A&A 409, 563-571 (2003)
DOI: 10.1051/0004-6361:20031082
Variation of cosmic ray injection across supernova shocks
H. J. Völk1, E. G. Berezhko2 and L. T. Ksenofontov2, 31 Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany
e-mail: Heinrich.Voelk@mpi-hd.mpg.de
2 Institute of Cosmophysical Research and Aeronomy, 31 Lenin Ave., 677891 Yakutsk, Russia
e-mail: berezhko@ikfia.ysn.ru
3 Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan
e-mail: ksenofon@icrr.u-tokyo.ac.jp
(Received 11 April 2003 / Accepted 28 May 2003)
Abstract
The injection rate of
suprathermal protons into the diffusive shock acceleration
process should vary strongly over the surface of
supernova remnant shocks. These variations and the absolute
value of
the injection rate are
investigated. In the simplest case, like for SN 1006,
the shock can be approximated as spherical in a uniform
large-scale magnetic field. The injection rate
depends strongly on the shock obliquity and diminishes as the angle
between the ambient field and the shock normal increases.
Therefore efficient particle injection, which leads to
conversion of a significant fraction of the
kinetic energy at a shock surface element, arises only
in relatively small regions near the "poles", reducing the
overall CR production. The sizes of these regions depend
strongly on the random background field and the Alfvén wave
turbulence generated due to the CR streaming instability. For
the cases of SN 1006 and Tycho's SNR they correspond
to about 20, and for Cas A to between 10 and 20 percent
of the entire shock
surface. In a first approximation, the CR production rate,
calculated under the assumption of spherical symmetry,
has therefore to be renormalized by this factor,
while the shock as such remains roughly spherical.
Key words: ISM: supernova remnants -- shock waves -- acceleration of particles -- ISM: cosmic rays -- ISM: magnetic fields
Offprint request: H. J. Völk, heinrich.voelk@mpi-hd.mpg.de
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