We examine resonant scattering of Lyα (Lyman-alpha) photons in the neutral hydrogen Intergalactic Medium (IGM) at high redshift. Lyα scattering plays a key role in the 21cm emission/absorption against the Cosmic Microwave Background via the 'Wouthuysen-Field Effect' Knowledge of the strength of Lyα scattering induced by the first sources will constitute a significant step in predicting and understanding the eventual observations of the impact of these objects on the signal from the IGM during the Epoch of Reionisation (EoR), using planned facilities such as the Square Kilometre Array. A quantitative analysis of the scattering rate requires formulation and solution of the radiative transfer equation for the system. We consider radiative transfer of Lyα scattering far from a source in the homogeneous expanding IGM for photons that free stream until scattering in the blue wing of the local line profile: we describe an approximation that ignores spatial diffusion of photons and assumes a locally homogeneous scattering medium, allowing the calculation of simple analytic solutions to examine the dependence of the local scattering rate on various physical effects such as local expansion/contraction, and extend our approach to determine time-dependent solutions. The more complex problem of Lyα photons scattering in both frequency and space within a spherically symmetric medium is subsequently solved for several test problems using both Monte Carlo methods and a method based on the ray and moment radiative transfer equations following an approach due to Mihalas et al. [1975, 1976]. We examine local Lyα scattering around a continuum source in the homogeneous expanding IGM using both methods and compare our results with an analytic solution in the zero-temperature diffusion regime derived from an analogous solution for a monochromatic source found by Loeb and Rybicki [1999]. Our results are used to make estimates of the resulting size of the spherical region around the source that is rendered detectable via 21cm observations against the CMB background. We also examine cases with different density and velocity profiles and determine the effect on the scattering rate.

The scattered radiation fields in spherical planetary atmospheres have been considered by a new method which is called the Quasi-Spherical method. This method is applicable to planets with radii which are much larger than the height of their atmosheres. The scattering of 0.5 (mu)m radiation in a conservative and vertically inhomogeneous atmosphere has been discussed. Results comparing the emerging radiation from plane-parallel and spherical models for the earth's atmosphere have been presented for four different aerosol distributions in addition to the normal molecular composition. These results indicate measurable differences on the order of 10 to 300% as the angle of observation and/or the angle of incident sun falls within 10(DEGREES) from the horizon. Also, the obtained results in the spherical atmosphere show that additional layers of aerosols in either the stratosphere or the troposphere can be detected by satellite or aircraft radiometric measurements, while the plane-parallel atmosphere does not permit such a detection. The accuracy of the obtained results by the present method can be increased by increasing the number of spherical shells in the spherical atmosphere. The emerging radiation in homogeneous and inhomogeneous Rayleigh atmospheres as computed by the Quasi-Spherical and the Monte Carlo methods compare quite well. By applying the divergence theorem it was shown by the present method that the total flux in the spherical atmosphere is conserved within 1.351%.

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Context. Understanding the diversity of planets requires studying the morphology and physical conditions in the protoplanetary disks in which they form. Aims. We aim to study the structure of the similar to 10 Myr old protoplanetary disk HD 100453, to detect features that can trace disk evolution and to understand the mechanisms that drive these features. Methods. We observed HD100453 in polarized scattered light with VLT/SPHERE at optical (0.6 mu m, 0.8 mu m) and near-infrared (1.2 mu m) wavelengths, reaching an angular resolution of similar to 0.02 '', and an inner working angle of similar to 0.09 ''. Results. We spatially resolve the disk around HD 100453, and detect polarized scattered light up to similar to 0.42 '' (similar to 48 au). We detect a cavity, a rim with azimuthal brightness variations at an inclination of similar to 38 degrees with respect to our line of sight, two shadows and two symmetric spiral arms. The spiral arms originate near the location of the shadows, close to the semi major axis. We detect a faint feature in the SW that can be interpreted as the scattering surface of the bottom side of the disk, if the disk is tidally truncated by the M-dwarf companion currently seen at a projected distance of similar to 119 au. We construct a radiative transfer model that accounts for the main characteristics of the features with an inner and outer disk misaligned by similar to 72 degrees. The azimuthal brightness variations along the rim are well reproduced with the scattering phase function of the model. While spirals can be triggered by the tidal interaction with the companion, the close proximity of the spirals to the shadows suggests that the shadows could also play a role. The change in stellar illumination along the rim induces an azimuthal variation of the scale height that can contribute to the brightness variations. Conclusions. Dark regions in polarized images of transition disks are now detected in a handful of disks and often interpreted as shadows due to a misaligned inner disk. However, the origin of such a misalignment in HD100453, and of the spirals, is still unclear, and might be due to a yet-undetected massive companion inside the cavity, and on an inclined orbit. Observations over a few years will allow us to measure the spiral pattern speed, and determine if the shadows are fixed or moving, which may constrain their origin.

Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables. This high dimensionality and presence of integral term present a serious challenge when trying to solve the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation have been introduced. These include, but are certainly not limited to, Monte Carlo methods, discrete-ordinate methods, spherical harmonics methods, spectral methods, finite difference methods, and finite element methods. Methods involving discrete ordinates have received particular attention in the literature due to their relatively high accuracy, flexibility, and relatively low computational cost. In this thesis we present a discrete-ordinate discontinuous Galerkin method for solving the radiative transfer equation. In addition, we present a generalized Fokker-Planck equation that may be used to approximate the radiative transfer equation in certain circumstances. We provide well posedness results for this approximation, and introduce a discrete-ordinate discontinuous Galerkin method to approximate a solution. Theoretical error estimates are derived, and numerical examples demonstrating the efficacy of the methods are given.

Thesis (Ph. D.)--University of California, San Diego, 1982. / Vita. Includes bibliographical references (leaves 136-139).

Because the bulk optical properties of dust are largely dependent on their chemical composition, published reports from numerous dust field studies enabled us to compile observation data sets to derive the effective complex refractive indices of Saharan and Asian dust. We considered the individual mineral components as aggregates and used the Bruggeman approximation to derive the effective refractive indices. Using the results, we calculated the single-scattering properties, including phase matrix, single-scattering albedo and asymmetry factor, with a combination of the T-matrix method and an improved geometric optics method (IGOM). The single-scattering properties were averaged by the measured particle size distribution to provide bulk optical properties for radiative transfer simulations. Using a Rapid Radiative Transfer Model (RRTM), the radiative forcing of mineral dust was computed at both the top of the atmosphere and the surface. By analyzing samples from various in-situ measurements, we assumed the Saharan and Asian dust to have average volume compositions and average aspect ratios. The effective refractive indices for Saharan and Asian dust were derived based on the assumed composition models. Bulk optical properties were integrated using the modified log-normal particle size distributions. The aspect ratio assumed in this study is 1.6 for both Saharan and Asian dust. The longwave radiative (IR) forcings at the top of the atmosphere (TOA) and at the surface were found to be positive and sensitive to wavelength. The shortwave (solar) radiative forcing at TOA, was also positive, but may possibly have been due to the strong absorption components considered in the composition models.

A Discontinuous Galerkin Time Domain method (DGTD), using a fourth order Runge-Kutta time-stepping of Maxwell's equations, was applied to the simulation of the optical properties of dielectric particles in two-dimensional (2-D) geometry. As examples of the numerical implementation of this method, the single-scattering properties of 2D circular and hexagonal particles are presented. In the case of circular particles, the scattering phase matrix was computed using the DGTD method and compared with the exact solution. For hexagonal particles, the DGTD method was used to compute single-scattering properties of randomly oriented 2-D hexagonal ice crystals, and results were compared with those calculated using a geometric optics method. Both shortwave (visible) and longwave (infrared) cases are considered, with particle size parameters 50 and 100. Ice in shortwave and longwave cases is absorptive and non-absorptive, respectively. The comparisons between DG solutions and the exact solutions in computing the optical properties of circular ice crystals reveal the applicability of the DG method to calculations of both absorptive and non-absorptive particles. In the hexagonal case scattering results are also presented as a function of both incident and scattering angles, revealing structure apparently not reported before. Using the geometric optics method we are able to interpret this structure in terms of contributions from varying numbers of internal reflections within the crystal.

An adding-doubling method is employed to calculate the reflected Stokes parameters for cirrus cloud layers composed of different habits and effective sizes. The elements of the Mueller matrix are determined from the reflected Stokes parameters by considering four different incident polarization states. The sensitivity of these elements is observed by comparing different ice crystal habits, effective sizes, and optical depth. The Mueller elements are strongly dependent on habit. The three habits, aggregate, bullet rosette, and plate, are observed and the M12/M11,M43/M11 and M44/M11 elements are discussed. The wavelength used is 0.532µm, which is the lidar wavelength used on the CALIPSO satellite. The linear depolarization ratio is also discussed. The method of subtracting the two depolarization ratios, is noted as another way to possibly better distinguish ice crystal habits. The sensitivity of the Mueller matrix to effective size is also observed. For three size distributions, the Mueller elements indicate no strong dependence. This may be due to the assumption of randomly oriented ice. Also, using an absorbing wavelength might provide dependence. Finally, the Mueller elements are dependent on optical depth. For a greater optical depth, the strength of reflection increases while the polarization decreases. As the optical depth increases, any peak-like features become non-existent.