Cut-offs and pile-ups in shock acceleration spectra

We have examined cut-offs and pile-ups due to various processes in the spec tra of particles produced by shock acceleration, and found that, even in th e absence of energy losses, the shape of the spectrum of accelerated partic les at energies well below the nominal maximum energy depends strongly on t he energy dependence of the diffusion coefficient. This has implications in many areas, for example, in fitting the observed cosmic ray spectrum with models based on power-law source spectra and rigidity dependent diffusive e scape from the galaxy. With continuous energy losses, prominent pile-ups ma y arise, and these should be included when modelling synchrotron X-ray and inverse Compton gamma-ray spectra from a shock-accelerated electron populat ion. We have developed a Monte Carlo/numerical technique to model the shape of t he spectrum for the case of non-continuous energy losses such as inverse Co mpton scattering in the Klein-Nishina regime. We find that the shapes of th e resulting cut-offs differ substantially from those arising from continuou s processes, and we suggest that such differences could be observable throu gh their effect on the spectrum of radiation emitted by a population of rec ently accelerated electrons as, for example, may exist in young supernova r emnants. (C) 1999 Elsevier Science B.V.