Interpretation of the surface brightness of Phobos

Analysis of disk resolved images of Phobos obtained by the Phobos 2 spacecraft allows us to study the surface scattering law and albedo variations. From low phase angle images we find variations in local geometric albedo approximately 10%, with a correlation length approximately 1km. The scattering law is reasonably well matched by the recent proposed LPI (Lumme et al. 1990a) model, which allows us to deduce a small scale (approximately 1 mm) surface roughness (approximately 0.5), defined here as the rms. tangent of the local surface normal relative to the mean surface normal in the Duxbury (1991) model of Phobos. This value is very close to what has been found for Mercury and the Moon.     

Results of TV imaging of Phobos (Experiment VSK-Fregat)

From February to March 1989 the Phobos 2 spacecraft took 37 TV images of Phobos at a distance of 190-1100 km. These images complement Mariner-9 and Viking data by providing higher-resolution coverage of a large region West of the crater Stickney (40-160 degrees W) and by providing disk-resolved measurements of surface brightness at a greater range of wavelengths and additional phase angles. These images have supported updated mapping and characterization of large craters and grooves, and have provided additional observations of craters' and grooves' bright rims. Variations in surface visible/near-infrared color ratio of almost a factor of 2 have been recognized; these variations appear to be associated with the ejecta of specific large impact craters. Updated determinations of satellite mass and volume allow calculation of a more accurate value of bulk density, 1.90 +/- 0.1 g cm-3. This is significantly lower than the density of meteoritic analogs to Phobos' surface, suggesting a porous interior perhaps containing interstitial ice.     

Predicted lightcurves of Phobos and Deimos

Using Mariner 9 results on the shapes, rotation periods and photometric functions of Phobos and Deimos we calculate approximate orbital lightcurves for the two Martian satellites. The prediction is that both Phobos and Deimos should show orbital brightness fluctuations detectable from Earth. For Phobos the detectable amplitude is predicted to be about 0.1 mag; for Deimos, 0.2 mag.     

Viking orbiter observations of the Mars opposition effect

The Viking Extended Mission has experienced two major dust storms that have changed the global photometric properties of Mars. Large quantities of atmospheric dust arising from the June 5, 1977, storm have been observed at very low phase angles to measure the opposition effect. These particles yield only a small increase in brightness at 0° phase angle with the least enhancement seen in violet light. The phase function is well modeled by nonspherical particles with a spectrally dependent single scattering albedo. It is doubtful, therefore, that atmospheric dust plays a significant role in the reported blue light brightness surge. Such particles as surface structure combined with a lunar photometric function could, however, produce the wavelength-dependent backscattering observed during the 1967 and 1969 oppositions under clearer conditions.     

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.     

Retrieval of ammonia abundances and cloud opacities on Jupiter from voyager IRIS spectra

A method is formulated to retrieve gaseous ammonia abundance and cloud opacities at 45 and 5 μm from Voyager IRIS data using a simplified atmospheric model and a two-stream radiative transfer approximation. Our goal is to obtain sufficient computational efficiency to permit global mapping of the relative horizontal variations of these parameters. A single cloud layer is invoked with a base pressure of 680 mbar and a scale height equal to 0.14 times the gas scale height. The NH₃ vertical distribution is modeled with a scale height equal to that of the cloud above 680 mbar and with a mole fraction independent of height at deeper levels. Measurements of brightness temperature as a function of emission angle from selected locations on the planet are used to verify the validity of the model and to constrain certain model parameters. It is found that the cloud particles can be treated as pure absorbers at 45 μm, but scattering must be included at 5 μm where a single scattering albedo of ∼0.75 is inferred. These results are used to develop a simple algorithm for the retrieval of ammonia abundance and cloud optical depths at 45 and 5 μm from measurements at 216, 225, and 2050 cm⁻¹.     

Near-Infrared Spectrophotometry of Phobos and Deimos

We have observed the leading and trailing hemispheres of Phobos from 1.65 to 3.5 μm and Deimos from 1.65 to 3.12 μm near opposition. We find the trailing hemisphere of Phobos to be brighter than its leading hemisphere by 0.24±0.06 magnitude at 1.65 μm and brighter than Deimos by 0.98±0.07 magnitude at 1.65 μm. We see no difference larger than observational uncertainties in spectral slope between the leading and trailing hemispheres when the spectra are normalized to 1.65 μm. We find no 3-μm absorption feature due to hydrated minerals on either hemisphere to a level of ∼5-10% on Phobos and ∼20% on Deimos. When the infrared data are joined to visible and near-IR data obtained by previous workers, our data suggest the leading (Stickney-dominated) side of Phobos is best matched by T-class asteroids. The spectral slope of the trailing side of Phobos and leading side of Deimos are bracketed by the D-class asteroids. The best laboratory spectral matches to these parts of Phobos are mature lunar soils and heated carbonaceous chondrites. The lack of 3-μm absorption features on either side of Phobos argues against the presence of a large interior reservoir of water ice according to current models of Phobos' interior (F. P. Fanale and J. R. Salvail 1989, Geophys. Res. Lett.16, 287-290; Icarus88, 380-395).     

Effects of subsurface volume scattering on the lunar microwave brightness temperature spectrum

The effects of volume scattering on the lunar microwave brightness temperature spectrum are evaluated for a broad range of plausible scattering fragment populations. Mie-scattering phase functions and the radiative transfer method are utilized. Results indicate that emission darkening of ～1–7°K is to be expected over the wavelength range 3–30 cm, dependent on the total volume fraction of centimeter-sized and larger fragments. Spectral variations can occur if the size distribution of scatterers is nonuniform in a power law sense. For mare regions representative of the Surveyor III, V, and VI sites, an increase in brightness temperature with wavelength is predicted which is smaller than the predicted spectral variation due to planetary heat flow. The amplitude of lunation variation in brightness temperature is particularly sensitive to the fraction of fragments in the upper 10-cm diurnal layer. Deductions of electrical loss based on purely absorptive models can overestimate loss tangent values by a factor of 1.5 or more if scattering effects are not accounted for. The absence of anomalies exceeding ～2°K in lunar night-time γ3.55-cm brightness temperature maps requires a remarkable uniformity of the surface layer (upper 10 cm) scattering properties on a 250-km scale.     

The photometric functions of Phobos and Deimos. III. Surface photometry of Phobos

At least three large areas on the surface of Phobos are covered by a dark material of complex texture which scatters light according to the Hapke-Irvine Law. The average 20° to 80° intrinsic and disc-integrated phase coefficients of this material are β_i = 0.020 ± 0.001 mag/deg and β = 0.033 mag/deg, respectively. These values are slightly greater than the values found for Deimos in Paper II (preceding article). On the largest scale the surface of Phobos is rougher than the surface of Deimos, perhaps accounting for the slightly greater phase coefficients. Contrary to the situation on Deimos, no definite regions of intrinsically brighter material are apparent on Phobos. This difference could account for the slightly lower average reflectance of Phobos relative to Deimos. No evidence for large exposures of solid rock has been found in the three areas studied.     

Vertical-structure effects on planetary microwave brightness temperature measurements: Applications to the lunar regolith

The effects of vertical variations in density and dielectric constant on nadir-viewing microwave brightness temperatures are examined. Stratification models as well as models of a continuous increase in density with depth are analyzed. Specific applications address the vertical structure of the lunar frontside regolith, utilizing combined constraints from Apollo data, bistatic radar signatures, and Earth-based measurements of the lunar microwave brightness temperature.Results have been analyzed in terms of the effects on the zeroth and first harmonic of the lunar disk-center brightness temperature variation over a lunation, and their wavelength dependence. Lunation-mean brightness temperatures, which are diagnostic of emissivity and steady-state sub-surface temperatures, are sensitive to both near-surface soil density gradients and single high-impedance dielectric contrasts. Models of the rapid density increase in the upper 5–10 cm of the lunar regolith predict brightness temperature decreases of 2–10°K between λ₀ = 3 and 30 cm. The magnitude of this spectral variation depends upon the thickness of a postulated low-density surface coating layer, and the magnitude of the density gradient in the transition soil layer. Comparable decreases in brightness temperature can be produced by a stratified two-layer model of soil overlaying bedrock if the high-density substrate lies within 1–2 m of the surface. Multiple soil layering on a centimeter scale, such as is observed in the Apollo core samples, is not likely to induce spectral variations in mean brightness temperature due to rapid regional variations in layer depths and thicknesses.The fractional variation in disk-center brightness temperature over a lunation (first harmonic) can be altered by vertical-structure effects only for the case in which a larger and abrupt dielectric contrast exists within the upper surface layer where the significant diurnal variations in physical temperature occur. Soil density variations do not cause scattering effects sufficient to significantly alter the microwave emission weighting function within the diurnal layer. For the Moon, this layer consists of the upper 10 cm. Since no widespread rock substrate as shallow as 10 cm exists in the lunar frontside, only volume scattering effects, due to buried shallow rock fragments, can explain the apparent high electrical loss inferred from Earth-based measurements of the amplitude of lunation brightness temperature variations.Representative models of the lunar frontside vertical structure have also been examined for their effects of radar cross-section measurements and resultant inferences of bulk dielectric constant. Models of the near-surface density gradient predict a significant increase in the remotely inferred dielectric constant value from centimeter to meter wavelengths. Such a model is in general agreement with the dielectric constant spectrum inferred from Earth-based brightness temperature polarization measurements, but is difficult to reconcile with the Apollo bistatic radar results at λ₀ = 13 and 116 cm.     

Darkening and visibility functions for the global five-minute oscillations

A theory for the brightness fluctuations of the Sun as a star under the effect of its global oscillations has been developed. Formulas for the darkening and visibility of p-modes are derived and their calculations are performed in the local approximation for adiabatic oscillations. Observational data from the DIFOS multichannel photometer onboard the CORONAS-F satellite are used to solve the inverse problem of determining the amplitude of the five-minute temperature fluctuations in the solar photosphere as a function of the height. Analysis of the solution and comparison with the results of other authors suggest that the predicted temperature waves resulting from a linear transformation of p-modes in the photosphere exist in the photosphere. The wavelength and phase velocity of the temperature waves are considerably smaller than those of acoustic waves. It turns out that the solar brightness fluctuations should be produced mainly by the temperature waves in the photosphere, not by the p-modes themselves. The darkening function for the brightness fluctuations is oscillatory in behavior, while the visibility function can differ markedly from that for the Doppler shifts of spectral lines produced by p-modes. These properties are important for interpreting the observations of stellar oscillations based on stellar brightness fluctuations.     

Phobos: Control network analysis

Initial analysis of the Mariner 9 high resolution pictures of Phobos surface features has been completed. A control network of 38 landmarks has been established and used to determine the physical size, shape, orientation, libration, and topography properties of Phobos. The results verified the synchronous rotation of Phobos and revealed a libration of approximately 5° in the orbit plane of Phobos. A preliminary map of Phobos, based on the control network analysis, is given.     

The Near-Infrared Continuum Slope of Martian Dark Region Reflectance Spectra

The planet Mars has a bimodal albedo distribution with bright and dark regions. Earth-boundreflectance spectra ofbright Martian regions are generally characterized by a flat to positive continuum slope in the near-infrared (NIR), while those of dark regions tend to have a negative slope. Spectra obtained with the instrument ISM (Imaging Spectrometer for Mars) onboard the Phobos 2 spacecraft usually show the same relationship between brightness and NIR continuum slope. Nevertheless, some ISM spectra show deviations from this relationship, the most conspicuous ones being observed in the Syrtis Major and Valles Marineris regions, where some dark areas are characterized by a flat continuum slope. So far, this was interpreted to indicate a basaltic material covered with a weathering coating or a thin layer of dust. The results of a new spectroscopic investigation of analog materials for the Martian crust revealed that reflectance spectra of bulk samples generally show a preference for a negative NIR continuum slope, in contrast to spectra of powder samples. This suggests a different interpretation of the ISM spectra, namely that the unusual dark regions, which are characterized by a flat NIR continuum slope, are covered by sand-sized basaltic particles. In contrast, the common dark regions, which are characterized by a blue continuum slope, are dominated by bedrock or blocky basalt rocks. This interpretation is in agreement with the findings of other methods of remote sensing. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Shadowing Effect for Regolith-like Surfaces

We describe a numerical model that allows the shadowing probability and photometric characteristics to be calculated in the general case of a disconnected multi-valued surface (regolith-like medium) in the single-scattering approximation when the phase function of a surface element is known. We investigate a statistically homogeneous medium and a medium with a density gradient (along the normal to the mean surface) with Gaussian and fractal statistical properties. A comparison of the phase functions of reflectance for a disconnected multi-valued surface with those for the previously developed model of a medium composed of opaque spherical particles shows qualitative agreement. The results of our calculations are also compared with the phase function of brightness for the Moon's surface. The model is shown to yield a function that matches the observed one for phase angles 10° at very low densities of the medium. Achieving better agreement requires invoking additional mechanisms for the formation of the phase function of brightness.     

The tilt effect for Saturn's rings

Multiple-scattering computations are carried out to explain the variation of the observed brightness of the A and B rings of Saturn with declination of the Earth and Sun. These computations are performed by a doubling scheme for a homogeneous plane-parallel scattering medium. We test a range of choices for the phase function, albedo for single scattering, and optical depth of both the rings. Isotropic scattering and several other simple phase functions are ruled out, and we find that the phase function must be moderately peaked in both the forward and backward directions. The tilt effect can be explained by multiple scattering in a homogeneous layer, but, for ring B, this requires a single-scattering albedo in excess of 0.8. The brightest part of ring B must have an optical depth greater than 0.9. We find that the tilt effect for ring A can be reproduced by particles having the same properties as those in ring B with the optical depth for the A ring in the range 0.4 to 0.6.     

Dynamics of Mars-orbiting dust: Effects of light pressure and planetary oblateness

This paper deals with dynamics of impact ejecta from Phobos and Deimos initially on near-circular equatorial orbits around Mars. For particles emitted in a wide size regime of 1 micron and greater, and taking into account the typical particle lifetimes to be less than 100 years, the motion is governed by two perturbing forces: solar radiation pressure and influence of Mars' oblateness. The equations of motion of particles in Lagrangian non-singular elements are deduced and solved, both analytically and numerically, for different-sized ejecta. We state that the coupled effect of both forces above is essential so that on no account can the oblateness of Mars are be neglected. The dynamics of grains prove to be quite different for the ejecta of Phobos and Deimos. For Deimos, the qualitative results are relatively simple and imply oscillations of eccentricity and long-term variations of orbital inclination, with amplitudes and periods both depending on grain size. For Phobos, the dynamics are shown to be much more complicated, and we discuss it in detail. We have found an intriguous peculiar behavior of debris near 300 µm in size. Another finding is that almost all the Phobos ejecta with radii less than 30 µm (against the values of 5 to 20 µm adopted earlier by many authors) should be rapidly lost by collisions with martian surface. The results of the paper may be the base for constructing an improved model of dust belts that presumably exist around Mars.     

The difference PDF of 21-cm fluctuations: a powerful statistical tool for probing cosmic reionization

A new generation of radio telescopes are currently being built with the goal of tracing the cosmic distribution of atomic hydrogen at redshifts 6–15 through its 21-cm line. The observations will probe the large-scale brightness fluctuations sourced by ionization fluctuations during cosmic reionization. Since detailed maps will be difficult to extract due to noise and foreground emission, efforts have focused on a statistical detection of the 21-cm fluctuations. During cosmic reionization, these fluctuations are highly non-Gaussian and thus more information can be extracted than just the one-dimensional function that is usually considered, i.e. the correlation function. We calculate a two-dimensional function that if measured observationally would allow a more thorough investigation of the properties of the underlying ionizing sources. This function is the probability distribution function (PDF) of the difference in the 21-cm brightness temperature between two points, as a function of the separation between the points. While the standard correlation function is determined by a complicated mixture of contributions from density and ionization fluctuations, we show that the difference PDF holds the key to separately measuring the statistical properties of the ionized regions.     

Estimates of the size of the particles in the rings of saturn and their cosmogonic implications

Very low values of the radio brightness temperature of the rings of Saturn indicate that their high refar reflectivity is not simply due to a gain effect in the backscattering direction. These two sets of observations are consistent with the ring particles having a very high single scattering albedo at radio wavelenghts, with multiple scattering effects being important. Comparison of scattering calculations for ice and silicate particles with the radio and radar observations imply a mean particle radius of ～1 cm. The ice bands observed in the rings' near-infrared reflectivity spectra are formed by scattering within a microstructure on the surface of the ring particles, with the scattering centers being 25–125 μm in size. The Poynting-Robertson effect has caused a significant spiraling-in of the ring particles, probably resulting in a broadening of the rings. The inferred mean size is consistent with a model in which meteoroid impacts have caused a substantial reduction in the mean particle size from its initial value.     

Characterization of terrestrial exoplanets based on the phase curves and albedos of Mercury, Venus and Mars

The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.     

Characteristics of Light Scattering at Small Phase Angles by Surfaces Consisting of Spherical Particles

We present the results of measurements of the phase dependences of brightness and of the polarization and depolarization characteristics for surfaces consisting of spherical glass particles in the phase-angle range from 0.1° to 5.0°. The measurements are performed using the laboratory photometer/polarimeter of Kharkov Astronomical Observatory and the photometer of Jet Propulsion Laboratory. An optically thick layer of transparent-glass spheres with mean size of about 57 m and refractive index of 1.44 exhibits a strong opposition effect due to single scattering. The contribution of interparticle scattering is nearly independent of the phase angle. At an angle of 0.4°, the spheres exhibit a glory ring that manifests itself in the phase behavior of all characteristics investigated. Small details are seen on the curves when a monochromatic radiation source is used for measurements. Their occurrence is confirmed by calculations based on the Mie theory. The unusual behavior of the phase dependences of reflectivity, degree of polarization, and color index for layers composed of spherical particles can be used to search for sites of possible deposits of spherical glass (or ice) particles in regoliths of atmosphereless celestial bodies.