Issue |
A&A
Volume 453, Number 1, July I 2006
|
|
---|---|---|
Page(s) | 181 - 191 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361:20054737 | |
Published online | 09 June 2006 |
Turbulence and particle acceleration in collisionless supernovae remnant shocks
I. Anisotropic spectra solutions
1
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
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
Centre d'Études Spatiales et du Rayonnement, CNRS, Université Paul Sabatier, 9 avenue du Colonel Roche, 31028 Toulouse Cedex, France e-mail: Alexandre.Marcowith@cesr.fr
Received:
20
December
2005
Accepted:
16
March
2006
This paper investigates the nature of the MHD turbulence
excited by the streaming of accelerated cosmic rays in a shock wave
precursor. The two recognised regimes (non-resonant and resonant) of
the streaming instability are taken into account. We show that the
non-resonant instability is very efficient and saturates through a balance between its growth and non-linear transfer. The cosmic-ray
resonant instability then takes over and is quenched by advection
through the shock. The level of turbulence is determined by the
non-resonant regime if the shock velocity Vsh is larger than
a few times , where
is the ratio of
the cosmic-ray pressure to the shock kinetic energy. The instability
determines the dependence of the spectrum with respect to
(wavenumbers along the shock normal). The transverse cascade of Alfvén waves simultaneously determines the dependence in
. We also study the redistribution of turbulent energy
between forward and backward waves, which occurs through the
interaction of two Alfvén and one slow magneto-sonic
wave. Eventually the spectra at the longest wavelengths are found
almost proportional to
. Downstream, anisotropy is
further enhanced through the compression at shock crossing.
Key words: acceleration of particles / shock waves / turbulence / ISM: supernova remnants
© ESO, 2006
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