Cosmic-ray transport and gamma-ray emission in supernova shells
The mixing and transport of cosmic rays accelerated by a pulsar inside an expanding supernova remnant are examined, and the resulting high-energy gamma-ray emission from nuclear interactions of these accelerated particles in the shell is investigated. Rayleigh-Taylor instability at the interface between a pulsar wind cavity and the inner supernova envelope is assumed to be the mixing mechanism. The analysis is applied to the model of Gaisser, Harding, and Stanev (1987), where protons are accelerated at the reverse shock in the pulsar wind. The instability time-scale is estimated from the dynamics of the pulsar wind cavity, and model the injection, diffusion, and interaction of protons in the shell. The resulting gamma-ray flux is lower than previous estimates due to proton adiabatic losses in the expanding pulsar wind. The protons mix and diffuse only into the innermost regions of the envelope before interacting. Energy-dependent diffusion causes the higher energy gamma-ray light curves to decay faster than those at lower energy.