Source position reconstruction and constraints on the galactic magnetic field from ultra-high energy cosmic rays

We study the possibility to reconstruct the position of ultra-high energy cosmic ray sources and some properties of the magnetic field along the line of sight towards them in the case that several events from the same source are detected. By considering an illustrative model for the galactic magnetic field, including both a regular and a turbulent component, we estimate the accuracy that can be achieved in the reconstruction. We analyse the effect of the experimental energy and angular resolutions on these results. We show that if about ten events with energies above 30 EeV are detected coming from the same source, it should be possible to reconstruct the source position with an accuracy of 0.5$^{\circ}$ and the integral of the orthogonal component of the magnetic field along the line of sight with an accuracy of 0.6 $\mu$G kpc Z$^{-1}$ (with Z the electric charge of the particles).Comment: Added references and referee comments, accepted for publicatio

The flux suppression at the highest energies

Almost half a century ago, Greisen, Zatsepin and Kuz'min (GZK) predicted a "cosmologically meaningful termination" of the spectrum of cosmic rays at energies around $10^{20}$ eV due to their interaction with the cosmic microwave background, as they propagate from distant extragalactic sources. A suppression of the flux above $4\times 10^{19}$ eV is now confirmed. We argue that current data are insufficient to conclude whether the observed feature is due to energy loss during propagation, or else to the fact that the astrophysical accelerators reach their limit, or indeed to a combination of both source properties and propagation effects. We discuss the dependence of the spectral steepening upon the cosmic-ray composition, source properties, and intervening magnetic fields, and speculate on the additional information that may be necessary to reach unambiguous conclusions about the origin of the flux suppression and of the mechanisms behind the acceleration of cosmic rays up to the highest observed energies.Comment: Invited review prepared for Comptes Rendus Physique (2014), in pres

Regenerative block empirical likelihood for Markov chains

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method cannot be directly applied on the data but rather on blocks of consecutive data catching the dependence structure. Generalization of empirical likelihood based on the construction of blocks of increasing nonrandom length have been proposed for time series satisfying mixing conditions. Following some recent developments in the bootstrap literature, we propose a generalization for a large class of Markov chains, based on small blocks of various lengths. Our approach makes use of the regenerative structure of Markov chains, which allows us to construct blocks which are almost independent (independent in the atomic case). We obtain the asymptotic validity of the method for positive recurrent Markov chains and present some simulation results

Detecting filaments in the ultra-high energy cosmic ray distribution

We propose and test new statistical tools to study the distribution of cosmic rays based on the use of the Minimal Spanning Tree. The method described is particularly sensitive to filamentary structures, as those expected to arise from strong sources of charged cosmic rays which get deflected by intervening magnetic fields. We also test the method with data available from the AGASA and SUGAR surface detector arrays.Comment: minor changes, matching the published version in Astroparticle Physic

Local-global principles for 1-motives

Building upon our arithmetic duality theorems for 1-motives, we prove that the Manin obstruction related to a finite subquotient \Be (X) of the Brauer group is the only obstruction to the Hasse principle for rational points on torsors under semiabelian varieties over a number field, assuming the finiteness of the Tate-Shaferevich group of the abelian quotient. This theorem answers a question by Skorobogatov in the semiabelian case and is a key ingredient of recent work on the elementary obstruction for homogeneous spaces over number fields. We also establish a Cassels-Tate type dual exact sequence for 1-motives, and give an application to weak approximation.Comment: 23 pages, minor modification

Arithmetic Duality Theorems for 1-Motives

We prove several duality theorems for the Galois and etale cohomology of 1-motives defined over local and global fields and establish a 12-term Poitou-Tate type exact sequence. The results give a common generalisation and sharpening of well-known theorems by Tate on abelian varieties as well as results by Tate/Nakayama and Kottwitz on algebraic tori.Comment: 44 pages, LaTeX, final version. Section 5 substantially rewritte

Effects of the galactic magnetic field upon large scale anisotropies of extragalactic Cosmic Rays

The large scale pattern in the arrival directions of extragalactic cosmic rays that reach the Earth is different from that of the flux arriving to the halo of the Galaxy as a result of the propagation through the galactic magnetic field. Two different effects are relevant in this process: deflections of trajectories and (de)acceleration by the electric field component due to the galactic rotation. The deflection of the cosmic ray trajectories makes the flux intensity arriving to the halo from some direction to appear reaching the Earth from another direction. This applies to any intrinsic anisotropy in the extragalactic distribution or, even in the absence of intrinsic anisotropies, to the dipolar Compton-Getting anisotropy induced when the observer is moving with respect to the cosmic rays rest frame. For an observer moving with the solar system, cosmic rays traveling through far away regions of the Galaxy also experience an electric force coming from the relative motion (due to the rotation of the Galaxy) of the local system in which the field can be considered as being purely magnetic. This produces small changes in the particles momentum that can originate large scale anisotropies even for an isotropic extragalactic flux.Comment: 11 pages, 4 figure