Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

New approximate formulae for radiative accelerations in stars

Radiative accelerations are quantities that are crucial in the study of diffusion processes in stars. Their calculation requires the use of large atomic and opacity data bases, and generally necessitates very heavy numerical computations. New approximate formulae for radiative accelerations in stars, arising from both bound–bound and bound–free transitions, are presented. These are written in a parametric form, which separate the terms depending on the local abundance of the element under consideration from those depending mainly on the atomic data. These formulae are shown to be significantly superior to those previously published. The main reason for this improvement comes form the use of monochromatic opacities instead of approximating these by the Rosseland mean. The principal advantage for the use of these parametric equations over other methods for calculating radiative accelerations is its numerical expediency. Results are shown for several elements (C, Ar, Ca and Fe) in a type A star.     

The expansion of scattering matrices for an isotropic medium in generalized spherical functions

It is shown that it is always possible to expand the scattering matrix for an isotropic medium in generalized spherical functions. Additional physical symmetry properties of the scattering process, e.g., time-reversal invariance or reflection invariance, give rise to simple symmetry relations for the expansion coefficents. The expansion in generalized spherical functions naturally leads to decomposition of variables and appears to be the simplest way to include the various symmetry relations for the scattering matrix discussed in the literature.     

Combined-Operations method for diffuse reflection by an isotropic,non-coherent scattering homogeneous sphere

Combined-Operations method has been utilised to solve the problem of diffuse reflection by a homogeneous, isotropic, non-coherent scattering spherical medium. The source function is considered to be frequency independent. The auxiliary equation has been formulated, the scattering function defined, and the integro-differential equation for this function deduced. A method for obtaining the emergent intensity and the internal source function for non-zero internal source distribution has been suggested for a given line profile.     

A fast and accurate DE-formula algorithm to evaluate Ambartsumian-Chandrarasekhar $H$ -function for isotropic scattering

Astrophysics and Space Science - Electrostatic (ES) waves generated in space plasmas, e.g., Langmuir and ion-acoustic waves, are subject to multiple applications, such as plasma diagnosis,...     

Semi-empirical model of absorption and scattering by isotropic fractal aggregates of spheres

Existing models of scattering by fractal aggregates of spheres are generally accurate but somewhat complicated and time consuming. Therefore, they are not easily usable for atmospheric studies that need intensive computations. We propose here a simple and fast model, based on Mie scattering and a set of empirical rules, that determines the scattering and absorption cross sections as well as the intensity phase function of isotropic fractal aggregates of identical spheres. This model is 10–50 times faster than the mean field model it is based on, and is easily derivable from a regular Mie code. The parameters of the present model are optimized for values of the real refractive index between 1.2 and 2.2, for imaginary refractive index less than 1 and for the product of real refractive index and spherical size parameter less than 10. This range was chosen as representative of typical particles in planetary atmospheres, for example, Titans aerosols.     

Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune

Raman scattering by H₂ in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ∼20% in a clear atmosphere and ∼10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH₄ bands is mainly Raman scattered is not valid for current estimates of the CH₄ vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ∼6% in the 0.22-0.26 μm range and by ∼13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH₄ absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ∼5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new approximation based on spectral tuning of the effective molecular single scattering albedo provides low errors for zenith angles below 70° in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.     

Exact solution of the problem of diffuse reflection for a combination of Rayleigh and isotropic scattering

We consider the basic vector equation of transfer for radiation in a semi-infinite atmosphere for diffuse reflection which scatters radiation in accordance with the phase matrix obtained from a combination of Rayleight and isotropic scattering. This equation will give an integral equation for emergent intensity while subjected to the Laplace transform. The integral equation will give rise to the emergent intensity matrix on application of the Wiener-Hopf technique. This is an exact method.     

Solution of the radiative transfer equation in combination with rayleigh and isotropic scattering

A theory is constructed for solving half-space, boundary-value problems for the Chandrasekhar equations, describing the propagation of polarized light, for a combination of Rayleigh and isotropic scattering, with an arbitrary probability of photon survival in an elementary act of scattering. A theorem on resolving a solution into eigenvectors of the discrete and continuous spectra is proven. The proof comes down to solving a vector, Riemann—Hilbert, boundary-value problem with a matrix coefficient, the diagonalizing matrix of which has eight branching points in the complex plane. Isolation of the analytical branch of the diagonalizing matrix enables one to reduce the Riemann—Hilbert problem to two scalar problems based on a [0, 1] cut and two vector problems based on an auxiliary cut. The solution of the Riemann—Hilbert problem is given in the class of meromorphic vectors. The conditions of solvability enable one to uniquely determine the unknown expansion coefficients and free parameters of the solution of the boundary-value problem. Translated from Astrofizika, Vol. 41, No. 2, pp. 263–276, April-June, 1998.     

Scattering in the Atmosphere of Venus. I. Line profiles and curves of growth for isotropic scattering

We have computed line profiles and curves of growth for both reflected and transmitted radiation for typical lines in CO₂ bands (in the photographic infrared) which occur in the spectrum of Venus. In our model the pressure variation with altitude was considered and the base of the cloud deck was set at the 2 bar level. The temperature was held constant at 250K and a Voigt profile was used for the lineshape. We also assumed that the scale height of the cloud particles was equal to the scale height of the gas. The calculations were made for four values of the scattering optical thickness (τ_c = 0.1, 1.0, 10, and 100) using a continuum single scattering albedo $\text{ω}{}_{\mathrm{<mtext>c</mtext>}}\text{= 0.9975}$ (which gives a Bond albedo of 0.896 for τ_c = 100, the value observed for Venus at these wavelengths). Curves of growth are also presented for reflected radiation which has been averaged over the visible disk for three values of the Venus phase angle (0, 86, and 166°).     

Asymmetry of compton scattering by relativistic electrons with an isotropic velocity distribution: Astrophysical implications

The angular distribution of low-frequency radiation after a single scattering by relativistic electrons with an isotropic velocity distribution differs markedly from the Rayleigh angular function. In particular, the scattering by an ensemble of ultrarelativistic electrons is described by the law p=1?cosα, where α is the scattering angle. Thus, photons are mostly scattered backward. We discuss some consequences of this fact for astrophysical problems. We show that a hot atmosphere of scattering electrons is more reflective than a cold one: the fraction of incident photons reflected after a single scattering can be larger than that in the former case by up to 50%. This must affect the photon exchange between cold accretion disks and hot coronae (or advective flows) near relativistic compact objects, as well as the rate of cooling (through multiple inverse-Compton scattering of the photons supplied from outside) of optically thick clouds of relativistic electrons in compact radio sources. Scattering asymmetry also causes the spatial diffusion of photons to proceed more slowly in a hot plasma than in a cold one, which affects the shapes of Comptonization spectra and the time delay in the detection of soft and hard radiation from variable X-ray sources.     

Relativistic corrections to the multiple scattering effect on the Sunyaev–Zel'dovich effect in the isotropic approximation

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev–Zel'dovich effect for clusters of galaxies and include the multiple scattering effects in the isotropic approximation. We present the results of the calculations by the Fokker–Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of     the ratio of both the contributions is −0.2 per cent in the Wien region. In the Rayleigh–Jeans region the ratio is −0.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.     

An approximate Riemann solver for relativistic magnetohydrodynamics

A Godunov-type scheme for relativistic magnetohydrodynamic (MHD) equations is developed. We consider the Maxwell equations and dynamic equations for a gas with perfect conductivity in hyperbolic form as was suggested by van Putten. To calculate the fluxes of conservative variables through cells' interfaces we suggest an algorithm for the solution of the linearized Riemann problem. 'Primitive' variables are calculated by solving a non-linear system using the Newton method .     

New properties of scalar-field dynamics in an isotropic cosmological model on the brane

We investigate some aspects of the scalar-field dynamics on the brane that differ from the corresponding regimes in standard cosmology. We consider asymptotic solutions near singularity, inflation and rebound conditions, and some features of chaos in the model on the brane. Our results are compared with their analogs in classical cosmology.     

An approximate solution for the polytropen=3

In general, the Lane-Emden equation for an arbitrary polytropic indexn does not admit of an analytic solution. Simple approximation to the numerical results can, however, be found; and, in particular, affords a hitherto unreported good approximation to then=3 model. This term is accurate to within 10% of the tabulated values over 78% of the polytropic interior.