Modeling crater populations on Venus and Titan

We describe a model for crater populations on planets and satellites with dense atmospheres, like those of Venus and Titan. The model takes into account ablation (or mass shedding), pancaking, and fragmentation. Fragmentation is assumed to occur due to the hydrodynamic instabilities promoted by the impactors’ deceleration in the atmosphere. Fragments that survive to hit the ground make craters or groups thereof. Crater sizes are estimated using standard laws in the gravity regime, modified to take into account impactor disruption. We use Monte Carlo methods to pick parameters from appropriate distributions of impactor mass, zenith angle, and velocity. Good fits to the Venus crater populations (including multiple crater fields) can be found with reasonable values of model parameters. An important aspect of the model is that it reproduces the dearth of small craters on Venus: this is due to a cutoff on crater formation we impose, when the expected crater would be smaller than the (dispersed) object that would make it. Hydrodynamic effects alone (ablation, pancaking, fragmentation) due to the passage of impactors through the atmosphere are insufficient to explain the lack of small craters. In our favored model, the observed number of craters (940) is produced by ∼5500 impactors with masses , yielding an age of (1-σ uncertainty) for the venusian surface. This figure does not take into account any uncertainties in crater scaling and impactor population characteristics, which probably increase the uncertainty to a factor of two in age.We apply the model with the same parameter values to Titan to predict crater populations under differing assumptions of impactor populations that reflect present conditions. We assume that the impactors (comets) are made of 50% porous ice. Predicted crater production rates are ≈190 craters . The smallest craters on Titan are predicted to be in diameter, and ≈5 crater fields are expected. If the impactors are composed of solid ice (density ), crater production rates increase by ≈70% and the smallest crater is predicted to be in diameter. We give cratering rates for denser comets and atmospheres 0.1 and 10 times as thick as Titan's current atmosphere. We also explicitly address leading-trailing hemisphere asymmetries that might be seen if Titan's rotation rate were strictly synchronous over astronomical timescales: if that is the case, the ratio of crater production on the leading hemisphere to that on the trailing hemisphere is ≈4:1.     

Far-infrared spectral observations of Venus,Mars, and Jupiter

Spectra of Venus, Mars, and Jupiter between 45 and 115 μm have been obtained at a resolving power of ～10, observing from the NASA Lear Jet at an altitude of 13.7 km. The results are calibrated with lunar observations, and show Mars and Venus to have relatively constant brightness temperatures over this wavelength region, with Venus appearing somewhat warmer at longer wavelengths. The brightness temperature of Jupiter decreases slightly toward longer wavelengths.     

Atmospheric acoustics of Titan, Mars, Venus, and Earth

Planetary atmospheres are complex dynamical systems whose structure, composition, and dynamics intimately affect the propagation of sound. Thus, acoustic waves, being coupled directly to the medium, can effectively probe planetary environments. Here we show how the acoustic absorption and speed of sound in the atmospheres of Venus, Mars, Titan, and Earth (as predicted by a recent molecular acoustics model) mirror the different environments. Starting at the surface, where the sound speed ranges from ∼200 m/s for Titan to ∼410 m/s for Venus, the vertical sound speed profiles reveal differences in the atmospheres' thermal layering and composition. The absorption profiles are relatively smooth for Mars, Titan, and Earth while Venus stands out with a noticeable attenuation dip occurring between 40 and 100 km. We also simulate a descent module sampling the sound field produced by a low-frequency “event” near the surface noting the occurrence of acoustic quiet zones.     

Ionospheric photoelectrons: Comparing Venus, Earth, Mars and Titan

The sunlit portion of planetary ionospheres is sustained by photoionization. This was first confirmed using measurements and modelling at Earth, but recently the Mars Express, Venus Express and Cassini-Huygens missions have revealed the importance of this process at Mars, Venus and Titan, respectively. The primary neutral atmospheric constituents involved (O and CO₂ in the case of Venus and Mars, O and N₂ in the case of Earth and N₂ in the case of Titan) are ionized at each object by EUV solar photons. This process produces photoelectrons with particular spectral characteristics. The electron spectrometers on Venus Express and Mars Express (part of ASPERA-3 and 4, respectively) were designed with excellent energy resolution (ΔE/E=8%) specifically in order to examine the photoelectron spectrum. In addition, the Cassini CAPS electron spectrometer at Saturn also has adequate resolution (ΔE/E=16.7%) to study this population at Titan. At Earth, photoelectrons are well established by in situ measurements, and are even seen in the magnetosphere at up to 7R_E. At Mars, photoelectrons are seen in situ in the ionosphere, but also in the tail at distances out to the Mars Express apoapsis (∼3R_M). At both Venus and Titan, photoelectrons are seen in situ in the ionosphere and in the tail (at up to 1.45R_V and 6.8R_T, respectively). Here, we compare photoelectron measurements at Earth, Venus, Mars and Titan, and in particular show examples of their observation at remote locations from their production point in the dayside ionosphere. This process is found to be common between magnetized and unmagnetized objects. We discuss the role of photoelectrons as tracers of the magnetic connection to the dayside ionosphere, and their possible role in enhancing ion escape.     

The abundances of ammonia in the atmospheres of Jupiter,Saturn, and Titan

An investigation of low-resolution ratio spectra of Jupiter, Saturn, and Titan in the region 5400–6500 Å has permitted new evaluations of ammonia absorption bands. The distribution of ammonia over the disk of Jupiter is very inhomogeneous. The carbon-to-nitrogen ratio is distinctly different from the solar value, but this is probably a result of uneven mixing of methane and ammonia, as suggested previously by Kuiper, rather than a compositional anomaly. The abundance of ammonia on Saturn also shows spatial variations, but appears constant in time over a 3-yr period. Two weak, unidentified absorptions were discovered in the red region of Titan's spectrum, in the absence of any detectable ammonia. The new upper limit is ηN < 120 cm-am.     

Polycyclic aromatic hydrocarbons in the atmospheres of Titan and Jupiter

Polycyclic aromatic hydrocarbons (PAHs) are important components of the interstellar medium and carbonaceous chondrites, but have never been identified in the reducing atmospheres of the outer solar system. Incompletely characterized complex organic solids (tholins) produced by irradiating simulated Titan atmospheres reproduce well the observed UV/visible/IR optical constants of the Titan stratospheric haze. Titan tholin and a tholin generated in a crude simulation of the atmosphere of Jupiter are examined by two-step laser desorption/multiphoton ionization mass spectrometry. A range of two- to four-ring PAHs, some with one to four alkylation sites are identified, with net abundance approximately 10(-4) g g-1 (grams per gram) of tholins produced. Synchronous fluorescence techniques confirm this detection. Titan tholins have proportionately more one- and two-ring PAHs than do Jupiter tholins, which in turn have more four-ring and larger PAHs. The four-ringed PAH chrysene, prominent in some discussions of interstellar grains, is found in Jupiter tholins. Solid state 13C NMR spectroscopy suggests approximately equal to 25% of the total C in both tholins is tied up in aromatic and/or aliphatic alkenes. IR spectra indicate an upper limit in both tholins of approximately equal to 6% by mass in benzenes, heterocyclics, and PAHs with more than four rings. Condensed PAHs may contribute at most approximately 10% to the observed detached limb haze layers on Titan. As with interstellar PAHs, the synthesis route of planetary PAHs is likely to be via acetylene addition reactions.     

Evidence for a low-altitude origin of lightning on Venus

Radio emissions attributed to lightning on Venus have been recorded by Venera 11 and 12 and by the Pioneer Venus Orbiter. The Venera descent records are compared to patterns of radio propagation within the Venusian atmosphere and an explanation is found for some timing trends that, if correct, indicates the lightning was below 33 km in altitude.     

Maintenance of equatorial superrotation in the atmospheres of Venus and Titan

This paper extends Leovy's theory on Venus’ equatorial superrotation by analytically examining additional terms in the mean zonal momentum equation that stably balances the momentum source of pumping by thermal tides. The general analytical solution is applied to the atmospheres of both Venus and Saturn's moon Titan. The main results are: (i) Venus’ equatorial superrotation of 118 m s⁻¹ results primarily from a balance between the momentum source of pumping by thermal tides and the momentum sink of meridional advection of wind shear by horizontal branches of the Hadley circulation; (ii) no solution is found for Titan's stratospheric equatorial superrotation centered at the 1-hPa level; (iii) however, if the main solar radiation absorption layer in Titan's stratosphere is lifted from 1 hPa (∼185 km) to 0.1 hPa (∼288 km), an equatorial superrotation of ∼110 m s⁻¹ centered at 0.1-hPa could be maintained. Titan's equatorial superrotation results mainly from a balance between the momentum source of tidal pumping and the momentum sink of frictional drag.     

Comparison study of magnetic flux ropes in the ionospheres of Venus, Mars and Titan

Magnetic flux ropes are created in the ionosphere of Venus and Mars during the interaction of the solar wind with their ionospheres and also at Titan during the interaction of the Saturnian magnetospheric plasma flow with Titan’s ionosphere. The flux ropes at Venus and Mars were extensively studied from Pioneer Venus Orbiter and Mars Global Surveyor observations respectively during solar maximum. Based on the statistical properties of the observed flux ropes at Venus and Mars, the formation of a flux rope in the ionosphere is thought first to arise near the boundary between the magnetic barrier and the ionosphere and later to sink into the lower ionosphere. Venus flux ropes are also observed during solar minimum by Venus Express and the observations of developing and mature flux ropes are consistent with the proposed mechanism. With the knowledge of flux rope structure in the Venus ionosphere, the twisted fields in the lower ionosphere of Titan from Cassini observations are studied and are found to resemble the Venus flux ropes.     

Optical signature of Venus lightning as seen from space

The calculations of M. A. Williams, L. W. Thomason, and D. M. Hunten (Icarus52, 166–170, 1982) for the light transmitted to space by a Venus lightning flash by dropping the use of similarity relations have been improved. This revised model increases their escape fractions and image sizes by about a factor of 2; however, their conclusions remain valid.     

Cloud base levels for Jupiter and Venus and the heteromolecular nucleation theory

For purified binary gas mixtures like NH₃H₂O or HClH₂O, partial pressures appreciably greater than the two saturation partial pressures are needed to condense the gas mixture into small solution droplets (“homogeneous hetero-molecular nucleation”). Thus without foreign nuclei, clouds are not as easily formed as in the theories of Lewis; the latter should be valid only if large condensation nuclei are available. We calculate here from classical homogeneous heteromolecular nucleation theory the threshold partial pressures necessary to achieve droplet nucleation for the gas mixtures NH₃H₂O (Jupiter,…), HClH₂O (Venus), H₂SO₄H₂O (Venus), and C₂H₅OHH₂O (laboratory). In the last case, theory and experiment agree satisfactorily. If no “dust” particles are available as condensation nuclei, then we expect in Jupiter's atmosphere the cloud base level to be around 40 km above the 400K level instead of 10–25 km in Lewis' models (1969) (similar upward shifts for the outer Jovian planets). For Venus, our corrections make the formation of HClH₂O clouds less probable for the 60-km layer at 0°C. If H₂SO₄ is formed by (photo-)chemical oxidation of SO₂ and if clouds are formed at that level where the H₂SO₄ production is largest, then the cloud base levels for H₂SO₄H₂O mixture clouds will not be shifted by our nucleation effects. For more reliable predictions, one needs more accurate data on the water vapor content of the planetary atmospheres and laboratory experiments testing the theoretically predicted nucleation behavior of these gaseous mixtures.     

Comparison of the responses of the atmosphere of Earth,Venus, Mars and Jupiter to heat sources and perturbations

The different characteristics of the structure and dynamics of the terrestial, the cytherean, the martian and the jovian atmospheres have been analysed. Our analyses with one-dimensional and three-dimensional models show the thermal structure of the martian and jovian atmosphere to be similar to that of the terrestrial atmosphere. For these three atmospheres the dimensionless parameter of thermal structure α is of the order 1, which is in contrast to the small α (5 × 10⁻²) for the cytherean atmosphere.     

The transmission to space of the light produced by lightning in the clouds of Venus

A Monte Carlo program by Thomason and Krider has been adapted to the Venus cloud geometry and optical properties. If lightning flashes occur within or just below the clouds, the fraction of photons of visible light escaping to space is 0.1–0.4, depending on the location of the flash. For flashes near the surface, only one blue photon in 10⁴ was found to escape; about 5% of the red ones are transmitted. Failure of the Pioneer Venus Orbiter to unambiguously detect optical lightning signals from space is not due to attenuation by the atmosphere and clouds. In any case, lightning is not acceptable as an explanation for ashen light.     

The optical properties of Venus and the Jovian planets I. The atmosphere of Jupiter according to polarimetric observations

Results are given for polarization measurements of both the entire Jupiter disk and its centre for seven wavelength regions in the 0.373–0.800 μm range. Interpretation of these observations is based on two model atmospheres: (A) The cloud layer particles and molecules are mixed with a constant ratio. (B) A gas layer with small optical thickness, τ₀, is situated above the cloud layer which consists of aerosol particles. The aerosol particles are considered to be non-absorbing spheres, their size distribution being normal Gaussian. The index of refraction for the particles is considered to be independent of wavelength in the above spectral range. An approximate method is used for the determination of parameters of the Jovian atmosphere. This method was tested by evaluation of the parameters for the Venus cloud layer: The refractive index was found to be n = 1.435 ± 0.015, the square of the logarithmic dispersion of the radius of particles σ² = 0.12 and the mean geometrical radius of particles r₀ = 0.74 μm which agree well with exact values given by Hansen and Arking (1971). For the atmosphere of Jupiter it was found: n = 1.36 ± 0.01, σ² ? 0.3, r₀ ? 0.2 μm. This refractive index for the particles agrees well with the ammonia cloud layer hypothesis.     

Atmospheric impacts, fragmentation, and small craters on Venus

We use high-resolution three-dimensional numerical models of aerodynamically disrupted asteroids to predict the characteristic properties of small impact craters on Venus. We map the mass and kinetic energy of the impactor passing though a plane near the surface for each simulation, and find that the typical result is that mass and energy sort themselves into one to several strongly peaked regions, which we interpret as more-or-less discrete fragments. The fragments are sufficiently well separated as to imply the formation of irregular or multiple craters that are quite similar to those found on Venus. We estimate the diameters of the resulting craters using a scaling law derived from the experiments of Schultz and Gault (1985, J. Geophys. Res. 90 (B5), 3701-3732) of dispersed impactors into targets. We compare the spacings and sizes of our estimated craters with measured diameters tabulated in a Venus crater database (Herrick and Phillips, 1994a, Icarus 111, 387-416; Herrick et al., 1997, in: Venus II, Univ. of Arizona Press, Tucson, AZ, pp. 1015-1046; Herrick, 2003, http://www.lpi.usra.edu/research/vc/vchome.html) and find quite satisfactory agreement, despite the uncertainty in our crater diameter estimates. The comparison of the observed crater characteristics with the numerical results is an after-the-fact test of our model, namely the fluid-dynamical treatment of large impacts, which the model appears to pass successfully.     

Limitations to growth of microorganisms on Uranus,Neptune, and Titan

We have examined a wide range of physical, chemical, and thermal models of the atmosphere of Uranus. In that model, which we believe maximizes favorable conditions for the support of life [Weidenschilling and Lewis, Icarus20, 465–476 (1973)], we find the probability of growth of a contaminant terrestrial microorganisms to be nil. If, as is likely, conditions are even more extreme on Neptune, the probability of contamination of both of the outer planets Uranus and Neptune is nil. The Wiedenschilling and Lewis model guarantees the presence of water droplets through the temperature range 0 to 100°C; other published models add water liquid at higher temperatures or fail to provide liquid water at all within this temperature range. In this model the heavy elements (C, N, O, etc.) are enhanced in Uranus by a factor sufficient to form a deep massive cloud layer of aqueous ammonia solution droplets. We can estimate the probability of growth with respect to the following factors: the presence of stable liquid water, convection of parcels of atmosphere to lethally hot depths, solar energy sources reaching the water layer, organic molecular production by solar ultraviolet light, ammonia concentration at the water cloud level, ionic species distribution, and concentrations at the water cloud level. The evaluation of these factors suggests that most terrestrial life as we know it would be excluded on the basis of any one of them. We know of no organism that would be adapted to all the stringent Uranus conditions simultaneously. The discovery of even a single species of Earth organism that can survive or grow under allowable outer planetary conditions would establish new principles in biology.Titan, the methane-rich moon of Saturn, may be more hospitable for terrestrial organisms than any of the other objects of the outer solar system. Even there we see formidable barriers to the growth of an Earth organism in Titan's atmosphere. We recognize that revision of our views concerning Titan must occur as more is learned about this satellite.We advocate the abandonment, in principle, of the probabilistic approach to the estimation of growth of terrestrial organisms on spacecraft, planets, and satellites in the solar system. We do not support an approach which estimates probabilities of qualitatively unknown phenomena. We recommend a strategy which involves identification and intensive study of those organisms most likely to thrive under known conditions for each of the planets respectively. (Unknown environmental conditions may be allowed to vary optimally.) Some explicit areas for Earth-based experimentation are indicated.     

Gravity,topography, and crustal evolution of Venus

The gravity anomalies of Venus, although small by comparison with those on Mars and the Moon, are still much larger than those on Earth for large features. On Venus, even the low-degree spherical harmonic terms for Venus' gravity field indicate a close association of broad positive gravity anomalies with major topographic highs. This is striking contrast to the situation on Earth, where the broad regional gravity anomalies show little correlation with continental masses or plate tectonic features, but instead appear to be caused by deep mass anomalies.A method for estimating radial gravity anomalies from line-of-sight acceleration data, their interpolation, and use of iteration for improved radial anomaly estimates is outlined. A preliminary gravity anomaly map of Venus at spacecraft altitude prepared using first estimate values is presented. A profile across the western part of Aphrodite along longitude 85 E was analyzed using time-series techniques. An elastic plate model would require a plate thickness of about 180 to 200 km to match the general amplitude of the observed gravity anomaly (about 33 mgal): a thickness much greater than that found for earth structures and, because of high surface temperatures, unlikely for Venus. An Airy isostatic model convolved with the topography across Aphrodite, however, provides a better match between the predicted and observed gravity anomalies if the nominal crustal thickness is about 70 to 80 km. This thickness is over twice that for continental crust on the earth, and considerably greater than that of the earth's basaltic ocean crust (only 5 km). A different differentiation history for Venus than that of the earth thus is anticipated. High gravity anomalies (+110 mgal) occur over Beta Regio and over the topographic high in eastern Aphrodite; both highs are associated with regions where detected lightning is clustered, and thus the topographic features may be active volcanic constructs. The large gravity anomalies at these two sites of volcanic activity require an explanation different than that indicated for western Aphrodite.     

Creation,detection, and evolution of Jupiter Trojan families

An investigation is carried out looking at correlations between the orbital elements of collisional targets and projectiles, estimating the number of interlopers in Trojan collisional families, and at the possibility of determining the ages of the Jupiter Trojan families by orbital integration. Real Trojans are integrated and close encounters are recorded in order to evaluate collisional circumstances between Trojans. Fictitious collisional families are created and integrated for 10 MJyr (million Julian years) forward in time and back again to the time of the collision in order to check the performance of the integrator, and the behaviour of the fictitious collisional fragments. Proper elements are calculated for the detection of family clustering using the hierarchically clustering method. This method presents little difficulty finding fictitious families in the Trojan swarms even in areas with densely populated backgrounds. However, even when the background is relatively sparse in objects, several interlopers can be connected to the family at velocity differences below 100 m s^–1. On the other hand, in densely populated backgrounds the contamination of interlopers should be less than 30%. Providing gravity is the only significant force acting on the Trojans and resonance effects are weak, the shape the collision fragments create in the proper element space are preserved on the GJyr scale, and collisions can be tracked with orbital integrations for ages of at least 100 MJyr. However, the shape of artificial families does not correspond to suggested real families. This points to the need of including non‐gravitational forces such as the Yarkovsky effect in order to simulate the family evolution. As a consequence age determination by orbital integration might be severely restricted and previous investigations involving long term orbital integrations might have tobe recalculated (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)