  As is well-known that the general radiation hydrodynamics models include two
mainly coupled parts: one is macroscopic fluid part, which is governed by the
compressible Navier-Stokes-Fourier equations, another is radiation field part,
which is described by the transport equation of photons. Under the two physical
approximations: "gray" approximation and P1 approximation, one can derive the
so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model
from the general one. In this paper we study the non-relativistic limit problem
for the Navier-Stokes-Fourier-P1 approximation model due to the fact that the
speed of light is much larger than the speed of the macroscopic fluid. Our
results give a rigorous derivation of the widely used macroscopic model in
radiation hydrodynamics.
