ELECTRON ACCELERATION IN TYCHO AND KEPLER SUPERNOVA-REMNANTS - SPECTRAL EVIDENCE OF FERMI SHOCK ACCELERATION

Relativistic electron energy spectra inferred from the synchrotron radio spectra Of supernova remnants (SNRs) are crudely consistent with the simplest test particle predictions of Fermi shock acceleration theory, supporting the operation of that mechanism as the source for the electrons. However, a few young SNRs have spectral indices considerably steeper than the test particle value of -0.5 expected for any sufficiently strong shock. Furthermore, more realistic shock acceleration models differ substantially from the test particle ones. Few calculations of particle spectra have been made in these improved models, and almost none of electron spectra in particular. Our previous work (Ellison & Reynolds 1991) on electron spectra in modified shocks predicted curved spectra differing markedly from proton spectra at the same energies, suggesting the possibility that synchrotron radiation from these electrons would in fact not be consistent with SNR observations. Here we present the first model synchrotron spectra calculated with a self-consistent, nonlinear shock model of first-order Fermi acceleration, and compare them with the observed radio spectra of Tycho's and Kepler's supernova remnants. We find excellent agreement. We have no difficulty reproducing the correct mean spectra indices approximately -0.64. The model spectra are slightly concave (hardening to higher energy), and there is evidence for such an effect in the data, enabling us to estimate the mean magnetic field strength in each remnant. The errors in the observations, and the steady state, planar, parallel shock simulation we used, make these numbers estimates only, but there is potential for improvements in both theory and observation which could allow accurate values of magnetic fields to be inferred from sufficiently precise integrated synchrotron spectra. We predict that when inconsistencies in the total flux radio spectrum of the remnant of SN 1006 AD are resolved, our curved models will fit as well there.