Phase curves of materials of Io: Interpretation in terms of Hapke's function

The photometric function developed by B. Hapke (1981,J. Geophys. Res.86, 3039–3054; 1984, Icarus59, 41–59) has been applied to near-opposition (α = 2–8°) disk-resolved phase curves for three color classes on Io, and the disk-integrated phase curve (α = 2–159°) of the satellite as a whole. Derived values of the Hapke compaction parameter h suggest that (1) a large percentage of the material on Io's surface has a porosity significantly greater significantly greater than 60%, supporting the estimate of high porosity made by D.L. Matson and D.B. Nash (1983,J. Geophys. Res.88, 4771–4783) and Nelson et al. (1984, Bull. Amer. Astron. Soc.16, 683–685; 1984,EOS65, 982–983); and (2) Average (“orange”) and Polar (“brown”) materials are significantly more porous than Bright (“white”) materials, a cottrast consistent with the Matson and Nash (1983) SO₂ cold trap model. The best-fit single particle phase function becomes more backscattering on moving from Polar to Average to Bright materials, with the surface of Io on average exhibiting significant backscattering comparable in magnitude to that of the lunar surface. For the color classes, and for Io as a whole, the degree of backscattering tends to increase toward longer wavelengths. The average macroscopic roughness of the Ionian surface, characterized by a mean slope angle of Ø ≃ 25°, is similar to that of other solid surface in the solar system. Consistency between observed limb darkening and that predicted by the Hapke model requires the presence of significant macroscopic roughness (Ø ≥ 20°) for the Average regions, but not necessarily for the Bright and Polar materials.     

Visible spectral reflectance measurements (0.33–1.1 μm) of the Galilean satellites at many orbital phase angles

One hundred eighty-seven reflectance spectra (0.33–1.10 μm) of the Galilean satellites have been obtained. Solar phase angle color correction coefficients were derived and the spectra corrected to a solar phase of 6°. Solar phase angle coefficients beyond 0.55 μm are presented for the first time. The spectra as a function of orbital phase angle are presented in the form of images to display hemispheric spectral variations. Io and Europa are redder on their trailing hemispheres while Callisto is redder on its leading hemisphere. Ganymede shows small longitudinal color variations despite the complex albedo structure visible in Voyager images. Comparisons of these data with previous measurements reveal that most differences can be attributed to the solar calibration. Reflectance measurements of Io at 0.73 μm observed 8.5 years apart show a 6% global reflectance decrease. However, it is difficult to unambigously attribute this particular decrease in reflectance to a change in Io's surface composition.     

Hyperion: Analysis of Voyager observations

A total of 82 images of Hyperion was returned by the Voyager spacecraft; the most detailed views have a nominal resolution of 8.7 km/line pair. Hyperion had a rotation period of about 13 days and a spin vector lying close to its orbital plane at the time of the Voyager 2 encounter in 1981. The satellite's shape is very irregular, and cannot be approximated suitably by an ellipsoid. The largest cross section (A × C) is about 370 × 225 km; the B × C cross section is approximately 280 × 225 km. Most prominent among the surface features is a 120-km-diameter crater with an estimated depth of 10 km, and a series of arcuate scarps 300 km long that have relief in excess of 5 km. The density of large craters of Hyperion is smaller than that on other small Saturnian satellites and suggests the possibility that the last significant fragmentation of Hyperion occurred near the end of or after initial heavy bombardment. Voyager photometry yields an average normal reflectance of the surface material of 0.21 in the clear filter (0.47 μm) and evidence of slight albedo mottling over the surface. The disk-integrated phase coefficient between phase angles of 22° and 82° is 0.018 mag/de; there is little indication of a strong opposition effect in Voyager data down to phase angles of 3°. Hyperion's average color is definitely redder than that of Phobe, but matches that of the dark material on the leading hemisphere of Iapetus quite well. The satellite's albedo and color are consistent with those of contaminated water ice but since no mass determinations of Hyperion exist we do not know whether the bulk composition is icy or rocky.     

Voyager photometry of Rhea,Dione, Tethys,Enceladus and Mimas

Voyager imaging observations provide new photometric data on Saturn's satellites at large phase angles (up to 133° in the case of Mimas) not observable from Earth. Significant new results include the determination of phase integrals ranging from 0.7 in the case of Rhea to 0.9 for Enceladus. For Enceladus we find an average geometric albedo p_v = 1.04 ± 0.15 and Bond albedo of 0.9 ± 0.1. The data indicate an orbital lightcurve with an amplitude of 0.2 mag, the trailing side being the brighter. For Mimas, the lightcurve amplitude is probably less than 0.1 mag. The value of the geometric albedo of Mimas reported here, p_v = 0.77 ± 0.15 (corresponding to a mean opposition magnitude V₀ = +12.5) is definitely higher than the currently accepted value of about 0.5. For Dione, the Voyager data show a well-defined orbital lightcurve of amplitude about 0.6 mag, with the leading hemisphere brighter than the trailing one.     

Albedo distribution on Io's surface

A visual albedo distribution model for all hemispheres of Io's surface has been synthesized from available Earth-based and spacecraft image and photometric data. The resulting model indicates some interesting patterns and symmetries on Io's surface: The dark polar caps are shifted off Io's rotational axis and are eliptical rather than circular in shape, with extensions toward the sub-Jupiter and anti-Jupiter points on Io; equatorial bright areas are located approximately on a great circle about Io, the plane of which is tilted approximately 15° toward Io longitude 60°. These and other indicated features may be clues to understanding the endogenic and exogenic processes that have resulted in Io's present observed surface characteristics.     

Voyager photometry of Europa

Ninety voyager images ranging in phase angle from 3 to 143° and covering the spectral range from 0.34 to 0.58 μm were analyzed to derive the photometric properties of Europa. At small phase angles the disk-integrated phase curve is remarkable in that it shows little or no evidence of an opposition effect (in agreement with earlier Earth-based observations by Millis and Thompson, Icarus26, 408, 1975). The phase integral determined in the Voyager clear filter (centered near 0.47 μm) is 1.09 ± 0.11, in good agreement with previous estimates based on radiometry. The bolometric Bond albedo is 0.62 ± 0.14. The scattering properties of Europa in general, and of the two major terrain types (bright plains and darker mottled terrain) in particular, cannot be represented by a lunar-like photometric law. However, an equation which is a linear superposition of a lunar-like scattering law and a Lambert component provides an adequate simple representation of the scattering properties. The plains are photometrically more homogeneous than the darker mottled terrain. In the Voyager clear filter, the average normal reflectance is 0.71 for the plains on both the leading and trailing hemispheres; for the darker mottled terrain the values are 0.60 on the leading hemisphere, and 0.48 on the trailing one.     

Amalthea: Implications of the temperature observed by Voyager

Voyager 1 IRIS observations of Amalthea, although initially indicating an unusually high temperature, now give a temperature of only 164 ± 5°K, a value consistent with the Earth-based measurement by G. H. Rieke [Icarus25, 333–334 (1975)] of 155 ± 15°K. We numerically modeled the temperature profile in the satellite's surface layer as a function of location and time of day, assuming a triaxial ellipsoid shape and thermal properties similar to those of the lunar soil. The major heat source is direct insolation, but temperatures are increased slightly by thermal radiation from Jupiter (?9°K), by sunlight reflected from the planet (?5°K), and by charged particle bombardment (?2°K). Maximum calculated temperatures reach 166°K, and we estimate that the temperature that Voyager would have measured under these circumstances is ≈160°K, in agreement with the observed temperature. Possible sources of error in the model are discussed in detail, including satellite shape effects, unusually low emissivity, uncommonly rough surface, abnormal thermal intertia, variability of the charged particle flux, and Joule heating. The IRIS observation strongly suggests that (i) the Amalthean surface has an emissivity near unity; (ii) the charged particle flux on the satellite at the time of observation was no more than 20 times larger than the flux indicated by Pioneer observations; and (iii) Joule heating of the satellite is insignificant (a conclusion also supported by rough calculations). The IRIS observation cannot, however, put any useful limits on the thermal inertia of the Amalthean surface layer.     

Color photometry of surface features on Ganymede and Callisto

Voyager imaging data demonstrate that the scattering properties (“phase curves”) of all major terrain types on Ganymede and callisto are not significantly wavelength dependent between 0.4 and 0.6 μm. Our data suggest that the phase curves may be slightly steeper at the shorter wavelengths, consistent with the trend of telescopic observations near opposition. However, the differences are small and entirely within the uncertainties of our analysis. Our result indicates that the phase integrals (0.8 for Ganymede and 0.6 for Callisto) derived by S. W. Squyres and J. Veverka [Icarus46, 137–155 (1981)] from the abundant Voyager clear filter observations are reliable measures of the radiometric phase integrals. The corresponding values of the Bond albedo turn out to be 0.35 for Ganymede and 0.11 for Callisto.     

Disk-resolved photometry of Io: I. Near-opposition limb darkening

We have determined the Minnaert limb-darkening parameters (B₀, k) for three color classes of regions on Io near opposition (solar phase angle = 4–5°). Bright (“white”) areas show k ≈ 0.6 independent of wavelength. k for Average (“orange”) regions starts slightly below 0.5 in the Voyager ultraviolet filter (≈0.35 μm), rises monotonically toward longer wavelengths, and reaches ≈0.6 in the orange (≈0.59 μm), a trend consistent with the globally averaged results of McEwen and Soderblom (NASA Technical Memorandum 86246, pp. 261–262 (1984)). For Polar (“brown”) materials, k lies in the range 0.6–0.7 in all filters longward of ultraviolet. The Bright and Average regions show significantly smaller limb darkening, and smaller wavelength dependence of k, than laboratory samples of sulfur, a discrepancy that might represent the influence of macroscopic surface roughness. From a study of the relative merits of two different techniques for determining limb darkening parameters, we find that the single-image method, involving a single spacecraft image and the choice of a group of “similar” regions, has serious consistency problems when applied to the multicolored surface of Io. In contrast, an adaptation of the two-image solution of McEwen and Soderblom, involving the use of two or more images and computation of the limb darkening for individual surface regions, gives consistent results for spectrally similar regions. We conclude that the two-image technique is the only way to accurately determine the limb darkening of Ionian surface materials.     

A low resolution map of Europa from four occultations by Io

Analysis of three occultations of JII (Europa) by JI (Io) has resulted in a preliminary reflectivity map of JII for the hemisphere centered on longitude 324°, a measurement of 1483±20 km for the radius of JII, estimates of the event impact parameters, determination of the mid event times, and a visual geometric albedo, p_ν = 0.74, for JII. A fourth occultation light curve was used after derivation of the results to confirm their validity.     

Photometry and polarimetry of Titan: Pioneer 11 observations and their implications for aerosol properties

The preliminary measurements by Pioneer 11 of the limb darkening and polarization of Titan at red and blue wavelenghts (M. G. Tomasko, 1980,J. Geophys. Res., 85, 5937–5942) are refined and the measurements of the brightness of the integrated disk at phase angles from 22 to 96° are reduced. At 28° phase, Titan's reflectivity in blue light at southern latitudes is as much as 25% greater than that at northern latitudes, comparable to the values observed by Voyager 1 (L. A. Sromovsky et al., 1981,Nature (London), 292, 698–702). In red light the reflectivity is constant to within a few percent for latitudes between 40°S and 60°N. Titan's phase coefficient between 22 and 96° phase angle averages about 0.014 magnitudes/degree in both colors—a value considerably greater than that observed at smaller phase from the Earth. Comparisons of the data with vertically homogeneous multiple-scattering models indicate that the single-scattering phase functions of the aerosols in both colors are rather flat at scattering angles between 80 and 150° with a small peak at larger scattering (i.e., small phase) angles. The models indicate that the phase integral, q, for Titan in both red and blue light is about 1.66 ± 0.1. Together with Younkin's value for the bolometric geometric albedo scaled to a radius of 2825 km, this implies an effective temperature in equilibrium with sunlight of 84 ± 2°K, in agreement with recent thermal measurements. The single-scattering polarizations produced by the particles at 90° scattering angle are quite large, >85% in blue light and >95% in red. A vertically homogeneous model in which the particles are assumed to scatter as spheres cannot simultaneously match the polarization observations in both colors for any refractive index. However, the observed polarizations are most sensitive to the particle properties near optical depth $\text{1}\text{2}$ in each color, and so models based on single scattering by spheres can be successful over a range of refractive indices if the size of the particles increases with depth and if the cross section of the particles increases sufficiently rapidly with decreasing wavelenght. For example, with n_r = 1.70, the polarization (and the photometry) are reproduced reasonably well in both colors when the area-weighted average radous of the particles, α, is given by α = (0.117 μm)(τ_red/0.5)^0.217. While this model does not reproduce the large increase in brightness from 129 to 160° phase observed by Voyager 1, the observed increase is determined by the properties of the particles in the top few hundredths of an optical depth. Thus the addition of a very thin layer of forward-scattering aerosols on top of the above model offers one way of satisfying both the Pioneer 11 and Voyager 1 observations. Of course, other models, using bimodal size distributions or scattering by nonspherical particles, may also be capable of reproducing these data.     

Four-color photometry of the Galilean satellites

Photometry obtained in 1973 on the uvby system yields high-precision rotational light curves for Io, Europa, and Ganymede at a mean phase angle of ～6°. By combining our observations with photometry obtained by others over a broader range of phase angle, we alsi derive improved values for the phase coefficients and opposition surges of the four Galilean satellites. The values of V(1, 0) obtained by linear extrapolation to zero phase are accurate to ±0.03 magnitudes. We also derive the colors of the sun of the uvby system and use these to obtain albedos of the satellites in four colors.     

Saturn's rings: 3-mm low-inclination observations and derived properties

Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r^?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material.     

The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data

A procedure of an a posteriori correction of the available data on the integral photometry of the Moon is described. This procedure reduces the regular errors of the integral phase curves caused by variations of the libration parameters; the effect due to libration can reach 4%. A method allowing the integral measurements of the Moon to be compared correctly with the photometric measurements of the lunar areas or laboratory samples imitating the lunar soil has been developed. To approximate the phase curves of integral albedo in the phase-angle range from 6° to 120°, we proposed a simple empirical formula A _eq(α) = m _l e ^?ρα + m ₂ e ^?0.7α, where α is the phase angle, ρ is the factor of effective roughness, and m ₁ + m ₂ is the surface albedo at a zero phase angle. An empirical phase dependence of the slope of the lunar spectrum in the 360–1060 nm range has been obtained. The results may be used to test various theoretical models of the light scattering by the lunar surface and to calibrate the data of ground-based and space-borne spectrophotometric observations.     

The infrared photometric function of Mars and its bolometric albedo

The photometric properties of local areas on Mars are studied using Minnaert's rule of surface scattering to analyze Mariner 6 and 7 Infrared Spectrometer data. Several bright deserts, Hellas, and the south polar cap are found to obey Minnaert's function well. The coefficients B₀(α, λ) and k(α, λ) are obtained at α = 39, 48, 56, 84° and λ = 1.85, 2.23, 3.50 μm. Observed bright regions all have similar values of k, except for Hellas and the south polar cap. The lower k of Hellas is apparently caused by microscopic effects rather than by large-scale roughness due to cratering. The higher k of the cap is similar to terrestrial snows in the visual at the same phase angle. Using existing Earth-based observations, at smaller α and λ, a bolometric Bond albedo of $\text{A}{}^1\text{= 0.24 ± 0.05}$ is calculated.     

Sulfur flows of Ra Patera,Io

Voyager 1 imaging data have been used to investigate the color and morphology of several radial flow-like features at Ra Patera, a broad volcanic structure at approximately 8° latitude and 325° longitude on the Galilean satellite Io (J1). It was found that downstream progressions of flow color and morphology are consistent with lava of a predominately sulfur composition cooling radiatively and erupting in the range of 470 to 520°K at effusion rates at 10¹⁰ to 10¹¹ cm³/sec. This implies global resurfacing rates by volcanic flows on Io of the order of 1 cm/year. Calculated energy content and effusion rates for flows at Ra Patera, using the physical parameters of sulfur, are of the order of the largest known terrestial basaltic eruptions and are consistent with calculations of globally available energy.     

Theoretical interpretation of the ground-based photometry of Saturn's B ring

New photographic photometry at small tilt angles during the 1979 and 1981 apparitions is combined with earlier data to yield several physical parameters for Saturn's B ring in red and blue colors. Phase curves are obtained for a mean tilt angle B ? 6°. The value of the volume density D is 0.020±0.004 with no indication of dependence on either the color or the tilt angle for 6°<B<26°. This conclusion is not altered significantly if the individual ring particles have a phase function similar to the phase curves of bright solar system objects. For the geometric albedo of a single particle we derive 0.61±0.04 (red) and 0.41±0.03 (blue), which are superior to earlier estimates because of the additional data now available. These values and the derived amount of multiple scattering as a function of tilt angle constrain the particle phase function in the red to be moderately backscattering. Inferred values of the particle single-scattering albedo are $\text{0.7≤}\text{ω}{}_0\text{(}\text{red}\text{) ≤0.92}$ and $\text{0.5≤}\text{ω}{}_0\text{(}\text{blue}\text{) ≤0.7}$, depending on the choice of phase function. No indication was found that the particle photometric properties might depend on the vertical distance from the central plane. Our results show that the ground-based photometry is entirely consistent with the classical, many-particle-thick ring model.     

Spectral reflectance change and luminescence of selected salts during 2–10 KeV proton bombardment: Implications for Io

Radiation damage and luminescence, caused by magnetospheric charged particles, have been suggested by several authors as mechanisms for explaining some of the peculiar spectral/albedo features of Io. We have pursued this possibility by measuring the uv-visual spectral reflectance and luminescent efficiency of several proposed Io surface constituents during 2 to 10-keV proton irradiation at room temperature and at low temperature (120 < T < 140°K). The spectral reflectance of NaCl and KCl during proton irradiation exhibits the well-known F-center absorption bands at 4580 and 5560 Å. Na₂SO₄ shows a generalized darkening which increases toward longer wavelengths. NaNO₃ shows a spectral reflectance change indicative of the partial alteration of NaNo₃ to NaNo₂. NaNO₂ shows no change. The luminescent efficiencies of NaCl and KCl are ～10^?4 at 300°K and increase by one-half order of magnitude at ～130°K. The efficiencies of K₂CO₃, Na₂CO₃, Na₂SO₄, and NaNO₃ are 10^?4, 10^?4, 10^?5 and 10^?6, respectively, at 300°K and they all decrease by one-half order of magnitude at ～130°K. These results indicate that magnetospheric proton irradiation of Io could cause spectral features in its observed ultraviolet and visible reflection spectrum if salts such as those studied here are present on its surface. However, because the magnitude of these spectral effects is dependent on competing factors such as surface temperature, incident particle energy flux, solar bleaching effects, and trace element abundance, we are unable at this time to make a quantitative estimate of the strength of these spectral effects on Io. The luminescent efficiencies of pure samples that we have studied in the laboratory suggest that charged-particle induced luminescence from Io's surface might be observable by a spacecraft such as Voyager when viewing Io's dark side.     

The opposition surge of Enceladus: HST observations 338-1022 nm

Hubble Space Telescope (HST) Wide-Field Planetary Camera (WFPC2) observations at phase angles in the range α=0.26°-6.4° obtained at every opposition and near quadrature between October 1996 and December 2002 reveal the opposition effect of Enceladus. We present a photometric analysis of nearly 200 images obtained through the five broadband UVBRI filters (F336W, F439W, F555W, F675W, and F814W) and the F785LP and F1042M filters from which we generate mutually consistent solar and rotational phase curves. Our solar phase curves reveal a dramatic, sharp increase in the albedo (from 0.11 mag in the F675W filter to 0.17 mag in the F785LP filter) as phase angles decrease from 2° to 0.26°. A slight opposition effect is evident in data from the F1042M filter (λ_eff=1022 nm); however, the smallest phase angle currently available for observations from this filter is α=0.58°. With the addition of data from the F255W filter we demonstrate the wavelength dependence of the albedo of the trailing hemisphere from 275 to 1022 nm. Our rotation curves show that the trailing hemisphere is ∼0.06 mag brighter than the leading when observed at wavelengths between 338 and 868 nm and 0.11 mag brighter than the leading at 1022 nm. We have supplemented the phase curve from the F439W filter (λ_eff=434 nm) with Voyager clear filter (λ_eff=480 nm) observations made at larger phase angles (α=13°-43°) to produce a phase curve with the most extensive phase angle coverage possible to date. This newly expanded range of phase angles enhances the ability of the Hapke photometric model (Hapke B., 2002, Icarus 157, 523-534) to relate physical characteristics of the surface of Enceladus to the manner in which incident light is reflected from it. We present Hapke 2002 model fits to solar phase curves from each UVBRI filter as well as from the F785LP and F1042M filters. Geometric albedos derived from these model fits range from p=0.92±0.01 at 1022 nm to p=1.41±0.03 at 549 nm, necessitating an increase of about 20% from previously derived values. Our Hapke fits demonstrate that the opposition surge of Enceladus is best described by a model which combines both moderate shadow-hiding and narrow coherent backscattering components.     

The photometric functions of Phobos and Deimos I. Disc-integrated photometry

We have used the integrated brightnesses from Mariner 9 high-resolution images to determine the large phase angle (20° to 80°) phase curves of Phobos and Deimos. The derived phase coefficients are β = 0.032 ± 0.001 mag/deg for Phobos and β = 0.030 ± 0.001 mag/deg for Deimos, while the corresponding phase integrals are q_Phobos = 0.52 and q_Deimos = 0.57. The predicted intrinsic phase coefficients of the surface material are β_i = 0.019 mag/deg and β_i = 0.017 mag/deg for Phobos and Deimos, respectively. The phase curves, phase coefficients and phase integrals are typical of objects whose surface layers are dark and intricate in texture, and are consistent with the presence of a regolith on both satellites. The relative reflectance of Deimos to Phobos is 1.15±0.10. The presence of several bright patches on Deimos could account for this slight difference in average reflectance.