Diffusive Synchrotron Radiation from Pulsar Wind Nebulae

Diffusive Synchrotron Radiation (DSR) is produced by charged particles as they random walk in a stochastic magnetic field. The spectrum of the radiation produced by particles in such fields differs substantially from those of standard synchrotron emission because the corresponding particle trajectories deviate significantly from gyration in a regular field. The Larmor radius, therefore, is no longer a good measure of the particle trajectory. In this paper we analyze a special DSR regime which arises as highly relativistic electrons move through magnetic fields which have only random structure on a wide range of spatial scales. Such stochastic fields arise in turbulent processes, and are likely present in pulsar wind nebulae (PWNe). We show that DSR generated by a single population of electrons can reproduce the observed broad-band spectra of PWNe from the radio to the X-ray, in particular producing relatively flat spectrum radio emission as is usually observed in PWNe. DSR can explain the existence of several break frequencies in the broad-band emission spectrum without recourse to breaks in the energy spectrum of the relativistic particles. The shape of the radiation spectrum depends on the spatial spectrum of the stochastic magnetic field. The implications of the presented DSR regime for PWN physics are discussed.