Transport of magnetic turbulence in Supernova remnants

TL;DR

This paper demonstrates that a time-dependent, self-consistent treatment of turbulence amplification and cosmic-ray transport near supernova remnants is essential to accurately reproduce observed cosmic-ray spectra, challenging steady-state models.

Contribution

It introduces a coupled, time-dependent numerical model for cosmic-ray and turbulence transport, highlighting the importance of turbulence evolution in cosmic-ray acceleration.

Findings

Steady state is not reached even after thousands of years.

Time-dependent spectra differ significantly from steady-state predictions.

Turbulence evolution is crucial for explaining observed cosmic-ray spectra.

Abstract

Context. Supernova remnants are known as sources of galactic cosmic rays for their non-thermal 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 Alfvenic 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 co-moving 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 non-linearity in addition to that imposed by cosmic-ray feedback.