On compressional modes in radiative plasmas

Dispersion relations associated with compressional modes in radiative fluids are derived from Israel's relativistic theory of transient thermodynamics. The main focus is on regimes where the photons dominate the thermal energy and pressure of the two-component fluid. Although the material gas can be entirely non-relativistic in this case, these plasmas exhibit typically relativistic features such as characteristic velocities $$v_\text c = \pm\sqrt {3/5}$$ and $$v_\text c = \pm\sqrt {1/3}$$. A comparison with standard results, derived earlier by Weinberg from conventional theory, shows that transient thermodynamics modifies not only the short-wavelength but also parts of the long-wavelength regime. Transient thermodynamics reduces an infinite zero-sound-band, predicted by conventional theory, to a compact triangular area. This clarifies the range of validity of a damping rate formula derived from conventional theory. It is shown that this standard result follows from transient thermo-dynamics as a long-wavelength approximation and that expansions in powers of the transport coefficients can be avoided. The question of the survival of protogalaxies during the acoustic phase in an expanding universe is touched upon at the end of this paper. The assumption that the modes expand spherically symmetrically proves to be crucial in the case of a low present density universe.