  Consider the linear Boltzmann equation of radiative transfer in a half-space,
with constant scattering coefficient $\sigma$. Assume that, on the boundary of
the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)
reflection law with albedo coefficient $\alpha$. Moreover, assume that there is
a temperature gradient on the boundary of the half-space, which radiates energy
in the half-space according to the Stefan-Boltzmann law. In the asymptotic
regime where $\sigma\to+\infty$ and $1-\alpha\sim C/\sigma$, we prove that the
radiation pressure exerted on the boundary of the half-space is governed by a
fractional diffusion equation. This result provides an example of fractional
diffusion asymptotic limit of a kinetic model which is based on the harmonic
extension definition of $\sqrt{-\Delta}$. This fractional diffusion limit
therefore differs from most of other such limits for kinetic models reported in
the literature, which are based on specific properties of the equilibrium
distributions (heavy tails) or of the scattering coefficient as in [U.
Frisch-H. Frisch: Mon. Not. R. Astr. Not. 181 (1977), 273-280].
