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Particle Transport in Young Pulsar Wind Nebulae

The model for pulsar wind nebulae (PWNe) as the result of the magnetohydrodynamic (MHD) downstream flow from a shocked, relativistic pulsar wind has been successful in reproducing many features of the nebulae observed close to the central pulsars. However, observations of well-studied young nebulae like the Crab Nebula, 3C 58, and G21.5--0.9 do not show the toroidal magnetic field on a larger scale that might be expected in the MHD flow model; in addition, the radial variation of spectral index due to synchrotron losses is smoother than expected in the MHD flow model. We find that pure diffusion models can reproduce the basic data on nebular size and spectral index variation for the Crab, 3C 58, and G21.5--0.9. Most of our models use an energy independent diffusion coefficient; power law variations of the coefficient with energy are degenerate with variation in the input particle energy distribution index in the steady state, transmitting boundary case. Energy dependent diffusion is a possible reason for the smaller diffusion coefficient inferred for the Crab. Monte Carlo simulations of the particle transport allowing for advection and diffusion of particles suggest that diffusion dominates over much of the total nebular volume of the Crab. Advection dominates close to the pulsar and is likely to play a role in the X-ray half-light radius. The source of diffusion and mixing of particles is uncertain, but may be related to the Rayleigh-Taylor instability at the outer boundary of a young PWN or to instabilities in the toroidal magnetic field structure.