Modelling spectral evolution of pulsar wind nebulae inside supernova remnants

We present a new model for the spectral evolution of pulsar wind nebulae (PWNe) inside supernova remnants (SNRs). The model couples the long-term dynamics of these systems, as derived in the 1D approximation, with a one-zone description (all quantities are assumed uniform in the nebula) of the spectral evolution of the emitting plasma. Our goal is to provide a simplified theoretical description that can be used as a tool to put constraints on unknown properties of PWN-SNR systems: a piece of work that is preliminary to any more accurate and sophisticated modelling. In this paper, we apply the newly developed model to a few objects of different ages and luminosities. We find that an injection spectrum in the form of a broken power law gives a satisfactory description of the emission for all the systems we consider. More surprisingly, we also find that the intrinsic spectral break turns out to be at a similar energy for all sources, in spite of the differences mentioned above. We discuss the implications of our findings on the workings of pulsar magnetospheres, pair multiplicity and on the particle acceleration mechanism(s) that might be at work at the pulsar wind termination shock.