A pulsar wind nebula (PWN) inside a supernova remnant provides a unique insight into the properties of the central neutron star, the relativistic wind powered by its loss of rotational energy, its progenitor supernova, and the surrounding environment. In this paper, we present a new semianalytic model for the evolution of such a PWN throughout its lifetime. This model couples the dynamical and radiative evolution of the PWNe, and predicts both the dynamical (e.g., radius and expansion velocity) and radiative (radio to TeV γ-ray spectrum) properties of the PWN during this period. As a result, it is well suited for using the observed properties of a PWN to constrain the physical characteristics of the neutron star, pulsar wind, progenitor supernova, and surrounding environment. We also discuss the expected evolution for a particular set of these parameters, and show that it reproduces the large spectral break inferred from the radio and X-ray spectrum of many young PWNe, and the low break frequency, low radio luminosity, high TeV γ-ray luminosity, and high magnetization observed for several older PWNe. The predicted spectrum of this PWN also contains spectral features which appear during different evolutionary phases detectable with new radio and γ-ray observing facilities such as the Extended Very Large Array and the Fermi Gamma-ray Space Telescope. Finally, this model has implications for determining if PWNe can inject a sufficient number of energetic electrons and positrons into their surroundings to explain the recent measurements of the cosmic-ray positron fraction by PAMELA and the cosmic-ray lepton spectrum by ATIC and HESS.
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