Pulsar wind nebulae: at last beyond compression

Even though pulsars are best-known for their periodic pulses, their pulsed electromagnetic radiation is usually not more than a few percent of their total energy release. Pulsars dissipate the bulk of their rotational energy via the emission of a relativistic wind of particles. We observe them as pulsar wind nebulae (PWNe)The vast majority of PWNe present in the Galaxy are middle-aged systems characterized by a strong interaction of the PWN itself with the supernova remnant (SNR). A phase in particular, when the reverse shock of the SNR reaches the PWN and the two begin to interact (reverberation) is critical for their evolution, and for correctly interpreting observations.This phase, however, has never been well-understood, and simplified models were -when not simply ignoring it- using untested assumptions. Among them, that the size of the pulsar wind nebulae shell (the contour of the PWN) is small in comparison with its size. Unfortunately, modelling these systems can be quite complex and numerically expensive, due to the non-linearity of the PWN-SNR evolution even in the simple one-dimensional (1D)/one-zone case.After 4 years of research (and four papers on the road up) we have finally introduced a new numerical technique that couples the numerical efficiency of the one-zone thin shell approach with the reliability of a full 'Lagrangian' evolution, able to correctly reproduce the PWN-SNR interaction during the reverberation, and to consistently evolve the particle spectrum beyond. We tested all such assumptions, finding their limitations. Our approach enable us for the first time to provide reliable spectral models of the along compression phases.For some PWNe, we found that the compression is less extreme than that obtained without such detailed dynamical considerations, leading to the formation of less structured spectral energy distributions, whereas for a few, factors of 10 to 100 are noted. Population studies will follow.