Confinement and anisotropy of ultrahigh-energy cosmic rays in isotropic plasma wave turbulence^*

I. Modification of the Hillas limit due to turbulence geometry

¹ Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany e-mail: rsch@tp4.ruhr-uni-bochum.de
² Department of Physics, University of Montenegro, Podgorica, Montenegro

Received: 14 December 2006
Accepted: 22 February 2007

Abstract

Context.The mean free path and anisotropy of galactic cosmic rays is calculated in weak plasma wave turbulence that is isotropically distributed with respect to the ordered uniform magnetic field.

Aims.The modifications on the value of the Hillas energy, above which cosmic rays are not confined to the Galaxy, are calculated. The original determination of the Hillas limit has been based on the case of slab turbulence where only parallel propagating plasma waves are allowed.

Methods.We use quasilinear cosmic ray Fokker-Planck coefficients to calculate the mean free path and the anisotropy in isotropic plasma wave turbulence.

Results.In isotropic plasma wave turbulence the Hillas limit is enhanced by about four orders of magnitude to  PeV resulting from the dominating influence of transit-time damping interactions of cosmic rays with obliquely propagating magnetosonic waves.

Conclusions.Below the energy E_c the cosmic ray mean free path and the anisotropy exhibit the well known  energy dependence. At energies higher than E_c both transport parameters steepen to a E³-dependence. This implies that cosmic rays even with ultrahigh energies of several hundreds of EeV can be rapidly pitch-angle scattered by interstellar plasma turbulence, and are thus confined to the Galaxy.