Multiple scattering in the atmosphere with a rough surface

In the present paper, the intensity of radiation emergent from the atmosphere bounded by a rough surface is discussed with the aid of the superposition method derived by Mukai (1973). The merit of this method is to express the laws of diffuse reflection and transmission for the planetary problem with a rough surface in terms of a scattering and a transmission function for the standard problem.Here the bottom surface is assumed to reflect light in accordance with the slope distribution given by Cox and Munk (1954a, b). The results are discussed in terms of the optical properties and roughness of the bottom surface.     

Polarization Models for Rayleigh Scattering Planetary Atmospheres

We present Monte Carlo simulations for the polarization of light reflected from planetary atmospheres. We investigate dependencies of intensity and polarization on three main parameters: single scattering albedo, optical depth of a scattering layer, and albedo of a Lambert surface underneath. The main scattering process considered is Rayleigh scattering, but isotropic scattering and enhanced forward scattering on haze particles are also investigated. We discuss disk integrated results for all phase angles and radial profiles of the limb polarization at opposition. These results are useful to interpret available limb polarization measurements of solar system planets and to predict the polarization of extra-solar planets as a preparation for VLT/SPHERE. Most favorable for a detection are planets with an optically thick Rayleigh-scattering layer. The limb polarization of Uranus and Neptune is especially sensitive to the vertically stratified methane mixing ratio. From limb polarization measurements constraints on the polarization at large phase angles can be set.     

Hubble Space Telescope imaging polarimetry of Mars during the 2003 opposition

We report results of polarimetric imaging observations of Mars with the Hubble Space Telescope during the 2003 opposition. Through careful calibration, the observations with the ACS camera allow measurements of the polarization degree with an absolute accuracy better than 0.5% and detection of features with polarization degree contrast as small as 0.2%. The general distribution of linear polarization parameters over the Mars disk and their dependence on phase angle and wavelength are well explained qualitatively by a combination of scattering separately by the martian surface and atmosphere. We have discovered transient polarization phenomena interpreted as clouds that are best observed in ultraviolet light. These clouds are optically thin but strongly polarizing, and their origin may be related to atmospheric ice condensation processes.     

Circular polarization of sunlight reflected by planetary atmospheres

Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined.     

A Monte Carlo Code to Compute Energy Fluxes in Cometary Nuclei

A Monte Carlo model designed to compute both the input and output radiation fields from spherical-shell cometary atmospheres has been developed. The code is an improved version of that by H. Salo (1988, Icarus76, 253-269); it includes the computation of the full Stokes vector and can compute both the input fluxes impinging on the nucleus surface and the output radiation. This will have specific applications for the near-nucleus photometry, polarimetry, and imaging data collection planned in the near future from space probes. After carrying out some validation tests of the code, we consider here the effects of including the full 4×4 scattering matrix in the calculations of the radiative flux impinging on cometary nuclei. As input to the code we used realistic phase matrices derived by fitting the observed behavior of the linear polarization as a function of phase angle. The observed single scattering linear polarization phase curves of comets are fairly well represented by a mixture of magnesium-rich olivine particles and small carbonaceous particles. The input matrix of the code is thus given by the phase matrix for olivine as obtained in the laboratory plus a variable scattering fraction phase matrix for absorbing carbonaceous particles. These fractions are 3.5% for Comet Halley and 6% for Comet Hale-Bopp, the comet with the highest percentage of all those observed.The errors in the total input flux impinging on the nucleus surface caused by neglecting polarization are found to be within 10% for the full range of solar zenith angles. Additional tests on the resulting linear polarization of the light emerging from cometary nuclei in near-nucleus observation conditions at a variety of coma optical thicknesses show that the polarization phase curves do not experience any significant changes for optical thicknesses τ?0.25 and Halley-like surface albedo, except near 90° phase angle.     

Light scattering by complex particles in the Moon's exosphere: Toward a taxonomy of models for the realistic simulation of the scattering behavior of lunar dust

It is suspected that the lunar exosphere has a dusty component dispersed above the surface by various physical mechanisms. Most of the evidence for this phenomenon comes from observations of “lunar horizon glow” (LHG), which is thought to be produced by the scattering of sunlight by this exospheric dust. The characterization of exospheric dust populations at the Moon is key to furthering our understanding of fundamental surface processes, as well as a necessary requirement for the planning of future robotic and human exploration.We present a model to simulate the scattering of sunlight by complex lunar dust grains (i.e. grains that are non-spherical and can be inhomogeneous in composition) to be used in the interpretation of remote sensing data from current and future lunar missions. We numerically model lunar dust grains with several different morphologies and compositions and compute their individual scattering signatures using the Discrete Dipole Approximation (DDA). These scattering properties are then used in a radiative transfer code to simulate the light scattering due to a dust size distribution, as would likely be observed in the lunar exosphere at high altitudes 10's of km. We demonstrate the usefulness and relevance of our model by examining mode: irregular grains, aggregate of spherical monomers and spherical grains with nano-phase iron inclusions. We subsequently simulate the scattering by two grain size distributions (0.1 and radius), and show the results normalized per-grain. A similar methodology can also be applied to the analysis of the LHG observations, which are believed to be produced by scattering from larger dust grains within about a meter of the surface.As expected, significant differences in scattering properties are shown between the analyses employing the widely used Mie theory and our more realistic grain geometries. These differences include large variations in intensity as well as a positive polarization of scattered sunlight caused by non-spherical grains. Positive polarization occurs even when the grain size is small compared to the wavelength of incident sunlight, thus confirming that the interpretation of LHG based on Mie theory could lead to large errors in estimating the distribution and abundances of exospheric dust.     

Prospects for Estimating the Properties of a Loose Surface from the Phase Profiles of Polarization and Intensity of the Scattered Light

It has been shown that the model of a scattering medium composed of clusters located in the far zones of each other allows some properties of regolith-like surfaces to be quantitatively estimated from the phase dependences of intensity and polarization measured in the backscattering domain. From the polarization profiles, the sizes of particles, the structure and porosity of the medium, and a portion of the surface area covered with a disperse material can be determined. At the same time, the intensity profiles of the scattered light weakly depend on the sizes and structure of particles; they are mainly controlled by the concentration of scatterers in the medium and the shadow-hiding contribution at small phase angles. Since the latter effect is beyond the considered model, a good agreement between the model and the measured intensity cannot be achieved. Nevertheless, if a portion of the surface that participates in coherent backscattering has been found from the phase profile of polarization, the present model makes it possible to determine the relative contribution of the shadow-hiding effect to the brightness surge measured at zero phase angle. This, in turn, may allow the roughness of the scattering surface to be estimated. The model contains no free parameters, but there is currently no possibility to verify it comprehensively by the data obtained in laboratory measurements of the samples with thoroughly controlled characteristics, because such measurements are rare for a wide range of the properties of particles in a medium, their packing density, and phase angles.

     

Limits on the size of aerosols from measurements of linear polarization in Titan’s atmosphere

The Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe into the atmosphere of Titan yielded information on the size, shape, optical properties, and vertical distribution of haze aerosols in the atmosphere of Titan [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., 2008. Planet. Space Sci. 56, 669-707] from photometric and spectroscopic measurements of sunlight in Titan’s atmosphere. This instrument also made measurements of the degree of linear polarization of sunlight in two spectral bands centered at 491 and 934 nm. Here we present the calibration and reduction of the polarization measurements and compare the polarization observations to models using fractal aggregate particles which have different sizes for the small dimension (monomer size) of which the aggregates are composed. We find that the Titan aerosols produce very large polarizations perpendicular to the scattering plane for scattering near 90° scattering angle. The size of the monomers is tightly constrained by the measurements to a radius of 0.04 ± 0.01 μm at altitudes from 150 km to the surface. The decrease in polarization with decreasing altitude observed in red and blue light is as expected by increasing dilution due to multiple scattering at decreasing altitudes. There is no indication of particles that produce small amounts of linear polarization at low altitudes.     

Optical reflectance polarimetry of Saturn globe and rings I. Measurements on B ring

The light reflected by the Saturn ring B acquires a polarization which varies with phase angle, wavelength, and position on the rings. This polarization results from the combined effects of two components P₀ and T. The component P₀ keeps its azimuth always parallel to the scattering plane and its amount varies with phase angle and wavelength, as for direct reflection at the surface of solid bodies. The polarization T has its azimuth all around the ring either parallel or perpendicular to the radius vector; unexpectedly its amount varies with time, often significantly in a few days in ways which are not predictable.     

Equatorial scattering and the structure of the broad-line region in Seyfert nuclei: evidence for a rotating disc

We present detailed scattering models confirming that distinctive variations in polarization across the broad Hα line, which are observed in a significant fraction of type 1 Seyfert galaxies, can be understood in terms of a rotating line-emitting disc surrounded by a coplanar scattering region (the equatorial scattering region). The predicted polarization properties are: (i) averaged over wavelength, the position angle (PA) of polarization is aligned with the projected disc rotation axis and hence also with the radio source axis; (ii) the polarization PA rotates across the line profile, reaching equal but opposite (relative to the continuum PA) rotations in the blue and red wings; and (iii) the degree of polarization peaks in the line wings and passes through a minimum in the line core. We identify 11 objects that exhibit these features to different degrees. In order to reproduce the large-amplitude PA rotations observed in some cases, the scattering region must closely surround the emission disc and the latter must itself be a relatively narrow annulus – presumably the Hα-emitting zone of a larger accretion disc. Asymmetries in the polarization spectra may be attributable to several possible causes, including bulk radial infall in the equatorial scattering region, or contamination by polar scattered light. The broad Hα lines do not, in general, exhibit double-peaked profiles, suggesting that a second Hα-emitting component of the broad-line region is present, in addition to the disc.     

Modeling the linear polarization of optical emission from red giants

We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N _d ∝ r ⁻², and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T _ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N _sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.     

Solar system observations by the Wisconsin Ultraviolet Photopolarimeter Experiment– III. The first ultraviolet linear spectropolarimetry of the Moon

Portions of the Moon were observed by the Wisconsin Ultraviolet Photopolarimeter Experiment ( WUPPE ) on 1995 March 12, 14 and 17, and represent the first ultraviolet (UV) spectropolarimetric observations of the Moon. The polarimetric observations confirm that a change in the dominant scattering process occurs in the UV, changing from volume scattering in the near-UV to surface scattering in the far-UV. The data are investigated empirically. It is found that Umov's relationship holds when the polarization is perpendicular to the scattering plane. It is also found that the degree of polarization can be modelled by a phase-angle-dependent polarization modified by a wavelength-dependent depolarization factor. The scattering function for each observation is determined.     

Interpreting photometry of regolith-like surfaces with different topographies: shadowing and multiple scattering

The effects of various types of topography on the shadow-hiding effect and multiple scattering in particulate surfaces are studied. Two bounding cases were examined: (1) the characteristic scale of the topography is much larger than the surface particle size, and (2) the characteristic scale of the topography is comparable to the surface particle size. A Monte Carlo ray-tracing method (i.e., geometric optics approximation) was used to simulate light scattering. The computer modeling shows that rocky topographies generated by randomly distributed stones over a flat surface reveal much steeper phase curves than surface with random topography generated from Gaussian statistics of heights and slopes. This is because rocks may have surface slopes greater than 90°. Consideration of rocky topography is important for interpreting rover observations. We show the roughness parameter in the Hapke model to be slightly underestimated for bright planetary surfaces, as the model neglects multiple scattering on large-scale topographies. The multiple scattering effect also explains the weak spectral dependences of the roughness parameter in Hapke's model found by some authors. Multiple scattering between different parts of a rough surface suppresses the effect of shadowing, thus the effects produced by increases in albedo on the photometric behavior of a surface can be compensated for with the proper decreases in surface roughness. This defines an effective (photometric) roughness for a surface. The interchangeability of albedo and roughness is shown to be possible with fairly high accuracy for large-scale random topography. For planetary surfaces that have a hierarchically arranged large-scale random topography, predictions made with the Hapke model can significantly differ from real values of roughness. Particulate media with surface borders complicated by Gaussian or clumpy random topographies with characteristic scale comparable to the particle size reveal different photometric behaviors in comparison with particulate surfaces that are flat or the scale of their topographies is much larger than the particle size.     

Polarization of Light Scattered by Surfaces with Complex Microstructure at Phase Angles 0.1°–3.5°

We present laboratory measurements of the phase dependences of linear polarization for surfaces with a complex microstructure in the range of phase angles 0.1°–3.5° A sample of freshly fallen snow (with particle sizes of about 50 × 500 m) exhibits a nearly zero polarization. Surfaces with submicron structure show a narrow branch of negative polarization at small phase angles, irrespective of whether the surface is powderlike or solid with microcrystalline structure. This polarization is similar to that exhibited by Jupiter's satellites. The negative polarization branch becomes deeper with decreasing porosity of light dielectric surfaces. At the phase angles between 0.5° and 3.0°, the polarization for quartz powder with 10-m particles is almost constant. The polarization for light dielectric surfaces depends on the geometry of illumination and observation. An inclination of the surface in the scattering plane produces a parallel shift of the negative polarization branch toward large values of the polarization modulus. The same inclination in a perpendicular direction produces the same shift toward positive degrees of polarization.     

Intensity and polarization line profiles in a semi-infinite Rayleigh-scattering planetary atmosphere. I. Integrated flux

Absorption and polarization line profiles as well as the curves of growth in the integrated light of a planet over the whole range of phase angles have been computed assuming a semi-infinite atmosphere scattering according to Rayleigh’s phase-matrix which takes polarization into account. The relative change in line depth and equivalent widths qualitatively agree with the observations of the CO₂ bands in Venus reported by Young, Schorn and Young (1980). It is pointed out that the bands might be formed in a part of the atmosphere which is different from that where continuum polarization originates.     

Photometric, spectroscopic and polarimetric variability of the weak-emission T Tauri star HD 288313

Photometric observations over three seasons show HD 288313 to be a light variable with a 2.2636-d period. The observed V amplitudes lie in the range of 0.06–0.15 mag. The star showed appreciable changes in the brightness at maximum and minimum of the light curve from season to season. The (   b − y   ) colour did not show any significant variation during the photometric cycle. The light variation appears to be caused by the rotational modulation of stellar flux by cool starspots distributed asymmetrically across the stellar longitudes. The Hα line strength in HD 288313 varied drastically from completely filled-in emission to almost full absorption, that is typical of a normal star of similar spectral type. The Hα equivalent width is found to show a clear rotational modulation only occasionally. Most of the time, chromospheric active regions are distributed well across the stellar longitudes, thereby suppressing obvious rotational modulations. Broad-band linear polarization measurements show HD 288313 to be a short period, low-amplitude polarization variable. The polarization variation is, apparently, rotationally modulated. Dust grain scattering in a non-spherical circumstellar envelope of a star with inhomogeneities in the surface brightness distribution seems to be the mechanism operating in producing the observed polarization.     

Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reflectance model for densely packed media: Estimates of the surface properties of the high-albedo satellites of Saturn

Interpretation of photometric and polarimetric observations of atmosphereless celestial bodies faces the problems connected with both the insufficient accuracy and level of details in groundbased observations and the current state of the theory of the multiple scattering of light. In application to sparse media, where the electromagnetic waves, propagating between the scatterers, can be considered as spherical (the socalled far-field approximation), this theory is rather well developed for both the diffuse and coherent components of the scattered radiation. In this paper, we show that this theory can be also successfully applied to the measurements of polarization of light scattered by densely packed, though nonabsorbing or weakly absorbing, media. For this purpose, we calculated the models for a semi-infinite layer of the medium composed of randomly oriented clusters of spherical particles and compared them with the data of laboratory and astronomical measurements. The potential of the present approach is illustrated by an example of the interpretation of the polarization measurements of the ice satellites of Saturn—Rhea and Enceladus—which allowed some properties of the surface of these celestial bodies to be estimated. In particular, the ratio of the surface area that makes no contribution to the negative polarization of light reflected at small phase angles to the area producing the negative polarization branch was found. Under the assumption of the same albedo of these areas, this ratio turned out to be 3.31–3.66 and 1.7–3.8 for Rhea and Enceladus, respectively. For Enceladus, it is difficult to obtain a sufficiently narrow range of the estimated parameters, since the number of measurement points in the phase dependence of polarization of this satellite is small. For the surface of Rhea, the estimated packing density of particles, participating in the opposition effects, is approximately 15%, while their smallest size is of the order of the wavelength of visible light.     

Polarization of radiation from a strongly magnetized accretion disk: The asymptotic spectral distribution

We calculate the polarization of the radiation from an optically thick accretion disk with a vertical averaged magnetic field. The polarization arises from the scattering of light by free electrons in a magnetized disk plasma. The Faraday rotation of the polarization plane during the propagation of a photon in a medium with a magnetic field is considered as the main effect. We discuss various models of optically thick accretion disks with a vertical averaged magnetic field. Our main goal is to derive simple asymptotic formulas for the polarization of radiation in the case where the Faraday rotation angle Ψ ≫ 1 at the Thomson optical depth τ = 1. The results of our calculations allow the magnetic field strength in the region of the marginally stable orbit near a black hole to be estimated from polarimetric observations, including X-ray observations expected in the future. Since the polarization spectrum of the radiation strongly depends on the accretion disk model, a realistic physical model of the accretion disk can be determined from data on the polarization of its radiation.