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# Photon diffusion

Photon diffusion refers to a situation where photons travel through a material with a high optical depth and very short mean free path. Their behavior is then dominated by scattering and the path of any given photon is effectively a random walk. A large ensemble of such photons can be said to exhibit diffusion in the material, described accurately with a diffusion equation.

Photon diffusion in Atmosphere In astrophysics, photon diffusions usually accrue inside a stellar atmosphere. To describe this phenomenon, one should develop the transfer equation in moments and use the Eddington limit (i.e. the diffusion approximation). In 3D the results are two equations for the photon energy flux (σ is the opacity), $\vec F = -\frac{c}{12\pi\sigma}\vec \nabla U,$ $\vec \nabla \cdot \vec F = 0.$ By substituting the first equation into the second, we get the diffusion equation for the photon energy density. $\nabla^2 U -\frac{1}{\sigma}\vec \nabla U \cdot \vec \nabla \sigma=0.$