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1.
A. G. Nikoghossian 《Astrophysics》2011,54(1):126-138
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. 相似文献
2.
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
3.
A. G. Nikoghossian 《Astrophysics》2004,47(3):412-421
The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented. 相似文献
4.
A. G. Nikoghossian 《Astrophysics》2004,47(1):104-116
This series of papers is devoted to multiple scattering of light in plane parallel, inhomogeneous atmospheres. The approach proposed here is based on Ambartsumyan's method of adding layers. The main purpose is to show that one can avoid difficulties with solving various boundary value problems in the theory of radiative transfer, including some standard problems, by reducing them to initial value problems. In this paper the simplest one dimensional problem of diffuse reflection and transmission of radiation in inhomogeneous atmospheres with finite optical thicknesses is considered as an example. This approach essentially involves first determining the reflection and transmission coefficients of the atmosphere, which, as is known, are a solution of the Cauchy problem for a system of nonlinear differential equations. In particular, it is shown that this system can be replaced with a system of linear equations by introducing auxiliary functions P and S. After the reflectivity and transmissivity of the atmosphere are determined, the radiation field in it is found directly without solving any new equations. We note that this approach can be used to obtain the required intensities simultaneously for a family of atmospheres with different optical thicknesses. Two special cases of the functional dependence of the scattering coefficient on the optical thickness, for which the solutions of the corresponding equations can be expressed in terms of elementary functions, are examined in detail. Some numerical calculations are presented and interpreted physically to illustrate specific features of radiative transport in inhomogeneous atmospheres. 相似文献
5.
6.
The problem of the passage of a plane electromagnetic wave through an arbitrary, inhomogeneous dielectric layer bounded on two sides by two different homogeneous, semi-infinite media is considered. Algebraic relations are obtained between the amplitudes of transmission and reflection (the scattering amplitudes) for the problem under consideration and the wave scattering amplitudes when the layer is bounded on both sides by a vacuum. It is shown that for s and p polarized fields the scattering problem (a boundary-value problem) can be formulated as a Cauchy problem directly for the s and p wave equations. It is also shown that the problem of finding the field inside the layer also reduces to a Cauchy problem in the general case. 相似文献
7.
A. G. Nikoghossian 《Astrophysics》2004,47(2):248-259
This paper is a continuation of a study of radiative transfer in one-dimensional inhomogeneous atmospheres. Two of the most important characteristics of multiple scattering in these media are calculated: the photon escape probability and the average number of scattering events. The latter is determined separately for photons leaving the medium and for photons that have undergone thermalization in the medium. The problem of finding the radiation field in an inhomogeneous atmosphere containing energy sources is also examined. It is assumed that the power of these sources, as well as the scattering coefficient, can vary arbitrarily with depth. It is shown that knowledge of the reflection and transmission coefficients of the atmosphere makes it possible to reduce all these problems to solving some first order linear differential equations with specified initial conditions. A series of new analytic results are obtained. Numerical calculations are done for two types of atmosphere with different depth dependences for the scattering coefficient. These are interpreted physically. 相似文献
8.
The influence of compressibility of media on both the statistical acceleration and the turbulent diffusion of cosmic-ray particles is investigated. The averaging over an ensemble of random velocity fields of the medium was performed in the kinetic equation. The kinetic coefficients, which are responsible for the particle acceleration, were obtained in the cases of weak and strong scattering due inhomogeneous magnetic fields. 相似文献
9.
In the present paper, with the aid of invariance principles in connection with the scattering matrix, we get the exact solution of diffuse reflection and transmission problems by finite inhomogeneous, anisotropically scattering atmospheres bounded by reflecting sufaces. On making use of the reflection and transmission integral operators, we show how to obtain the non-linear integro-differential equations for these operators, which do not depend on the initial condition. Then, we have a system of the required integro-differential equations for the scattering and transmission functions. The obtained result is new, so far as we know. Finally, using the scattering matrix, we reduce the diffuse reflection and transmission problems for planetary atmospheres with reflecting surfaces to the standard diffuse reflection and transmission problems.Supported by the National Science Foundation under Grant No. GP29049 and the Atomic Energy Comminission, Division of Research under Contract No. AT(40-3)-133, Project 19. 相似文献
10.
H. F. Machali 《Astrophysics and Space Science》1993,208(1):33-39
The time-dependent equation of radiative transfer for a finite, plane-parallel, non-radiating, and isotropically scattering atmosphere of arbitrary stratification is solved by using the integral equation method. The medium is taken to be inhomogeneous. The Laplace transform is used in the time domain. It is seen that the obtained solutions are reducible to the corresponding ones for steady-state problems by simply changing the Laplace transform parameter to zero. 相似文献
11.
D. Lorenz-Petzold 《Journal of Astrophysics and Astronomy》1986,7(3):155-170
We present a detailed study of the inhomogeneous Stephani-Krasinski solution with time-dependent curvature index. In general,
the cosmological behaviour of the models depends on six arbitrary functions of time. Such models are termed ‘private universes’
and cannot be in accord with observation in the most general case. Two simple models with changing topology are considered
as illustrating examples. In one of these models the pressure turns out to be negative and hence a violation of the weak energy
condition in the singularity theorems is possible. A brief review of other inhomogeneous cosmologies is included for the sake
of clarity. It is shown that the geodesic equation can be reduced to a complicated differential equation, which depends on
the three arbitrary functions involved. Therefore, it is difficult to obtain explicit formulas for the various observational
relations. 相似文献
12.
Asymptotic calculations for reflection and transmission coefficients for particles incident on an inhomogeneous plane parallel medium are performed. The medium is assumed to consist of several different optically thick homogeneous layers. Functional relations between the reflection and transmission coefficients for the sublayers are obtained. The invariant embedding concepts are used to calculate the albedo for sublayers. Numerical calculations and comparisons are performed. 相似文献
13.
We present Monte Carlo simulations for the polarization of light reflected from planetary atmospheres. We investigate dependencies of intensity and polarization on three main parameters: single scattering albedo, optical depth of a scattering layer, and albedo of a Lambert surface underneath. The main scattering process considered is Rayleigh scattering, but isotropic scattering and enhanced forward scattering on haze particles are also investigated. We discuss disk integrated results for all phase angles and radial profiles of the limb polarization at opposition. These results are useful to interpret available limb polarization measurements of solar system planets and to predict the polarization of extra-solar planets as a preparation for VLT/SPHERE. Most favorable for a detection are planets with an optically thick Rayleigh-scattering layer. The limb polarization of Uranus and Neptune is especially sensitive to the vertically stratified methane mixing ratio. From limb polarization measurements constraints on the polarization at large phase angles can be set. 相似文献
14.
The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scattering particles. Here, we present results of calculations with a three-dimensional Monte Carlo code that simulates the transmitted flux during occultations or transits. For isotropically scattering particles, like gas molecules, the transmitted flux appears to be well-described by the total atmospheric optical thickness. Strongly forward-scattering particles, however, such as commonly found in atmospheres of Solar System planets, can increase the transmitted flux significantly. For exoplanets, such added flux can decrease the apparent radius of the planet by several scale heights, which is comparable to predicted and measured features in exoplanet transit spectra. We performed detailed calculations for Titan’s atmosphere between 2.0 and 2.8 μm and show that haze and gas abundances will be underestimated by about 8% if forward-scattering is ignored in the retrievals. At shorter wavelengths, errors in the gas and haze abundances and in the spectral slope of the haze particles can be several tens of percent, also for other Solar System planetary atmospheres. We also find that the contribution of forward-scattering can be fairly well described by modelling the atmosphere as a plane-parallel slab. This potentially reduces the need for a full three-dimensional Monte Carlo code for calculating transmission spectra of atmospheres that contain forward-scattering particles. 相似文献
15.
A clue towards a retrieval of the zodiacal brightness gathering along a line of sight in the ecliptic plane consists in introducing the other intersection of that line with the terrestrial orbit (Fig. 1). The distribution of the elemental contribution to the brightness, or of the local quantity [directional scattering coefficient, i.e. cross-section of the unit-volume, which gives very simple expressions (1), (2) for the brightness integral] can then be approached with reduced uncertainty. The assumptions-steady state of the zodiacal cloud; smooth distribution of —are strongly suggested by the observations, and are much less controversial than the classical assumption of uniform composition and size everywhere.The scattering coefficient may vary along the line of sight as seen in Fig. 3 : an uncertainty bar highly dependent of the abscissa, and considerably reduced in the vicinity of two “nodes”. Both in abscissae and in ordinates, these nodes are conspicuously insensitive to the arbitrary choice of a mathematical model (Table 1).The node exterior to the Earth's orbit (“martian node”) remains at r ? 1.5 a.u. from the Sun (Fig. 4). It gives access to a range of the scattering phase function near Mars' orbit, deconvolved from any radial dependence of that function (Fig. 5). The backscattering effect obtained is a new confirmation of the non-terrestrial origin of the gegenschein.The node interior to the Earth's orbit remains located not far from the middle of each chord (“quasi-radial node”. Fig. 4). It allows to retrieve the radial dependence of , partly deconvolved from its angular dependence, between 0.5 and 1 a.u. (Fig. 6 and Table 4).The uncertainty bars on at the two observing locations yield two uncertainty bars of the phase function σ(θ) at 1 a.u. (Fig. 7). At θ = 30°, the forward scattering efficiency (normalized to θ = 90°) cannot exceed 6 and more likely 4. This disagrees with higher values obtained assuming spherical particles, and even obtained in part of the more realistic studies (assuming irregularly shaped particles, or mainly observational) reviewed in Table 5.All of these results are derived, with fair agreement, from three independent observational sources. 相似文献
16.
A general theory of scattering of waves in a magnetoactive plasma by particles of arbitrary energy is presented. The cross-section
for the scattering of magnetoionic waves by thermal particles is derived and discussed. Conditions under which the effect
of the spiralling motion of the scattering electron can be neglected in treating inverse Compton radiation are found. 相似文献
17.
Equipartition magnetic fields can dramatically affect the polarization of radiation emerging from accretion disc atmospheres in active galactic nuclei. We extend our previous work on this subject by exploring the interaction between Faraday rotation and absorption opacity in local, plane-parallel atmospheres with parameters appropriate for accretion discs. Faraday rotation in pure scattering atmospheres acts to depolarize the radiation field by rotating the polarization planes of photons after last scattering. Absorption opacity in an unmagnetized atmosphere can increase or decrease the polarization compared to the pure scattering case, depending on the thermal source function gradient. Combining both Faraday rotation and absorption opacity, we find the following results. If absorption opacity is much larger than scattering opacity throughout the atmosphere, then Faraday rotation generally has only a small effect on the emerging polarization because of the small electron column density along a photon mean free path. However, if the absorption opacity is not too large and it acts alone to increase the polarization, then the effects of Faraday rotation can be enhanced over those in a pure scattering atmosphere. Finally, while Faraday rotation often depolarizes the radiation field, it can in some cases increase the polarization when the thermal source function does not rise too steeply with optical depth. We confirm the correctness of the analytic calculation by Silant'ev of the high magnetic field limit of the pure scattering atmosphere, which we incorrectly disputed in our previous paper. 相似文献
18.
Viik Tõnu 《Earth, Moon, and Planets》1989,46(3):261-284
The vector equation of radiative transfer is solved both for conservative and non-conservative planetary atmospheres using the method of discrete ordinates. The atmosphere, bounded by a Lambert bottom, is considered plane-parallel and homogeneous. The scattering in the atmosphere obeys the Rayleigh or Rayleigh-Cabannes law. The compiled package of FORTRAN codes allows us to find the Stokes parameters for such an atmosphere at arbitrary optical depth. 相似文献
19.
Yoshiyuki Kawata 《Icarus》1978,33(1):217-232
Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined. 相似文献
20.
《Astronomische Nachrichten》1976,297(5):217-227
The published data on the abundance determinations for magnetic Ap-stars were considered critically. The traditional methods of curve of growth were shown to be unsufficient for quantitative analysis of the atmospheres of magnetic Ap-stars due to inhomogeneous structure of the surface of these stars. Only qualitative results can be obtained by these methods. Correlations between overabundances of different elements are considered. Very distinct correlations exist between overabundances of Mn and Zr, between Fe and rare earths and others. No correlation could be found between overabundance of elements and Teff. The methods of determination of local abundances and the results obtained — overabundances of some elements in spots and underabundances of them out of spots - are considered. The significanse of these data for the theory of chemical anomalies in magnetic Ap stars are mentioned. 相似文献