Circular polarization of sunlight reflected by planetary atmospheres

Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined.     

Photometry of Venus: II. Theoretical brightness distribution over the disk

Theoretical brightness distributions over the Venus disk have been computed for homogeneous and multilayered cloud models. With homogeneous models, the relative brightness does not depend very much on the optical properties of the cloud, except near the limb or for small phase angles. For multilayered cloud structures, the relative brightness is nearly fixed by the structures and the relative brightness is nearly fixed by the scattering function of the uppermost cloud; the vertical distribution of the absorption is unimportant if the spherical albedo of the planet is given. If the horizontal inhomogeneities currently seen on Venus are due to a layered structure, with an optical thickness of the upper cloud varying from point to point, large simplifications seem possible, and measured contrasts at various wavelengths should permit a test of such a model.     

Polarization Models for Rayleigh Scattering Planetary Atmospheres

We present Monte Carlo simulations for the polarization of light reflected from planetary atmospheres. We investigate dependencies of intensity and polarization on three main parameters: single scattering albedo, optical depth of a scattering layer, and albedo of a Lambert surface underneath. The main scattering process considered is Rayleigh scattering, but isotropic scattering and enhanced forward scattering on haze particles are also investigated. We discuss disk integrated results for all phase angles and radial profiles of the limb polarization at opposition. These results are useful to interpret available limb polarization measurements of solar system planets and to predict the polarization of extra-solar planets as a preparation for VLT/SPHERE. Most favorable for a detection are planets with an optically thick Rayleigh-scattering layer. The limb polarization of Uranus and Neptune is especially sensitive to the vertically stratified methane mixing ratio. From limb polarization measurements constraints on the polarization at large phase angles can be set.     

Intensity and polarization line profiles in a semi-infinite Rayleigh-scattering planetary atmosphere. I. Integrated flux

Absorption and polarization line profiles as well as the curves of growth in the integrated light of a planet over the whole range of phase angles have been computed assuming a semi-infinite atmosphere scattering according to Rayleigh’s phase-matrix which takes polarization into account. The relative change in line depth and equivalent widths qualitatively agree with the observations of the CO₂ bands in Venus reported by Young, Schorn and Young (1980). It is pointed out that the bands might be formed in a part of the atmosphere which is different from that where continuum polarization originates.     

Magnetic fields of mars and venus: Solar wind interactions

Recent U.S.S.R. studies of the magnetic field and solar wind flow in the vicinity of Mars and Venus confirm earlier U.S.A. reports of a bow shock wave developed as the solar wind interacts with these planets. Mars 2 and 3 magnetometer experiments report the existence of an intrinsic planetary magnetic field, sufficiently strong to form a magnetopause, deflecting the solar wind around the planet and its ionosphere. This is in contrast to the case for Venus, where it is assumed to be the ionosphere and processes therein which are responsible for the solar wind deflection. An empirical relationship appears to exist between planetary dipole magnetic moments and their angular momentum for Moon, Mars, Venus, Earth and Jupiter. Implications for the magnetic fields of Mercury and Saturn are discussed.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973     

Venus phase function and forward scattering from H2SO4

Ground-based and spacecraft photometry covering phase angles from 2° to 179° has been acquired in wavelength bands from blue to near infrared. An unexpected brightness surge is seen in the B and V bands when the disk of Venus is less than 2% illuminated. This excess luminosity appears to be the result of forward scattering from droplets of H₂SO₄ (sulfuric acid) in the high atmosphere of Venus. The fully sunlit brightness of Venus, adjusted to a distance of one AU from the Sun and observer, was found to be V=−4.38, and the corresponding geometric albedo is 67%. The phase integral is 1.35 and the resulting spherical albedo is 90%. Comparison between our data and photometry obtained over the past 50 years indicates a bias in the older photoelectric results, however atmospheric abundance variations suggest that brightness changes may have occurred too.     

Absorption line studies of reflection from horizontally inhomogeneous layers

A discussion of literature relevant to horizontal inhomogeneities in planetary atmospheres shows this to be an increasingly important yet largely unexplored topic. Section II details an inhomogeneous reflecting layer (IRFL) model designed to survey absorption line behavior from a Squires-like cloud cover (which is characterized by convection cell structure). Computational problems and procedures are discussed in detail, with results presented for center to limb equivalent width variations at phase angles α = 0° and 90°, followed by equivalent width variations as a function of phase angle for specific points across the planetary equator. We examine a range of cloud and gas configurations, of line and continuum opacities, and we compare phase variations of bright versus dark limbs.The results in general show trends quite dissimilar to (usually opposite) those predicted by a simple reflecting layer model. Percent equivalent width variations for the tower model are usually somewhat greater for weak than for relatively strong absorption lines, with differences of a factor of about two or three. Also, IRFL equivalent width variations do not differ drastically as a function of geometry when the total volume of absorbing gas is held constant. The IRFL results are in many instances consistent with observed equivalent width variations of Jupiter, Saturn, and Venus. Thus, consideration of horizontal inhomogeneities evidently worsens current uniqueness problems. Future more detailed observations will ameliorate this impass if, it is argued, interpretive studies encompass the complexities of realistic horizontal cloud structure.     

Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Is jupiter getting brighter ?

For a given planet there is a critical distance from the Sun when the planet is first or last seen. This is called Jian-Fu-Du (JFD) by ancient Chinese astronomers. TABLE 1 lists the values of JFD for the five planets as given in 33 Chinese calendars between −103 and +1368. The data show that 1) in order of decreasing brightness, we have Venus, Jupiter, Saturn and Mars, while the brightness of Mercury is the same as the last two; 2) the JFD of Jupiter is decreasing in time; and 3) the JFDs of the other four planets are increasing in time. Perhaps changes in the transparency of the Earth's atmosphere and in the brightness of the Sun cause a general increase in JFD. Then the decreasing JFD of Jupiter means that Jupiter is getting brighter in time. A rough estimate for the rate of brightening is 0.003 mag per thousand years.     

Solar wind origin of 36Ar on Venus

A hypothesis is considered in which the ³⁶Ar found on Venus is of solar origin. This possibility is quantitatively discussed within the framework of present theories of planetary accumulation by sweep up of planetesimals under gas-free conditions. Solar wind implantation of ³⁶Ar would take place by irradiation of accumulating material during the first ≈10⁵ years of planetary growth, provided that the flux of solar wind was enhanced by a factor of ≈100 at that time. Enrichment of Venus in implanted gas would be a consequence of the irradiated material being initially confined to the innermost edge of the radially opaque circusolar planetesimal disk predicted by these theories. The observed atmospheric data require a Ne/Ar fractionation by a factor of ≈100 during the planetesimal stage. It is also necessary that there be very little mixing of irradiated planetesimals from the inner edge of disk to the distance (≈1 AU) at which the Earth formed. The hypothesis can be tested by measurement of the abundance of Kr and Xe in the Venus atmosphere. Venera data indicate a terrestrial ³⁶Ar/Kr ratio, in disagreement with the solar wind hypothesis. In contrast, the Pioneer experiments find a lower limit to this ratio, well above the terrestrial value, that is compatible with the hypothesis. These experiments also show that Venus' ³⁶Ar/Xe ratio does not correspond to the so-called “planetary” trapped inert gas composition. The inert of Venus could be related to result of admixture of gas with solar composition. The inert gas on Venus could be related to that found in enstatite chondrites.     

Latitudinal and longitudinal variation of a planetary atmosphere and the occultation experiment

The distribution of neutral and ionized particles about a planet depends, at any time, on angular coordinates (latitude and longitude) as well as altitude. Measurements of the Venusian and Martian atmospheres and ionospheres have been made by means of the ‘occultation’ experiment on-board the Mariner spacecrafts, and the same or similar experiment is planned for future missions to the planets. The conventional method of reducing the residual doppler data assumes spherical symmetry, in which the refractivity of the medium depends only on radius from the center of the planet, or altitude. It is shown that the neglect of angular dependence may introduce serious errors, even for media in which this dependence is slight compared to that in the radial direction, when the plane of motion of the spacecraft about the planet is inclined with respect to the direction of the Earth. The magnitude of the errors may be greatest for a planet such as Mercury and least for Jupiter, if planetary size and atmospheric temperature are the principal factors considered. Mars and Venus being intermediate. These results are most significant for an orbiter in which the orbital plane is inclined to obtain planetary coverage in a matter of months of measurements. Results of calculations for a particular model show that scale height measurements, and, thereby, atmospheric temperature, may be in error by a factor greater than 2 for inclined orbital configurations.     

The effect of surface roughness on the transmission of microwave radiation through a planetary surface

To account for surface roughness, the transmission of microwave radiation through a planetary surface to an observer is treated by a Monte Carlo technique. Sizable effects are found near the limb of the planet, and they should be included in analyses of high-resolution observations and high-precision integrated disk observations.     

Deep radio occultations and “evolute flashes”; their characteristics and utility for planetary studies

Radio occultation studies of the structure of planetary atmospheres have generally involved relatively shallow penetration of the spacecraft behind the limb of the planet in the plane of the sky. Current radio link sensitivities allow detection of the radio signals at all occultation depths, whenever the planet-spacecraft distance is sufficiently large for the refraction to occur at atmospheric heights where microwave absorption is not too large. Voyager 1 at Jupiter and Voyager 2 at Saturn will pass almost directly behind the planets as viewed from the Earth. Thus they will pass through the caustics that corresponds to the focal line of a spherical planet, expanded by oblateness into a surface approximating a four-cusp cylinder. In the plane of the sky, the projection of this surface approximates the evolute of the planet's limb. As the spacecraft passes behind the planet with its antenna tracking the occulting limb, the strength of the radio signals received on Earth will at first decrease due to defocusing in the atmosphere, but then increase as the evolute is approached, because of the focusing caused by limb curvature. Inside the evolute there are four simultaneous signal paths over four limb positions. If we neglect absorption, focused signals for an instant could become orders of magnitude stronger than for the unocculted spacecraft. Measurements of the frequency and intensity of deep occultation signals, and of the timing and character of these “evolute flashes”, could provide information on atmospheric absorption, turbulence, and structure, and on details of the shape of the atmosphere at the focusing limbs as affected, for example, by planetary gravitational moments, rotation, and zonal winds. Such observations will be attempted with Voyager and potentially could be very fruitful in the Pioneer Venus and Galileo (Jupiter) orbiting missions.     

X-rays from solar system objects

During the last few years our knowledge about the X-ray emission from bodies within the solar system has significantly improved. Several new solar system objects are now known to shine in X-rays at energies below 2 keV. Apart from the Sun, the known X-ray emitters now include planets (Venus, Earth, Mars, Jupiter, and Saturn), planetary satellites (Moon, Io, Europa, and Ganymede), all active comets, the Io plasma torus (IPT), the rings of Saturn, the coronae (exospheres) of Earth and Mars, and the heliosphere. The advent of higher-resolution X-ray spectroscopy with the Chandra and XMM-Newton X-ray observatories has been of great benefit in advancing the field of planetary X-ray astronomy. Progress in modeling X-ray emission, laboratory studies of X-ray production, and theoretical calculations of cross-sections, have all contributed to our understanding of processes that produce X-rays from the solar system bodies.At Jupiter and Earth, both auroral and non-auroral disk X-ray emissions have been observed. X-rays have been detected from Saturn's disk, but no convincing evidence of an X-ray aurora has been observed. The first soft (0.1–2 keV) X-ray observation of Earth's aurora by Chandra shows that it is highly variable. The non-auroral X-ray emissions from Jupiter, Saturn, and Earth, those from the disk of Mars, Venus, and Moon, and from the rings of Saturn, are mainly produced by scattering of solar X-rays. The spectral characteristics of X-ray emission from comets, the heliosphere, the geocorona, and the Martian halo are quite similar, but they appear to be quite different from those of Jovian auroral X-rays. X-rays from the Galilean satellites and the IPT are mostly driven by impact of Jovian magnetospheric particles.This paper reviews studies of the soft X-ray emission from the solar system bodies, excluding the Sun. Processes of production of solar system X-rays are discussed and an overview is provided of the main source mechanisms of X-ray production at each object. A brief account on recent development in the area of laboratory studies of X-ray production is also provided.     

Exchange of global mean angular momentum between an atmosphere and its underlying planet

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.     

Optical reflectance polarimetry of Saturn's globe and rings: IV. Aerosols in the upper atmosphere of Saturn

From 1958 to 1976 the degree and direction of polarization of the light at Saturn's disk center were measured in orange light over 74 nights and at five wavelenghts over 19 nights. Measurements were also recorded at limb, terminator, and pole. In addition, extensive regional polarization measurements were collected over Saturn's disk and several polarization maps were produced. These data were analyzed on the basis Mie scattering theory and of transfer theory in planetary atmospheres. A model of the Saturn upper atmosphere aerosol structure is derived in which the top part of the the main cloud layer is composed of spherical transparent particles of radius 1.4 μm and refractive index 1.44. Above this layer, a fine haze of submicron-sized grains was detected by its production of a component of polarization which is always directed poleward; this upper haze is interpreted as having nonspherical particles which are systematically oriented. This upper haze layer covers approximately the whole planet uniformly but varies in thickness from year to year. The clear gas above the cloud layer has an optical thickness of around 0.1.     

Orbital resonances and planetary formation sites

Orbital resonances may have played an important role in determining the locations where the planetesimal swarm eventually accreted into full-size planets. Several pairs of planets do indeed have commensurable orbital periods at present, but the case for control of planet formation by resonances is weakened by the fact that many pairs are not commensurable and that those which are do not necessarily exist at the strongest resonances. However, the mass loss and redistribution that occurred in the early solar system evolution can substantially alter the positions of planets and planetary embryos within the swarm. A cascaded resonance structure is hypothesized where planetesimal growth was accelerated at 2:1 interior and 1:2 exterior resonances with an early-formed Jupiter producing runaway growth of planetary embryos. These embryos produce their own resonances which, in turn, lead to additional embryos in a process that successively propagates inward and outward to generate a resonant configuration of embryos. In this manner, the early presence of Jupiter imposed a harmonic structure on the accumulating planetesimal swarm. For an accretion disk with surface density obeying a power law of index ?1.2 the positions of the planetary embryos can be moved into a reasonably good agreement with most of the present planetary positions that is as good as that given by the Titius-Bode law.     

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.     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.