Multiple Scattering of Light in Regolith-like Media: Geometric Optics Approximation

We present a numerical model that allows us to calculate the contribution of a specified scattering order in the geometric optics approximation for media composed of large particles with an arbitrary phase function. It has been demonstrated that the correlated propagation of the incident and emergent rays, which is disregarded in the classical radiative-transfer theory, markedly affects the contributions of different orders of scattering, especially the first-order scattering. If the theory describing the photometric properties of regolith-like media ignores the shadowing effect, the errors of its application may reach several tens of percent even for bright surfaces. The packing density of a medium essentially influences the phase dependence of the first-order scattering, although its effect on the value and the phase curve of the higher scattering orders is relatively weak. The backscattering peaks calculated on the basis of the Hapke theory are narrower than those obtained from the numerical simulations, because the Hapke theory is an approximate approach.     

Calculation of single-scattering albedos: Comparison of Mie results with Hapke approximations

The grain size of water ice can be determined from its near-infrared spectrum, which has numerous diagnostic absorption bands of different opacities. Models that have been used to determine water ice grain size from infrared spectra of icy outer Solar System objects have shown discrepancies in modeled grain size of a factor of two or more. Here the single-scattering albedo calculated using the commonly used Hapke model given by Roush [Roush, T.L., 1994. Icarus 108, 243-254] is compared with the exact calculation for spheres from a Mie series. An earlier approximation of single-scattering albedo called the Hapke “slab” model is also used in the comparison. All three models are implemented using the same optical constants for water ice at ∼110 K. Results are displayed for a large range of grain sizes from 1 μm to 1 mm. In general neither Hapke model can mimic the Rayleigh effects from particles sized near the wavelength of light that the Mie model predicts. For 10 μm particles, the slab model matches the Mie calculation quite well, but larger sizes are more discrepant. The Hapke/Roush model grain size needs to be ∼2.5 times larger to mimic the Mie results, and there are additional discrepancies in the continuum levels and band strengths. The Mie calculation for spheres is recommended for analysis of unknown remote sensing measurements, as it can mimic the spectra of oblate, prolate, and hollow particles given by equivalent sphere theories.     

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.     

On the Light-Absorbing Surface Layer of Cometary Nuclei: I. Radiative Transfer

A small but increasing volume of observations of cometary nuclei has accumulated during the past two decades. This development is accelerating with upcoming space missions such as Stardust, Contour, and Rosetta. In response to the growing need for a theoretical understanding of optical properties of cometary nuclei, we have calculated synthetic reflectance spectra in the wavelength region 0.2-2.0 μm, photometric colors in the Johnson-Kron-Cousins UBVRI system, and visual geometric albedos for a large number of porous ice-dust mixtures with differing composition, regolith grain sizes, and grain morphologies, such as core-mantle grains, dense clusters of such grains, and large irregular particles with internal scatterers. The calculations are based on Mie theory, the discrete dipole approximation, Hapke theory, and a numerical solution to the equation of radiative transfer in particulate media. In addition, wavelength-integrated directional-hemispherical albedos and flux attenuation profiles in the regolith as functions of depth have been calculated in order to improve the energy budget and treatment of energy boundary conditions in thermal models of cometary nuclei.Our results are compared with spectra and colors of observed cometary nuclei. Our main conclusions are that only regolith consisting of relatively large core-mantle grains, or clusters of smaller core-mantle grains, is capable of reproducing the red colors seen in comets; that ice-dust mixtures actually can be darker than ice-free regolith in certain circumstances; and that solar radiation sometimes penetrates to a depth that is comparable to the region in which diurnal temperature variations occur.     

On Hapke photometric model predictions on reflectance of closely packed particulate surfaces

In a recent paper Hapke et al. (Hapke, B., Shepard, M., Nelson, R., Smythe, W., Piatek, J. [2009]. Icarus 199, 210-218) performed bi-directional reflectance measurements on closely-packed particulate surfaces of micrometer-sized particles and compared these with both the Hapke IMSA photometric model, and a numerical radiative transfer algorithm, the MDYZ (Mishchenko, M., Dlugach, J., Yanovitskij, E., Zakharova, N. [1999a]. J. Quant. Spectrosc. Radiat. Trans. 63, 409-432). To account for the effects of close packing, Hapke et al. applied a diffraction truncation scheme to remove the diffraction spike and supplied the renormalized single scattering phase function to the IMSA. They found that the IMSA prediction is a better match with measurement than that of MDYZ. In this work we demonstrate that the diffraction truncation procedure outlined by Hapke et al. contains an error. By following Hapke et al.’s intended truncation scheme, we have found that the IMSA model is not sufficiently anisotropic to describe the reflectance pattern of measurements on surface reflectance of closely packed large spherical particles.     

Light Scattering from Regolith: Intensity Versus Particle Size Behavior

Nature of the photometric phase curves of the regolith like surfaces (like those of the asteroids) are believed to be dependent on the single particle characteristics like particle size, shape, composition etc. and physical characteristics of the surface like porosity and roughness. Most of the phase curves have a rapid surge of intensity at small phase angles (typically below 5^°) known as opposition effect, followed by a linear less decreasing trend at larger phase angles. Average intensity of the linear region has been found to be mostly dependent on the average particle size and its composition, in many laboratory observations. Generally, it is difficult to explain the nature of light scattering by an ensemble of irregular shaped inhomogeneous particles with a theoretical model, just by studying the phase curves. In the present work, we have investigated whether the theoretically expected variation of the scattered light intensity (at a given phase angle) with the average particle size of the grains constituting regoliths, for a given material of the particle is in agreement with the experimental results or not? If yes, this can be a simpler but efficient way to study light scattering by regolith like surfaces. For theoretical analysis, Hapke formula has been used with Mie theory for single particle phase function, where we have neglected the influence of porosity and roughness presently. The data are also fitted with an empirical formula. It has been found that this empirical formula may also be used to estimate the unknown average particle size of a real regolith with known composition.     

Gusev photometric variability as seen from orbit by HRSC/Mars-express

Minnaert and two-term phase function Hapke models are used to describe the photometric properties of the martian surface using HRSC (High Resolution Stereo Camera) multi-angular observations acquired along the ongoing Mars-Express mission. These observations can be pieced together to derive integrated phase functions over a wide range of phase angles. The photometric diversity at 675 nm, as seen from orbit, of the martian surface properties across Gusev is depicted with seven units. Three photometric units widespread across the flanks of Apollinaris Patera flank and the floor of Gusev Crater are identified as having high single scattering albedo with rather forward scattering properties, low to intermediate macroscopic roughness and porous or not compacted powdered surface state as indicated by the opposition parameters. Another unit has the highest single scattering albedo, the smoothest surface in terms of macroscopic roughness, associated with an extremely forward scattering behavior. The opposition parameters are consistent with the presence of transparent particles in the surface powder layer. The distribution of this unit appears quite intermittent across the crater and does not seem to indicate any relationship with a given morphological structure. It may correspond to sparse areas where the structure of the surface dust layer is the most preserved. The most pronounced photometric changes are observed in three units associated with the low-albedo features corresponding to dark wind streaks. These units have a low single scattering albedo, are the most backscattering surfaces across Gusev, have a high surface roughness and present variable surface states as shown by the opposition parameters estimates, consistent with the occurrence of large grains organized in more or less packed layers. Clear differences are seen among these units in terms of opposition effect. While one exhibits typical characteristics for the opposition effect, another appears more unusual in terms of lobe width and the third suggests the occurrence of a packed/compressed/narrow size distribution powder surface. The opposition effect thus appears to play a significant role suggesting that the surface state optical properties across Gusev are strongly influenced by the porosity and packing characteristics or grain size distribution of the upper layer of the martian soil. The mapping aspect of the investigation is quite useful to get a better sense of the meaning of the observed photometric variations. Indeed, the Hapke modeling suggests that surface organization (surface roughness, packing state) is more important than the simple physical characterization of the intrinsic optical properties of the constitutive particles. Given the overall spatial patterns derived from the photometric analysis, the variations, at least for the western and central part of Gusev Crater, are likely partly driven by the prevailing wind regimes, considered to be oriented north-northwest/south-southeast and disturbing the very upper surface layer. The present photometric results agree with independent investigations based on thermal inertia, reflectance spectroscopy, in situ photometric and microscopic imaging and support the idea of a thin layer of fine-grained dust, being stripped off in the low albedo units to reveal a dark basaltic substrate comprising coarse-grained materials.     

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.     

A Study of Saturn's Ring Phase Curves from HST Observations

Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains (d∼λ for the C ring particles, d∼1-10 μm for the other rings).     

Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88°. This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 μm. We suggest characterizing the lunar regolith with the parameter a(Pmax)A, where Pmax,A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax-A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface.     

Bidirectional reflectance spectroscopy: 6. Effects of porosity

It is well known that the bidirectional reflectance of a particulate medium such as a planetary regolith depends on the porosity, in contrast to predictions of models based on the equation of radiative transfer as usually formulated. It is shown that this failure to predict porosity dependence arises from an incorrect treatment of the light that passes between the particles. In this paper a more physically correct treatment that takes account of the necessity of preventing particles from interpenetrating is used together with the two-stream approximation to solve the radiative transfer equation and derive improved expressions for the bidirectional and directional-hemispherical reflectances. It is found that increasing the filling factor (decreasing the porosity) increases the reflectance of low and medium albedo powders, but decreases it for ones with very high albedos. The model agrees qualitatively with measured data.     

Constraints on Mercury’s surface composition from MESSENGER and ground-based spectroscopy

The composition and chemistry of Mercury’s regolith has been calculated from MESSENGER MASCS 0.3-1.3 μm spectra from the first flyby, using an implementation of Hapke’s radiative transfer-based photometric model for light scattering in semi-transparent porous media, and a linear spectral mixing algorithm. We combine this investigation with linear spectral fitting results from mid-infrared spectra and compare derived oxide abundances with mercurian formation models and lunar samples. Hapke modeling results indicate a regolith that is optically dominated by finely comminuted particles with average area weighted grain size near 20 μm. Mercury shows lunar-style space weathering, with maturation-produced microphase iron present at ∼0.065 wt.% abundance, with only small variations between mature and immature sites, the amount of which is unable to explain Mercury’s low brightness relative to the Moon. The average modal mineralogies for the flyby 1 spectra derived from Hapke modeling are 35-70% Na-rich plagioclase or orthoclase, up to 30% Mg-rich clinopyroxene, <5% Mg-rich orthopyroxene, minute olivine, ∼20-45% low-Fe, low-Ti agglutinitic glass, and <10% of one or more lunar-like opaque minerals. Mercurian average oxide abundances derived from Hapke models and mid-infrared linear fitting include 40-50 wt.% SiO₂, 10-35 wt.% Al₂O₃, 1-8 wt.% FeO, and <25 wt.% TiO₂; the inferred rock type is basalt. Lunar-like opaques or glasses with high Fe and/or Ti abundances cannot on their own, or in combination, explain Mercury’s low brightness. The linear mixing results indicate the presence of clinopyroxenes that contain up to 21 wt.% MnO and the presence of a Mn-rich hedenbergite. Mn in M1 crystalline lattice sites of hedenbergite suppresses the strong 1 and 2 μm crystal field absorption bands and may thus act as a strong darkening agent on Mercury. Also, one or more of thermally darkened silicates, Fe-poor opaques and matured glasses, or Mercury-unique Ostwald-ripened microphase iron nickel may lower the albedo. A major part of the total microphase iron present in Mercury’s regolith is likely derived from FeO that is not intrinsic to the crust but has been subsequently delivered by exogenic sources.     

Application of a radiative transfer model to bright icy satellites

A radiative transfer model, derived largely from the work of B.W. Hapke (1981, J. Geophys. Res.86, 3039–3054) and J.D. Goguen (1981, Ph.D. thesis, Cornell University, Ithaca, N.Y.), is fit to Voyager imaging observations of Europa, Mimas, Enceladus, and Rhea. It is possible to place constraints on the single-scattering albedo, the porosity of the optically active upper regolith, the single-particle phase functions, and, in the cases of Europa and Mimas, the mean slope angle of macroscopic surface features. The texture of the surfaces of the Saturnian satellites appears to be similar to the Earth's moon. However, Europa is found to have a distinctly more compact regolith and a more forward-scattering single-particle phase function.     

NEAR Infrared Spectrometer Photometry of Asteroid 433 Eros

We present near-infrared spectrometer (NIS) observations (0.8 to 2.4 μm) of the S-type asteroid 433 Eros obtained by the NEAR Shoemaker spacecraft and report results of our Hapke photometric model analysis of data obtained at phase angles ranging from 1.2° to 111.0° and at spatial resolutions of 1.25×2.5 to 2.75×5.5 km/spectrum. Our Hapke model fits successfully to the NEAR spectroscopic data for systematic color variations that accompany changing viewing and illumination geometry. Model parameters imply a geometric albedo at 0.946 μm of 0.27±0.04, which corresponds to a geometric albedo at 0.550 μm of 0.25±0.05. We find that Eros exhibits phase reddening of up to 10% across the phase angle range of 0-100°. We observe a 10% increase in the 1-μm band depth at high phase angles. In contrast, we observe only a 5% increase in continuum slope from 1.486 to 2.363 μm and essentially no difference in the 2-μm band depth at higher phase angles. These contrasting phase effects imply that there are phase-dependent differences in the parametric measurements of 1- and 2-μm band areas, and in their ratio. The Hapke model fits suggest that Eros exhibits a weaker opposition surge than either 951 Gaspra or 243 Ida (the only other S-type asteroids for which we possess disk-resolved photometric observations). On average, we find that Eros at 0.946 μm has a higher geometric albedo and a higher single-scatter albedo than Gaspra or Ida at 0.56 μm; however, Eros's single-particle phase function asymmetry and average surface macroscopic roughness parameters are intermediate between Gaspra and Ida. Only two of the five Hapke model parameters exhibit a notable wavelength dependence: (1) The single-scatter albedo mimics the spectrum of Eros, and (2) there is a decrease in angular width of the opposition surge with increasing wavelength from 0.8 to 1.7 μm. Such opposition surge behavior is not adequately modeled with our shadow-hiding Hapke model, consistent with coherent backscattering phenomena near zero phase.     

Polarization of Light Scattered by Solar System Bodies and the Aggregate Model of Dust Particles

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 m. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.     

Comparison between the Shkuratov and Hapke Scattering Theories for Solid Planetary Surfaces: Application to the Surface Composition of Two Centaurs

This project examines the different approaches which deal with the theory of radiative transfer on atmosphereless bodies. We present the relative merits of two scattering theories based on the equivalent slab model: the extensively used Hapke theory (Hapke 1981, J. Geophys. Res.86, 3039-3054) and the Shkuratov theory (Shkuratov et al. 1999, Icarus141, 132-155). We found that their main difference is the role of the phase function of individual particles of regolith, which is predicted (and generally forward directed) in the case of the Shkuratov model instead of being a free parameter as formulated in the Hapke model. We also emphasize that different assumptions as to the manner in which different constituents are physically mixed in either model have a substantial effect on the synthetic spectra inferred. This leads to a significant extension of the validity of Hapke's or similar practical approaches to areas where these approaches are valid.We used two objects (the Centaurs 5145 Pholus and 8405 Asbolus) as examples. Previous modeling of the spectra of these two bodies with the Hapke approach gave suspect results in terms of the derived grain sizes, which were smaller than the wavelength, violating key assumptions of the model (Cruikshank et al. 1998, Icarus135, 389-407 for Pholus; Barucci et al. 2000, Astron. Astrophys.357, L53-56 for Asbolus). We considered several different types of powdered surfaces to interpret the surface composition of these two Centaurs. The effect of fine-scale contamination of water ice grains by small amounts of carbon and/or tholins is also explored. We can explain the strong red color and the rich near-infrared spectral signatures of Pholus using a five-component surface (contaminated water ice, amorphous carbon, Titan tholin, olivine, and methanol ice) where the grain sizes are consistent with the model assumptions. These components are similar to those inferred by Cruikshank et al. (1998), but we obtain very different grain sizes and relative abundances. For example, we obtain a relative abundance of water ice on the surface of Pholus of about 40% instead of 6% found with the Hapke model. Organic and carbonaceous components change by similar amounts. In the case of Asbolus, a tholin and amorphous carbon areal mixture can reproduce the spectrum, with water remaining at 9% or less. Using the albedo published by Fernandez et al. (2002, Astron. J.123, 1050-1055) which is higher than most workers assume for Centaurs and Kuiper belt objects, a surface composition similar to that of Pholus is found. It appears that model-based uncertainties in relative compositions must be regarded with more attention.     

First measurements with the Physikalisches Institut Radiometric Experiment (PHIRE)

We have constructed an experiment to perform bidirectional reflectance distribution function (BRDF) measurements of laboratory samples, and have used the experiment to characterize a sample of JSC-1 lunar regolith simulant. Characterizations relied on in-plane BRDF measurements in visible and near-infrared (NIR) bandpasses. The optical properties of the simulant sample were found to be similar to those observed for bright, lunar highland regions. Reflectance models (Hapke 1981. Bidirectional reflectance spectroscopy 1. Theory. J. Geophys. Res. 86(B4), 3,039−3,054; 1984. Bidirectional reflectance spectroscopy 3. Correction for macroscopic roughness. Icarus 59, 41−59; 1986. Bidirectional reflectance spectroscopy 4. The extinction coefficient and the opposition effect. Icarus 67, 264−280; 2002. Bidirectional reflectance spectroscopy 5. The coherent backscatter opposition effect and anisotropic scattering. Icarus 157, 523−534) made excellent fits to fixed incidence angle, variable emission angle data sets. However, the models were not found to extrapolate well to fixed, near-zero phase angle data at varying incidence angles, and no solutions were found that provided simultaneous, high quality fits to the two types of data sets. Except for the single-scattering albedo, the best-fit parameters of the fixed incidence angle data were statistically the same in the visible and NIR. Correlations between the reflectance model parameters were systematically examined, and strong correlations were found between single-scattering albedo and the two two-stream Henyey-Greenstein scattering parameters and, to a lesser extent, the small-scale mean surface roughness.     

Global photometric properties of Asteroid (4) Vesta observed with Dawn Framing Camera

Dawn spacecraft orbited Vesta for more than one year and collected a huge volume of multispectral, high-resolution data in the visible wavelengths with the Framing Camera. We present a detailed disk-integrated and disk-resolved photometric analysis using the Framing Camera images with the Minnaert model and the Hapke model, and report our results about the global photometric properties of Vesta. The photometric properties of Vesta show weak or no dependence on wavelengths, except for the albedo. At 554 nm, the global average geometric albedo of Vesta is 0.38 ± 0.04, and the Bond albedo range is 0.20 ± 0.02. The bolometric Bond albedo is 0.18 ± 0.01. The phase function of Vesta is similar to those of S-type asteroids. Vesta’s surface shows a single-peaked albedo distribution with a full-width-half-max ∼17% relative to the global average. This width is much smaller than the full range of albedos (from ∼0.55× to >2× global average) in localized bright and dark areas of a few tens of km in sizes, and is probably a consequence of significant regolith mixing on the global scale. Rheasilvia basin is ∼10% brighter than the global average. The phase reddening of Vesta measured from Dawn Framing Camera images is comparable or slightly stronger than that of Eros as measured by the Near Earth Asteroid Rendezvous mission, but weaker than previous measurements based on ground-based observations of Vesta and laboratory measurements of HED meteorites. The photometric behaviors of Vesta are best described by the Hapke model and the Akimov disk-function, when compared with the Minnaert model, Lommel–Seeliger model, and Lommel–Seeliger–Lambertian model. The traditional approach for photometric correction is validated for Vesta for >99% of its surface where reflectance is within ±30% of global average.     

Galileo Photopolarimetry of Jupiter at 678.5 nm

Brightness and linear polarization measurements at 678.5 nm for four south-north strips of Jupiter are studied. These measurements were obtained in 1997 by the Galileo photopolarimeter/radiometer. The observed brightness exhibits latitudinal variations consistent with the belt/zone structure of Jupiter. The observed degree of linear polarization is small at low latitudes and increases steeply toward higher latitudes. No clear correlations were observed between the degree of linear polarization and the brightness. The observed direction of polarization changes from approximately parallel to the local scattering plane at low latitudes to perpendicular at higher latitudes. For our studies, we used atmospheric models that include a haze layer above a cloud layer. Parameterized scattering matrices were employed for the haze and cloud particles. On a pixel-wise basis, the haze optical thickness and the single-scattering albedo of the cloud particles were derived from the observed brightness and degree of linear polarization; results were accepted only if they were compatible with the observed direction of polarization. Using atmospheric parameter values obtained from Pioneer 10 and 11 photopolarimetry for the South Tropical Zone and the north component of the South Equatorial Belt, this analysis yielded acceptable results for very few pixels, particularly at small phase angles. However, for almost all pixels, acceptable results were found when the parameterized scattering matrix of the cloud particles was adjusted to produce more negative polarization for single scattering of unpolarized light, especially at large scattering angles, similar to some laboratory measurements of ammonia ice crystals. Using this adjusted model, it was found that the derived latitudinal variation of the single-scattering albedo of the cloud particles is consistent with the belt/zone structure, and that the haze optical thickness steeply increases toward higher latitudes.     

The optical effects of small iron particles that darken but do not redden: Evidence of intense space weathering on Mercury

Submicroscopic iron particles larger than about 50 nm, infused throughout mineral grains or glasses, are abundant in planetary materials altered by their environment such as shocked meteorites and lunar agglutinate glasses. Such particles darken their host material but do not redden their spectra but to date there has been no theoretical treatment of their optical effects. Using Mie theory, we modify the Hapke (2001) radiative transfer model of the effects of space weathering to include these effects. Comparison with laboratory measurements shows that the new treatment reproduces the relationship between submicroscopic iron size, abundance and reflectance. We apply this new model to near-IR spectra of Mercury recently obtained by the MESSENGER spacecraft and find that submicroscopic iron is much more abundant on Mercury than in lunar soils, with typical total submicroscopic iron abundances near 3.5 wt.% compared to about 0.5 wt.% for lunar soils We also find that the ratio of iron particles that darken but do not redden to the abundance of very small iron particles that impart the red slope to space weathered material is much larger than lunar (6 vs. 2). Both the total submicroscopic iron abundance and ratio of particle size fractions are consistent with the higher production of melt and vapor in micrometeorite impact on Mercury relative to the Moon (Cintala, 1992) that enables more accumulation of space weathering products before sequestration by regolith overturn. The radiative transfer model cannot directly constrain the abundance of opaque minerals on Mercury because of ambiguities between the darkening effects of opaques and submicroscopic iron particles larger than 50 nm, but assuming the opaques are the ultimate source of the submicroscopic iron, our results place a lower limit of 4-20 wt.% on opaque abundance on Mercury depending on the composition of the opaque phase and whether titanium metal also contributes to the space weathering effect.