Pulsar wind nebulae (PWNe) are a prominent class of very high energy ( E > 0.1 TeV) Galactic sources. Their γ-ray spectra are interpreted as due to inverse Compton scattering of ultrarelativistic electrons on the ambient photons, whereas the X-ray spectra are due to synchrotron emission. We investigate the relation between the γ- and X-ray emission and the pulsars' spin-down luminosity and characteristic age. We find that the distance-independent γ-ray to X-ray flux ratio of the nebulae is inversely proportional to the spin-down luminosity, ( ), while it appears proportional to the characteristic age, (∝τ 2.2 c ), of the parent pulsar. We interpret these results as due to the evolution of the electron energy distribution and the nebular dynamics, supporting the idea of so-called relic PWNe. These empirical relations provide a new tool to classify unidentified diffuse γ-ray sources and to estimate the spin-down luminosity and characteristic age of rotation-powered pulsars with no detected pulsation from the X-ray and γ-ray properties of the associated PWNe. We apply these relations to predict the spin-down luminosity and characteristic age of four (so far unpulsing) candidate pulsars associated with wind nebulae.
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Mattana et al. (2009) studied this question.