ............................. 61 v vi CONTENTS 3.2.1 Compositioninthetransitionregion . 62 3.2.2 Primaryphotons .. .. .. .. .. .. .. .. .. .. 63 3.2.3 Neutrinos ........................... 65 3.3 Anisotropy .............................. 65 3.3.1 Large-scaleanisotropy . 65 3.3.2 Intermediatescaleanisotropy . 67 3.3.3 Smallscaleanisotropy . 67 3.4 Crosssection ............................. 71 3.5 Summaryoftheresults .. .. .. .. .. .. .. .. .. .. 72 3.6 Importanceofthetransitionregion . 73 4 The transition region: spectrum 75 4.1 SNRGalacticspectrum
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