Pulsar Wind Nebulae and the Non-thermal X-Ray Emission of Millisecond   Pulsars
  The non-thermal, non-pulsed X-ray emission of MSPs is investigated. As in young pulsars, MSPs emit a relativistic wind, which interacting with the interstellar medium and/or a binary companion can significantly contribute to the non-pulsed emission of these pulsars. An application and extension of a simple model developed for young pulsars is applied to the old recycled MSP B1957+20. It is found that the pulsar wind can, indeed, contribute to both the resolved and unresolved X-ray emission. For other MSP in the Galactic field where the spectral index of the non-pulsed component has been measured (i.e., PSR B1937+21, J0218+4232) the contribution of the pulsar wind to the non-pulsed X-ray luminosity is estimated. For the MSPs in the core regions of globular clusters, the pulsar wind nebula is likely affected by its interaction with the dense stellar environment, possibly leading to a diminished contribution to the total X-ray emission. In this case, the existence of non-thermal non-pulsed X-ray emission is more likely for binary rather than isolated MSPs with the emission arising from the interaction of the relativistic pulsar wind with a binary companion. Our study suggests that the magnetization parameter in the pulsar wind nebulae of MSPs is significantly larger than that of the Crab nebula by about a factor of 10. The emission from MSPs moving at high velocities may appear spatially extended with a tail-like morphology, which may contribute to the faint filamentary X-ray source subpopulation in the Galaxy. 
K. S. Cheng, Ronald E. Taam, and W. Wang