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1.
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 (v
2/c
2), and (2) the transfer equation and moment equations for a radial flow in curved spacetime with the Schwarzschild-type metric. 相似文献
2.
Rabindra Nath Das 《Astrophysics and Space Science》1980,67(2):335-342
The key equation which commonly appears for radiative transfer in a finite stellar atmosphere having ground reflection according to Lambert's law is considered in this paper. The exact solution of this equation is obtained for surface quantities in terms of theX-Y equations of Chandrasekhar by the method of Laplace transform and linear singular operators. This exact method is widely applicable for obtaining the solution for surface quantities in a finite atmosphere. 相似文献
3.
Myeong-Gu Park 《Monthly notices of the Royal Astronomical Society》2006,367(4):1739-1745
Radiation interacts with matter via exchange of energy and momentum. When matter is moving with a relativistic velocity or when the background space–time is strongly curved, rigorous relativistic treatment of hydrodynamics and radiative transfer is required. Here, we derive fully general relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations can be applied to any three-dimensional problems and are rather straightforward to understand compared to the comoving frame-based equations. The current approach is applicable to any space–time or coordinates, but in this work we specifically choose the Schwarzschild space–time to show explicitly how the hydrodynamic and the radiation moment equations are derived. Some important aspects of relativistic radiation hydrodynamics and the difficulty with the radiation moment formalism are discussed as well. 相似文献
4.
The coupled set of equations of hydrodynamics and radiative transfer is derived for small disturbances in a plane, grey atmosphere. Only radiative transfer is taken into account in the energy equation; dynamical effects of radiation are ignored. A mean stationary radiative flux through the photosphere is taken into account. The radiative transfer equation is used by assuming the Eddington approximation, moreover, an exponential height profile of the temperature and an analytical opacity formula are supposed. For this model we obtained an asymptotic solution for plane nonadiabatic acoustic waves and radiation waves. The approach provides a detailed discussion of the interaction of nonadiabatic p‐modes and radiation waves in a realistic model of the photosphere of a solar‐like star. 相似文献
5.
A complete set of transfer equations required for the order-of-scattering analysis of partially polarized radiation in inhomogeneous, anisotropically scattering atmospheres is provided. The equations have been derived for both a local study using the radiative transfer equation and its associated auxiliary equation for the source-matrix, and a global study in terms of the scattering and transmission matrices; they account for the polarity of the scattering medium. Their derivations for the finite order scattering and the finitely cumulative scattering, in particular, have yielded important new equations expressing the invariance principles and the integro-differential recurrences for the scattering and transmission matrices. These novel expressions contain as a special case Bellmanet al's (1972) equations for the simpler case of isotropic scattering of unpolarized light in homogeneous atmospheres. 相似文献
6.
A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF
n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source. 相似文献
7.
The aim of the present paper will be to establish the explicit form of the equations of radiative transfer, in plane-parallel atmospheres surrounding the stars which are distorted by axial rotation or tides, in curvilinear coordinates which parallel the distorted surface; with particular attention to the circumstances under which the effects arising from limb- and gravity-darkening are multiplicative and admit of algebraic separation. In Section 2 (which follows a general outline of our problem) the fundamental equations of the radiativetransfer problem will be formulated for the ‘grey’ case; and rewritten in Section 3 in terms of non-orthogonal coordinates in which the potential over a level surface in hydrostatic equilibrium replaces the radial coordinate of spherical polars. In Section 4 we shall proceed to construct an explicit solution of the corresponding transfer problem in a plane-parallel approximation; and to prove that the effects of limb- and gravity-darkening remain factorizable only to terms which are linear in the cosines μ of the angle of foreshortening. Lastly, in Section 5 we shall list additional problems, arising in this connection, which still await appropriate treatment. 相似文献
8.
The equation for radiative transfer in the case of resonance radiation for isotropic scattering has been solved by the method of the Laplace transformation and linear singular operators. The solution for emergent intensities have come out in terms ofX- andY-functions. 相似文献
9.
A moment method with three stream division of the radiation field was suggested by Wilson, Wan and Sen (1980) for solving radiative transfer problems in stationary, non-grey extended shells surrounding a central star. Use was made of the generalised Eddington relations as the closure conditions of the moment equations. In the present paper the same method has been utilised to study the radiative transfer problems in a non-grey, expanding gaseous spherical shells surrounding a central star. The transfer equation has been set in comoving frame in spherical geometry. The radiation and material quantities, angles and frequencies have been expressed in comoving frame. The mean intensity, flux and K-integrals have been calculated for extensive atmospheres in the presence of different velocity fields. 相似文献
10.
S. I. Grachev 《Astrophysics》2001,44(4):505-517
A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity of t, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + t, and so forth. The method enables one to analyze nonsteady tradiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples. 相似文献
11.
The time-dependent equation of radiative transfer for isotropic scattering has been solved by integral equation technique in terms ofX- andY-functions appropriate for the problem. It is seen thatX- andY-functions are reducible to the corresponding function for steady-state problems by simply changing the Laplace transform parameters-i.e., byS0. 相似文献
12.
J. S. Aliyev 《Astrophysics and Space Science》1986,121(2):283-300
The functional analytic method of solution is applied to investigation of the radiative transfer equation in spectral lines. A problem of scattering in the spectral line with the frequency redistribution in anisotropic-scattering infinite and semi-infinite media is considered. Continuum absorption in the line is also taken into account.The solution is presented as the exponential function of the operatorA and the functional calculus is developed. The eigenfunction and the expansion coefficients, in terms of which the explicit solution is expressed, have been found. The nonlinear equation and the explicit expressions for theX-function are derived. The albedo problem with the determined expansion coefficients and the intensity of the emergent radiation is given as an example. 相似文献
13.
Rabindra Nath Das 《Astrophysics and Space Science》1980,71(1):37-43
The simplest form of the equation of transfer for a time dependent radiation field in finite atmosphere is considered. This equation of transfer is an integro-differential equation, the solution of this equation is based on the theory of separation of variables, the Laplace transform and the theory of linear singular operators. The emergent intensities from the bounding faces of the finite atmosphere are determined in terms ofX-Y equations of Chandrasekhar. 相似文献
14.
A. Adriani M. L. Moriconi G. L. Liberti A. Gardini R. Orosei E. D’Aversa G. Filacchione A. Coradini 《Earth, Moon, and Planets》2005,96(3-4):109-117
An attempt to evaluate the preliminary values of the Titan's surface albedo at 2 μm from the first Cassini-VIMS observations of the moon is presented. The methodology is based on the application of radiative transfer calculations and a microphysical model of the Titan atmosphere based on fractal aerosol. As a first guess, the surface has been considered flat and lambertian. The results are presented as a function of the geographical coordinates associated to the image pixels. The libRadtran package, using the radiative transfer equation solver DISORT 2.0, has been applied for the calculations. A test run to evaluate the model performances, using ground based observations of Titan as reference in the range of wavelengths 0.3-1.0 μm, has been carried out.The retrieved values of the surface albedo range between 0.03 and 0.22. 相似文献
15.
We have calculated prominence thread models for different values of the center temperature and pressure. We have simultaneously solved the radiative transfer, statistical equilibrium and ionization equilibrium equations assuming a three-level atom plus continuum. We have also computed the energy balance equation including the hydrogen radiative losses from our calculations, plus other radiative losses and heat conduction. Some models have been calculated assuming possible variations in thermal conductivity and heating terms. We computed the lines and continua emitted by a number of threads, in order to compare with the observations and evaluate how the different values of the parameters affect the profiles and absolute intensities of L, L, H, and Ly continuum.Member of the Carrera del Investigador, CONICET, Argentina.c.c.67 Suc. 28 Buenos Aires 1428, Argentina. 相似文献
16.
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). 相似文献
17.
Radiative transfer 总被引：1，自引：0，他引：1
George B. Rybicki 《Journal of Astrophysics and Astronomy》1996,17(3-4):95-112
Chandrasekhar’s work in radiative transfer theory began in 1944 and culminated with the publication of his influential treatiseRadiative Transfer in 1950. In this review his major contributions to radiative transfer will be recounted and evaluated. These include his
development of the discrete ordinates method, the invariance principles, and his formulation and solution of the transfer
equation for polarized light. 相似文献
18.
19.
J. Sánchez Almeida 《Solar physics》1992,137(1):1-14
Two formal solutions of the radiative transfer equation for polarized light have been proposed. One uses the Stokes parameters to describe the polarization, while the other uses the coherency matrix. It is shown in the present work that they are equivalent. Both can be used to compute response and contribution functions for the Stokes parameters and both require the solution of systems of differential equations with similar numbers of independent variables. New equations to solve the radiative transfer problem using the Stokes parameters formalism are presented. In addition, a computer code which synthesizes the Stokes profiles by means of these equations is described.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
20.
In connection with Chandrasekhar's planetary problem of radiative transfer the total scattering and the diffuse transmission functions have been discussed by several authors (cf. Chandrasekhar, 1950; van de Hulst, 1948; Sobolev, 1948; Bellman,et al., 1967; Kagiwada and Kalaba, 1971). With the aid of the Bellman-Krein formula for the resolvent kernel of the auxiliary equation governing the source function, we show how the invariant imbedding equations governing the diffuse scattering and transmission functions can readily be obtained. So far as we know, the Cauchy system of the functional equations for the scattering and transmission functions is new and is well-suited for the numerical computation.Supported by the National Science Foundation under Grant No. GP 29049, and by the Atomic Energy Commission under Grant No. AT (40-3)-113 Project 19. 相似文献