On the formation of energy spectra in synchrotron sources

The observed energy spectra in synchrotron sources are power laws,N (E)=KE^–, with the distribution in peaked around 2.5. These are consistent with initially injected spectra with between 1 and 2, subsequently steepened by synchrotron losses. Contrary to the results of Kardashev (1962), it is shown that statistical acceleration when coupled with synchrotron losses lead naturally to the formation of flat stationary spectra with 1. These stationary spectra have bends near the energy at which synchrotron losses balance the energy gains by acceleration. Above this bend the spectrum tends to =2. The time evolution of an initial spectrum towards the stationary spectrum is investigated. It is suggested that the initially flat spectra with 1 to 1.5 observed in some variable sources result from an incomplete approach to the stationary spectrum, and that in sources with constant acceleration spectra with 2 are to be expected.