Time dependent cosmicray shock acceleration with selfconsistent injection
Abstract
One of the key questions to understanding the efficiency of diffusive shock acceleration of the cosmic rays (CRs) is the injection process from thermal particles. A selfconsistent injection model based on the interactions of the suprathermal particles with selfgenerated magneto hydrodynamic waves has been developed recently by Malkov (\cite{Malk98}). By adopting this analytic solution, a numerical treatment of the plasmaphysical injection model at a strong quasiparallel shock has been devised and incorporated into the combined gas dynamics and the CR diffusionconvection code. In order to investigate selfconsistently the injection and acceleration efficiencies, we have applied this code to the CR modified shocks of both high and low Mach numbers (M=30 and M=2.24) with a Bohm type diffusion model. Both simulations have been carried out until the maximum momentum (p_{max}/m_{p}c) ~ 1 is achieved to illustrate early evolution of a Bohm type diffusion. We find the injection process is selfregulated in such a way that the injection rate reaches and stays at a nearly stable value after quick initial adjustment. For both shocks about 10^{3} of the incoming thermal particles are injected into the CRs. For the weak shock, the shock has reached a steady state within our integration time and $\sim 10\%$ of the total available shock energy is transfered into the CR energy density. The strong shock has achieved a higher acceleration efficiency of ~ 20% by the end of our simulation, but has not yet reached a steadystate. With such efficiencies shocks do not become CRdominated or smoothed completely during the early stages when the particles are only mildly relativistic. Later, as the CR pressure becomes dominated by highly relativistic particles that situation should change, but is difficult to compute, since the maximum CR momentum increases approximately linearly with time for this model. In the near future we intend to extend such shock simulations as these to include much higher CR momenta using an adaptive mesh refinement technique currently under development.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 2000
 arXiv:
 arXiv:astroph/0011058
 Bibcode:
 2000A&A...364..911G
 Keywords:

 Acceleration of Particles;
 Hydrodynamics;
 Shock Waves;
 Methods: Numerical;
 ISM: Cosmic Rays;
 Astrophysics
 EPrint:
 13 pages, 10 figures, LaTeX209 (epsf.sty, laa.sty), Astron.Astrophys. in press