Showing papers on "Radiative transfer published in 1976"

The observation and analysis of stellar photospheres

Abstract: 1. Background 2. Fourier transforms 3. Spectroscopic tools 4. Light detectors 5. Radiation terms and definitions 6. The black body and its radiation 7. Radiative and convective energy transport 8. The continuous absorption coefficient 9. The model photosphere 10. The measurement of stellar continua 11. The line absorption coefficient 12. The measurement of spectral lines 13. The behavior of spectral lines 14. The measurement of stellar radii and temperatures 15. The measurement of photospheric pressure 16. Chemical analysis 17. Velocity fields in stellar photospheres 18. Stellar rotation.

Fluid dynamics of relativistic blast waves

Abstract: A fluid dynamical treatment of an ultra‐relativistic spherical blast wave enclosed by a strong shock is presented. A simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and this is generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius. Radiative shocks, in which the escaping photons carry away momentum as well as energy, are also discussed. Formulas that interpolate between the non‐ and ultra‐relativistic limits are proposed.

The delta-Eddington approximation for radiative flux transfer

Abstract: This paper presents a rapid yet accurate method, the “delta-Eddington” approximation, for calculating monochromatic radiative fluxes in an absorbing-scattering atmosphere. By combining a Dirac delta function and a two-term approximation, it overcomes the poor accuracy of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is taken proportional to the square of the phase function asymmetry factor, which distinguishes the delta-Eddington approximation from others of similar nature. Comparisons of delta-Eddington albedos, transnmissivities and absorptivities with more exact calculations reveal typical differences of 0–0.022 and maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo and phase function asymmetry. Delta-Eddington fluxes are in error, on the average, by no more than 0.5%0, and at the maximum by no more than 2% of the incident flux. This computationally fa...

A two-temperature accretion disk model for Cygnus X-1: structure and spectrum.

Abstract: We present a model for Cygnus X-1, involving an accretion disk around a black hole, which can explain the observed X-ray spectrum from 8 to 500 keV. In particular we construct a detailed model of the structure of an accretion disk whose inner region is considerably hotter and geometrically thicker than previous disk models. The inner region of the disk is optically thin to absorption, is gas-pressure dominated, and yields, from first principles, electron temperatures of 10/sup 9/ K and ion temperatures 3--300 times hotter. The spectrum above 8 keV is produced by inverse Compton scattering of soft X-ray photons in the two-temperature inner region of the disk. This spectrum is computed by numerical integration of the Kompane'ets equation, modified to account for escape of photons from a region of finite (order unity) electron scattering optical depth. (AIP)

Double optical resonance

Abstract: A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.

Volcanic explosions and climatic change: A theoretical assessment

Abstract: A theoretical assessment is presented of the influence of volcanic activity on the climate. The methodology of radiative transfer calculations is described and the sources of the adopted parameters are considered. The dependence of various quantities of interest is plotted as a function of the change in the optical depth of the stratosphere at a reference wavelength. An investigation is conducted concerning the increase in optical depth produced by volcanic explosions. An estimate is obtained regarding the magnitude of the mean surface temperature change resulting from the added aerosols.

Accretion onto magnetized neutron stars: structure and interchange instability of a model magnetosphere.

Abstract: A self-consistent model is analyzed for the spherical infall of weakly magnetized plasma into the magnetosphere of a slowly rotating, strongly magnetized neutron star. It is shown that spherical infall is probably a good approximation for X-ray sources which accrete from a stellar wind. The location of the standoff shock which halts the hypersonic infall is estimated along with the emission from the shocked layer. The location of the equilibrium magnetopause and the structure of the magnetic field within it are calculated; it is found that the magnetic poles are true cusps and that the entry of gas due to equilibrium flow across a cusp is almost certainly dominated by the interchange instability near the magnetic equator. The energy principle is applied to derive necessary conditions for the occurrence of this instability. The results indicate that the strong magnetic-pressure gradient stabilizes the gas unless moderately strong radiative cooling takes place and that the cooled plasma enters the magnetosphere as long filaments capable of moving between field lines. The rate at which the equilibrium magnetopause can 'absorb' mass and momentum is derived, the validity of the approximations employed is discussed, and the likely evolution of the sinking filaments is outlined to show that the spatial distribution of the plasma is determined mainly by the dynamics and thermodynamics of the filaments rather than the magnetic-field structure.

A global average model of atmospheric aerosols for radiative transfer calculations

Abstract: A global average model is proposed for the size distribution, chemical composition, and optical thickness of stratospheric and tropospheric aerosols. This aerosol model is designed to specify the input parameters to global average radiative transfer calculations which assume the atmosphere is horizontally homogeneous. The model subdivides the atmosphere at multiples of 3 km, where the surface layer extends from the ground to 3 km, the upper troposphere from 3 to 12 km, and the stratosphere from 12 to 45 km. A list of assumptions made in construction of the model is presented and discussed along with major model uncertainties. The stratospheric aerosol is modeled as a liquid mixture of 75% H2SO4 and 25% H2O, while the tropospheric aerosol consists of 60% sulfate and 40% soil particles above 3 km and of 50% sulfate, 35% soil particles, and 15% sea salt below 3 km. Implications and consistency of the model are discussed.

Orientation of cosmic dust grains

Abstract: Orientation of nonspherical cosmic dust grains is found in anisotropic corpuscular or radiative fluxes and in the presence of the magnetic field; cosmic grains being approximated by axially symmetric ellipsoids. A comparatively small twisting of grains is shown to cause differences in scattering right-hand and left-hand circularly polarized photons and growth of the angular momentum. If the period of the grain's angular momentum precession induced by the magnetic field is shorter than the time of orientation by corpuscular or radiative flux, distribution of grains' axes becomes symmetric relative to the magnetic lines. This orientation mechanism easily explains interstellar linear polarization observed in our Galaxy. The mechanisms of grains' orientation near the Becklin-Neugebauer infrared source, in the B 96 reflected cloud near RY Tau and in cometary heads are proposed.

2.3. Absorption and Emission by Atmospheric Gases

Abstract: Publisher Summary This chapter focuses on absorption and emission by atmospheric gases. At centimeter and shorter wavelengths, absorption and emission by atmospheric gases can significantly affect the propagation of electromagnetic radiation through the atmosphere. At frequencies from 1 to 300 GHz, referred to as “microwave frequencies,” absorption by atmospheric gases is dominated by water vapor lines at 22 and 183 GHz, oxygen lines near 60 GHz and at 118 GHz, and relatively narrow and weaker ozone lines above 100 GHz. Non-resonant absorption by water vapor and oxygen has significant effects in the window regions away from the dominant lines. The radiative transfer expressions appropriate for calculating absorption and emission by atmospheric gases are formulated. The general expressions for the spectral-line absorption coefficient are provided, followed by specific expressions for calculating absorption by water vapor and oxygen. Problems associated with the calculation of absorption by these two molecules are discussed. The absorption by microwave lines of ozone and other minor constituents is considered. Finally, the results of calculations of atmospheric absorption and emission, as well as the measured values are presented in the chapter.

Radiative Transfer Within the Earth's Troposphere and Stratosphere: A Simplified Radiative-Convective Model

Abstract: A radiative transfer model of the troposphere and stratosphere is presented which includes both long-wave cooling and solar heating due to H2O, CO2 and O3 and has a simplified formulation which facilitates the inclusion of Doppler broadening, H2O continuum bands, hot and minor isotopic bands of CO2, and overlap of H2O bands with CO2 and O3 bands. The radiative model is used to develop an accurate radiative-convective model for studying the global surface temperature, stratospheric thermal structure and the net outgoing long-wave flux.

Stratospheric Aerosol Measurements III: Optical Model Calculations

Abstract: : Articles in the literature dealing with light scattering properties of atmospheric aerosols are numerous and of great variety. Many fall into two general categories: those in which the effect of aerosols on radiative transfer processes in the atmosphere is studied, and those in which aerosol size distribution or composition information is obtained (or shown possible to be obtained) from light scattering measurements in the atmosphere. The results reported here, although limited to the stratospheric aerosol layer, are believed to be based on the most consistent and globally extensive measurements of the aerosol size distribution made to date. From this comprehensive set of data and other data on aerosol composition, the authors have constructed appropriate optical models which are used in Mie single-scattering calculations of the aerosol total extinction, absorption, 180 degree lidar backscattering, angular scattering, outward (2 pie hemispheric) scattering for a given solar zenith angle and finally, values of the global stratospheric aerosol albedo.

The structure of supernova shock waves.

Abstract: The structure of strong shock waves is calculated over the range of shock energies (1 to 100 MeV nucleon/sup -1/) and initial number densities (10/sup 15/--10/sup 22/ cm/sup -3/) believed likely to occur in the red-giant-like envelopes of stars undergoing Type II supernova explosions. The general equations governing the structure of such shocks are developed on the basis of a plasma composed of ions, electrons, positrons, and photons, making use of diffusion theory to evaluate the dissipative and transfer terms. The present treatment differs from previous calculations in that the effects of radiation transport on the energy and momentum balance in the shock are taken into account, as well as the relativistic contributions to radiative emission rates due to nondipole electron-ion bremsstrahlung, electron-electron bremsstrahlung, and radiative Compton scattering. An implicit treatment of inverse Compton scattering is also developed in terms of the creation and diffusion of effective photons.Severalmodels of strong shock structure are formulated and solved on the basis of these equations and physical processes. (AIP)

Radiative opacity tables for 40 stellar mixtures.

Abstract: Using improved methods, radiative opacities for 40 mixtures of elements are given for use in calculations of stellar structure, stellar evolution, and stellar pulsation. The major improvements over previous Los Alamos data are increased iron abundance in the composition, better allowance for the continuum depression for bound electrons, and corrections in some bound-electron energy levels. These opacities have already been widely used, and represent a relatively homogeneous set of data for stellar structures. Further improvements to include more bound-bound (line) transitions by a smearing technique and to include molecular absorptions are becoming available, and in a few years these tables, as well as all previous tables, will be outdated. At high densities the conduction of energy will dominate radiation flow, and this effect must be added separately. (AIP)

Resonance and Relaxation in Light Scattering

Abstract: Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of “damping operator” in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.

Satellite measurement of mass of Sahara dust in the atmosphere

Abstract: Landsat 1 measurements of nadir radiance are used to obtain the mass of particulates in a vertical column of dust from the Sahara Desert. A radiative transfer model, constructed with knowledge of a few values of optical parameters measured from a ship, is developed to account for the measured radiance values. Measurement and model accuracies are discussed. It is found that the mass of particulates with smaller than a 10 micron radius in a vertical column is 1.6 g/sq m.

Inversion of the OH 1720-MHz Line

Abstract: It is shown that the OH 1720-MHz line can be strongly inverted by collisions which excite the rotation states, preferentially the $sup 2$$pi$$sub 3$/$sub 2$ ladder. It is also argued that radiative pumps (of any wavelength) can strongly invert only the 1612-MHz line. Inversion of the 1720-MHz line with vertical-bartauvertical-barapproximately-less-than1 can be achieved by either collisional or radiative pumps at low OH densities (n/sub OH/10$sup -3$-10$sup - 4$ cm$sup -3$). (AIP)

Nonisothermal band model theory

Abstract: Theoretical formulations of radiation band models for general nonuniform optical paths are presented. The models are framed within the statistical band model for an array of Lorentz lines and an inverse line strength distribution. Radiative transfer for an isolated line in a general nonuniform medium and the statistical model for a uniform optical path are reviewed in order to provide the foundation required for the band model formulations. Two approaches to the development of these models are taken. The first is based on making approximations to such radiative transfer functions as transmittance or equivalent width and yields models equivalent or similar to the traditional Curtis-Godson approximation. The second treats approximations to the spatial derivatives of these functions. From the standpoint of computing line or band radiance, the spatial derivatives are more fundamental quantities than the transfer functions themselves; consequently, these latter “derivative approximations” are instrinsically more accurate than the Curtis-Godson type approximations. All of the models are formulated to give the spatial derivative of the mean equivalent width function W (s) δ in the form 1 δ d W (s) ds =c(s)p(s) k (s)y(s) , where c(s), p(s) and k(s) are the concentration, total pressure and absorption band model parameter, respectively, at the local path position s. The functional form of the derivative function y(s) is derived for each of the models. In general, y(s) is a function of both local and path-averaged (subscript e) band model parameters. These local and averaged parameters are used to define a dimensionless optical depth parameter x e = u k e β e and three nonuniformity indexes ρ= γ γ e , r= β β e and θ = δ e δ (γ is line width, ḡd is the mean line spacing band model parameter, and β = 2μ γ γ ). The explicit manner in which these parameters enter into the various functional forms for y(s) is derived and discussed. The introduction of the parameter q is an important aspect of the new models and is an explicit measure of nonisothermality along the optical path. In addition to the traditional Curtis-Godson definitions for the effective parameters ke and βe, new definitions for the path averages γe and δe are derived. These new definitions are obtained from the fundamental properties of the assumed inverse line strength distribution. A summary of all the models is given as a table of relevant equations for use in practical calculations.

The physics of electron beam excited rare gases at high densities

Abstract: The unique properties of charged particle excited high density rare gases are reviewed in terms of the basic collisional and radiative processes upon which they depend. Both low and high excitation density conditions are considered and a kinetic model of the important processes is formulated using available and estimated rate coefficients.

Ultraviolet photometry from the orbiting astronomical observatory. XXV. Diffuse galactic light in the 1500--4200 A region and the scattering properties of interstellar dust grains

Abstract: New measurements of the ultraviolet surface brightness of the night sky in 71 fields in the galactic longitude range 65degree< or =l/sub i//sub i/< or =145degree are presented. The data were obtained with the Orbiting Astronomical Observatory (OAO-2) at nine wavelengths between 1500 A and 4200 A and have been corrected for the contributions due to zodiacal light and integrated starlight. The residual brightnesses were analyzed with radiative transfer models for the diffuse galactic light which incorporate a z-dependent source function. The results qualitatively confirm earlier findings for this wavelength region, yielding a wavelength dependent albedo of the interstellar grains of approximately ..cap alpha..=0.7 +- 0.1 longward of lambda3000, ..cap alpha..=0.35 +- 0.05 around the pronounced minimum near lambda2200, and ..cap alpha..=0.6 +- 0.05 at lambda1550. The true absorption nature of the bump in the interstellar extinction curve near lambda2200, as well as the increase of the albedo shortward of lambda2000 are thus reconfirmed. The phase function asymmetry factor is found to lie between g=0.6 and g=0.9 for the entire wavelength range, indicating the interstellar grains are strongly forward scattering. (AIP)

Mass ejection from the O4f star Zeta Puppis

Abstract: Profiles of P Cygni lines and displaced absorption lines observed in high-resolution Copernicus UV scans of Zeta Pup from 907 to 1738 A are compared with profile calculations to derive an optical-depth scale of the lines as a function of height or velocity in the expanding envelope. The degrees of ionization of the elements C, N, O, Si, and S under equilibrium conditions at electron temperatures of 20,000 to 1 million K, radiation temperatures of 20,000 to 50,000 K, and electron number densities of 100 million to 1 trillion per cu cm are computed with a dilution factor of 0.1, taking into account collisional ionization by electrons, radiative ionization from the ground state, radiative recombination, and dielectric recombination. Observed and predicted relative ionization fractions are then compared to determine the electron and radiation temperatures. Crude and refined estimates of the mass-loss rate and velocity law are made, and radiative acceleration in the expanding envelope is analyzed. The derived model for Zeta Pup is found to have a mass-loss rate of about 7.2 millionths of a solar mass per year, a wind velocity that increases slowly outward and reaches 700 km/s about 28 solar masses, and a nearly isothermal envelope with an electron temperature of approximately 200,000 K.

Effect of molecular multiple scattering and surface albedo on atmospheric photodissociation rates

Abstract: Results are presented from an extensive theoretical investigation aimed at evaluating the effect of molecular multiple scattering and surface albedo on photodissociation rates. Results are compared with similar calculations typical of most atmospheric photochemical models which only describe absorption in a direct solar beam. The effect of molecular multiple scattering and surface albedo on photodissociation rates, which can be sizable, depends strongly on solar zenith angle, surface albedo, altitude, and wavelength regime. Various atmospheric photodissociation processes are categorized by spectral type based upon the wavelength regime in which the photodissociation process occurs. Three basic wavelength regimes are noted, and results characteristic of each regime are presented. Adjustment factors are provided for generalizing the pure absorption calculations. (auth)

New theory of radiative energy transfer in free electromagnetic fields

Abstract: A new theory of radiative energy transfer in free, statistically stationary electromagnetic fields is presented. It provides a model for energy transport that is rigorous within the framework of the stochastic theory of the classical field as well as within the framework of the theory of the quantized field. Unlike the usual phenomenological model of radiative energy transfer that centers around a single scalar quantity (the specific intensity of radiation), our theory brings into evidence the need for characterizing the energy transport by means of two (related) quantities: a scalar and a vector that may be identified, in a well-defined sense, with "angular components" of the average electromagnetic energy density and of the average Poynting vector, respectively. Both of them are defined in terms of invariants of certain new electromagnetic correlation tensors. In the special case when the field is statistically homogeneous our model reduces to the usual one and our angular component of the average electromagnetic energy density, when multiplied by the vacuum speed of light, then acquires all the properties of the specific intensity of radiation. When the field is not statistically homogeneous our model reduces in good approximation to the usual phenomenological one, provided that the angular correlations between plane wave modes of the field extend over a sufficiently small solid angle of directions about the direction of propagation of each mode. It is tentatively suggested that, when suitably normalized, our angular component of the average electromagnetic energy density may be interpreted as a quasiprobability (general quantum-mechanical phase-space distribution function, such as Wigner's) for the position and the momentum of a photon.

Sensitivity of surface temperature and atmospheric temperature to perturbations in the stratospheric concentration of ozone and nitrogen dioxide

Abstract: A radiative-convective model is proposed for estimating the sensitivity of the atmospheric radiative heating rates and atmospheric and surface temperatures to perturbations in the concentration of O3 and NO2 in the stratosphere. Contribution to radiative energy transfer within the atmosphere from H2O, CO2, O3, and NO2 is considered. It is found that the net solar radiation absorbed by the earth-atmosphere system decreases with a reduction in O3; if the reduction of O3 is accompanied by an increase in NO2, there is a compensating effect due to solar absorption by NO2. The surface temperature and atmospheric temperature decrease with decreasing stratospheric O3. Another major conclusion is the strong sensitivity of surface temperature to the vertical distribution of O3 within the atmosphere. The results should be considered as reflecting the sensitivity of the proposed model rather than the sensitivity of the actual earth-atmosphere system.

Structure and spectrum of quiescent prominences: energy balance and hydrogen spectrum

Abstract: In this paper we present theoretical models of quiescent prominences which satisfy the constraints of radiative, magnetohydrostatic, and statistical equilibrium We obtain reasonable models only if we assume that the exciting ultraviolet radiation field can penetrate diffusely into the slab, or that there is a source of nonradiative energy input The computed temperatures in our models are in good agreement with observational estimates The models reproduce most observed features of these objects quite well, and should provide a good starting point to study further the formation of prominence spectra and the effects of nonradiative energy inputs (AIP)

On the effect of radiative exchange on the growth by condensation of a cloud or fog droplet

Abstract: The effect of radiative heat transfer on droplet growth is assessed. It is estimated that radiative cooling is the principal agent of droplet growth in radiation fog, and that supersaturations are very small – slight undersaturation may even occur – and may be relatively unimportant for droplet growth in this environment. Gravitational settling is shown to be the principal limiting factor on droplet growth in radiation fog. It is also suggested that radiative transfer may have some relevance to the unexpectedly large numbers of 5μm radius droplets observed in cumulus clouds by Warner (1969).