Issue |
A&A
Volume 453, Number 1, July I 2006
|
|
---|---|---|
Page(s) | 193 - 202 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361:20054738 | |
Published online | 09 June 2006 |
Turbulence and particle acceleration in collisionless supernovae remnant shocks
II. Cosmic-ray transport
1
Centre d'Études Spatiales et du Rayonnement, CNRS, Université Paul Sabatier Toulouse 3, 9 avenue du Colonel Roche, 31028 Toulouse Cedex, France e-mail: Alexandre.Marcowith@cesr.fr
2
Institut d'Astrophysique de Paris, UMR 7095 CNRS, Université Pierre & Marie Curie, 98bis boulevard Arago, 75014 Paris, France e-mail: lemoine@iap.fr
3
Laboratoire d'Astrophysique de Grenoble, CNRS, Université Joseph Fourier II, BP 53, 38041 Grenoble, and Institut Universitaire de France, France e-mail: Guy.Pelletier@obs.ujf-grenoble.fr
Received:
20
December
2005
Accepted:
16
March
2006
Supernovae remnant shock waves could be at the origin of
cosmic rays up to energies in excess of the knee (eV) if the magnetic field is efficiently amplified by the
streaming of accelerated particles in the shock precursor. This paper
follows up on a previous paper (Pelletier et al. 2006, A&A, in press) which derived the
properties of the MHD turbulence so generated, in particular its
anisotropic character, its amplitude and its spectrum. In the present
paper, we calculate the diffusion coefficients, also accounting for
compression through the shock, and show that the predicted
three-dimensional turbulence spectrum
(with
and
the wavenumber components along and
perpendicular to the shock normal) generally leads to Bohm diffusion
in the parallel direction. However, if the anisotropy is constrained
by a relation of the form
, which
arises when the turbulent energy cascade occurs at a constant rate
independent of scale, then the diffusion coefficient loses its Bohm
scaling and scales as in isotropic Kolmogorov turbulence. We show that
these diffusion coefficients allow to account for X-ray observations
of supernova remnants. This paper also calculates the modification of
the Fermi cycle due to the energy lost by cosmic rays in generating
upstream turbulence and the concomittant steepening of the energy
spectrum. Finally we confirm that cosmic rays can produced an
amplified turbulence in young SNr during their free expansion phase
such that the maximal energy is close to the knee and the spectral
index is close to 2.3 in the warm phase of the interstellar medium.
Key words: acceleration of particles / shock waves / turbulence / ISM: supernova remnants
© ESO, 2006
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