Evolution and observational signatures of the cosmic ray electron
  spectrum in SN 1006
  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
$\gamma$-ray emission. The remnant SN 1006 is an ideal particle acceleration
laboratory because it is observed across all electromagnetic wavelengths from
radio to $\gamma$-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 $\gamma$-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 $\gamma$-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 $\gamma$-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.
