Determination of acceleration mechanism characteristics directly and nonparametrically from observations: Application to supernova remnants

Abstract

We have developed an inversion method for determination of the characteristics of the acceleration mechanism directly and non-parametrically from observations, in contrast to the usual forward fitting of parametric model variables to observations. In two recent papers (Petrosian & Chen 2010, Chen & Petrosian 2013), we demonstrate the efficacy of this inversion method by its application to acceleration of electrons in solar flares based on stochastic acceleration by turbulence. Here we explore its application for determining the characteristics of shock acceleration in supernova remnants (SNRs) based on the electron spectra deduced from the observed nonthermal radiation from SNRs and the spectrum of the cosmic ray electrons observed near the Earth. These spectra are related by the process of escape of the electrons from SNRs and energy loss during their transport in the galaxy. Thus, these observations allow us to determine spectral characteristics of the momentum and pitch angle diffusion coefficients, which play crucial roles in both direct acceleration by turbulence and in high Mach number shocks. Assuming that the average electron spectrum deduced from a few well known SNRs is representative of those in the solar neighborhood we find interesting discrepancies between our deduced forms for these coefficients and those expected from well known wave-particle interactions. This may indicate that the standard assumptions made in treatment of shock acceleration need revision. In particular, the escape of particles from SNRs may be more complex than generally assumed.