Supernova remnant dynamics and particle acceleration in elliptical galaxies

Spherically symmetric numerical models of supernova remnants (SNRs) evolving from the initial explosion up to their final dispersal within the interstellar medium (ISM) and exploding into a tenuous and hot plasma are presented. The parameters of the exploding stars are typical for an old stellar population (Type I SNe) and the external medium is characterized by a temperature between 106K and 3 107K with a corresponding number density of 3 10 3cm 3 and 10 4cm 3 representative for the ISM of elliptical galaxies. The magnetic fields vary between 1 G and 5 G. These models include the diffusive acceleration of charged particles at shock waves by the first order Fermi mechanism, injection of energetic particles at shock waves as well as dissipation of Alfvén waves. Due to the high temperatures and low densities of the ambient medium, the sound velocity is at all evolutionary stages comparable to the SNR expansion velocity leading to a number of differences compared e.g. to the standard Sedov-phase. It is shown that the acceleration efficiency of cosmic rays in SNRs is significantly reduced. Due to the importance of energetic particles advected into the shock front for these low Mach numbers, injection of particles plays a minor role and the amount of the SN-explosion energy transferred into cosmic rays depends on the external population of energetic particles. For standard parameters the mean cosmic ray energy density within an elliptical galaxy is determined by their surrounding extragalactic values and in the case of no intergalactic cosmic rays the losses of energetic particles into the extragalactic space can hardly be compensated by acceleration of cosmic rays in SNRs and hence it is difficult to establish an equilibrium situation for a cosmic ray population within an elliptical galaxy.