Abstract
We study the fundamental modes of radiation hydrodynamic waves arising from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium using the Eddington approximation. The dispersion relation analyzed is the same as that of Paper I (Kaneko et al., 2000), but is solved as a quintic in angular frequency ω while a quadratic in k 2 in Paper I. Numerical results reveal that wave patterns of five solutions are distinguished into three types of the radiation-dominated and type 1 and type 2 matter-dominated cases. The following wave modes appear in our problem: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusion modes, adiabatic sound wave, cooling-damped and drag–force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. The radiation-dominated case is characterized by the gap between the isothermal sound and isentropic radiation-acoustic speeds within which there is not any acoustic wave propagating with real phase speed. One of the differences between type 1 and type 2 matter-dominated cases is the connectivity of the constant-volume diffusion mode, which originates from the radiative mode in the former case, while from the Newtonian-cooling wave in the latter case. Analytic solutions are derived for all wave modes to discuss their physical significance. The criterion, which distinguishes between radiation-dominated and type 1 matter-dominated cases, is given by Γ0 = 9, where Γ0 = C p (tot)/C V (tot) is the ratio of total specific heats at constant pressure and constant volume. Waves in a scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.
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Kaneko, N., Morita, K., Satoh, T. et al. Small-Amplitude Disturbances In A Radiating And Scattering Grey Medium Ii. Solutions Of Given Real Wave Number k . Astrophys Space Sci 299, 263–306 (2005). https://doi.org/10.1007/s10509-005-8189-2
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DOI: https://doi.org/10.1007/s10509-005-8189-2