# On the Gamma-Ray Nebula of Vela Pulsar. I. Very Slow Diffusion of Energetic Electrons within the TeV Nebula

## TL;DR

This study models the slow diffusion of TeV electrons in the Vela pulsar's nebula, using analytical solutions to match observed spectral and spatial data, revealing diffusion rates much lower than in the interstellar medium.

## Contribution

The paper provides the first analytical modeling of TeV electron diffusion in Vela X PWN, constraining the diffusion coefficient and suggesting slow diffusion is common in PWNe.

## Key findings

- Diffusion coefficient for 10 TeV electrons is ~1×10^{26} cm^2/s.
- Diffusion rate is over three orders of magnitude lower than in the ISM.
- Results align with recent HAWC observations of Geminga nebula.

## Abstract

High-energy particle transport in pulsar wind nebulae (PWNe) plays an essential role in explaining the characteristics revealed in multiwavelength observations. In this paper, the TeV-gamma-ray-emitting electrons in the Vela X PWN are approximated to be injected impulsively when the cocoon is formed due to the interaction between the SNR reverse shock and the PWN. By solving the diffusion-loss equation analytically, we reproduce the broadband spectral energy distribution and surface brightness profile simultaneously. The diffusion coefficient of TeV electrons and positrons, which is well constrained by the spectral and spatial properties of the TeV nebula, is thus determined to be $1 \times 10^{26}$\,cm$^{2}$\,s$^{-1}$ for 10\,TeV electrons and positrons. This coefficient is more than three orders of magnitude lower than that in the interstellar medium, in agreement with a constraint recently obtained from HAWC observations of a TeV nebula associated with the Geminga pulsar. These results suggest that slow diffusion of high-energy particles might be common in PWNe.