A model for the X-ray luminosity of pulsar nebulae

A one-zone, shocked wind model is developed for the X-ray luminosity of pulsar nebulae. If the electrons and positrons cool rapidly by synchrotron radiation and the initial particle spectrum is similar to that of the Crab Nebula, the X-ray luminosity is produced from the pulsar power with high efficiency and is insensitive to the model parameters. If the electrons are not in the cooling regime, the X-ray luminosity is produced with lower efficiency, as appears to be the case for the compact nebula around the Vela pulsar, The observed X-ray spectral index is an indicator fur which case applies and thus plays a role in estimating the pulsar power needed to produce an observed X-ray luminosity.