Testing the Hapke photometric model: Improved inversion and the porosity correction

In conjunction with a companion paper (Shepard, M.K., Helfenstein, P. [2011]. Icarus, submitted for publication), we derive, test, and apply a detailed approach for visualizing the phase angle dependence of light scattering in particulate soils from both whole-disk and disk-resolved observations. To reduce the number of model parameters and provide stronger constraints on model fits, we combine Hapke’s (Hapke, B. [2008]. Icarus 195, 918-926) recent correction for effects of porosity with his (Hapke, B. [1986]. Icarus 67, 264-280) model of the shadow hiding opposition effect. We further develop our method as a tool for least-squares fitting of Hapke’s model to photometric data. Finally, we present an improved method for estimating uncertainties in retrieved values of Hapke model parameters. We perform a preliminary test of the model on spectrogoniometric measurements from three selected laboratory samples from Shepard and Helfenstein (Shepard, M.K., Helfenstein, P. [2007]. J. Geophys. Res. 112 (E03001), 17). Our preliminary suite of test samples is too small and selective to permit the drawing of general conclusions. However, our results suggest that Hapke’s porosity correction improves the fidelity of fits to samples composed of low- and moderate-albedo particles and may allow for more reliable retrieval of porosity estimates in these materials. However, we find preliminary evidence that in high-albedo surfaces, the effects of porosity may be difficult to detect.     

Re-analysis of previous laboratory phase curves: 1. Variations of the opposition effect morphology with the textural properties,and an application to planetary surfaces

Typical variations in the opposition effect morphology of laboratory samples at optical wavelengths are investigated to probe the role of the textural properties of the surface (roughness, porosity and grain size). A previously published dataset of 34 laboratory phase curves is re-analyzed and fit with several morphological models. The retrieved morphological parameters that characterize the opposition surge, amplitude, width and slope (A, HWHM and S respectively) are correlated to the single scattering albedo, the roughness, the porosity and the grain size of the samples. To test the universality of the laboratory samples’ trends, we use previously published phase curves of planetary surfaces, including the Moon, satellites and rings of the giant planets. The morphological parameters of the surge (A and HWHM) for planetary surfaces are found to have a non-monotonic variation with the single scattering albedo, similar to that observed in asteroids (Belskaya, I.N., Shevchenko, V.G. [2000]. Icarus 147, 94–105), which is unexplained so far. The morphological parameters of the surge (A and HWHM) for laboratory samples seem to exhibit the same non-monotonic variation with single scattering albedo. While the non-monotonic variation with albedo was already observed by Nelson et al. (Nelson, R.M., Hapke, B.W., Smythe, W.D., Hale, A.S., Piatek, J.L. [2004]. Planetary regolith microstructure: An unexpected opposition effect result. In: Mackwell, S., Stansbery, E. (Eds.), Proc. Lunar Sci. Conf. 35, p. 1089), we report here the same variation for the angular width.     

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.     

A new look at photometry of the Moon

We use ROLO photometry (Kieffer, H.H., Stone, T.C. [2005]. Astron. J. 129, 2887-2901) to characterize the before and after full Moon radiance variation for a typical highlands site and a typical mare site. Focusing on the phase angle range 45° < α < 50°, we test two different physical models, macroscopic roughness and multiple scattering between regolith particles, for their ability to quantitatively reproduce the measured radiance difference. Our method for estimating the rms slope angle is unique and model-independent in the sense that the measured radiance factor I/F at small incidence angles (high Sun) is used as an estimate of I/F for zero roughness regolith. The roughness is determined from the change in I/F at larger incidence angles. We determine the roughness for 23 wavelengths from 350 to 939 nm. There is no significant wavelength dependence. The average rms slope angle is 22.2° ± 1.3° for the mare site and 34.1° ± 2.6° for the highland site. These large slopes, which are similar to previous “photometric roughness” estimates, require that sub-mm scale “micro-topography” dominates roughness measurements based on photometry, consistent with the conclusions of Helfenstein and Shepard (Helfenstein, P., Shepard, M.K. [1999]. Icarus 141, 107-131). We then tested an alternative and very different model for the before and after full Moon I/F variation: multiple scattering within a flat layer of realistic regolith particles. This model consists of a log normal size distribution of spheres that match the measured distribution of particles in a typical mature lunar soil 72141,1 (McKay, D.S., Fruland, R.M., Heiken, G.H. [1974]. Proc. Lunar Sci. Conf. 5, Geochim. Cosmochim. Acta 1 (5), 887-906). The model particles have a complex index of refraction 1.65-0.003i, where 1.65 is typical of impact-generated lunar glasses. Of the four model parameters, three were fixed at values determined from Apollo lunar soils: the mean radius and width of the log normal size distribution and the real part of the refraction index. We used FORTRAN programs from Mishchenko et al. (Mishchenko, M.I., Dlugach, J.M., Yanovitskij, E.G., Zakharova, N.T. [1999]. J. Quant. Spectrosc. Radiat. Trans. 63, 409-432; Mishchenko, M.I., Travis, L.D., Lacis, A.A. [2002]. Scattering, Absorption and Emission of Light by Small Particles. Cambridge Univ. Press, New York. <http://www.giss.nasa.gov/staff/mmishchenko/books.html>) to calculate the scattering matrix and solve the radiative transfer equation for I/F. The mean single scattering albedo is ω = 0.808, the asymmetry parameter is 〈cos Θ〉 = 0.77 and the phase function is very strongly peaked in both the forward and backward scattering directions. The fit to the observations for the highland site is excellent and multiply scattered photons contribute ?80% of I/F. We conclude that either model, roughness or multiple scattering, can match the observations, but that the strongly anisotropic phase functions of realistic particles require rigorous calculation of many orders of scattering or spurious photometric roughness estimates are guaranteed. Our multiple scattering calculation is the first to combine: (1) a regolith model matched to the measured particle size distribution and index of refraction of the lunar soil, (2) a rigorous calculation of the particle phase function and solution of the radiative transfer equation, and (3) application to lunar photometry with absolute radiance calibration.     

An experimental study of Hapke’s modeling of natural granular surface samples

A series of natural granular surfaces composed of volcanic samples that widely vary in grain sizes (from the micron-scale to the millimeter-scale), shapes, surface aspects, origins, and including glass and minerals, has been measured in the visible domain with the spectro-imaging device ISEP (Observatoire Midi-Pyrénées, Toulouse, France) and inverted by photometric modeling. The experimental protocol makes use of a specific set of multiangular configurations (on the order of a few tens) with sufficient angular diversity and coverage of the bidirectional space to resolve differences in particle phase function behavior and surface texture. This restrained set delivers comparable results in terms of photometric parameters to those produced with a dense set of hundreds of measurements. The considered samples in this work have been chosen to assess the influence of varied physical properties on light scattering behavior. The following specific photometric trends are found. Samples comprising fresh glass or monocrystals in a proportion on the order of 30% or more (from binocular magnifying glass inspection) are extremely forward scattering with narrow scattering lobes, and the larger the particles, the narrower the scattering lobe; also, round particles tend to be more backscattering than irregularly-shaped ones of similar texture, and the presence of voids within particles tends to increase the backscattering character of the sample. Particles with broad scattering lobes (phase function asymmetry parameter b ? 0.5) display relatively large modeled surface macroscopic roughness values (15-25°), while particles with narrow scattering lobes (b ? 0.5) show smaller modeled surface macroscopic roughness (between 15° and ∼3°).The comparison between the present results for the scattering parameters b and c, and those obtained in previous studies from artificial particles shows a similar trend and general agreement although some discrepancies were observed. The granular surface samples analyzed in the present study that contain a high proportion of isolated translucent monocrystals and/or fresh glass appear extremely forward-scattering and clearly chart a new part of the c vs. b trend. This is further supported by recent similar findings for martian in situ data and lunar regolith simulants. These results should help to better interpret present and future orbital and landed photometric data from bodies’ surfaces such as the Moon’s, Mars’, Vesta’s or Mercury’s regolith.     

A quantitative test of the ability of models based on the equation of radiative transfer to predict the bidirectional reflectance of a well-characterized medium

Predictions of two widely-used regolith reflectance models, a numerically exact computer code and an approximate analytic equation, based on the equation of radiative transfer were tested against the measured reflectance of a medium of close-packed spheres, whose properties supposedly can be well-characterized. Surprisingly, the approximate analytic model was a better match to the experimental data than the numerically exact computer solution. Other approximate regolith models were tested briefly with similar results. Discrepancies between the two models and between models and experiment can be explained if the phase functions and albedos of the spheres are not the same as when the particles are isolated. Differences include the absence of the Fraunhoffer diffraction peak, which is an intrinsic assumption of the approximate analytical model but not the exact numerical model, and increased scattering in the mid-range of phase angles, which the approximate analytic model fortuitously describes more accurately than the exact numerical model. These changes may be caused by the close proximity of surrounding particles. If they are taken into account, models based on the radiative transfer equation appear able to quantitatively predict the reflectances of regoliths and other particulate media. Interparticle perturbations are also predicted to cause a coherent backscatter opposition effect in the backward direction that was observed, but its angular width was found to be much larger than predicted by theories for sparsely-packed media.     

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.     

Scattering properties of planetary regolith analogs

The physics of scattering of electromagnetic waves by media in which the particles are in contact, such as planetary regoliths, has been thought to be relatively well understood when the particles are larger than the wavelength. However, this is not true when the particles are comparable with or smaller than the wavelength. We have measured the scattering parameters of planetary regolith analogs consisting of suites of well-sorted abrasives whose particles ranged from larger to smaller than the wavelength. We measured the variation of reflectance as the phase angle varied from 0.05° to 140°. The following parameters of the media were then deduced: the single scattering albedo, single scattering phase function, transport mean free path, and scattering, absorption, and extinction coefficients. A scattering model based on the equation of radiative transfer was empirically able to describe quantitatively the variation of intensity with angle for each sample. Thus, such models can be used to characterize scattering from regoliths even when the particles are smaller than the wavelength. The scattering parameters were remarkably insensitive to particle size. These results are contrary to theoretical predictions, but are consistent with earlier measurements of alumina abrasives that were restricted to small phase angles. They imply that a basic assumption made by virtually all regolith scattering models, that the regolith particles are the fundamental scattering units of the medium, is incorrect. Our understanding of scattering by regoliths appears to be incomplete, even when the particles are larger than the wavelength.     

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.     

The surface properties of small asteroids: Peculiar Betulia—A case study

We present the results of extensive thermal-infrared observations of the C-type near-Earth Asteroid (1580) Betulia obtained in June 2002 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii. Betulia is a highly unusual object for which earlier radiometric observations, interpreted on the basis of simple thermal models, indicated a surface of high thermal inertia. A high thermal inertia implies a lack of thermally insulating regolith. Radiometric observations of other asteroids of comparable size indicate that regolith is present in nearly all cases. Knowledge of the surface thermal properties of small near-Earth asteroids is crucial for meaningful calculations of the Yarkovsky effect, which is invoked to explain the delivery of collisional fragments from the main belt into near-Earth orbits, and apparently has a significant influence on the orbital evolution of potentially hazardous near-Earth asteroids. Furthermore, apart from being an indicator of the presence of thermally insulating regolith on the surface of an asteroid, the thermal inertia determines the magnitude of the diurnal temperature variation and is therefore of great importance in the design of instrumentation for lander missions to small asteroids. In the case of Betulia our database is sufficiently broad to allow the use of more sophisticated thermal models than were available for earlier radiometric observations. The measured fluxes have been fitted with thermal-model emission continua to determine the asteroid's size and geometric albedo, pv. Fits obtained with a new thermophysical model imply an effective diameter of 4.57±0.46 km and an albedo of 0.077±0.015 and indicate a moderate surface thermal inertia of around 180 J m⁻² s^−0.5 K⁻¹. It is difficult to reconcile our results with earlier work, which indicate a larger diameter for Betulia and a high-thermal-inertia surface of bare rock.     

Light scattering by media composed of semitransparent particles of different shapes in ray optics approximation: consequences for spectroscopy, photometry, and polarimetry of planetary regoliths

Computer simulations of light scattering by particulate surfaces and single particles forming these surfaces are presented. The ray optics approximation is used. Three types of particles are studied: spheres, cubes, and very irregular particles that are generated with an auxiliary random Gaussian field. The surfaces of the particles are represented as an arrangement of triangular facets. For the Monte Carlo ray tracing 10⁶−10⁷ rays were used. The ray tracing verifies Shkuratov et al.'s (Icarus 137 (1999) 235-246) spectral albedo model for powder-like media. We derive a useful relationship between the hemispheric albedo, A_int, and the bi-directional reflectance, R, at phase angle 30°: logR(30°)=1.088logA_int. This relationship provides a way to estimate bi-directional reflectance spectra from laboratory spectra measured with an integrating sphere for surfaces composed of particles of irregular shapes. We study also phase angle curves of the nonzero scattering matrix elements, F₁₁, −F₁₂/F₁₁, F₂₂/F₁₁, F₃₃/F₁₁, F₃₄/F₁₁, F₄₄/F₁₁, for single particles and media thereof. Randomly shaped particles show smoother phase angle behavior than particles with regular shapes that display distinct features. For media consisting of spheres the glory and primary rainbow both are prominent even in the case of conservative (nonabsorbing) scattering. On the other hand, such media clearly exhibit the depolarization effect, showing a significant role of multiple scattering between particles. For media composed of semitransparent cubes the retroreflector spike and a very deep negative polarization branch at small phase angles are observed. We demonstrate that, in the geometric optics approximation, neither a medium of spherical particles nor one of cubic particles is appropriate for modeling light scattering behavior of regolith-like surfaces.     

A survey of Karin cluster asteroids with the Spitzer Space Telescope

The Karin cluster is one of the youngest known families of main-belt asteroids, dating back to a collisional event only 5.8±0.2 Myr ago. Using the Spitzer Space Telescope we have photometrically sampled the thermal continua (3.5-22 μm) of 17 Karin cluster asteroids of different sizes, down to the smallest members discovered so far, in order to make the first direct measurements of their sizes and albedos and study the physical properties of their surfaces. Our targets are also amongst the smallest main-belt asteroids observed to date in the mid-infrared. The derived diameters range from 17.3 km for 832 Karin to 1.5 km for 75176, with typical uncertainties of 10%. The mean albedo is pv=0.215±0.015, compared to 0.20±0.07 for 832 Karin itself (for H=11.2±0.3), consistent with the view that the Karin asteroids are closely related physically as well as dynamically. The albedo distribution (0.12?pv?0.32) is consistent with the range associated with S-type asteroids but the variation from one object to another appears to be significant. Contrary to the case for near-Earth asteroids, our data show no evidence of an albedo dependence on size. However, the mean albedo is lower than expected for young, fresh “S-type” surfaces, suggesting that space weathering can darken main-belt asteroid surfaces on very short timescales. Our data are also suggestive of a connection between surface roughness and albedo, which may reflect rejuvenation of weathered surfaces by impact gardening. While the available data allow only estimates of lower limits for thermal inertia, we find no evidence for the relatively high values of thermal inertia reported for some similarly sized near-Earth asteroids. Our results constitute the first observational confirmation of the legitimacy of assumptions made in recent modeling of the formation of the Karin cluster via a single catastrophic collision 5.8±0.2 Myr ago.     

Physical characterization of the potentially hazardous high-albedo Asteroid (33342) 1998 WT24 from thermal-infrared observations

The potentially hazardous Asteroid (33342) 1998 WT₂₄ approached the Earth within 0.0125 AU on 2001 December 16 and was the target of a number of optical, infrared, and radar observing campaigns. Interest in 1998 WT₂₄ stems from its having an orbit with an unusually low perihelion distance, which causes it to cross the orbits of the Earth, Venus, and Mercury, and its possibly being a member of the E spectral class, which is rare amongst near-Earth asteroids (NEAs). We present the results of extensive thermal-infrared observations of 1998 WT₂₄ obtained in December 2001 with the 3-m NASA Infrared Telescope Facility (IRTF) on Mauna Kea, Hawaii and the ESO 3.6-m telescope in Chile. A number of thermal models have been applied to the data, including thermophysical models that give best-fit values of 0.35±0.04 km for the effective diameter, 0.56±0.2 for the geometric albedo, pv, and 100-300 J m⁻² s^−0.5 K⁻¹ for the thermal inertia. Our values for the diameter and albedo are consistent with results derived from radar and polarimetric observations. The albedo is one of the highest values obtained for any asteroid and, since no other taxonomic type is associated with albedos above 0.5, supports the suggested rare E-type classification for 1998 WT₂₄. The thermal inertia is an order of magnitude higher than values derived for large main-belt asteroids but consistent with the relatively high values found for other near-Earth asteroids. A crude pole solution inferred from a combination of our observations and published radar results is β=−52°, λ=355° (J2000), but we caution that this is uncertain by several tens of degrees.     

Vestoid surface composition from analysis of faint absorption bands in visible reflectance spectra

Faint absorption bands in the visible range of the smoothed vestoid spectra have been found. The bands centered near 505, 530, and 550 nm are attributed to ferrous iron in low-calcium pyroxene and are typical for pyroxene-bearing vestoid surfaces. In accordance with characteristics of the faint absorption bands around 600 and 650 nm the studied vestoid spectra can be sorted into five types. Since the same absorptions are also seen in the laboratory spectra of the minerals and meteorites, which appear to be similar to vestoid material, spectral types of the vestoids can be related to their surface compositions. Regolith of the Type-I vestoids consists of pure low-calcium pyroxenes. Minor amount of olivine along with pyroxene appear to be on the Type-II vestoids whereas the mixtures of low-calcium pyroxene with minor chromite define the Type-III and -IV. The causes for the fifth spectral type in terms of minor mineral phases are unclear now. Simulation of the spectra of vestoids was employed to estimate content of olivine (∼6-12 vol%) and chromite (∼12-30 vol%) on their surfaces.     

Visible/near-infrared spectrogoniometric observations and modeling of dust-coated rocks

Interpretations of visible/near-infrared reflectance spectra of Mars are often complicated by the effects of dust coatings that obscure the underlying materials of interest. The ability to separate the spectral reflectance signatures of coatings and substrates requires an understanding of how their individual and combined reflectance properties vary with phase angle. Toward this end, laboratory multispectral observations of rocks coated with different amounts of Mars analog dust were acquired under variable illumination and viewing geometries using the Bloomsburg University Goniometer (BUG). These bidirectional reflectance distribution function (BRDF) data were fit with a two-layer radiative transfer model, which replicated BUG observations of dust-coated basaltic andesite substrates relatively well. Derived single scattering albedo and phase function parameters for the dust were useful in testing the model's ability to derive the spectrum of a “blind” substrate (unknown to the modeler) coated with dust. Subsequent tests were run using subsets of the BUG data restricted by goniometric or coating thickness coverage. Using the entire data set provided the best constraints on model parameters, although some reductions in goniometric coverage could be tolerated without substantial degradation. Predictably, the most thinly coated samples provided the best information on the substrate, whereas the thickest coatings best replicated the dust. Dust zenith optical thickness values ∼0.6-0.8 best constrain the substrate and coating simultaneously, particularly for large ranges of incidence or emission angles. The lack of sufficient angles can be offset by having a greater number and range of coatings thicknesses. Given few angles and thicknesses, few constraints can be placed concurrently on the spectral properties of the coating and substrate.     

Physical characteristics of Hayabusa target Asteroid 25143 Itokawa

In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.     

Keck observations of near-Earth asteroids in the thermal infrared

We present the results of thermal-infrared observations of 20 near-Earth asteroids (NEAs) obtained in the period March 2000-February 2002 with the 10-m Keck-I telescope on Mauna Kea, Hawaii. The measured fluxes have been fitted with thermal-model emission continua to determine sizes and albedos. This work increases the number of NEAs having measured albedos by 35%. The spread of albedos derived is very large (p_v=0.02−0.55); the mean value is 0.25, which is much higher than that of observed main-belt asteroids. In most cases the albedos are in the ranges expected for the spectral types, although some exceptions are evident. Our results are consistent with a trend of increasing albedo with decreasing size for S-type asteroids with diameters below 20 km. A number of objects are found to have unexpectedly low apparent color temperatures, which may reflect unusual thermal properties. However, the results from our limited sample suggest that high thermal-inertia, regolith-free objects may be uncommon, even amongst NEAs with diameters of less than 1 km. We discuss the significance of our results in the light of information on these NEAs taken from the literature and the uncertainties inherent in applying thermal models to near-Earth asteroids.     

Asteroid observations at low phase angles: III. Brightness behavior of dark asteroids

The results of photometric observations of eight main-belt asteroids with low surface albedo are presented. The magnitude-phase dependences including low phase angles (<1 deg) have been obtained for Asteroids 76 Freia (down to phase angle 0.1 deg, P-type), 190 Ismene (0.3 deg, P-type), 303 Josephina (0.2 deg, C-type), 309 Fraternitas (0.1 deg, C-type), 313 Chaldaea (0.1 deg, C-type), 444 Gyptis (0.8 deg, P-type), 615 Roswitha (0.1 deg, C-type), and 954 Li (0.03 deg, FCX-type). The behavior of brightness in the range of opposition effect is found to be practically linear for 190 Ismene with amplitude of opposition effect only 0.03 mag. Amplitudes of the opposition effect for other asteroids are close to a mean for this type. The obtained data allowed us also to determine the rotation periods of asteroids: 303 Josephina (12.497±0.001 h), 309 Fraternitas (11.205±0.005 h), 615 Roswitha (4.422±0.001 h) and 954 Li (7.207±0.002 h). The color indexes B-V, V-R and R-I have been determined for some asteroids.     

Comment on “Modeling of opposition effects with ensembles of clusters: Interplay of various scattering mechanisms” by Elena V. Petrova, Victor P. Tishkovets, Klaus Jockers, 2007 [Icarus 188, 233-245]

We show that the mechanism called “near-field effect” [e.g., Petrova, E.V., Tishkovets, V.P., Jockers, K., 2007. Icarus 188, 233-245], which is used to explain wide-phase-angle negative polarization branch observed for planetary regoliths and cometary comas, is not realistic as it contradicts laboratory experiments and results of modeling with discrete dipole approximation calculations.     

Exploration of faint absorption bands in the reflectance spectra of the asteroids by method of optimal smoothing: Vestoids

An optimization method of smoothing noisy spectra was developed to investigate faint absorption bands in the visual spectral region of reflectance spectra of asteroids and the compositional information derived from their analysis. The smoothing algorithm is called “optimal” because the algorithm determines the best running box size to separate weak absorption bands from the noise. The method is tested for its sensitivity to identifying false features in the smoothed spectrum, and its correctness of forecasting real absorption bands was tested with artificial spectra simulating asteroid reflectance spectra. After validating the method we optimally smoothed 22 vestoid spectra from SMASS1 [Xu, Sh., Binzel, R.P., Burbine, T.H., Bus, S.J., 1995. Icarus 115, 1-35]. We show that the resulting bands are not telluric features. Interpretation of the absorption bands in the asteroid spectra was based on the spectral properties of both terrestrial and meteorite pyroxenes. The bands located near 480, 505, 530, and 550 nm we assigned to spin-forbidden crystal field bands of ferrous iron, whereas the bands near 570, 600, and 650 nm are attributed to the crystal field bands of trivalent chromium and/or ferric iron in low-calcium pyroxenes on the asteroids' surface. While not measured by microprobe analysis, Fe³⁺ site occupancy can be measured with Mössbauer spectroscopy, and is seen in trace amounts in pyroxenes. We believe that trace amounts of Fe³⁺ on vestoid surfaces may be due to oxidation from impacts by icy bodies. If that is the case, they should be ubiquitous in the asteroid belt wherever pyroxene absorptions are found. Pyroxene composition of four asteroids of our set is determined from the band position of absorptions at 505 and 1000 nm, implying that there can be orthopyroxenes in all range of ferruginosity on the vestoid surfaces. For the present we cannot unambiguously interpret of the faint absorption bands that are seen in the spectra of 4005 Dyagilev, 4038 Kristina, 4147 Lennon, and 5143 Heracles. Probably there are other spectrally active materials along with pyroxenes on the surfaces of these asteroids.