Advances in radiative transfer

This review describes advances in radiative transfer theory since about 1985. We stress fundamental aspects and emphasize modern methods for the numerical solution of the transfer equation for spatially multidimensional problems, for both unpolarized and polarized radiation. We restrict the discussion to two-level atoms with noninverted populations for given temperature, density and velocity fields. Unfortunately this article was originally published with typesetter's errors: The correct publication date was 25 February 2006, not 3 January 2006. The content was not in the final form. The publishers wish to apologize for this mistake. The online version of the original version can be found at /10.1007/s00159-005-0025-8.     

OnH-functions of radiative transfer

Chandrasekhar'sH-functionH(z) corresponding to the dispersion functionT(z)=| _rs –frs(z)|, where [f _rs (z)] is of rank 1, is obtained in terms of a Cauchy integral whose density functionQ(x, ₁, ₂,...) can be approximated by approximating polynomials (uniformly converging toQ(x)) having their coefficients expressed as known functions of the parameters _r 's. A closed form approximation ofH(z) to a sufficiently high degree of accuracy is then readily available by term by term integration.     

Factorization methods in radiative transfer theory

Published in Astrofizika, Vol. 38, No. 4, pp. 706–708, October–December, 1995.     

Numerical methods in polarized radiative transfer

This paper looks at three aspects of numerical methods for solving polarized radiative transfer problems associated with spectral line formation in the presence of a magnetic field. First we prove Murphy's law for Stokes evolution operators which is the basis of the efficient algorithm used in the SPSR software package to compute the Stokes line depression contribution functions. Then we use a two-stream model to explain the efficacy of the field-free method in which the non-LTE line source function in a uniform magnetic field is approximated by the source function neglecting the magnetic field. Finally we introduce a totally new and computationally efficient approach to solving non-LTE problems based on a method of sparsely representing integral operators using wavelets. As an illustration, the wavelet method is used to solve the source function integral equation for a two-level atomic model in a finite atmosphere with coherent scattering, ignoring polarization.     

The interaction principle in radiative transfer

We describe the interaction principle which is of fundamental importance to the theory of radiative transfer in one-, two-, and three-dimensional geometry. We also describe the practical difficulties associated with this principle in these geometries.     

On multi-region problems in radiative transfer

TheF _N method is used to solve radiative transfer problems, based on the general anisotropically scattering model, in multi-layer atmospheres.     

Contribution functions for polarized radiative transfer

The concepts of contribution functions (CF) and of mean depths of line formation of unpolarized light as well as of Stokes profiles will be critically discussed. After having outlined the historical development arguments are given in favour of the use of directly observable quantities such as the emergent line intensity or the polarized components seen through polarization optics only. The arguments are provided by a probability interpretation of the CF; the ambiguities of line depression CF as well as some physically strange features in Stokes profiles are avoided if the rules based on this interpretation are observed. Some problems of the interpretation of measurements in chromospheric lines will be discussed as well.     

尘埃辐射转移模型

尘埃辐射转移模型对解释和探索宇宙中众多的多尘埃天体的观测现象可发挥重要的作用。目前所见的四种球对称系统中的尘埃辐射转移方法可被总结为：二流Ｅｄｄｉｎｇｔｏｎ近似模型方法,Ｅｄｄｉｎｇｔｏｎ因子迭代模型方法、射线跟踪法和Ｍｏｎｔｅ－Ｃａｒｌｏ模型方法,除了第一种方法外,其余方法在原理上都没有近似性。现在使用最多的是后两种方法。Ｍｏｎｔｅ－Ｃａｒｌｏ方法是其中最灵活的一种,它可被用于对非球对称系统的辐     

3D hydrodynamics and radiative transfer

Finite difference codes for the solution of the fully three dimensional equations of hydrodynamics, self-gravitation, and radiative transfer have been developed for use on relatively modest computers. Originally developed to study the collapse and fragmentation of protostellar clouds, this family of codes has been used to study a variety of astrophysical problems, with a particular emphasis on cosmogonical issues.     

An inverse problem in a three-dimensional radiative transfer

In a series of papers (cf. Bellmanet al., 1965a, b; Kagiwadaet al., 1975), an estimation of optical properties of turbid media has been made, in the least-squared sense, with the aid of quasi-linearization and invariant imbedding. Recently, an extension of the above procedure to the three-dimensional case with horizontally inhomogeneous albedo of the underlying surface has been attempted (Ueno, 1982). From computational aspects the numerical evaluation is not so easy, even by means of high-speed electronic computers. In the present paper it is shown that the latin-square algorithm is a useful estimate for the least-squares inference of the optical properties of turbid media bounded by an inhomogeneous reflecting surface.     

Multigroup radiative transfer in supernova shock breakout models

The physical peculiarities of supernova shock breakout are discussed. A number of models for various types of supernovae have been constructed based on multigroup radiative transfer by taking these peculiarities into account. The results of numerical simulations and the influence of the effects of photon scattering by electrons and the thermalization depth on them are considered. It is shown under which conditions the appearance of hard X-ray emission is possible at shock breakout. It is pointed out what refinements are necessary in the computational algorithms for radiative transfer and hydrodynamics.     

Group-theoretical description of radiative transfer in one-dimensional media

Group theory is used to describe a procedure for adding inhomogeneous absorbing and scattering atmospheres in a one-dimensional approximation. The inhomogeneity originates in the variation of the scattering coefficient with depth. Group representations are derived for the composition of media in three different cases: inhomogeneous atmospheres in which the scattering coefficient varies continuously with depth, composite or multicomponent atmospheres, and the special case of homogeneous atmospheres. We extend an earlier proposal to solve problems in radiative transfer theory by first finding global characteristics of a medium (reflection and transmission coefficients) and then determining the internal radiation field for an entire family of media without solving any new equations. Semi-infinite atmospheres are examined separately. For some special depth dependences of the scattering coefficients it is possible to obtain simple analytic solutions expressed in terms of elementary functions. An algorithm for numerical solution of radiative transfer problems in inhomogeneous atmospheres is described.     

Probabilistic approach to radiative transfer in supersonic flows

The relationship J=(1 – )S + _c I _c common to most supersonic radiative transfer theories, is given a detailed interpretation in terms of atomic rates and probabilities. It is also generalized to cases whereI _c depends on angle. The nature of the escape process and the expressions for the escape probability are clarified.On leave from Michigan State University.     

Diffusion approximation in the theory of radiative transfer

The transfer process of hard X-ray radiation passing through a cold plasma is studied in this paper under the diffusion approximation. We call such a particular transfer process a down-Comptonization. A diffusion equation describing this process is derived and its potential applications in astrophysics and radiation physics are also pointed out.     

General integral operator for radiative transfer problems

General integral operator for radiative transfer problems is considered and will be denoted asK ^k {g(t)}.General theorems for theK-operator valid to any smooth functiong(t) will be established. The effect of the operator to the functions oftenly occur in transfer problems will also be established analytically and computationally.     

Bilinear integrals of the radiative transfer equation

It is shown that the group of problems in the theory of radiative transfer that are reducible to the sourcefree problem admits a class of integrals involving quadratic moments of the intensity of arbitrarily high orders. Based on a variational principle, it is found that these integrals, which include the R-integral, follow from the corresponding conservation laws. Some of the results are generalized to the case of anisotropic scattering.