Diffusion and advection model for particle transport in young pulsar wind nebulae

The magnetohydrodynamic (MHD) model for young pulsar wind nebulae (PWN) has been successful in reproducing many features of the nebulae. The model is characterized by a termination shock (TS) between the PWN and unshocked pulsar wind. Relativistic particles are injected at the TS and follow an advective flow to the outer boundary. However, toroidal structure of well studied young PWN like the Crab Nebula, 3C 58 and G21.5-0.9 is only present in the region close to the TS. In the outer parts of the nebulae, filamentary and loop-like structure is observed. Also, the radial variation of spectral index due to synchrotron losses is smoother than expected in the MHD flow model. We find that a pure diffusion model with energy independent diffusion and a transmitting boundary can reproduce the basic data on nebular size and spectral index variation for the Crab, 3C 58, and G21.5-0.9. Energy dependent diffusion is also discussed. Power law variations of the coefficient with energy are degenerate with variation in the input particle energy distribution index in the steady state case. Monte Carlo simulations of particle transport with both diffusion and advection for the Crab nebula and 3C 58 suggest a picture in which advection dominates the inner part of the PWN where toroidal structure is clearly present. Diffusion dominates the outer part of the PWN where filamentary and loop-like structure is observed. The source of the chaotic field is uncertain, but may be related to Rayleigh-Taylor instability at the outer boundary of young nebulae and/or the kink instability of the toroidal magnetic field.