Inhomogeneous extragalactic magnetic fields and the second knee in the cosmic ray spectrum

Various experiments indicate the existence of a second knee around energy E=3×10¹⁷eV in the cosmic ray spectrum. This feature could be the signature of the end of the galactic component and of the emergence of the extragalactic one, provided that the latter cuts off at low energies. Recent analytical calculations have shown that this cutoff could be a consequence of the existence of extragalactic magnetic fields (Refs. [M. Lemoine, Phys. Rev. D 71, 083007 (2005).PRVDAQ0556-282110.1103/PhysRevD.71.083007][R. Aloisio and V. Berezinsky, Astrophys. J. 625, 249 (2005).ASJOAB0004-637X10.1086/429615]): low energy protons diffuse on extragalactic magnetic fields and cannot reach the observer within a given time. We study the influence of inhomogeneous magnetic fields on the magnetic horizon, using a new semianalytical propagation code. Our results indicate that, at a fixed value of the volume averaged magnetic field ⟨B⟩, the amplitude of the low energy cutoff is mainly controlled by the strength of magnetic fields in the voids of the large-scale structure distribution.