Michael J. Price

Mars: Clearing of the 1971 dust storm

Abstract A semiquantitative analysis of clearing in the 1971 great dust storm on Mars is presented as a function of time and altitude, using Mariner 9 orange- and visual-light photos. Steady settling of dust approximately accounts for the decline of the storm after December 22, 1971. Continuous settling cannot be invoked prior to that date; injection of dust into the atmosphere, i.e., a storm resurgence, occurred in mid-December 1971. Theoretical models of optical depth versus time are developed for various distributions of particles in the atmosphere. By intespreting settling in terms of Stokes law, estimates of the maximum radii of dust particles throughout the atmosphere have been obtained. Models which best account for the dust-storm decline indicate particles ⪷ 5μm in diameter high in the atmosphere, with a concentration of larger particles (⪷ 10μm) near the ground in the lowest parts of Mars. Long-term thin high hazes should persist through much of the Martian year, perhaps clearing before perihelion.

Optical scattering properties of Saturn's ring. II

Abstract Further analysis of visual (V) wavelength photometric function data for Saturns ring is presented. Evidence indicating both that primary scattering dominates, and that mutual shadowing is an irrelevant concept, is reviewed. Simple anisotropic scattering radiative transfer models are used to define the probable ranges in the single scattering albedo, and in the general shape of the scattering phase function of the individual particles. Limitations on the mean perpendicular optical thickness of the ring are also obtained. Results indicate that the ring particles are highly efficient back-scatterers of visual radiation. Macroscopic particles account for the basic shape of the scattering phase function. Based on an infinite optical thickness for the ring, a minimum single scattering albedo ≈0.75 is found. Use of conservative scattering leads to a minimum optical thickness ≈0.7. The analysis is consistent with the ring particles being centimeter-size pieces of ice.

Limb brightening on Uranus: An interpretation of the λ7300 Å methane band

Abstract Measurements of limb brightening on the Uranus disk within the λ7300 A CH 4 band are interpreted using an elementary inhomogeneous radiative transfer model to describe the atmosphere. A two layer model which consists of a finite, optically thin, region of conservatively scattering particles overlying a semi-infinite clear H 2 ue5f8CH 4 atmosphere satisfactorily explains the observations. The maximum optical thickness of the upper layer appears to lie in the range 0.1 to 0.2. The CH 4 /H 2 mixing ratio in the lower layer is larger than the corresponding solar value by a factor on the order of three or greater. The results are discussed briefly in terms of current models of the Uranus atmosphere.

Saturn: UBV photoelectric pinhole scans of the disk

Abstract UBV pinhole scans of the Saturn disk have been made with a photoelectric area-scanning photometer. Limb profiles, spaced parallel to the equator, were obtained over the entire southern hemisphere of the planet. Saturn was found to exhibit strong limb brightening in the ultraviolet, moderate limb brightening at blue wavelengths, and strong limb darkening in the visual region of the spectrum. Latitudinal variations in the disk profiles were found. In general, the degree of limb brightening decreases towards the polar region. Pronounced asymmetry is apparent in the disk profiles in each color. The sunward limb is significantly brighter than the opposite limb. This asymmetry depends on phase angle; approaching zero at opposition, it reaches a maximum near quadrature. Our observations are interpreted using an elementary radiative transfer model. The Saturn atmosphere is approximated by a finite homogeneous layer of isotropically scattering particles overlying a Lambert scattering haze or cloud layer. The reflectivity of the haze or clouds is a strongly dependent function of wavelength. Our best-fitting model consists of a clear H 2 layer of column density ∼31 km-am above the haze or clouds; the maximum permitted H 2 column density is ∼46 km-am. The H 2 column density above the equatorial region appears to be less than at temperate latitudes. The phase-dependent asymmetry in the disk profiles is a natural consequence of the scattering geometry. Our results are consistent with current knowledge of the Saturn atmosphere.

Illumination of Saturn's ring by the ball. I. Preliminary results

Abstract Indirect solar illumination of Saturns ring via scattering from the ball of the planet provides a new ground-based observational technique for studying the single scattering albedo and phase function of the individual particles. Information concerning optical thickness may also be obtained. Essentially complete phase angle coverage can be achieved by studying the variation with azimuth of the indirect contribution to the surface brightness of the ring. Initial application of the technique is reported. The indirect contribution to the radiation scattered from the ring has been marginally detected by electronographic areal photometry. The results have been interpreted using simple scattering models. The photometric accuracy was insufficient to permit investigation of departures from isotropic scattering. But high single scattering albedos, and an essentially opaque ring, are indicated.

The scattering mean free path in the Uranian atmosphere

New measurements of the equivalent widths of the 4-0 S(0) and S(1) H2 quadrupole lines in the Uranian spectrum have been obtained using high dispersion (4.12 A/mm) image-tube spectrography. The measured equivalent widths are 62 ± 19mA and 58 ± 13 mA for the S(0) and S(1) lines, respectively. Curve-of-growth analysis in terms of a reflecting layer model yields an H2 column-density of 780−330+940km amagat and a temperature of 78−24+80°K. Interpretation using a semi-infinite, homogeneous, isotropically scattering model for line formation yields a scattering mean free path at λ6400 A of 550 ± 250 km amagat. Quoted errors for both the H2 column-density and the scattering mean free path include the effect of uncertainty in the choice of atmospheric temperature. The results are discussed in terms of current models for the Uranian atmosphere.

Infrared thermal models for Saturn's ring

Abstract Infrared (10 and 20 μm) thermal emission data for Saturns rings are discussed in terms of simple isothermal radiative transfer models of finite optical thickness. Recent brightness temperature measurements, corresponding to essentially maximum ring tilt, indicate that optical single scattering albedos less than 0.75 are required to provide sufficient heating of the ring material. Reconciliation with analyses of the optical scattering properties of the ring requires the back-scattering efficiency to be even higher than for a macroscopic sphere. Historical brightness temperature measurements are used to show that no unique isothermal ring model exists. Instead, a temperature gradient perpendicular to the ring plane appears to be present.

Saturn's rings and Pioneer 11

Abstract Quantitative predictions of the diffuse reflection and transmission properties of Saturns rings, relevant to the September 1979 Pioneer 11 flyby, are presented. Predictions are based on an elementary anisotropic scattering model. Interparticle separations are considered to be sufficiently large that mutual shadowing is negligible. Likely ranges in both the single scattering albedo and perpendicular optical thickness of the ring are considered. Situations of pronounced back-scattering and of isotropic scattering are treated individually. Spacecraft measurement of the radiation suffering diffuse scattering by the ring can provide a useful test of the basic ring model.

Anisotropic optical scattering within Saturn's rings

Abstract Visual photometric function data for Saturns rings are analyzed in terms of elementary anisotropic scattering radiative transfer models which involve the Henyey-Greenstein function. Limits are placed on the combinations of single scattering albedo and backscattering directivity which are permitted by observation. Particles with both microscopic and macrscopic lunar-like scattering properties are excluded by the analysis. Results are consistent with the ring particles being nearly pure spherical conglomerates of H 2 O frost.