A&A 427, 525-536 (2004)

DOI: 10.1051/0004-6361:20041111

## The theory of synchrotron emission from supernova remnants

**E. G. Berezhko**

^{1}and H. J. Völk^{2}^{1}Institute of Cosmophysical Research and Aeronomy, 31 Lenin Av., 677891 Yakutsk, Russia

e-mail: berezhko@ikfia.ysn.ru

^{2}Max Planck Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany

e-mail: Heinrich.Voelk@mpi-hd.mpg.de

(Received 16 April 2004 / Accepted 9 July 2004)

** Abstract **

The time-dependent nonlinear kinetic theory for cosmic ray
(CR) acceleration
in supernova remnants (SNRs) is applied
studying the
properties of the synchrotron emission from SNRs, in
particular,
the surface brightness-diameter (
) relation. Detailed
numerical calculations are performed for the expected range of
the relevant physical parameters, namely the ambient
density and the supernova explosion energy. The magnetic field
in SNRs is assumed to be significantly amplified by the
efficiently accelerating nuclear CR component. Due to the growing
number of
accelerated CRs the expected SNR luminosity increases during the
free
expansion phase, reaches a peak value at the
beginning of the Sedov phase and then decreases again, since in
this stage the overall CR number remains nearly constant,
whereas the effective magnetic field diminishes with time.
The theoretically predicted brightness-diameter relation
in the radio range in the Sedov phase is close to
. It
fits the observational data in a very
satisfactory way. The observed spread of
at a given
SNR size
*D* is the result of the spread of supernova explosion
energies and interstellar medium densities.

**Key words:**X-rays: stars

**--**stars: supernovae: general

**--**shock waves

**--**acceleration of particles

**--**radiation mechanisms: non-thermal

**--**magnetic fields

**©**

*ESO 2004*