Search

We reanalyze the propagation of one-dimensional small-amplitude disturbances of given real frequency ω in a radiating and scattering grey medium using the Eddington approximation, which has been studied previously by us (Kaneko et al., 1976). Numerical results reveals three frequency regimes to be distinguished, and two wave modes always appear in each frequency regime. The governing equations and analytic solutions are derived for all wave modes using Whitham's method modified into quadratic form and approximate methods based on radiation thermodynamics. In the high-frequency regime appear the radiation-wave and adiabatic sound modes, which are damped by opacity and radiative cooling, respectively. Wave patterns in the intermediate-frequency and low-frequency regimes depend critically on the importance of radiation, for which the criterion is given in terms of the ratio of total specific heats at constant pressure and constant volume. When the radition overwhelms the matter (radiation-dominated case), the radiative mode in the intermediate-frequency regime is the constant-volume diffusion mode. When the matter overwhelms the radiation (matter-dominated case), damped radiation-wave and damped radiation-diffusion modes newly appear between the radiation-wave and constant-volume diffusion modes. The acoustic mode in the intermediate-frequency regime is the isothermal sound mode,which is damped by radiative cooling at higher frequencies and by radiation-thermal drag force at lower frequencies. Two modes appearing in the low-frequency regime are the isentropic radiation-acoustic and constant-pressure diffusion modes. The absorption coefficient derived for the former is shown to be a radiation-thermodynamic extension of that of Landau and Lifshitz (1987). The transition frequencies between all adjacent two modes are also derived to discuss the implications of them.

The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When τeff≪1, the sound speeda

The comoving-frame equations of radiative transfer and moment equations to accurate terms of all orders inv/c are derived in the modified Lagrangian form. The equations exactly describe the interaction of radiation with matter in a relativistically moving medium in flat or curved spacetime. Two specialized sets of equations are presented: (1) the equation of radiative transfer and moment equations accurate to terms of second order (v2/c2), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric.

The general-relativistic equations of hydrodynamics for a nonideal fluid are derived in the modified Lagrangian form. Together with the zeroth and first moment equations of radiative transfer derived by Morita and Kaneko (1986), the equations provide a complete set of the modified Lagrangian equations of radiation hydrodynamics. The equations of hydrodynamics are specialized for a thermally conducting, Newtonian viscous fluid in the modified Lagrangian form, which are the generalization of the specialrelativistic equations of hydrodynamics derived by Greenberg (1975).

The equation of radiative acoustics is derived by taking into account the effect of a transverse magnetic field, which is quite similar to the acoustic equation derived in Paper I. The only difference is that theadiabatic, isothermal, andisentropic speeds of sound and theradiation-acoustic speed are replaced by theadiabatic, isothermal, andisentropic magnetoacoustic speeds and theradiation-magnetoacoustic speed, respectively. The main results shown in Paper I are valid even in the presence of a transverse magnetic field.

Integrated colors of M3, M5, M13, and M92 are calculated from the luminosity function, the color-magnitude diagram, and the two-color diagram to compare them with observed ones. The results show good agreements for M3, M13, and M92 and the discrepancy for M5. Possible causes for this discrepancy are discussed.

Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of $$\mathfrak{M} = \mathfrak{M}_ \odot $$ is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn0=108 cm-3 andT0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s-1, which primarily arises from the optical surface (t~1) ofT~104 K. The accretion flow is characterized by t~1 and (v/c)t~10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at t~1. The radiative equilibrium is strictly realized at (v/c)t~10.

Assuming a dust model of Reeset al. (1969), we study the time dependence of the infrared emission from grains which absorb variable ultraviolet radiation. A time scale for the variability is shown to be fairly small compared with the light travel-time across the infrared emitting region, of which size depends on the wavelength strongly. Comparison of calculated infrared light curves with observations of NGC 4151 leads to the conclusion that the variability at 2.2 µ is consistent with interpretation by the infrared emission on the basis of thermal process.