Distortion of the ultrahigh energy cosmic ray flux from rare transient sources in inhomogeneous extragalactic magnetic fields

¹ Institut d’Astrophysique de Paris, CNRS – Université Pierre & Marie Curie, 98bis boulevard Arago, 75014 Paris, France
e-mail: kalli@iap.fr
² Université Mohamed Boudiaf, Msila, Algérie
³ Laboratoire de Physique Mathématique et Physique Subatomique (LPMPS), Université Mentouri, Constantine, Algérie
⁴ Department of Astronomy & Astrophysics, Enrico Fermi Institute, and Kavli Institute for Cosmological Physics, The University of Chicago, Chicago, Illinois 60637, USA

Received: 3 September 2010
Accepted: 29 December 2010

Abstract

Detecting and characterizing the anisotropy pattern of the arrival directions of the highest energy cosmic rays are crucial steps towards the identification of their sources. We discuss a possible distortion of the cosmic ray flux induced by the anisotropic and inhomogeneous distribution of extragalactic magnetic fields in cases where sources of ultrahigh energy cosmic rays are rare transient phenomena, such as gamma-ray bursts and/or newly born magnetars. This distortion does not involve an angular deflection but the modulation of the flux related to the probability of seeing the source on an experiment lifetime. To quantify this distortion, we construct sky maps of the arrival directions of these highest energy cosmic rays for various magnetic field configurations and appeal to statistical tests proposed in the literature. We conclude that this distortion cannot affect present experiments but should be considered when performing anisotropy studies with future large-scale experiments that record as many as hundreds of events above 6 × 10¹⁹ eV.