Modeling statistical properties of the X-ray emission from aged Pulsar Wind Nebulae

The number of known PWNe has recently increased considerably, and the majority of them are now middle-age objects. Recent studies have shown a clear correlation of both X-ray luminosity and size with the PWN age, but fail in providing a thorough explanation of the observed trends. Here I propose a different approach to these effects, based on the hypothesis that the observed trends do not simply reproduce the evolution of a "typical" PWN, but are a combined effect of PWNe evolving under different ambient conditions, the leading parameter being the ambient medium density. Using a simple analytic approach, I show that most middle-age PWNe are more likely observable during the reverberation phase, and I succeed in reproducing trends consistent with those observed, provided that the evolution of the X-ray emitting electrons keeps adiabatic over the whole reverberation phase. As a direct consequence, I show that the X-ray spectra of older PWNe should be harder: also this is consistent with observations.