ELECTRON ACCELERATION IN A NONLINEAR SHOCK MODEL WITH APPLICATIONS TO SUPERNOVA-REMNANTS

We present Monte Carlo calculations of ion and electron spectra produced by Fermi acceleration in a steady state, plane, parallel, modified shock for Mach numbers of 170 and 43. The simulation assumes isotropic, elastic scattering in the local fluid frame, consistent with results from plasma simulations. The shock structure is calculated taking into account the back pressure of accelerated ions, and includes self-consistent pickup and acceleration of thermal ions. In a steady state, particle acceleration is balanced by particle escape; we assume that particles escape above some energy E(max), and show results for various values of E(max) ranging up to 1 TeV. Results are described for two dependences of scattering mean free path on rigidity. Our ion spectra include the entire continuous distribution function from thermal particles to E(max). We show that these shocks are extremely efficient, with up to 98% of the entering energy flux emerging as relativistic ions. Since the physics of electron injection is not understood, we inject electrons at various superthermal energies, producing the first electron spectra calculated in a modified shock profile. Electron spectra are steeper than ion spectra at virtually all energies relevant for radio emission from supernova remnants (0.3-30 GeV) and are slightly concave upward (hardening with energy), with mean spectral indices near 2 [i.e., N(E) is-proportional-to E-2]. While results from time-dependent, evolving shocks may be different, they are almost certain to be less compressive, to be less efficient, and to produce softer spectra. We compare our spectral results with integrated radio spectra of young supernova remnants.