On the interpretation of the “inverse phase effect” for CO2 equivalent widths on Venus

Computations of the equivalent widths of absorption lines as a function of planetary phase angle are made for a homogeneous cloud with particles having the properties (shape, refractive index, and size distribution) deduced from polarimetry of Venus. The computed equivalent widths show an “inverse phase effect” comparable to that which is observed for CO₂ lines on Venus. This result verifies a recent suggestion of Regas et al. that the existence of an inverse phase effect does not by itself imply the presence of multiple layers of scattering particles in the atmosphere of Venus.     

Scattering in the Atmosphere of Venus. I. Line profiles and curves of growth for isotropic scattering

We have computed line profiles and curves of growth for both reflected and transmitted radiation for typical lines in CO₂ bands (in the photographic infrared) which occur in the spectrum of Venus. In our model the pressure variation with altitude was considered and the base of the cloud deck was set at the 2 bar level. The temperature was held constant at 250K and a Voigt profile was used for the lineshape. We also assumed that the scale height of the cloud particles was equal to the scale height of the gas. The calculations were made for four values of the scattering optical thickness (τ_c = 0.1, 1.0, 10, and 100) using a continuum single scattering albedo $\text{ω}{}_{\mathrm{<mtext>c</mtext>}}\text{= 0.9975}$ (which gives a Bond albedo of 0.896 for τ_c = 100, the value observed for Venus at these wavelengths). Curves of growth are also presented for reflected radiation which has been averaged over the visible disk for three values of the Venus phase angle (0, 86, and 166°).     

Observations of the phase variation of Venus CO2 equivalent widths

We present equivalent widths of Venus CO₂ scans of the P branch (P8–P32) of the 5ν₃ band at 8689 Å, the P16 line of the 5ν₃ band, and the P14 line of the ν₁ + 5ν₃ band at 7820 Å covering phase angles between 5°.1 and 170°. The equivalent widths reach a minimum at 10°, in agreement with a phase function with a backward lobe at 160° which is caused by a single internal reflection within the cloud particles. This is evidence that Venus cloud particles are composed of liquid droplets. Maximum equivalent widths are observed at ～60°, a value which is closer to the maximum of single-layer Mie scattering models than to that of two-layer models. At high phase angles we observe equivalent widths greater than those computed from homogeneous scattering models, indicating that at high altitudes the mixing ratio of scattering particles to CO₂ increases with depth. At all phase angles, particularly at large phase angles, the temporal and spatial variations in the observed equivalent widths confuse the phase variation.     

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.     

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.     

Theoretical interpretation of the 0.7820 μm CO2 band and 0.8226 μm H2O line on Venus

We have analyzed the P6, P8, and P10 lines in the 0.7820 μm CO₂ band of Venus using a scattering model. Our new results compare favorably with previous results from the 1.05 μm CO₂ band. We considered nonabsorbing and absorbing clouds. We found that the anisotropic scattering mean free path for both models at the 0.2atm level is between 0.55 and 0.73km, a range close to the value of 1 km for terrestrial hazes. We used our scattering models to synthesize the 0.8226 μm H₂O line, assuming that the clouds are composed of sulfuric acid drops, and found our nonabsorbing cloud required a sulfuric acid concentration of 82% by weight, while our thicker absorbing cloud required a concentration of 89%. A comparison of the variation of optical depth with height for our cloud models with the variation reported by Prinn (1973, Science182, 1132–1134) showed that, within a factor of 2, the variation for Prinn's thinnest cloud agreed with ours. Whitehill and Hansen (1973, Icarus20, 146–152) have recently confirmed the work of Regas et al. (1973a, J. Quant. Spectry. Radiative Transfer13, 461–463) which showed that two cloud layers are not required to explain the CO₂ phase variation of Venus. Prinn's recent photochemical study of sulfuric acid clouds further supports a single, continuous cloud layer in the line formation region instead of two cloud layers with an extensive clear region between. The single layer model appears more likely because the maximum particle density in Prinn's cloud occurs in the clear region between the two layers in the models of Hunt (1972, J. Quant. Spectry. Radiative Transfer12, 405–419) and Carleton and Traub (1972, Bull. Amer. Astron. Soc.4, 362.).     

Scattering in the atmosphere of Venus: II. Effect of varying the scale height of the scattering particles

We have made calculations for the variation of equivalent width with phase angle (for a Venus-like atmosphere except that the cloud particles scatter isotropically). The effect of temperature variations, within our model atmosphere, is shown to be small. The effect of changing the scale height of the cloud relative to the scale height of the gas is much larger.     

Monte Carlo Radiative Transfer Modeling of Lightning Observed in Galileo Images of Jupiter

We study lightning on Jupiter and the clouds illuminated by the lightning using images taken by the Galileo orbiter. The Galileo images have a resolution of ∼25 km/pixel and are able to resolve the shape of single lightning spots, which have half widths (radii) at half the maximum intensity in the range 45-80 km. We compare the shape and width of lightning flashes in the images with simulated flashes produced by our 3D Monte Carlo light-scattering model.The model calculates Monte Carlo scattering of photons in a 3D opacity distribution. During each scattering event, light is partially absorbed. The new direction of the photon after scattering is chosen according to a Henyey-Greenstein phase function. An image from each direction is produced by accumulating photons emerging from the cloud in a small range (bins) of emission angles. The light source is modeled either as a point or a vertical line.A plane-parallel cloud layer does not always fit the data. In some cases the cloud over the light source appears to resemble cumulus clouds on Earth. Lightning is estimated to occur at least as deep as the bottom of the expected water cloud. For the six flashes studied, we find that the clouds above the lightning are optically thick (τ>5). Jovian flashes are more regular and circular than the largest terrestrial flashes observed from space. On Jupiter there is nothing equivalent to the 30-40-km horizontal flashes that are seen on Earth.     

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.     

Jupiter: An inhomogeneous atmospheric model analysis of spatial variations of the H2 4-0 S(1) line

An analysis of the structure of the Jovian atmosphere, primarily based on center-to-limb variations (CTLV) of the equivalent width of the hydrogen quadrupole 4-0 S(1) line, is presented. These data require that the atmosphere have regions of both long- and short- scattering mean free paths. Two alternative cloud structures which fit the data are developed. The first is a two-cloud model (TCM) consisting of a thin upper cloud and a lower semi-infinite cloud, with absorbing gas between the clouds and above the upper cloud. The second model is a reflecting-scattering model (RSM), in which a gas layer lies above a haze consisting of scattering particles and absorbing gas. The cloud-scattering phase function in both models must have a strong forward peak. The CTLV data require, however, the presence of a backscattering lobe on the phase function, with the backscattering intensity about 4% of the forward scattering. The decrease in reflectivity of all regions from the visible to the ultraviolet is explained by the presence of dust particles mixed with the gas. Most of the ultraviolet absorption in the atmosphere must occur above the upper cloud layer. Particles with a uniform distribution of radii from 0.0 to 0.1 μm with a complex index of refraction varying as λ^?2.5 are used. The contrast in reflectivity between belts and zones may be explained by the larger concentration of dust in the belts than in the zones. Spatially resolved ultraviolet limb-darkening curves will help to determine the dust distribution of the Jovian atmosphere. The visible methane bands at λλ 6190, 5430, and 4860 Å are analyzed in terms of these models. We derive a methane-to-hydrogen mixing ratio of 2.8 × 10^?3, which is about 4.5 times the value for solar composition.     

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.     

Observable effects of convection and gravity waves on the Venus condensational cloud

We present results of a simple two-dimensional model investigating the observable effects that convective motions and gravity waves can have on the condensational Venus cloud. Gravity waves have been observed in the Venus atmosphere in the form of temperature scintillations in the Magellan and Pioneer Venus occultation data. Multiple in situ probes and long-duration remote observations indicate the presence of convective motions in the Venus clouds. Dynamical studies by others have suggested that gravity waves can exist in the stable regions of the Venus atmosphere above the middle clouds and beneath the middle clouds, and likely are triggered by flow past sub-cloud plumes caused by convective overshooting. We find that a simplified treatment of convective kinematics generates variation in the Venus condensational cloud consistent with the observed variability of optical depth and brightness temperature. Specifically, we find that the downdraft regions in our simulated convective cell exhibit a decrease in cloud optical depth of around Δτ∼10. The brightness temperature ranges from about 460 K in the downdraft regions of the simulated convective cells, to about 400 K in the simulated updrafts. We also find that gravity waves launched by obstacles (such as overshooting convective plumes) near the cloud base exhibit horizontal wavelengths comparable to the separation between convective cells, and generate variations in brightness temperature that should be observable by instruments such as VIRTIS on Venus Express. However, a more robust treatment of the atmospheric dynamics is needed to address adequately these interactions between the clouds and the mesoscale dynamics.     

Photometry and polarimetry of Jupiter at large phase angles: I. Analysis of imaging data of a prominent belt and a zone from pioneer 10

Limb-darkening curves are derived from Pioneer 10 imaging data for Jupiter's STrZ (?18 to ?21° latitude) and SEBn (?5 to ?8° latitude) in red and blue light at phase angles of 12, 23, 34, 109, 120, 127, and 150°. Inhomogeneous scattering models are computed and compared with the data to constrain the vertical structure and the single-scattering phase functions of the belt and the zone in each color. The very high brightness observed at a 150° phase angle seems to require the presence of at lleast a thin layer of reasonably bright and strongly forward-scattering haze particles at pressure levelsof about 100 mbar or less above both belts and zones. Marginally successful models have been constructed in which a moderate optical thickness (τ ≥ 0.5) of haze particles was uniformly distributed in the upper 25 km-amagats of H₂. Excellent fits to the data were obtained with models having a thin (optical depths of a few tenths) haze conentraated above most of the gas. Following recent spectrospcopicanalyses, we have placed the main “cloud” layer or layers beneath about 25 km-amagats of H₂, although successful fits to our continuum data probably could be achieved also if the clouds were permitted to extend all the way up to the thin haze layer. Similarly, below the haze level our data cannot distinguish between models having two clouds separated by a clear space as suggested by R. E. Danielson and M. G. Tomasko and models with a single extensive diffuse cloud having an H₂ abundance of a few kilometer-amagats per scattering mean free path as described by W. D. Cochran. In either case, the relative brightness of the planet at each phase angle primarily serves to constrain the single-scattering phase functions of the Jovian clouds at the corresponding scattering angles. The clouds in these models are characterized by single-scattering phase functions having strong forward peaks and modest backward-scattering peaks, indicating cloud particles with dimensions larger than about 0.6 μm. In our models, a lower single-scattering albedo of the cloud particles in the belt relative to the zone accounts for the contrast between these regions. If an increased abundance of absorbing dust above uniformly bright clouds is used to explain the contrast between belts and zones at visible wavelengths, the limb darkening is steeper than that observed for the SEBn in blue light at small phase angles. The phase integral for the planet calculated for either the belt or the zone model in either color lies in the range 1.2 to 1.3. If a value of 1.25 is used with D.J. Taylor's bolometric geometric albedo of 0.28, the planet emits 2.25 or 1.7 times the energy it absorbs from the Sun if it effective temperature is 134 or 125°K, respectively—roughly as expected from current theories of the cooling of Jupiter's interior.     

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.     

An investigation of possible causes of the holes in the condensational Venus cloud using a microphysical cloud model with a radiative-dynamical feedback

Near-infrared observations of the nightside of Venus reveal regions of high brightness temperatures. These regions of high brightness temperatures are caused by the localized evaporation of the middle and lower cloud decks, which are about 50 to 60 km above the surface of the planet. We simulate the Venus condensational middle and lower cloud deck with the University of Colorado/NASA Ames Community Aerosol and Radiation Model for Atmospheres (CARMA). Our simulated clouds have similar characteristics to the observed Venus clouds. Our radiative transfer model reproduces the observed temperature structure and atmospheric stability structure within the middle cloud region. A radiative-dynamical feedback occurs which generates mixing due to increased absorption of upwelling infrared radiation within the lower cloud region, as previously suggested by others. We find that localized variations in temperature structure or in sub-grid scale mixing cannot directly explain the longevity and optical depth of the clouds. However, vertical motions are capable of altering the cloud optical depth by a sufficient magnitude in a short enough timescale to be responsible for the observed clearings.     

Measuring Venus’ winds using the Absolute Astronomical Accelerometer: Solid super-rotation model of Venus’ clouds

We present a new method of measuring the Venus winds by Doppler velocimetry on the full visible spectrum of solar light scattered by the clouds. In January 2003, we carried out observations to measure the winds of Venus, using the EMILIE high-resolution, cross-dispersed spectrograph and its associated calibrating instrument the Absolute Astronomical Accelerometer (AAA), at Observatoire de Haute-Provence, France. The motivation of this type of measurements is that it measures the actual velocity of cloud particles, while the other method (track of cloud features) may be sensitive to the deformation of the clouds. During observations, Venus was near maximum western elongation, at a phase angle near 90°. The EMILIE-AAA system allows us to measure accurately the Doppler shift induced in the reflected solar spectrum by the radial component of the motion of the clouds of Venus. We present the measurements and compare them with a forward simulation of a solid super-rotation of the atmosphere of Venus. Taking into account the Doppler shift relative to the Sun and that relative to the Earth, the theoretical total Doppler shift induced in the solar spectra is easily computed as a function of the velocity of the reflecting target. A first forward simulation is computed, with a wind model considering a purely horizontal and zonal wind. The magnitude of the wind is assumed to depend on cos(latitude), as for a solid-body rotation. The comparison with the measurements at various points on the illuminated semi-disc allowed us to determine an equatorial velocity of 66, 75, 91 and 85 m/s on 4 consecutive mornings, consistent with previous ultraviolet cloud tracking wind measurements, showing that wave propagation is not a major factor in the apparent motion of the cloud marks. Further, we discuss the effect of the finite angular size of the Sun and its rapid equatorial rotation (that we call the Young effect). It mainly affects measurements taken near the terminator, where the largest discrepancies are found. These discrepancies are alleviated when the Young effect is taken into account in the model but then the retrieved Venus equatorial velocity is reduced to only 48±3 m/s. This is well below classical ultraviolet markings velocities, but the altitude at which the visible photons are scattered (66 km) that we use is 5 km below the UV markings, confirming the vertical gradient of the horizontal winds shown by previous in-situ measurements.     

Are the clouds of venus sulfuric acid?

Water solutions of sulfuric acid, containing about 75% H₂SO₄ by weight, have a refractive index within 0.01 of the values deduced from polarimetric observations of the Venus clouds. These solutions remain liquid at the cloud temperature, thus explaining the spherical shape of the cloud particles (droplets). The equilibrium vapor pressure of water above such solutions is 0.01 that of liquid water or ice, which accounts for the observed dryness of the cloud region. Furthermore, H₂SO₄ solutions of such concentration have spectra very similar to Venus in the 8–13 μm region; in particular, they explain the 11.2 μm band. Cold sulfuric acid solutions also seem consistent with Venus spectra in the 3–4 μm region. The amount of acid required to make the visible clouds is quite small, and is consistent with both the cosmic abundance of sulfur and the degree of out-gassing of the planet indicated by known atmospheric constituents. Sulfuric acid occurs naturally in volcanic gases, along with known constituents of the Venus atmosphere such as CO₂, HCl, and HF ; it is produced at high temperature by reactions between these gases and common sulfate rocks. The great stability and low vapor pressure of H₂SO₄ and its water solutions explain the lack of other sulfur compounds in the atmosphere of Venus—a lack that is otherwise puzzling.Sulfuric acid precipitation may explain some peculiarities in Venera and Mariner data. Because sulfuric acid solutions are in good agreement with the Venus data, and because no other material that has been proposed is even consistent with the polarimetric and spectroscopic data, H₂SO₄ must be considered the most probable constituent of the Venus clouds.     

Effects of shock processing on Serkowski polarization curves

This paper presents a semi-empirical model for variations of interstellar polarization curves based upon the Serkowski-Wilking law for optical and near-infrared wavebands. The model assumes that nonspherical dust grains producing interstellar polarization are core-mantle particles shaped like oblate spheroids. The physical picture is one in which large (a ₀ 0.1µm) particles in the dense cloud phase are deposited into the diffuse cloud medium and thereafter undergo mantle processing by galactic shocks and UV starlight. It is shown that polarization curves vary their widths mainly as a consequence of the nonthermal sputtering of mantles by low-velocity shocks. Mantle sputtering by shocks in low density clouds tends to broaden the curves, whereas mantle sputtering by shocks in denser clouds produce narrow curves. Hence, shock processing of grain mantles can explain the observed correlation between the width of polarization curves and the dust grain environment.     

Photometry of Venus: I. Observation of the brightness distribution over the disk

Isophotes of the luminance distribution over the disk of Venus at several phase angles and in several wavelengths are constructed by means of isodensitometry of high-quality photographic negatives of Venus. Twenty-three plates were selected from more than 2000 original negatives available at the IAU Planetary Photographs Center of Meudon Observatory. Six isophote maps were made from a series of yellow light images (λ = 5850Å), corresponding to phase angles from 22° to 129°. Special attention was paid to the rare occurrences of distinct features in yellow light. A sequence of isophote maps was taken in six wavelengths from λ = 5850 to 3250Å. The ultraviolet cloud markings appear as changes in the isophote configurations for different wavelengths. Variations of contrast with wavelengths are deduced. Dark features, almost invisible at 4500Å, reach a contrast of 25% at 3500Å which then no longer increases toward ultraviolet. The polar bright clouds give contrasts of 40% to 60% in ultraviolet. A series of images taken in ultraviolet at 3500Åshows configurations characteristic of observations at short wavelengths for both the waxing and the waning crescent.In Parts II and III of this series of papers, the isophote maps will be compared with theoretical curves computed from the theory of multiple-order scattering by aerosol particles.     

Spectropolarimetry of comets Austin and Churyumov-Gerasimenko

Spectropolarimetric observations from 5000 to 8000 Å have been obtained for comets P/Austin (1982g) and P/Churyumov-Gerasimenko (1982f). The observations were spaced over phase angles of 50–125° for comet Austin and 10–40° for comet Churyumov-Gerasimenko. The use of spectropolarimetry allowed an evaluation of continuum polarization without molecular line contamination. Especially for comet Churyumov-Gerasimenko, the curve of polarization versus phase angle resembles curves for asteroids, where the polarization is negative (electric vector maximum parallel to the scattering plane) for phase angles less than 20° and the most negative polarization is from ?1 to ?2%. The negative polarization at backscattering angles may be due to multiple scattering in agglomerated grains, as assumed for asteroids, or to Mie scattering by small dielectric particles. If multiple scattering is important in comet dust, polarization measurements may imply a low albedo, less than 0.08. The polarization of comet Austin remained steady during a large change in the dust production rate. Both comets increased continuum flux by a factor of 2 near perihelion. The continuum of comet Churyumov-Gerasimenko had the shape of the solar spectrum with derivations less than 5%. The equivalent width of spectral features of C₂, NH₂, and O varied as r^?2.