Effect of synchtrotron losses on multiple diffusive shock acceleration

Abstract

The effect of synchrotron losses on diffusive shock acceleration (DSA) at many shocks is treated numerically. Synchrotron losses determine a maximum energy to which electrons can be accelerated through DSA, and this is referred to as the synchrotron cutoff, p_c. The distribution of accelerated electrons after many shocks is found (a) for a distribution injected at the initial shock, to tend to a plateau (f(p) independent of p <~ 0.1 p_c), and (b) for the cumulative distribution from injection at each shock to tend to f(p) proptional to p^-b with b approximately 3 well below the synchrotron cutoff with a peak in the slope (b_min approx 2) at p <~ 0.1 p_c. It is suggested that the latter result might account for the flat synchrotron spectra observed in some Galactic Centre sources.