Numerical Treatment of Radiative Transfer

We present a numerical treatment of radiative transfer in three dimensions. The radiation is modeled by the grey moment M ₁ system. The introduced scheme is able to compute accurate numerical solutions over a broad class of regimes from the transport to the diffusive limit. We discuss numerical issues concerning the resolution and the parallelization of this scheme for multi-dimensional simulations. Several numerical results are then presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. We also present a comparison in two dimensions of our code with a Monte-Carlo transfer code.     

Conservation Laws in Time-Dependent Radiative Transfer Problems

Astrophysics - The classical problem of radiative transfer with the escape of a photon from a semi-infinite scattering and absorbing atmosphere is generalized by the author to the case where the...     

Radiative Transfer Reconsidered as a Quantum Kinetic Theory Problem

We revisit the radiative transfer theory from first principles approach, inspired from quantum kinetic theory. The radiation field is described within the second quantization formalism. A master equation for the radiation density operator is derived and transformed into a balance relation in the phase space, which involves nonlocal terms owing to radiation coherence. In a perturbative framework, we focus on the lowest order term in ?-expansion and show that the radiation coherence results in an alteration of the photon group velocity. An application to the formation of hydrogen lines in stellar atmospheres is performed as an illustration.     

Basics of Gas-Dynamics and Radiative Transfer

This article is intended to review some basics of gas-dynamics (Sect. 1) and radiative transfer (Sect. 2) which are the necessary background to introduce out-of-equilibrium high energy flows. The two first sections deal with general aspects, the more specific problem of out-of-equilibrium flows is tackled in Sect. 3 through the example of radiative shock waves. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radiative Transfer in Spherically Symmetric Dust Nebulae

In this paper the mathematical tools for future calculations of the diffuse radiation field inside a homogeneous spherically symmetric dust nebula are made available. The solution of the equation of radiative transfer is represented as an expansion after LEGENDRE polynomials. Making use of the operator calculus a system of ordinary differential equations is derived the solution of which yields the coefficients of this expansion. The method developped here is more general as well as more rigorous than previous work in this field.     

Radiative Transfer in Inhomogeneous Atmospheres. II

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.     

Radiative Transfer in Inhomogeneous Atmospheres. I

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.     

Radiative Transfer in Inhomogeneous Atmospheres. III

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.     

五维Bianchi-Ⅴ型宇宙模型的辐射解

本文给出了理想流体五维Bianchi-V型的宇宙模型的严格解,并讨论了解的奇性,发现该解随着时间的增长将趋于五维膨胀各向同性宇宙模型。     

New Periodic Solution for Planar 8-body Problems

For planar Newtonian 8-body problems with equal masses, we prove the existence of the new non-collision periodic solution such that two pair bodies move clockwise and the other two pairs counter-clockwise. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radiative Transfer Models of Dust Shells Around Post-AGB Stars

We present a radiative transfer analysis of circumstellar dust shells around the Post-AGB stars HD 179821, HD 56126, HD 101584 and early R star HD 100764, using the code DUSTY. Parameters like mass-loss, shell inner radius, dust temperature, outflow velocity etc., are derived for HD 179821and HD 56126 whose observed SED could be reproduced by our models. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monte Carlo Radiative Transfer Modeling of Lightning Observed in Galileo Images of Jupiter

We study lightning on Jupiter and the clouds illuminated by the lightning using images taken by the Galileo orbiter. The Galileo images have a resolution of ∼25 km/pixel and are able to resolve the shape of single lightning spots, which have half widths (radii) at half the maximum intensity in the range 45-80 km. We compare the shape and width of lightning flashes in the images with simulated flashes produced by our 3D Monte Carlo light-scattering model.The model calculates Monte Carlo scattering of photons in a 3D opacity distribution. During each scattering event, light is partially absorbed. The new direction of the photon after scattering is chosen according to a Henyey-Greenstein phase function. An image from each direction is produced by accumulating photons emerging from the cloud in a small range (bins) of emission angles. The light source is modeled either as a point or a vertical line.A plane-parallel cloud layer does not always fit the data. In some cases the cloud over the light source appears to resemble cumulus clouds on Earth. Lightning is estimated to occur at least as deep as the bottom of the expected water cloud. For the six flashes studied, we find that the clouds above the lightning are optically thick (τ>5). Jovian flashes are more regular and circular than the largest terrestrial flashes observed from space. On Jupiter there is nothing equivalent to the 30-40-km horizontal flashes that are seen on Earth.     

The Standard Problem of Nonlocal Thermodynamic Equilibrium Radiative Transfer in the Rovibrational Band of the Planetary Atmosphere

The standard problem of radiative transfer in a rovibrational band is formulated for an optically semi-infinite plane-parallel planetary atmosphere using a model of a linear molecule with two vibrational states. The solution of the problem describes the variation with height of the population of the excited vibrational state due to the existence of the upper boundary of the atmosphere. We seek this solution as a function of the specially introduced dimensionless parameters—the atmosphere depth and four similarity parameters—and study it for the parameter values that can be realized in the planetary atmospheres, including the atmospheres of extrasolar planets. It is shown that an increase in the optical density of the atmosphere can reduce the population of an excited vibrational state in the band at the upper boundary of the atmosphere by as much as several orders of magnitude as compared to the population corresponding to the optically thin band limit. The anomalous decrease in the opacity of the atmosphere, when only several lines of the band are involved in radiative transfer, is predicted. We also determined the accuracy of calculating the population in the approximation of the Doppler line profile. An approximate formula is obtained for the dimensionless height of the boundary of the layer in which the local thermodynamic equilibrium exists for vibrational states. We propose a model and the formula following from this model to roughly evaluate the decrease in this height due to the impact on the population of additional radiative transitions between the state being considered and the underlying state belonging to another vibrational mode of the molecule.     

More Microwave Observations of Saturn: Modeling the Ring with a Monte Carlo Radiative Transfer Code

We present a second epoch of Very Large Array Saturn observations taken in February 1997 spanning wavelengths 1.3-21 cm. These observations complement earlier observations at Saturn's autumnal equinox in November 1995. In this epoch, however, we generally have better signal-to-noise ratios and the ring inclination of the present observations was −5.0°, whereas the previous observations were made with ring inclination +2.7°.Our observations confirm the latitudinal structure on the saturnian disk as seen at 2.0, 3.6, and 6.1 cm. We also see some latitudinal structure at 1.3 cm for the first time. The details of this structure have changed dramatically from those reported by I. de Pater and J. R. Dickel (1991, Icarus94, 474-492) for the 1980s and are consistent with those seen in F. van der Tak et al. (1999, Icarus142, 125-147). The most prominent features are a pair of brightness enhancements just inside the edges of the Equatorial Zone.The rings do not show the east-west asymmetry seen in our previous epoch, perhaps indicative of a viewing angle effect on the scattering properties of the rings. The radial trend in brightness in the ansae is generally consistent with that expected from optical depth variations and increasing distance from the source of scattered light. In particular the increased optical depth towards the center of the C ring is evident. Azimuthal variation in brightness in the C ring shows the forward scattering expected of Mie scattering. By contrast, the A and B rings show little or no azimuthal variation.We present Monte Carlo simulations of the ring brightness under the assumptions of isotropic and Mie scattering. These are the first synthetic maps of Saturn which can be directly compared to the images we obtained. Neither model fits all the data well. However, a hybrid model combining isotropic and Mie scattering does fit well. We interpret the consistency with isotropic scattering in the outer rings as an indication that near-field effects may be important. This in turn implies geometrically thin rings, as predicted by dynamical simulations of these rings.