Propagation of Ultra-High Energy Cosmic Rays and anisotropy studies with the Pierre Auger Observatory: the multiscale approach

The main goal of this thesis is the investigation of the arrival directions of ultra-high energy cosmic rays (UHECRs). The clustering of such events, collected by the Pierre Auger Observatory, is used to infer the nature of sources and their density, as well as other physical unknowns. Results are based on the comparison between real and simulated data. Hence, an ad hoc Monte Carlo code (HERMES) for the realistic simulation of UHECR propagation in the Universe and a novel method (MAF) to quantify the amount of clustering in a data set of few UHECR events have been developed. In the first chapter, a general overview of UHECR physics is given, with particular attention to the Auger Observatory and the most recent results regarding its measurements. In the second and third chapters, we present the general structure of HERMES and we discuss the procedures adopted to simulate the propagation of UHECRs in a magnetized Universe. In the second chapter, magnetic fields are treated, and their impact on the propagation of UHECRs is discussed. In particular, we simulate the diffusion of charged particles in both turbulent and structured magnetic fields for energy values ranging from 10^17 to 10^21 eV. In the third chapter, the propagation of protons and heavier nuclei is treated. We define the cosmological framework of HERMES and we parameterize the cosmic background radiation (CBR). The parameterizations for the cross section of the interactions between nuclei and CBR photons are discussed, as well as the relevant energy-loss processes. The impact of propagation on the GZK horizon of UHE protons is investigated, and comparisons between our results and the literature those obtained with other simulators are presented. In the fourth chapter, a novel method is introduced to estimate the statistical significance of clustering in the arrival direction distribution of few events, a necessary requirement because of the current small number of events observed above 5x10^19 eV. The method involves a multiscale procedure, based on information theory and extreme value statistics, providing high discrimination power, even in presence of strong background isotropic contamination. It is extended to allow correlation analysis with catalogues of sources. Here, the term "multiscale" explicitly indicates the dependence on the angular scale adopted to investigate the arrival directions of UHECRs. It is shown that MAF has some valuable features, it is: i) semi-analytical, ii) very sensitive to small, medium and large scale clustering, iii) not biased against the null hypothesis. Finally, in the fifth, sixth and seventh chapters, Monte Carlo simulations are extensively adopted to investigate real data. In the fifth chapter we use multiscale methods to explore the effects of experimental uncertainties on clustering and correlation of UHECRs with catalogues. In the sixth chapter, energy losses due to secondary particle production or photo-disintegration, as well as deflections due to galactic (GMF) and extragalactic magnetic fields (EMF), are taken into account. All of such interactions, together with the distribution of sources, produce different arrival directions of events at Earth. Hence, clustering in events detected with the Auger Observatory and in simulated sky maps of UHECRs, mimicking realistic astrophysical scenarios, is used to put bounds on some relevant unknowns, as the fraction of protons in the data, the density of sources and the strength of the turbulent component of the EMF. Moreover, the possibility that nearby active galactic nuclei and black holes could be responsible for the observed flux of UHECRs is explored in detail. In the seventh chapter, we perform a more extended study which takes into account additional observables, as the elongation rate and the energy spectrum. By varying the underlying assumptions, we have outlined an astrophysical scenario able to explain Auger data from a phenomenological point of view.