Cosmic ray (CR) electrons reveal key insights into the non-thermal physics of the interstellar medium (ISM), galaxies, galaxy clusters, and active galactic nuclei by means of their inverse Compton γ-ray emission and synchrotron emission in magnetic fields. While magnetohydrodynamical (MHD) simulations with CR protons capture their dynamical impact on these systems, only few computational studies include CR electron physics because of the short cooling time-scales and complex hysteresis effects, which require a numerically expensive, high-resolution spectral treatment. Since CR electrons produce important non-thermal observational signatures, such a spectral CR electron treatment is important to link MHD simulations to observations. We present an efficient post-processing code for Cosmic Ray Electron Spectra that are evolved in Time (crest) on Lagrangian tracer particles. The CR electron spectra are very accurately evolved on comparably large MHD time steps owing to an innovative hybrid numerical-analytical scheme. crest is coupled to the cosmological MHD code arepo and treats all important aspects of spectral CR electron evolution such as adiabatic expansion and compression, Coulomb losses, radiative losses in form of inverse Compton, bremsstrahlung and synchrotron processes, diffusive shock acceleration and reacceleration, Fermi-II reacceleration, and secondary electron injection. After showing various code validations of idealized one-zone simulations, we study the coupling of crest to MHD simulations. We demonstrate that the CR electron spectra are efficiently and accurately evolved in shock-tube and Sedov-Taylor blast wave simulations. This opens up the possibility to produce self-consistent synthetic observables of non-thermal emission processes in various astrophysical environments.
Supernova remnants (SNRs) are believed to be the source of Galactic cosmic rays (CRs). SNR shocks accelerate CR protons and electrons which reveal key insights into the non-thermal physics by means of their synchrotron and γ-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to γ-rays. We perform three-dimensional (3D) magnetohydrodynamics (MHD) simulations where we include CR protons and follow the CR electron spectrum. By matching the observed morphology and non-thermal spectrum of SN 1006 in radio, X-rays and γ-rays, we gain new insight into CR electron acceleration and magnetic field amplification. 1. We show that a mixed leptonic-hadronic model is responsible for the γ-ray radiation: while leptonic inverse-Compton emission and hadronic pion-decay emission contribute equally at GeV energies observed by Fermi, TeV energies observed by imaging air Cherenkov telescopes are hadronically dominated. 2. We show that quasi-parallel acceleration (i.e., when the shock propagates at a narrow angle to the upstream magnetic field) is preferred for CR electrons and that the electron acceleration efficiency of radio-emitting GeV electrons at quasi-perpendicular shocks is suppressed at least by a factor ten. This precludes extrapolation of current one-dimensional plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. 3. To match the radial emission profiles and the γ-ray spectrum, we require a volume-filling, turbulently amplified magnetic field and that the Bell-amplified magnetic field is damped in the immediate post-shock region. Our work connects micro-scale plasma physics simulations to the scale of SNRs.
The γ-ray emission of star-forming (SF) galaxies is attributed to hadronic interactions of cosmic ray (CR) protons with the interstellar gas and contributions from CR electrons via bremsstrahlung and inverse Compton (IC) scattering. The relative importance of these processes in different galaxy types is still unclear. We model these processes in three-dimensional magneto-hydrodynamical (MHD) simulations of the formation of isolated galactic discs using the moving-mesh code Arepo, including dynamically coupled CR protons and adopting different CR transport models. We calculate steady-state CR spectra and also account for the emergence of secondary electrons and positrons. This allows us to produce detailed γ-ray maps, luminosities and spectra of our simulated galaxies at different evolutionary stages. Our simulations with anisotropic CR diffusion and a low CR injection efficiency at supernovae (SNe, ζSN = 0.05) can successfully reproduce the observed far-infrared (FIR)-γ-ray relation. Starburst galaxies are close to the calorimetric limit, where CR protons lose most of their energy due to hadronic interactions and hence, their γ-ray emission is dominated by neutral pion decay. However, in low SF galaxies, the increasing diffusive losses soften the CR proton spectra due to energy-dependent diffusion, and likewise steepen the pionic γ-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to ∼40 per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed γ-ray spectra of starburst galaxies, we require a weaker energy dependence of the CR diffusion coefficient, D∝E0.3, in comparison to Milky Way-like galaxies.
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