  In the dynamic diffusion limit of radiation hydrodynamics, advection
dominates diffusion; the latter primarily affects small scales and has
negligible impact on the large scale flow. The radiation can thus be accurately
regarded as an ideal fluid, i.e., radiative diffusion can be neglected along
with other forms of dissipation. This viewpoint is applied here to an analysis
of simple waves in an ideal radiating fluid. It is shown that much of the
hydrodynamic analysis carries over by simply replacing the material sound
speed, pressure and index with the values appropriate for a radiating fluid. A
complete analysis is performed for a centered rarefaction wave, and expressions
are provided for the Riemann invariants and characteristic curves of the
one-dimensional system of equations. The analytical solution is checked for
consistency against a finite difference numerical integration, and the validity
of neglecting the diffusion operator is demonstrated. An interesting physical
result is that for a material component with a large number of internal degrees
of freedom and an internal energy greater than that of the radiation, the sound
speed increases as the fluid is rarefied. These solutions are an excellent test
for radiation hydrodynamic codes operating in the dynamic diffusion regime. The
general approach may be useful in the development of Godunov numerical schemes
for radiation hydrodynamics.
