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Proof of a simple relation between directional emissivity and directional hemispherical reflectivity for an isothermal coherent scattering and absorptive atmosphere, and also for the case of a complete redistribution in a line. The proof is generalized to a noncoherent situation.
The relationship of directional hemispherical reflectivity to emissivity is investigated for a nonisothermal medium with isotropic coherent scattering and absorption. Departures from a generalized Kirchhoff's Law occur due to the long range nature of the scattering process. Such departures occur in lunar thermal emission at microwave but not at infrared frequencies.
Line driven O-B stellar winds are unstable to perturbations of short spatial wavelength and the growth rates for such instabilities are very rapid. The nature of the nonlinear development of this instability is unknown, but might possibly be one of blobs of gas driven through ambient gas or a quasiregular train of outward moving shocks. In either case the resulting dissipation of mechanical energy might explain the observed anomalous heating n O-B stars as evidenced by their X-ray emission and high ionization state. It also might explain the observed fine structure of the absorption lines and their time variability. The driving due to the absorption of the stellar continuum flux was considered and the effects of the diffuse, scattered radiation field were neglected. It was shown that under certain special conditions the effect of scattering could reduce the instability growth rate to zero. A stability analysis that includes scattering, but that uses the more physically realistic assumption of complete redistribution instead of coherent scattering, and that includes the effects of transverse velocity gradients, which become important as the flow moves away from the stellar surface is presented. It is found that the instability is eliminated right at the base of the wind, but that as the flow moves outward the instability rate rapidly becomes equal to a substantial fraction of the calculated value, the fraction asymptotically reaching 80% at large radii. Since this still implies many e folds in a characteristic outflow time, the primary conclusion that these winds are highly unstable is unchanged.
The reflection of electromagnetic radiation from a planetary regolith involves a combination of geometric and physical optics processes which contribute to the signal returned to the remote observer. The geometric optics effects are the product of singly and multiply scattered radiation from the surfaces of the regolith particles, combined with radiation which has undergone various combinations of transmission through one or more regolith grains followed by one or more scatterings from other particles. The physical optics effects include diffraction of radiation around the edges of large irregular particles and cooperative coherent scattering between particles which are small when compared to the wavelength of the incident radiation. These effects produce measurable changes in the intensity and polarization of reflected light as a function of illumination and viewing geometry. In particular, as phase angle becomes small, the reflectance of a particulate material will increase non-linearly and exhibit the 'opposition effect'. In the planetary science context, the phase curve, and in particular the size of the opposition surge and the width of the phase curve near zero degrees, have been attributed to two processes commonly called 'shadow hiding' (SHOE) and 'coherent backscattering' (CBOE).
VHF radar data from the Summer 1990 Equatorial Spread F campaign on Kwajalein are presented. The Cornell 50 MHz portable radar interferometer (CUPRI) operated concurrently with the Altair UHF incoherent scatter radar throughout July and August and supported two sounding rocket flights on July 30 and August 2. This experiment provided the first opportunity to simultaneously diagnose equatorial spread F using the three prime experimental techniques: VHF/UHF coherent scatter, incoherent scatter, and in situ probe measurements of electric field and density fluctuations. The intensity of the coherent echoes observed was consistent with typical Jicamarca spread F observations, but chains of periodic, large-scale plasma upwellings were observed more often and for much longer durations on Kwajalein than have been seen over Peru. CUPRI also measured Doppler frequencies in one upwelling corresponding to 1200-m/s plasma drift velocities. This measurement agrees with recent observations of supersonic drift rates at the magnetic equator by spacecraft. Near the most active localized plasma upwellings, interferometer data reveal that the zonal drift rate of plasma irregularities can vary sharply in space, as one would expect for two-dimensional incompressible flow. We introduce a semiempirical model of the three-dimensional spectrum of F region irregularities that is consistent with the one-dimensional spectra of density fluctuations observed by sounding rockets and with the axial ratio of irregularities determined recently. Normalized to data from one of the rocket flights on Kwajalein, the model predicts the 3-m scattering cross-section measured by CUPRI to within a few decibels.
The paper presents approximate solutions obtained for a radiative transfer problem that represents a highly-idealized description of the multiple scattering of solar resonance radiation in the nearby interstellar medium. The problem of a point source in the center of a spherically symmetric cavity imbedded in an infinite uniform medium is solved for a range of cavity radii. First and second-order scattering contributions are calculated, and the Eddington approximation is used to estimate the higher order components of the radiation field. It is shown that for coherent scattering at very large cavity radii, the backscattered intensity from the cavity approaches three times the value deduced from the optically thin solution, in agreement with previous work. It is concluded that an accurate analysis of sky background will require including not only the frequency redistribution, but also the correct spatial distribution of density.
In this paper we treat the multiple scattering theory of radiative transfer in plane-parallel inhomogeneous atmospheres. The treatment presented here may be adopted to model atmospheres characterized by an optical depth dependent coherent scattering phase function. For the purpose of illustration we consider the semi-infinite medium in which the absorption property of the atmosphere is characterized by an exponential function. The methodology employed here is the extension of the case treated previously by the author for homogeneous atmospheres.
Atmospheric dust detection of size, nature and distribution by laser light scattering
From a comparison between observed and computed wings of the Mg II resonance lines, distributions of temperature versus mass column density for solar photospheric layers in plages and in the chromospheric network are derived. The theoretical profiles are computed assuming partial coherent scattering. In the active regions, temperatures exceed those in the quiet sun by up to 200 K near the temperature minimum and up to 400 K in deeper layers. In the observed network structure, the temperature is enhanced by 200 K at the temperature minimum but is the same as that in the quiet sun at greater depths. The difference in the slope of the temperature distribution between the network and plages is real, but may refer only to long elements of the network rather than to the brightest portions. Adjacent to the network is a region in which the temperatures are similar to those in the quiet sun, except immediately below the temperature minimum, where the temperatures are depressed by 150 K.
The results of a redetermination of the rotational periods of Uranus and Neptune, based on spectrograms obtained with the coude spectrograph of the 5 m Hale telescope, are presented. The effects of image motion on the shape of the spectral lines reflected by a planet rotating as a solid body and coherently scattering solar light, has been studied analytically. A general relation between the seeing transformed velocities at any point on the disk and those at the equator is established. It is shown that, for the case of Gaussian seeing, the brightness continuum of the smeared disk contains all the information required to derive the shape of the reflected lines. The shift, change in r.m.s. width, and asymmetry of the seeing transformed lines at the equator have been numerically evaluated for the brightness distribution of Uranus determined from Stratoscope II.
The present analysis is an application of the theory described by Lucy (1971) for the calculation of P Cygni resonance line profiles formed by isotropic and coherent scattering in spherically symmetric expanding circumstellar envelopes. Copernicus satellite measurements of resonance features in the FUV spectrum of the O 7 supergiant UW Canis Majoris (= HD 57060) are compared with theoretical P Cygni profiles. Grids of line profiles are computed using four free parameters which contain information about the velocity law, ionization equilibrium, temperature, and envelope density. Thus, with the assumption of a spherically symmetric steady flow, and of solar element abundances, the stellar mass loss rate and the electron temperature of the expanding shell can be derived. The mass flow is treated in a fully transonic way, i.e., the Sobolev approximation is applied.
The ultraviolet spectrum of the close binary UW CMa, obtained with the Copernicus (OAO-3) and IUE satellites in the wavelength region from 1010 to 1510 A and from 1200 to 3000 A, respectively, is analyzed. The observed P Cygni line profiles are compared with theoretically predicted profiles formed by isotropic and coherent scattering in a spherically symmetric expanding circumstellar envelope. Tables illustrate the identified stellar lines, laboratory wavelengths, and line strengths in terms of peak height for emission or central depth for absorption components, normalized to the local stellar continuum.
A microcomputer-video system was used to measure both spatial and temporal variations of two dimensional fluid flow velocity fields. The system utilizes two methods: the first method is the traditional one in which tracers are introduced into the fluid and their position compared at two closely spaced times; and the second method involves scattering coherent light in the fluid and obtaining motion by analyzing the multiple exposed speckle pattern recorded on photographic film.
The effects of atmospheric turbulence and the basis for the coherent scatter radar techniques are discussed. The reasons are given for upgrading the Radar system to a larger steerable array. Phase array theory pertinent to the system design is reviewed, along with approximations for maximum directive gain and blind angles due to mutual coupling. The methods and construction techniques employed in the UHF model study are explained. The antenna range is described, with a block diagram for the mode of operation used.
A form for the Lyman-alpha redistribution function that is modified to include the effects of collisional coupling between different energy states is presented. It is noted that this extends the work of Yelnik et al. (1981) and Roussel-Dupre(1982). By separating the source function into its primary components at all heights, the formation of Lyman-alpha radiation is investigated in detail. Frequencies in the line wing can be mapped back in such a way that the heights of formation for a change in lambda of plus or minus 0.5-6 A span the entire solar chromosphere. The usefulness of the Lyman-alpha wing as an atmospheric probe, however, is limited by long thermalization lengths, which result from almost coherent scattering outside of the Doppler core. When the line profiles calculated from the chromospheric models of Vernazza et al. (1981) are compared with the quiet-sun observations of Roussel-Dupre, agreement is found in integrated core intensities and in the line wing shape and normalized center-to-limb behavior. The calculated wing intensities, however, are a factor of four too small.
The term Mesosphere-Stratosphere-Troposphere radar (MST) was invented to describe the use of a high power radar transmitter together with a large vertically, or near vertically, pointing antenna to study the dynamics and structure of the atmosphere from about 10 to 100 km, using the very weak coherently scattered radiation returned from small scale irregularities in refractive index. Nine topics were addressed including: meteorological and dynamic requirements for MST radar networks; interpretation of radar returns for clear air; techniques for the measurement of horizontal and vertical velocities; techniques for studying gravity waves and turbulence; capabilities and limitations of existing MST radar; design considerations for high power VHF radar transceivers; optimum radar antenna configurations; and data analysis techniques.
The 41-MHz coherent-scatter radar located northeast of the University of Illinois at Urbana is being used for studies of the troposphere, stratosphere and mesosphere regions. The antenna consists of 1008 halfwave dipoles with a physical aperture of 11000 sq m. Transmitted peak power is about 750 kW. Clear-air returns may be received from 6 km to 90 km altitude. Autocorrelation functions of the scattered signal are calculated on-line. From the autocorrelation functions the scattered power, line-of-sight velocity and signal correlation time are calculated. Some aspects of the troposphere/stratosphere and the mesosphere observations are discussed. Capabilities and limitations of the Urbana MST radar are pointed out, and recent and planned improvements to the radar are described.
The theory of sound propagation over randomly irregular, nominally plane terrain of finite impedance is discussed. The analysis is an extension of the theory of coherent scatter originally proposed by Biot for an irregular rigid surface. It combines Biot's approach, wherein the surface irregularities are modeled by a homogeneous distribution of hemispherical bosses, with more conventional analyses in which the ground is modeled as a smooth plane of finite impedance. At sufficiently low frequencies the interaction of the surface irregularities with the nearfield of a ground-based source leads to the production of surface waves, which are effective in penetrating the ground shadow zone predicted for a smooth surface of the same impedance.