Microphysics of shock acceleration from observations of X-ray synchrotron emission from supernova remnants Original Research Article

Recent observations of non-thermal X-rays from supernova remnants have been attributed to synchrotron radiation from the loss-steepened tail of a non-thermal distribution of electrons accelerated at the remnant blast wave. In the test-particle limit of diffusive shock acceleration, in which the energy in shock-accelerated particles is unimportant, the slope of a shock-accelerated power-law is independent of the diffusion coefficient κ and on how κ depends on particle energy. However, the maximum energy to which particles can be accelerated depends on the rate of acceleration and that does depend on the energy-dependence of the diffusion coefficient. If the time to accelerate an electron from thermal energies to energy E≫mec2 is τ(E) and if κ∝Eβ, then τ(E)∝Eβ in parallel shocks and τ∝E2−β in perpendicular shocks. Most work on shock acceleration has made the plausible assumption that κ∝rg (where rg is the particle gyroradius), so that β=1 at relativistic energies, implying a particular (wavelength-independent) spectrum of MHD turbulence, where Kolmogorov or Kraichnan spectra might be more physically plausible. I derive the β dependence of the maximum electron energy resulting from limitations due to radiative (synchrotron and inverse-Compton) losses and to finite remnant age (or size). I then exhibit calculations of synchrotron X-ray spectra, and model images, for supernova remnants as a function of β and compare to earlier β=1 results. Spectra can be considerably altered for β<1 and images are dramatically different for values of β corresponding to Kolmogorov or Kraichnan spectra of turbulence. The predicted images are quite unlike observed remnants, suggesting that the turbulence near SNRs is generated by the high-energy particles themselves.