The synchrotron spectrum of diffuse radio sources: Effects of particle and field distributions

We present analytic and numerical calculations of the synchrotron spectrum arising from a distribution of magnetic field strengths as well as particle energies. We find that power-law photon spectra can arise either from power-law particle distributions, or power-law field distributions. We also find that high-frequency steepening of the photon spectrum is common; this steepening need not be due to synchrotron aging. Different underlying distributions do lead to different rates of high-frequency steepening, and this may provide observational discriminants between different physical pictures.