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A Comprehensive Study of the Spectral Variation and the Brightness Profile of Young Pulsar Wind Nebulae

We present a systematic study of particle transport by diffusion in young pulsar wind nebulae (PWNe). We selected nine bright sources that are well resolved with the Chandra X-ray Observatory. We analyzed archival data to obtain their radial profiles of photon index ($Γ$) and surface brightness ($Σ$) in a consistent way. These profiles were then fit with a pure diffusion model that was tested on Crab, 3C 58 and G21.5$-$0.9 before. In addition to the spectral softening due to the diffusion, we calculated the synchrotron power and built up the theoretical surface brightness profile. For each source, we performed separate fits to the $Γ$ and the $Σ$ profiles. We found these two profiles of most PWNe are similar, except for Crab and Vela. Both profiles can be well described by our model, suggesting that diffusion dominates the particle transport in most sampled PWNe. The discrepancy of parameters between the $Γ$ profile and $Σ$ profiles is relatively large for 3C 58 and G54.1+0.3. This difference could be attributed to the elongated shape, reflecting boundary, and the non-uniform magnetic field. Finally, we found no significant correlations between diffusion parameters and physical parameters of PWN and pulsar.