What shape are your spectra in? - Rudnick, L (2002)
The shapes of synchrotron spectra contain important information about the origin and evolution of the relativistic electron distributions. The analyses of spectral shapes that appear in the literature are inadequate, at best, to address the important scientific issues. A proper analysis of spectra can illuminate the energy distribution of particles as they are "injected" into diffuse regions, the acceleration and loss processes, the bulk and microscopic transport of electrons and the role of inhomogeneities in the magnetic field. I describe some observational difficulties we face in isolating the actual particle distributions, highlight some of the interpretational "sins" we have committed, and make some modest recommendations.