Scattering matrices and expansion coefficients of martian analogue palagonite particles

We present measurements of ratios of elements of the scattering matrix of martian analogue palagonite particles for scattering angles ranging from 3° to 174° and a wavelength of 632.8 nm. To facilitate the use of these measurements in radiative transfer calculations we have devised a method that enables us to obtain, from these measurements, a normalized synthetic scattering matrix covering the complete scattering angle range from 0° to 180°. Our method is based on employing the coefficients of the expansions of scattering matrix elements into generalized spherical functions. The synthetic scattering matrix elements and/or the expansion coefficients obtained in this way, can be used to include multiple scattering by these irregularly shaped particles in (polarized) radiative transfer calculations, such as calculations of sunlight that is scattered in the dusty martian atmosphere.     

Detection of Leonids meteoric dust in the upper atmosphere by polarization measurements of the twilight sky

A new method for the meteoric dust detection in the upper atmosphere based on the polarimetric observations of the twilight sky is proposed. Polarization measurements are effective for detection of the meteoric dust scattering on the background consisting basically of troposphere multiple scattering. The method is based on the observed and explained polarization properties of the sky background during different stages of twilight. It is used to detect the mesosphere dust after the Leonids maximum in 2002, estimate its altitude range and to investigate its evolution—slow decrease of the altitude. The polarization method takes into account the multiple scattering and sufficient contribution of moonlight scattering background and turns out to be more sensitive than existing analogs used in the present time.     

Exact solution of a problem in a stellar atmosphere using the Laplace transform and the Wiener-Hopf technique

The general equation for radiative transfer of line scattering intensity — including the effects of scattering, absorption and thermal emission — in the Milne-Eddington model is considered here. The scattering function is assumed to be quadratically anisotropic in the cosine of the scattering angle, and Planck's intensity function is assumed for thermal emission. The exact solutions for emergent intensity from the bounding face and the intensity at any optical depth are obtained by the method of the Laplace transform in combination with the Wiener-Hopf technique.     

The approximation of neutrino heat conduction with neutrino scattering

We have developed an algorithm for taking into account the neutrino scattering in the approximation of neutrino heat conduction. We show that in the case of incoherent neutrino scattering (e.g., by electrons), the coefficients of the temperature and chemical potential gradients are averaged over the neutrino energy using functions that can be found by numerically solving integral equations. The coherent scattering by free nucleons and atomic nuclei can be described by introducing a transport cross section. We suggest a new method for calculating the neutrino—electron scattering functions that is based on Fermi—Dirac functions of integer indices.     

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.     

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.     

Derivatives of theH-function

The first two derivatives and the mixed derivative of theH-function with respect to the angular variable and the albedo of single scattering are studied in the case of isotropic scattering using the kernel approximation method. This allows to obtain simple formulae the accuracy of which is estimated to be very good in rather low orders of approximation. Some samples of numerical results are given with eight decimal accuracy.     

Inverse radiation modeling of Titan's atmosphere to assimilate solar aureole imager data of the Huygens probe

During the descent of the Huygens probe through Titan's atmosphere in January 2005, the Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking measurements at various spectral ranges and spatial resolutions. This internal radiation density could be estimated by radiative transfer calculations for Titan's atmosphere. However, to do this, the optical properties—i.e. volume extinction coefficient, single scattering albedo and scattering phase function—have to be prescribed at every altitude, and these are apriori not known. Herein, an inverse approach is investigated, which retrieves the single scattering albedo and the phase function of the aerosols from DISR observations. The method uses data from a DISR subinstrument, the Solar Aureole imager (SA), to estimate the optical properties of the atmospheric layer between two successive observation altitudes. A unique solution for one layer can in principle be calculated directly from a linear system of equations, but due to the sparseness of the data and the unavoidable noise in the measurements, the inverse problem is ill-posed. The problem is stabilized by the regularization method requiring smoothness of the resultant solution. A consistent set of solutions for all layers is obtained by iterating several times downward and upward through the layers. The method is tested in a simulated radiation density scenario for Titan, which is based on a microphysical aerosol model for the haze layer. Within this scenario, the expected coverage of SA data allows a reconstruction of the angular dependence of the scattering phase function with an explained variance better than 90%.     

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.     

Scattering Law Analysis Based on Hapke and Lommel-Seeliger Models for Asteroidal Taxonomy

In deriving the physical properties of asteroids from their photometric data, the scattering law plays an important role, although the shape variations of asteroids result in the main variations in lightcurves. By following the physical behaviors of light reflections, Hapke et al. deduced complex functions to represent the scattering process, however, it is very hard to accurately simulate the surface scattering law in reality. For simplicity, other numerical scattering models are presented for efficiently calculating the physical properties of asteroids, such as the Lommel-Seeliger(LS) model. In this article,these two models are compared numerically. It is found that in some numerical applications the LS model in simple form with four parameters can be exploited to replace the Hapke model in complex form with five parameters. Furthermore, the generated synthetic lightcurves by the Cellinoid shape model also show that the LS model can perform as well as the Hapke model in the inversion process. Finally, by applying the Principal Component Analysis(PCA) technique to the parameters of the LS model, we present an efficient method to classify C and S type asteroids, instead of the conventional method using the parameters of the Hapke model.     

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions \(\vert \mu \vert \geq0.1 \) is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.     

Emergent radiation from the atmosphere bounded by the two halves of the Lambert surface with different albedos

For the evaluation of the effect of the nonuniform surface albedo to the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two-halves of the Lambert surface with different albedos is computed. The principal plane is assumed to be perpendicular to the boundary of surfaces. The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are 0.25, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is approximated by the contributions due to the multiple scattering in the atmosphere, directly attenuated radiation, and radiation due to single scattering in the atmosphere which is reflected by the Lambert surface (up to 4 interactive radiative modes between atmosphere and surface). For quantitative analysis, results are compared with those of the atmosphere-uniform surface model, where the multiple scattering is considered. The numerical simulation exhibits the extraordinary effect near the surface boundary of different albedos. The effect decreases exponentially with the distance from the boundary. It is a function of the observational position, difference of surface albedos, optical thickness and aerosol type.The upward radiance would simply be evaluated using the present scattering approximation method if the atmosphere is in clear condition. Whereas in hazy condition, the effect of multiple scattering in the atmosphere should be considered more precisely, since the upward radiance exhibit a strong dependence on observational nadir angles due to multiple scattering in the atmosphere. Furthermore, it depends on the optical characteristics of aerosols.     

Quantum string theory in curved space-times

A general method to quantize strings in curved space-times is exposed. It treats the space-time metric exactly and the string excitations small as compared with the energy scale of the geometry. The method is applied to cosmological (de Sitter) and black-hole (Schwarzschild) geometries. The critical dimension decreases in one for de Sitter and stays unaltered for black-holes as compared with flat space-time values. Bogoliubov transformations in the context of string theory are derived and the Bogoliubov coefficients describing elastic and inelastic scattering and excitation of modes are computed explicitely. The string-black-hole cross section is derived and a pair mode creation phenomena is found. The quantization and scattering of strings in shockwave geometries (ultrarelativistic boosted black-holes or Aichelburg-Sexl space time) is found to be exactly solvable.     

Slope variations on the surface of Phobos

It has been suggested that slope fluctuations on the scale of pixel dimensions could be determined by statistical photoclinometry. A closer study of the surface of Phobos reveals variations in the scattering properties of single particles and micro-structures formed by the particles. In the present context, the photoclinometric method of brightness moments is extended to account for these variations by allowing statistical fluctuations in the phase function of the assumed Lommel-Seeliger scattering law. The mean slope on the investigated regions of Phobos has been found to vary from approximately 12 degrees on a 61m scale to approximately 7 degrees on a 216-272m scale. On the same scales, a value of the order of 2% has been obtained for the standard deviation of the scattering phase function. Hints of a fractal-like scale-invariance have been noticed in the covariance function of brightness.     

On the effect of coronal outflow on spectra formation in galactic black hole systems

We present the results of both analytical and numerical calculations of the amplitude of the reflection component in X-ray spectra of galactic black hole systems. We take into account the anisotropy of Compton scattering and the systematic relativistic bulk motion of the hot plasma. In the case of the single scattering approximation, the reflection from the disc surface is significantly enhanced owing to the anisotropy of Compton scattering. On the other hand, the calculations of multiple scattering obtained using the Monte Carlo method show that the anisotropy effect is much weaker in that case. Therefore, the enhanced back-scattered flux may affect the observed spectra only if the disc surface is highly ionized, which reduces the absorption in the energy band corresponding to the first Compton scattering.     

Radiative transfer in spectral lines by noncoherent scattering

A functional analytic method of solution of the operator equations is used to obtain a solution of the radiative transfer equation in spectral lines. A problem of scattering in the spectral line with frequency redistribution in an isotropic scattering medium is considered.     

A photometric investigation of the packing state of apollo 11 lunar regolith samples

The angular light scattering properties of an Apollo 11 lunar regolith ‘fines’ sample have been determined experimentally for both flat and undulating sample surface preparations. The light scattering curves, whose shapes are known to be a function of the porosity and slope distribution of the measured surface, have been compared with corresponding Earth-based lunar measurements. The comparison method involves the numerical fitting of theoretical photometric functions to both the astronomical and laboratory data.It is deduced that regolith material can, under favourable circumstances, maintain a very underdense structure (porosity of the surface layer greater than 90 per cent) in air, so that vacuum cold-welding is not essential in the formation of such a structure. Photometric scanning is shown to provide a rapid method of determining the effective porosity of regolith sample surfaces in the laboratory.     

Albedo-shift method in the problem of anisotropic light scattering in a plane atmosphere

A standard problem of radiative transfer theory — calculating the diffuse reflection and transmission of radiation by a plane scattering atmosphere — is considered. The recently proposed albedoshift method is used to calculate the X and Y functions (and the H function) for the case of anisotropic scattering with a Henyey-Greenstein indicatrix. The method enables one to “suppress” scattering and obtain iterative solutions of high accuracy in only a few iterations, even when the mean number of photon scatterings in the atmosphere is very large. Translated from Astrofizika, Vol. 41. No. 4, pp. 623–646, October–December, 1998.     

On the DC ratio in the atmosphere of Uranus

A method for deriving mixing ratios in the outer planets, mostly independent of scattering processes, is applied to Uranus. It is shown that scattering processes play a major role in the line formation in the atmospheres of Uranus and Neptune; consequently, abundance ratios derived from a reflecting-layer model can be questionable. Using our method, we derive for Uranus $\text{D}\text{C}\text{< 6 × 10}{}^{\mathrm{?3}}$, which is significantly smaller than our result on Jupiter. The simplest explanation implies a C/H enrichment by at least a factor of 6 relative to the solar value.     

Second-order scattering approximation to X-ray photon transport at balloon altitudes

A numerical solution of the transport equation, based on the iterative method of expansion in order of scattering, is proposed to evaluate the effect of multiple Compton scattering on the cosmic X-ray spectrum from balloon experiments. Computation up to the second order of scattering is performed in the hard X-ray range (10–200 keV). It is shown that this approximation is sufficient to evaluate the X-ray flux at typical balloon atmospherical depths.INFN sez. Rome. On leave from CNR, Istituto di Astrofisica Spaziale.