On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation

摘要

The cosmic-ray streaming instability creates strong magnetohydrodynamic turbulence in the precursor of a SN shock. The level of turbulence determines the maximum energy of cosmic-ray particles accelerated by the diffusive shock acceleration mechanism. In this paper we present the continuation of previous work (Ptuskin Zirakashvili 2003). We assume that Kolmogorov type nonlinear wave interactions together with ion-neutral collisions restrict the amplitude of the random magnetic field. As a result, the maximum energy of the accelerated particles strongly depends on the age of a SNR. The average spectrum of cosmic rays injected in the interstellar medium in the course of the adiabatic SNR evolution (the Sedov stage) is approximately Q(p)p(2) proportional to p(-2) at energies larger than 10-30 GeV/nucleon and with a maximum particle energy that is close to the position of the knee in the cosmic-ray spectrum observed at similar to4 x 10(15) eV. At an earlier stage of SNR evolution-the ejecta-dominated stage described by the Chevalier-Nadyozhin solution, the particles are accelerated to higher energies and have a rather steep power-law distribution. These results suggest that the knee may mark the transition from the ejecta-dominated to the adiabatic evolution of SNR shocks which accelerate cosmic rays.