  We introduce a model concerning radiational gaseous stars and establish the
existence theory of stationary solutions to the free boundary problem of
hydrostatic equations describing the radiative equilibrium. We also concern the
local well-posedness of the moving boundary problem of the corresponding
Navier-Stokes-Fourier-Poisson system and construct a prior estimates of strong
and classical solutions. Our results explore the vacuum behaviour of density
and temperature near the free boundary for the equilibrium and capture such
degeneracy in the evolutionary problem.
