Non-thermal bremsstrahlung from supernova remnants and the effect of Coulomb losses

Abstract

Aims: We investigate the shape of the electron cosmic ray spectrum in the range up to ~1000 keV, assuming that the acceleration process at the shock results in a power law in momentum, and that downstream of the shock the spectrum is affected by Coulomb interactions with background electrons only.
Methods: In the non-relativistic regime one can analytically determine the energy of an electron starting with a certain energy, and use this result to produce an electron cosmic ray spectrum, modified by Coulomb losses.
Results: An analytic expression for the electron spectrum is obtained that depends on the parameter n_et, which can be estimated from a similar parameter used to characterize the line spectra of supernova remnants.
Conclusions: For the brightest supernova remnants n_et > 10¹¹ cm^-3 s, and most of the electrons accelerated to <100 keV have lost their energy. Because of its high radio flux, Cas A is the most likely candidate for non-thermal bremsstrahlung. Although it has n_et ~ 2 × 10¹¹ cm^-3 s, one may expect to pick up non-thermal bremsstrahlung above 100 keV with current hard X-ray detectors.