Hard spectra in pulsar-wind nebula and diffusive shock-acceleration

To date, there is no self-consistent model for the exceptionally hard radio spectra of pulsar-wind nebulae (PWN). We examine if diffusive acceleration in the underlying ultra-relativistic shocks (DSA) can generate a spectrum as hard as that observed. To this end, we generalize a semi-analytic moment-expansion code that solves the transport equation for arbitrary shock and angular diffusion-function, and provides statistics such as the particle distribution-function, anisotropy, escape probability, and energy gain. Unlike previous studies, we find that an anisotropic diffusion function can generate very hard spectra, down to the p~1 limit. However, such hard spectra arise from a vanishing escape probability associated with the confinement of particles near the shock, severely constraining the integrated emissivity, and thus ruling out such DSA as the origin of PWN synchrotron emission. Indeed, a different mechanism is needed to explain the acceleration of the radiating particles.