Could giant impacts cripple core dynamos of small terrestrial planets?

Large impacts not only create giant basins on terrestrial planets but also heat their interior by shock waves. We investigate the impacts that have created the largest basins existing on the planets: Utopia on Mars, Caloris on Mercury, Aitken on Moon, all formed at ∼4 Ga. We determine the impact-induced temperature increases in the interior of a planet using the “foundering” shock heating model of Watters et al. (Watters, W.A., Zuber, M.T., Hager, B.H. [2009]. J. Geophys. Res. 114, E02001. doi:10.1029/2007JE002964). The post-impact thermal evolution of the planet is investigated using 2D axi-symmetric convection in a spherical shell of temperature-dependent viscosity and thermal conductivity, and pressure-dependent thermal expansion. The impact heating creates a superheated giant plume in the upper mantle which ascends rapidly and develops a strong convection in the mantle of the sub-impact hemisphere. The upwelling of the plume rapidly sweeps up the impact-heated base of the mantle away from the core-mantle boundary and replaces it with the colder surrounding material, thus reducing the effects of the impact-heated base of the mantle on the heat flux out of core. However, direct shock heating of the core stratifies the core, suppresses the pre-existing thermal convection, and cripples a pre-existing thermally-driven core dynamo. It takes about 17, 4, and 5 Myr for the stratified cores of Mars, Mercury, and Moon to exhaust impact heat and resume global convection, possibly regenerating core dynamos.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Deep versus shallow origin of gravity anomalies, topography and volcanism on Earth, Venus and Mars

The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs.     

Size and compositional constraints of Ganymede's metallic core for driving an active dynamo

Ganymede has an intrinsic magnetic field which is generally considered to originate from a self-excited dynamo in the metallic core. Driving of the dynamo depends critically on the satellite's thermal state and internal structure. However, the inferred structure based on gravity data alone has a large uncertainty, and this makes the possibility of dynamo activity unclear; variations in core size and composition significantly change the heat capacity and alter the cooling history of the core. The main objectives of this study is to explore the structural conditions for a currently active dynamo in Ganymede using numerical simulations of the thermal history, and to evaluate under which conditions Ganymede can maintain the dynamo activity at present. We have investigated the satellite's thermal history using various core sizes and compositions satisfying the mean density and moment of inertia of Ganymede, and evaluate the temperature and heat flux at the core-mantle boundary (CMB). Based on the following two conditions, we evaluate the possibility of dynamo activity, thereby reducing the uncertainty of the previously inferred interior structure. The first condition is that the temperature at the CMB must exceed the melting point of a metallic core, and the second is that the heat flux through the CMB must exceed the adiabatic temperature gradient. The mantle temperature starts to increase because of the decay of long-lived radiogenic elements in the rocky mantle. After a few Gyr, radiogenic elements are exhausted and temperature starts to decrease. As the rocky mantle cools, the heat flux at the CMB steadily increases. If the temperature and heat flux at the CMB satisfy these conditions simultaneously, we consider the case as capable of driving a dynamo. Finally, we identify the Dynamo Regime, which is the specific range of internal structures capable of driving the dynamo, based on the results of simulations with various structures. If Ganymede's self-sustained magnetic field were maintained by thermal convection, the satellite's metallic core would be relatively large and, in comparison to other terrestrial-type planetary cores, strongly enriched in sulfur. The dynamo activity and the generation of the magnetic field of Ganymede should start from a much later stage, possibly close to the present.     

Venus’ internal structure,temperature and core composition

The mass and radius of our closest neighbour Venus are only slightly smaller than those of the Earth indicating a similarity in composition. However, the lack of self-sustained internal magnetic field in Venus points to a difference in the core structure. The theory of tricritical phenomena has recently been used to study solidification at the high pressures and temperatures of the Earth, revealing how the Earth’s core works. This theoretical approach is here applied to Venus. While keeping Venus’ mantle density similar to the Earth’s, one obtains the gravitational acceleration g inside Venus, its moment of inertia factor, the size, pressure and density of its core, together with the planet’s temperature profile. Mainly due to the temperature difference between the core–mantle boundary and surface being 21% smaller than on the Earth, and the 11.5% smaller gravitational acceleration, Venus’ Rayleigh number Ra parameterizing mantle convection is only 54% of the Earth’s, offering a possible explanation for the present lack of plate tectonics on Venus. The theory as discussed predicts that Venus is molten at the centre, with temperature about 5200 K, and has 8 mol.% impurities there, slightly more impurities than in the Earth’s inner core boundary fluid. These impurities are likely to be a combination of MgO and MgSiO₃.     

Did 26Al and impact‐induced heating differentiate Mercury?

Numerical models dealing with the planetary scale differentiation of Mercury are presented with the short‐lived nuclide, ²⁶Al, as the major heat source along with the impact‐induced heating during the accretion of planets. These two heat sources are considered to have caused differentiation of Mars, a planet with size comparable to Mercury. The chronological records and the thermal modeling of Mars indicate an early differentiation during the initial ~1 million years (Ma) of the formation of the solar system. We theorize that in case Mercury also accreted over an identical time scale, the two heat sources could have differentiated the planets. Although unlike Mars there is no chronological record of Mercury's differentiation, the proposed mechanism is worth investigation. We demonstrate distinct viable scenarios for a wide range of planetary compositions that could have produced the internal structure of Mercury as deduced by the MESSENGER mission, with a metallic iron (Fe‐Ni‐FeS) core of radius ~2000 km and a silicate mantle thickness of ~400 km. The initial compositions were derived from the enstatite and CB (Bencubbin) chondrites that were formed in the reducing environments of the early solar system. We have also considered distinct planetary accretion scenarios to understand their influence on thermal processing. The majority of our models would require impact‐induced mantle stripping of Mercury by hit and run mechanism with a protoplanet subsequent to its differentiation in order to produce the right size of mantle. However, this can be avoided if we increase the Fe‐Ni‐FeS contents to ~71% by weight. Finally, the models presented here can be used to understand the differentiation of Mercury‐like exoplanets and the planetary embryos of Venus and Earth.     

Planetary dynamos: effects of electrically conducting flows overlying turbulent regions of magnetic field generation

A fully three-dimensional, nonlinear, time-dependent, multi-layered spherical kinematic dynamo model is used to study the effect on the observable external magnetic field of flow in an electrically conducting layer above a spherical turbulent dynamo region in which the α effect generates the magnetic field. It is shown that the amplitude and structure of an observable planetary magnetic field are largely determined by the magnitude and structure of the flow in the overlying layer. It is also shown that a strong-field planetary dynamo can be readily produced by the effect of an electrically conducting flow layer at the top of a convective core. The overlying layer and the underlying convective region constitute a magnetically strongly coupled system. Such overlying layers might exist at the top of the Earth's core due to chemical or thermal causes, in the cores of other terrestrial planets for similar reasons, and in Saturn due to the differentiation of helium from hydrogen. An electrically conducting and differentially rotating layer could exist above the metallic hydrogen region in Jupiter and affect the jovian magnetic field similar to the overlying layers in other planets. Lateral temperature gradients resulting in thermal winds drive the flow in the overlying layers. All planetary magnetic fields could be maintained by similar turbulent convective dynamos in the field-generation regions of planets with the differences among observable magnetic fields due to different circulations in the overlying electrically conducting layers.     

Earth and Venus: A comparative study

The observed density of Venus is about 2% smaller than would be expected if Venus were a twin planet of the Earth, possessing an identical internal composition and structure. In principle, this could be explained by a process of physical segregation of metal particles from silicate particles in the solar nebula prior to accretion, so that Venus accreted from relatively metal-depleted material. However, this model encounters severe difficulties in explaining the nature of the physical segregation process and also the detailed chemical composition of the Earth's mantle. Two alternative hypotheses are examined, both of which attempt to explain the density difference in terms of chemical fractionation processes. Both of these hypotheses assume that the relative abundances of the major elements Fe, Si, Mg, Al, and Ca are similar in both planets. According to the first hypothesis, a larger proportion of the total iron in Venus is present as iron oxide in the mantle, so that the core-to-mantle ratio is smaller than in the Earth. This model implies that Venus is more oxidized than the Earth, with its lower intrinsic density (i.e., corrected to equivalent pressures and temperatures) due to the larger amount of oxygen present. The difference between oxidation states is attributed to differing degrees of accretional heating arising from the relatively smaller mass of Venus. On the other hand, the second hypothesis maintains that Venus is more reduced than the Earth, with its mantle essentially devoid of oxidized iron. The difference intrinsic densities is attributed to the Earth accreting at a lower temperature than Venus as a result of the Earth's greater distance from the center of the nebula. As a result, large amounts of sulfur accreted on the Earth but not on Venus. The sulfur, which entered the core, is believed to have increased the mean density of the Earth because of its relatively high atomic weight. The hypothesis also implies that most of the Earth's potassium, because of its chalcophile properties, entered the core.These hypotheses are evaluated in the light of existing data. The second hypothesis leads to an intrinsic density for Venus which is only 0.4% smaller than that of the Earth. This difference is much smaller than is believed to exist. A wide range of chemical evidence is found to be unfavorable to this second hypothesis, but to be consistent with the interpretation that Venus is more oxidized than the Earth, as required by the first hypothesis.     

Formation of the terrestrial planets

The early phases of formation in the inner solar system were dominated by collisions and short-range dynamical interactions among planetesimals. But the later phases, which account for most of the differences among planets, are unsure because the dynamics are more subtle. Jupiter's influence became more important, leading to drastic clearing out of the asteroid belt and the stunting of Mars's growth. Further in, the effect of Jupiter-- both directly and indirectly, through ejection of mass in the outer solar system-- was probably to speed up the process without greatly affecting the outcome. The great variety in bulk properties of the terrestrial bodies indicate a terminal phase of great collisions, so that the outcome is the result of small-N statistics. Mercury, 65 percent iron, appears to be a residual core from a high-velocity collision. All planets appear to require a late phase of high energy impacts to erode their atmospheres: including the Earth, to remove CO₂ so that its ocean could form by condensation of water.Consistent with this model is that the largest collision, about 0.2 Earth masses, was into the proto-Earth, although the only property that appears to require it is the great lack of iron in the Moon. The other large differences between the Earth and Venus, angular momentum (spin plus satellite) and inert gas abundances, must arise from origin circumstances, but neither require nor forbid the giant impact. Venus's higher ratio of light to heavy inert gases argues for it receiving a large icy impactor, about 10^–6 Earth masses from far out, requiring some improbable dynamics to get a low enough approach velocity. Core formation in both planets probably started rather early during accretion.Some geochemical evidences argue for the Moon coming from the Earth's mantle, but are inconclusive. Large scale melting of the mantle by the giant impact would plausibly have led to stratification. But the "lock-up" at the end of turbulent mantle convection is a trade-off between rates: crystallization of constituents of small density difference versus overall freezing. Also, factors such as differences in melting temperatures and densities, melt compressibilities, and phase transitions may have had homogenizing effects in the subsequent mantle convection.     

Impact-induced mantle dynamics on Mars

At least 20 impact basins with diameters ranging from 1000 to 3380 km have been identified on Mars, with five exceeding 2500 km. The coincidental timing of the end of the sequence of impacts and the disappearance of the global magnetic field has led to investigations of impact heating crippling an early core dynamo. The rate of core cooling (and thus dynamo activity) is limited by that of the overlying mantle. Thus, the pre-existing thermal state of the mantle controls the extent to which a sequence of impacts may affect dynamo activity. Here, we examine the effects of the initial thermal structure of the core and mantle, and the location of an impact with respect to the pre-existing convective structure on the mantle dynamics and surface heat flux.We find that the impacts that formed the five largest basins dominate the impact-driven effects on mantle dynamics. A single impact of this size can alter the entire flow field of the mantle. Such an impact promotes the formation of an upwelling beneath the impact site, resulting in long-lived single-plume convection. The interval between the largest impacts is shorter than the initial recovery time for a single impact. Hence, the change in convective pattern due to each impact sets up a long term change in the global heat flow. These long-term changes are cumulative, and multiple impacts have a synergistic effect.     

Giant impacts and the initiation of plate tectonics on terrestrial planets

Earth is the only terrestrial planet with present-day lithosphere recycling through plate tectonics. However, theoretical models of mantle convection based on general considerations find that all the terrestrial planets should be operating in the stagnant lid regime, in which the planets are one-plated and there is no lithosphere recycling. The stagnant lid regime is a consequence of the strong viscosity contrast across the convective layer, and therefore the upper lid (roughly equivalent to the lithosphere) must be sufficiently weakened in order to be mobilized. Here I propose that giant impacts could have provided the upper layer weakening required for surface recycling, and hence for plate tectonics, to initiate on the early Earth. Additionally, giant impacts originated lithosphere thickness and density differences, which might contribute to the initiation of subduction. Impacts are more energetic for Earth than for Mars, which could explain the likely early existence of plate tectonics on the Earth whereas Mars never had lithosphere recycling. On the other hand, convection on Mercury and the Moon might be sluggish or even inexistent, implying a reduced influence of giant impacts on their internal dynamics, whereas there is no record of the earliest geological history of Venus, which obscures any discussion on the influence of giant impacts on their internal dynamics.     

Mars

Mars is the fourth planet out from the sun. It is a terrestrial planet with a density suggesting a composition roughly similar to that of the Earth. Its orbital period is 687 days, its orbital eccentricity is 0.093 and its rotational period is about 24 hours. Mars has two small moons of asteroidal shapes and sizes (about 11 and 6 km mean radius), the bigger of which, Phobos, orbits with decreasing semimajor orbit axis. The decrease of the orbit is caused by the dissipation of tidal energy in the Martian mantle. The other satellite, Deimos, orbits close to the synchronous position where the rotation period of a planet equals the orbital period of its satellite and has hardly evolved with time. Mars has a tenous atmosphere composed mostly of CO with strong winds and with large scale aeolian transport of surface material during dust storms and in sublimation-condensation cycles between the polar caps. The planet has a small magnetic field, probably not generated by dynamo action in the core but possibly due to remnant magnetization of crustal rock acquired earlier from a stronger magnetic field generated by a now dead core dynamo. A dynamo powered by thermal power alone would have ceased a few billions of years ago as the core cooled to an extent that it became stably stratified. Mars' topography and its gravity field are dominated by the Tharsis bulge, a huge dome of volcanic origin. Tharsis was the major center of volcanic activity, a second center is Elysium about 100° in longitude away. The Tharsis bulge is a major contributor to the non-hydrostaticity of the planet's figure. The moment of inertia factor together with the mass and the radius presently is the most useful constraint for geophysical models of the Martian interior. It has recently been determined by Doppler range measurements to the Mars Pathfinder Lander to be (Folkner et al. 1997). In addition, models of the interior structure use the chemistry of the SNC meteorites which are widely believed to have originated on Mars. According to the models, Mars is a differentiated planet with a 100 to 200 km thick basaltic crust, a metallic core with a radius of approximately half the planetary radius, and a silicate mantle. Mantle dynamics is essential in forming the elements of the surface tectonics. Models of mantle convection find that the pressure-induced phase transformations of -olivine to -spinel, -spinel to -spinel, and -spinel to perovskite play major roles in the evolution of mantle flow fields and mantle temperature. It is not very likely that the -spinel to perovskite transition is present in Mars today, but a few 100 km thick layer of perovskite may have been present in the lower mantle immediately above the core-mantle boundary early in the Martian history when mantle temperatures were hotter than today. The phase transitions act to reduce the number of upwellings to a few major plumes which is consistent with the bipolar distribution of volcanic centers of Mars. The phase transitions also cause a partial layering of the lower mantle which keeps the lower mantle and the core from extensive cooling over the past aeons. A relatively hot, fluid core is the most widely accepted explanation for the present lack of a self-generated magnetic field. Growth of an inner core which requires sub-liquidus temperatures in the core would have provided an efficient mechanism to power a dynamo up to the present day. Received 10 May 1997     

Effects of impacts on the atmospheric evolution: Comparison between Mars, Earth, and Venus

Classified as a terrestrial planet, Venus, Mars, and Earth are similar in several aspects such as bulk composition and density. Their atmospheres on the other hand have significant differences. Venus has the densest atmosphere, composed of CO₂ mainly, with atmospheric pressure at the planet's surface 92 times that of the Earth, while Mars has the thinnest atmosphere, composed also essentially of CO₂, with only several millibars of atmospheric surface pressure. In the past, both Mars and Venus could have possessed Earth-like climate permitting the presence of surface liquid water reservoirs. Impacts by asteroids and comets could have played a significant role in the evolution of the early atmospheres of the Earth, Mars, and Venus, not only by causing atmospheric erosion but also by delivering material and volatiles to the planets. Here we investigate the atmospheric loss and the delivery of volatiles for the three terrestrial planets using a parameterized model that takes into account the impact simulation results and the flux of impactors given in the literature. We show that the dimensions of the planets, the initial atmospheric surface pressures and the volatiles contents of the impactors are of high importance for the impact delivery and erosion, and that they might be responsible for the differences in the atmospheric evolution of Mars, Earth and Venus.     

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.     

2000—2049年行星天象（一）

本文给出 2 0 0 0 - 2 0 4 9年行星天象的一部分 ,包括水星、金星的东、西大距 ,留及上、下合日 ;金星最亮和最接近地球 ;外行星冲日、最接近地球、合日、留 ;地球和外行星过远近日点计1 5个表     

Interplanetary dust dynamics: I. Long-term gravitational effects of the inner planets on zodiacal dust

Whereas the inner planets' perturbations on meteoroids' and larger interplanetary bodies' orbits have been studied extensively, they are usually neglected in studies of the dynamics of smaller particles producing the zodiacal light through scattering of sunlight. Forces acting on these dust particles are fairly well known and include radiation forces and interaction with the solar wind. This article is the first in a series aimed at improving our knowledge of the dynamical evolution of dust in interplanetary space by studying the combined effects of these perturbations including gravitational perturbations by the planets Venus, Earth, Mars, and Jupiter. The necessity of including effects of the inner planets in dust dynamics investigations is established. Sample trajectories are presented to illustrate commonly occurring phenomenae, such as nonmonotonic changes in semimajor axis, eccentricity, inclination, and in the line of nodes. These perturbations are shown to be due to the inner planets as opposted to Jupiter or nongravitational forces.     

On the internal structures of mercury and venus

Recent radar measures of the radius and mass of Mercury imply a composition for the planet containing about 60% iron. One or other of two conclusions seems inescapable: either that Mercury is a highly exceptional object among terrestrial planets, or that all measures to date of the planet involve substantial systematic error. In either case the situation is such that independent checking of the radius and mass of Mercury by some entirely different means has become of the greatest importance to planetary physics and cosmogony.The recent radar and other determinations of the solid radius of Venus imply an internal structure similar to that of the Earth, namely a liquid core surrounded by a solid mantle and outer-shell zone. The theory also implies that the temperatures within Venus should be slightly higher than at the corresponding parts of the Earth. The proportion of mass in the core of Venus (about 25% of the whole) is entirely consistent with the phase-change hypothesis as to its nature, as of course is also the absence of any liquid or iron core in both Mars and the Moon. On the older iron-core hypothesis, Venus with considerably less iron content by mass than the Earth, and Mars and the Moon with none, would all present problems in different degrees to account for the differences of composition.If Venus began as an all-solid planet, the initial radius would have been about 6300 km, and the total amount of surface reduction to date owing to contraction of the planet would have been almost 40 million km², and as a proportion of the total area only slightly less than the contraction of the Earth. The theory thus predicts the existence of folded and thrusted mountain-systems of terrestrial type at the surface of Venus.     

Convection and heat exchange during rapid rotation

Convection is highly geostrophic in the liquid cores of planets. A three-dimensional Boussinesq model in a plane rotating layer is considered in this study, and an analysis is given of the mechanism of the nonlinear interaction of Fourier waves that results in energy transfer through the spectrum. The structure of the wave triangle is demonstrated to be strongly different on scales smaller (or larger) than those of the leading mode of cyclonic turbulence. The differences in the structure of the triads of the thermal turbulence from that in the Kolmogorov model of homogeneous and isotropic turbulence are shown. The regimes with rotation considered in the study are typical of the modern models of convection and dynamo in the cores of planets, including the 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.     

Volatiles on Earth and Mars: A comparison

Based on our new and previous determinations of halogens in SNC meteorites, the bulk concentrations of halogens in the SPB, which is thought to be Mars, are estimated. The two-component model for the formation of terrestrial planets as proposed byA. E. Ringwood (Geochem. J. 11, 111–135 (1977) andOn the Origin of the Earth and Moon, Springer-Verlag, New York, 1979) andH. Wa¨nke (Philos. Trans. Roy. Soc. London, Ser. A 303, 287–302 (1981) is further substantiated. It is argued that almost all of the H₂O added to Mars during its homogeneous accretion was converted on reaction with metallic Fe to H₂, which escaped. By comparing the solubilities of H₂O and HCl in molten silicates, the amount of H₂O left in the mantle of Mars at the end of accretion can be related to the abundance of Cl. In this way an H₂O content in the Martian mantle of 36 ppm is obtained, corresponding to an ocean covering the whole planet to a depth of about 130 m.The huge quantities of H₂ produced by the reaction of H₂O with metallic iron should also have removed other volatile species by hydrodynamic escape. Thus it is postulated that the present atmospheres of Venus, Earth, and Mars were formed by degassing the interiors of the planets, after the production of H₂ had ceased, i.e., after metallic iron was no longer available. It is also postulated that the large differences in the amounts of primordial rare gases in the atmospheres of Venus, Earth, and Mars are due mainly to different loss factors.Except for gaseous species, Mars is found to be richer in volatile (halogens) and moderately volatile elements than the Earth. The resulting low release factor of⁴⁰Ar for Mars is attributed to a low degree of fractionation, leading to a relatively small crustal enrichment of even the most incompatible elements like K.