EDP Sciences
Free access
Volume 403, Number 1, May III 2003
Page(s) 1 - 10
Section Cosmology
DOI http://dx.doi.org/10.1051/0004-6361:20030323

A&A 403, 1-10 (2003)
DOI: 10.1051/0004-6361:20030323

Limits on diffusive shock acceleration in supernova remnants in the presence of cosmic-ray streaming instability and wave dissipation

V. S. Ptuskin and V. N. Zirakashvili

Institute for Terrestrial Magnetism, Ionosphere and Radiowave Propagation of the Russian Academy of Sciences, Troitsk, Moscow Region 142190, Russia
(Received 23 January 2003 / Accepted 6 February 2003 )

The instability in the cosmic-ray precursor of a supernova shock moving in interstellar medium is studied. The level of magnetohydrodynamic turbulence in this region determines the maximum energy of particles accelerated by the diffusive shock acceleration mechanism. A high efficiency of cosmic ray acceleration is accepted, and the consideration is not limited by the case of weak turbulence. It is assumed that Kolmogorov-type nonlinear wave interactions together with the ion-neutral collisions restrict the amplitude of the random magnetic field. As a result, the maximum energy of accelerated particles strongly depends on the age of the supernova remnant. The maximum energy can be as high as ${\sim}10^{17}Z$ eV in young supernova remnants and falls to about ${\sim}10^{10}Z$ eV at the end of the Sedov stage. Thus the standard estimate of maximum particle energy based on the Bohm limit calculated for the interstellar magnetic field strength is not justified in this case. This finding may explain why supernova remnants with age of more than a few thousand years are not prominent sources of very high energy gamma-rays.

Key words: ISM: supernova remnants -- ISM: cosmic rays -- acceleration of particles -- shock waves -- turbulence -- gamma rays: theory

Offprint request: V. S. Ptuskin, vptuskin@izmiran.rssi.ru

© ESO 2003