摘要：Context. Supernova remnants are known as sources of Galactic cosmic rays
for their nonthermal emission of radio waves, X-rays, and gamma rays. However, the
observed soft broken power-law spectra are hard to reproduce within standard acceleration
theory based on the assumption of Bohm diffusion and steady-state calculations.
Aims. We point out that a time-dependent treatment of the acceleration
process together with a self-consistent treatment of the scattering turbulence
amplification is necessary.
Methods. We numerically solve the coupled system of transport equations
for cosmic rays and isotropic Alfvénic turbulence. The equations are coupled through the
growth rate of turbulence determined by the cosmic-ray gradient and the spatial diffusion
coefficient of cosmic rays determined by the energy density of the turbulence. The system
is solved on a comoving expanding grid extending upstream for dozens of shock radii,
allowing for the self-consistent study of cosmic-ray diffusion in the vicinity of their
acceleration site. The transport equation for cosmic rays is solved in a test-particle
approach.
Results. We demonstrate that the system is typically not in a steady
state. In fact, even after several thousand years of evolution, no equilibrium situation
is reached. The resulting time-dependent particle spectra strongly differ from those
derived assuming a steady state and Bohm diffusion. Our results indicate that proper
accounting for the evolution of the scattering turbulence and hence the particle diffusion
coefficient is crucial for the formation of the observed soft spectra. In any case, the
need to continuously develop magnetic turbulence upstream of the shock introduces
nonlinearity in addition to that imposed by cosmic-ray feedback.
关键词：ISM: supernova remnants;acceleration of particles;turbulence
