Transport of magnetic turbulence in supernova remnants

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 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 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.

Modeling of the spatially resolved nonthermal emission from the Vela Jr. supernova remnant

“…The type of the diffusion determines the shape of the cut off in the resulting particle spectrum: Kolmogorov-type diffusion implies a slower cut-off than Bohm diffusion. We also calculate the diffusion coefficient by solving the transport equation for magnetic turbulence dominated by Alfvén waves (Brose et al 2016). The equation is solved in 1D for spherical symmetry assuming that Alfvénic turbulence is isotropic and accounting for compression, advection, cascading, damping and growth due to resonant amplification of Alfvén waves.…”

“…In this regard we consider two different profiles of the magnetic field downstream of the shock, damped magnetic field and transported magnetic field, to test which of the two effects described above determines X-ray filaments and spectral softening observed in these filaments. For our simulation we use the Radiation Acceleration Transport Parallel Code (RATPaC) described in a number of previous papers (Telezhinsky et al 2012(Telezhinsky et al , 2013Brose et al 2016). The code solves the time-dependent transport equation for cosmic rays in one dimension (1D) in the test particle regime and subsequently simulates the non-thermal radiation from accelerated particles.…”

“…The shock evolution is simulated using 1D hydrodynamic simulations performed by the Pluto code (Mignone et al 2007) which is the most recent addition to RATPaC. The calculation of the particle acceleration can also be coupled to the evolution of isotropic Alfvénic turbulence upstream of the shock (Brose et al 2016).…”

Nonthermal emission from the reverse shock of the youngest Galactic supernova remnant G1.9+0.3

“…Here, ζ = 1 represents the lowest diffusion coefficient possible in a given magnetic field and ζ > 1 might be a more common situation. Alternatively the amplification of Alfvénic turbulence can be explicitely treated by solving a separate wave transport equation and thus calculating the diffusion coefficient self-consistently (Brose et al 2016).…”

“…where D k is the diffusion coefficient in wavenumber space representing cascading and Γ g and Γ d are the growth and the damping rates, respectively (Brose et al 2016, and references therein). We are thus able to track the growth and damping, the cascading, compression, and the propagation of the Alfvénic turbulence in the CR precursor and inside the SNR.…”