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.     

Ice table depth variability near small rocks at the Phoenix landing site, Mars: A pre-landing assessment

We combine thermal simulations of ground ice stability near small rocks with extrapolations of the abundance of rocks at the Phoenix landing site based on HiRISE rock counts to estimate the degree of ice table depth variability within the 3.8 m² workspace that can be excavated during the mission. Detailed predictions of this kind are important both to test current ground-ice theory and to optimize soil investigations after landing. We find that Phoenix will very likely have access to at least one rock in the diameter range 5 cm to 1 m. Our simulations, which assume the ice to be in diffusive equilibrium with atmospheric water vapor, indicate that all rocks in this size range are associated with an annulus of deep ice-free soil. Ice table depth variability of 1-5 cm is very likely at the landing site due to the presence of small rocks. Further, there are scenarios in which Phoenix might exploit the presence of individual large rocks and/or the arrangement of small rocks to sample soils at depths >10 cm below the average depth predicted from orbit (∼4 cm). Scale analysis to constrain uncertainties in simulation results indicates that estimates of maximum depths may be somewhat conservative and that ice table depressions associated with individual rocks could be deeper and laterally more extended than indicated by formal predictions by mm to cm.     

Particle sieving and sorting under simulated martian conditions

We report on sorting of small grained material under simulated martian conditions in order to better understand the nature of particle movement in the acquisition-to-analysis chain for future martian missions. We find that triboelectric charging when material is sieved is a major phenomenon that has to be understood and mitigation strategies explored in order to be able to successfully move particles under these types of conditions while minimizing cross sample talk. In different experimental set-ups, we have observed such phenomena as caking of the sieve, adhesion of particles to hardware, clodding of dry fines, and electrostatic repulsion. These phenomena occur when different experimental testing is performed with varied configurations and environmental conditions. Identifying these electrostatic effects can help us understand potential bias in the analytical instruments and to define the best operational protocols to collect samples on the surface of Mars. These experiments demonstrate the need for end-to-end system testing under the most realistic environmental conditions and platforms before mission configurations can be demonstrated before launch.     

Cratering saturation and equilibrium: A new model looks at an old problem

Recent advances in computing technology and our understanding of the processes involved in crater production, ejecta production, and crater erasure have permitted me to develop a highly-detailed Cratered Terrain Evolution Model (CTEM), which can be used to investigate a variety of questions in the study of impact dominated landscapes. In this work, I focus on the manner in which crater densities on impacted surfaces attain equilibrium conditions (commonly called crater ‘saturation’) for a variety of impactor population size-frequency distributions: from simple, straight-line power-laws, to complex, multi-sloped distributions. This modeling shows that crater density equilibrium generally occurs near observed relative-density (R) values of 0.1-0.3 (commonly called ‘empirical saturation’), but that when the impactor population has a variable power-law slope, crater density equilibrium values will also be variable, and will continue to reflect, or follow the shape of the production population long after the surface has been ‘saturated.’ In particular, I demonstrate that the overall level of crater density curves for heavily-cratered regions of the lunar surface are indicative of crater density equilibrium having been reached, while the shape of these curves strongly point to a Main Asteroid Belt (MAB) source for impactors in the near-Earth environment, as originally stipulated in Strom et al. [Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A., 2005. Science 309 (September), 1847-1850]. This modeling also validates the conclusion by Bottke et al. [Bottke, W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. Icarus 175 (May), 111-140] that the modern-day MAB continues to reflect its ancient size-frequency distribution, even though severely depleted in mass since that time.     

Photometric anomalies of the lunar surface studied with SMART-1 AMIE data

We present new results from the mapping of lunar photometric function parameters using images acquired by the spacecraft SMART-1 (European Space Agency). The source data for selected lunar areas imaged by the AMIE camera of SMART-1 and the data processing are described. We interpret the behavior of photometric function in terms of lunar regolith properties. Our study reveals photometric anomalies on both small (sub-kilometer) and large (tens of kilometers) scales. We found the regolith mesoscale roughness of lunar swirls to be similar in Mare Marginis, Mare Ingenii, and the surrounding terrains. Unique photometric properties related to peculiarities of the millimeter-scale regolith structure for the Reiner Gamma swirl are confirmed. We identified several impact craters of subkilometer sizes as the source of photometric anomalies created by an increase in mesoscale roughness within the proximal crater ejecta zones. The extended ray systems reveal differences in the photometric properties between proximal and distant ejecta blankets. Basaltic lava flows within Mare Imbrium and Oceanus Procellarum indicate higher regolith porosity for the redder soils due to differences in the chemical composition of lavas.     

New estimates for the sublimation rate for ice on the Moon

The strong hydrogen signal that the Lunar Prospector saw at the Moon's poles suggests that water ice may be present near the surface of the lunar regolith. A robotic mission to obtain in situ samples and to quantify the amount of this valuable resource must be designed carefully to avoid dissipating too much heat in the regolith during coring or drilling and, thus, causing the ice to sublimate before it is processed. Here I use new results for the saturation vapor pressure of water ice to extend previous estimates of its sublimation rate down to a temperature of 40 K, typical of the permanently shaded craters near the lunar poles where the water ice is presumed to be trapped. I find that, for temperatures below 70 K, the sublimation rate of an exposed ice surface is much less than one molecule of water vapor lost per square centimeter of surface per hour. But even if a small ice sample (∼4 ng) were heated to 150 K, it could exist for over two hours without sublimating a significant fraction of its mass. Hence, carefully designed sampling and sample handling should be able to preserve water ice obtained near the lunar poles for an accurate measurement of its in situ concentration.     

Rebuttal to 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]

Shkuratov and Zubko [Shkuratov, Yu.G., Zubko, E., 2008. Icarus 194, 850-852] criticize our paper [Petrova, E.V., Tishkovets, V.P., Jockers, K., 2007. Icarus 188, 233-245]. With this comment we reply to this criticism. We show that the experimental data and the modeling calculations presented by these authors cannot disprove the near-field effect as an important contributor to the scattering mechanisms considered in our paper.     

Laboratory studies into the effect of regolith on planetary X-ray fluorescence spectroscopy

In the analysis of X-ray fluorescence spectra from planetary surfaces, it is traditionally assumed that the observed surface is a plane-parallel, smooth, and homogeneous medium. The spectral and spatial resolutions of the instruments that have been used to measure X-ray emission from planetary surfaces to date have been such that this has been a reasonable assumption, but a new generation of X-ray spectrometers will provide enhanced spectral and spatial resolutions when compared with previous instrumentation. In light of these improvements in performance, it is important to assess how the requirements on the methodology of analysis of spectra may change when the surface is considered as a regolith. At other wavelengths, varying physical properties of planetary regoliths, such as the packing density, are known to have an effect on the observed signal as a function of viewing geometry. In this paper, the results from laboratory X-ray fluorescence measurements of regolith analogue materials at different viewing geometries are presented. Characteristic properties of the regolith such as particle sizes and packing density are found to affect the measured elemental line ratios. A semiempirical function is introduced as a tool for fitting fluorescent line intensity dependences as a function of viewing geometry. The importance of the results is discussed and recommendations are made for the future analysis of planetary X-ray fluorescence data.     

Velocity distributions of high-velocity ejecta from regolith targets

We measured the velocity distributions of impact ejecta with velocities higher than ∼100 m s⁻¹ (high-velocity ejecta) for impacts at variable impact angle α into unconsolidated targets of small soda-lime glass spheres. Polycarbonate projectiles with mass of 0.49 g were accelerated to ∼250 m s⁻¹ by a single-stage light-gas gun. The impact ejecta are detected by thin aluminum foils placed around the targets. We analyzed the holes on the aluminum foils to derive the total number and volume of ejecta that penetrated the aluminum foils. Using the minimum velocity of the ejecta for penetration, determined experimentally, the velocity distributions of the high-velocity ejecta were obtained at α=15°, 30°, 45°, 60°, and 90°. The velocity distribution of the high-velocity ejecta is shown to depend on impact angle. The quantity of the high-velocity ejecta for vertical impact (α=90°) is considerably lower than derived from a power-law relation for the velocity distribution on the low-velocity ejecta (less than 10 m s⁻¹). On the other hand, in oblique impacts, the quantity of the high-velocity ejecta increases with decreasing impact angle, and becomes comparable to those derived from the power-law relation. We attempt to scale the high-velocity ejecta for oblique impacts to a new scaling law, in which the velocity distribution is scaled by the cube of projectile radius (scaled volume) and a horizontal component of impactor velocity (scaled ejection velocity), respectively. The high-velocity ejecta data shows a good correlation between the scaled volume and the scaled ejection velocity.