Polarization of continuum radiation in magnetic atmospheres

A numerical solution is presented for the problem of continuum radiative transfer in a magnetoactive medium. The continuum opacities are calculated in the presence of a strong magnetic field (H=10⁷ G) typical of magnetic white dwarfs. The L.T.E. pure absorption model is assumed for calculating the polarized radiation field emitted by a realistic model atmosphere in the plane parallel approximation. The wavelength dependence of the linear and circular polarizations are calculated for both uniform and dipole field configurations.     

Diffusion of radiation in planetary atmospheres

The problem of interaction of the solar radiation with the turbid Earth atmosphere, containing complicated polydispersive aerosol systems, is discussed in this paper. Equations for computing the angular functions ofn-th order scattering are derived. On the basis of these functions the spectral radiance, radiation flows and radiation balance of the atmosphere in the short-wave spectral range are calculated. The relations obtained can be used to calculate the complex index of refraction, distribution function and other characteristics of the submicron aerosol fraction, by solving the inverse problems.     

Polarization effect on radiative transfer in planetary composite atmospheres with interacting interface

A procedure of computing the radiance and the polarization parameters of radiation diffusely reflected and transmitted by an inhomogeneous, plane-parallel terrestrial atmosphere bounded by a ruffled ocean surface is discussed with the aid of the adding method. If the atmosphere and the ocean are simulated by a number of homogeneous sublayers, the matrices of radiation reflected and transmitted diffusely by the atmosphere-ocean system can be expressed in terms of these matrices of sublayers by using only a couple of iterative equations in which the polarity effect of radiation is included. Furthermore, the upwelling radiance and the polarization degree of radiation at the top of the atmosphere can be calculated by using a single iterative equation without requiring the equation for the diffuse transmission matrix of radiation. The ruffled ocean surface can be treated as an interacting interface, where the transmitted radiation from beneath the ocean surface into the atmosphere is also taken into account into the derivation of equations. Finally, sample computations of the upwelling radiance and the polarization degree of radiation from the top of the atmosphere are carried out at the wavelength of 0.60 micron.     

A generalised principle of invariance and radiation field in multilayer atmospheres

A generalized principle of invariance is derived for a plane-parallel atmosphere. On the basis of this principle a method for determining the radiation field in a multilayer atmosphere is proposed. This method, the first part of which is the well-known adding method, permits the application to problems involving optically finite as well as semi-infinite atmospheres. The reflecting boundaries may be incorporated, though in that case it is not possible to use the adding method.Some numerical results are given for the standard and Milne problems and for the problem with internal sources.     

Curvature effects in extended stellar atmospheres — Pure absorption

The effects of curvature in an atmosphere with pure absorption are investigated. Numerical solution of the transfer equation has been obtained in the framework of the Discrete Space Theory of Radiative Transfer. Two cases have been considered: (a) the atmosphere is irradiated at the bottom and there is no incident radiation at the top of the atmosphere; and (b) no radiation is incident on either side of the atmosphere. It is found that the thermal sources inside the atmosphere dominantly influence the emergent radiation and this is very much so, in the spherical case and for large optical thickness. The emergent luminosities increase with the geometrical thickness although the emergent specific intensities are reduced and the former seems to be because of the larger surface area and later seems to be because of the effects of curvature.     

Average photon path-length of radiation emerging from finite atmospheres

The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.To solve this problem we have used the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions (or matrices). By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries.As in the case of scalar transfer the principles of invariance by Chandrasekhar may be used to find an adding scheme to obtain both the scattering and transmission matrices and their derivatives with respect to the albedo of single scattering. These derivatives are crucial in determining the average path length.The numerical experiments have shown that the impact of the polarisation on the average pathlength of the emergent radiation is the largest in the atmospheres with optical thickness less than, or equal to, three, reaching 6.9% in the reflected radiation.     

Solution of linear radiative transport problems in plane-parallel atmospheres. I.

A new method for determining various quantities describing the radiation field in an inhomogeneous, plane-parallel atmosphere is proposed in this two-part paper. The essence of this method is the reduction of the boundary value problems which arise during the customary statement of various astrophysical problems associated with solving the radiative transfer equations to initial value problems. Compared to previous attempts in this area, the proposed method is universal and simple. The first part of this paper deals with one-dimensional media. Scalar, as well as vector–matrix problems relating to the diffusion of radiation in spectral lines with frequency redistribution are examined.     

Functional equations in emitting atmospheres

Astrophysics and Space Science - Starting with the equation of transfer in a plane-parallel inhomogeneous atmosphere which emits and scatters radiation anisotropically, we obtain a set of...     

Radiative transfer in spherical shell atmospheres: II. Asymmetric phase functions

In this paper we investigate the effects of sphericity on the radiation reflected from a planet with a homogeneous, conservative scattering atmosphere of optical thicknesses of 0.25 and 1.0. We considered a Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7. Significant differences were found when these results were compared with the plane-parallel calculations. Also, large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle. These results will be useful to researchers in the field of remote sensing and planetary spectroscopy.     

Rayleigh-Cabannes scattering in planetary atmospheres III. The Milne problem in conservative atmospheres

The discrete ordinale method by Chandrasekhar is used to solve the conservative Milne problem in a homogeneous plane-parallel atmosphere which scatters the radiation according to the Rayleigh-Cabannes law.The approximate solution which is supposed to converge uniformly to an exact one when increasing the order of approximation is obtained explicitly. In addition to a tabulation of the Hopf vector for different factors of depolarization, the extrapolation distance, the values of c, q and the Rubenson degrees of polarization at the limb are given.     

Depolarization of multiple scattered light in atmospheres due to anisotropy of small grains and molecules

Freely oriented small anisotropic grains and molecules depolarize radiation both in single scattering and in the process of multiple scattering. Especially large depolarization occurs for resonant scattering corresponding to the electron transitions between the energy levels with very different quantum numbers. The existence of light absorption also changes essentially the angular distribution and polarization of radiation, outgoing from an atmosphere. In the present paper we consider these effects in detail both for continuum radiation and for resonant lines. Because the term describing the depolarization deals with isotropic radiation, we consider the axially symmetric part of radiation. We derived the formulas for observed intensity and polarization using the invariance-principles both for continuum and resonant scattering. We confine ourselves to two problems—the diffuse reflection of the light beam from semi-infinite atmosphere, and the Milne problem.     

Hydrogen-model atmospheres for white dwarf stars

We present a detailed calculation of model atmospheres for DA white dwarfs. Our atmosphere code solves the atmosphere structure in local thermodynamic equilibrium with a standard partial linearization technique, which takes into account the energy transfer by radiation and convection. This code incorporates recent improved and extended data base of collision-induced absorption by molecular hydrogen. We analyse the thermodynamic structure and emergent flux of atmospheres in the range 2500 T _eff60 000 K and 6.5log  g 9.0. Bolometric correction and colour indices are provided for a subsample of the model grid. Comparison of the colours is made with published observational material and results of other recent model calculations.
Motivated by the increasing interest in helium-core white dwarfs, we analyse the photometric characteristics of these stars during their cooling, using evolutionary models recently available. Effective temperatures, surface gravities, masses and ages have been determined for some helium-core white dwarf candidates, and their possible binary nature is briefly discussed.     

A relaxation method for the computation of model stellar atmospheres

A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Rayleigh scattering in planetary atmospheres

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.     

Mean values in inhomogeneous atmospheres

A brief summary of observations of inhomogeneities in the solar atmosphere and progress in the theoretical analysis of two-dimensional model atmospheres is given. In particular, it is asserted that reliable reference models of the mean temperature, pressure, etc. may be derived only by averaging over the horizontal coordinates of a two- or three-dimensional model. In discussion of a wide variety of cases including strong chromospheric lines, weak photospheric lines, and continuum radiation, it is shown that although the derivation of mean values by first averaging over the fluctuations in the data and then applying a one-dimension analysis is an obvious first approximation, it may lead to errors of a gross qualitative nature. Thus the recent deductions by several authors of very small temperature gradients in the upper regions of sunspots are shown to be subject to considerable doubt.     

The solar radiation incident at the top of the atmospheres of Uranus and Neptune

The latitudinal and seasonal variation of the direct solar radiation incident at the top of the atmosphere of Uranus and Neptune has been recalculated by use of updated values for the period of axial rotation and the oblateness. Values for the solar radiation are given in Watt per square meter instead of the unit used in earlier papers (calories per square centimeter per planetary day). The solar radiation averaged over a season and a year as a function of planetocentric latitude has also been reviewed. In addition, attention is made to the ratio of the solar radiation incident on an oblate planet to that incident on a spherical planet.     

Convective energy transport in stellar atmospheres

We discuss a theoretical method of computing the temperature structure of hot and cool streams in convective stellar atmospheres. The method is based on the model that the streams are due to organized cells whose diameters are greater than the thickness of the photosphere. The excess thermal energy of matter rising from the deeper layers, where the entropy is higher than in the photosphere, is converted to radiation in a steady front. This model, applied to the solar case, exhibits a peak-to-peak contrast of 30–40% between granules and lanes. This contrast agrees with the Stratoscope data reduced by Namba and Diemel (1969). As a necessary part of the theory, we obtain an expression for the perturbation in radiative heat exchange which may be used in a medium with a strongly preferred direction such as a stellar atmosphere.Supported in part by the National Science Foundation [GP-15911 (formerly GP-9433), GP-9114] and the Office of Naval Research [Nonr-220(47)].     

Polarization of radiation from stellar atmospheres. The grey case

An accurate numerical method is presented for the solution of the transfer equations in a plane-parallel atmosphere in which scattering occurs according to Rayleigh's law. Some results are given for the polarization and limb darkening of both integrated and monochromatic radiation emerging from grey atmospheres with various ratios of scattering to absorption. The method is equally applicable to non-grey atmospheres.     

Ray propagation in oblate atmospheres

We evaluate the departures from Bouguer's law for the case of an oblate atmosphere. We show that, to lowest order, the plane of refraction is defined by the normal to the atmosphere at closest approach. In next order, however, the ray path is “warped” by the oblateness, which changes slightly the plane of refraction.     

The neutral atmospheres of comets

In this paper we have endeavored to critically evaluate our present understanding of cometary atmospheres. Following a brief introduction of the significance of the study of cometary atmospheres (Section 1), the relevant photometric and spectroscopic observations are summarized in Section 2.The interaction with the solar radiation, with regard to both the excitation of the observed species as well as the dissociation of stable molecules evaporating from the nucleus, is considered in Sections 3 and 4. The gas phase chemistry likely to take place in the dense inner coma is next considered in Section 5.The exospheric and hydrodynamic models of the expanding cometary atmosphere are considered in detail in Section 6, and both their limitations as well as possible improvements are discussed.The observed chemical composition of the neutral atmosphere and the inferred chemical composition of the volatile component of the nucleus, together with possible variations between different classes of comets is next considered in Section 7, and their possible cosmogonic significance is discussed.In conclusion, some of the important directions in which future research should progress, in order to provide more complete and secure knowledge of cometary atmospheres, are stressed (Section 8).Astrophysics and Space Science Review Paper.