Protocore destabilization in planetary embryos formed by cold accretion: Feedbacks from non-Newtonian rheology and energy dissipation

It is suggested that a distinct population of Mars-sized planetary embryos can form by cold accretion in the outer part of the terrestrial zone. A possible radial structure for such embryos consists of an outer silicate-rich layer and an undifferentiated solid protocore. The protocore is divided in a cold undifferentiated central region, a layer of iron, and an outer shell of undifferentiated material. This structure is gravitationally unstable. We investigate the influence of the rheology of the silicate-rich material and of the thermal effects on the protocore destabilization and on the iron core formation. We use a 2D thermomechanical numerical model of a self-gravitating planetary body. The planetary surface is treated as a free surface by imposing a massless weak medium. Our calculations include a non-Newtonian temperature-, pressure-, and strain rate-dependent viscoplastic rheology and thermal contributions from shear heating. We explored the influence of rheology by varying the activation volume, friction angle, and the maximum yield strength of silicate-rich layers. We distinguished three different core formation regimes: exposure mode, fragmentation mode, and transition mode. Like in previous models with Newtonian rheology, the core experiences large deviations from the spherical shape and is temporarily exposed at the surface in the exposure mode. In contrast to the Newtonian models the destruction of the protocores in the fragmentation modes is driven by (i) the spontaneous strain localization along planetary-scale shear zones forming inside the protocore, and/or (ii) descending localized iron diapirs/sheets penetrating the protocore. Feedback from energy dissipation notably modifies the thermal structure of the deforming planetary body. In particular it causes a temperature increase of up to several hundred Kelvin (i) around the moving and deforming protocore and (ii) along planetary scale rupture zones that form inside the protocore. If the protocore is large and has a high viscosity, a large fraction of the dissipated heat is used to increase the temperature of iron.     

Anthropic selection of a Solar System with a high Al/Al ratio: Implications and a possible mechanism

Since our technological civilisation depends on our planet's properties, anthropic selection can explain the close match between the high ²⁶Al/²⁷Al ratios in the earliest Solar System solids, which are difficult to produce in models of star-formation, and the limiting value required to cause (the widely observed) thermal processing of planetesimals. We suggest that volatile loss on heating of planetesimals favours future development of technological civilisations in Solar Systems with elevated concentrations of ²⁶Al.     

Origin of water in the inner Solar System: A kinetic Monte Carlo study of water adsorption on forsterite

The origin of water in the inner Solar System is not well understood. It is believed that temperatures were too high in the accretion disk in the region of the terrestrial planets for hydrous phases to be thermodynamically stable. Suggested sources of water include direct adsorption of hydrogen from the nebula into magma oceans after the terrestrial planets formed, and delivery of asteroidal or cometary material from beyond the zone of the terrestrial planets. We explore a new idea, direct adsorption of water onto grains prior to planetary accretion. This hypothesis is motivated by the observation that the accretion disk from which our planetary system formed was composed of solid grains bathed in a gas dominated by hydrogen, helium, and oxygen. Some of that hydrogen and oxygen combined to make water vapor. We examine quantitatively adsorption of water onto grains in the inner Solar System accretion disk by exploring the adsorption dynamics of water molecules onto forsterite surfaces via kinetic Monte Carlo simulations. We conclude that many Earth oceans of water could be adsorbed.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: I. Effects of interaction with planetesimals and other protoplanets

We have performed N-body simulations on the stage of protoplanet formation from planetesimals, taking into account so-called “type-I migration,” and damping of orbital eccentricities and inclinations, as a result of tidal interaction with a gas disk without gap formation. One of the most serious problems in formation of terrestrial planets and jovian planet cores is that the migration time scale predicted by the linear theory is shorter than the disk lifetime (10⁶-10⁷ years). In this paper, we investigate retardation of type-I migration of a protoplanet due to a torque from a planetesimal disk in which a gap is opened up by the protoplanet, and torques from other protoplanets which are formed in inner and outer regions. In the first series of runs, we carried out N-body simulations of the planetesimal disk, which ranges from 0.9 to 1.1 AU, with a protoplanet seed in order to clarify how much retardation can be induced by the planetesimal disk and how long such retardation can last. We simulated six cases with different migration speeds. We found that in all of our simulations, a clear gap is not maintained for more than 10⁵ years in the planetesimal disk. For very fast migration, a gap cannot be created in the planetesimal disk. For migration slower than some critical speed, a gap does form. However, because of the growth of the surrounding planetesimals, gravitational perturbation of the planetesimals eventually becomes so strong that the planetesimals diffuse into the vicinity of the protoplanets, resulting in destruction of the gap. After the gap is destroyed, close encounters with the planetesimals rather accelerate the protoplanet migration. In this way, the migration cannot be retarded by the torque from the planetesimal disk, regardless of the migration speed. In the second series of runs, we simulated accretion of planetesimals in wide range of semimajor axis, 0.5 to 2-5 AU, starting with equal mass planetesimals without a protoplanet seed. Since formation of comparable-mass multiple protoplanets (“oligarchic growth”) is expected, the interactions with other protoplanets have a potential to alter the migration speed. However, inner protoplanets migrate before outer ones are formed, so that the migration and the accretion process of a runaway protoplanet are not affected by the other protoplanets placed inner and outer regions of its orbit. From the results of these two series of simulations, we conclude that the existence of planetesimals and multiple protoplanets do not affect type-I migration and therefore the migration shall proceed as the linear theory has suggested.     

The formation and habitability of terrestrial planets in the presence of close-in giant planets

‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.     

Orbital evolution and accretion of protoplanets tidally interacting with a gas disk: II. Solid surface density evolution with type-I migration

This paper investigates the surface density evolution of a planetesimal disk due to the effect of type-I migration by carrying out N-body simulation and through analytical method, focusing on terrestrial planet formation. The coagulation and the growth of the planetesimals take place in the abundant gas disk except for a final stage. A protoplanet excites density waves in the gas disk, which causes the torque on the protoplanet. The torque imbalance makes the protoplanet suffer radial migration, which is known as type-I migration. Type-I migration time scale derived by the linear theory may be too short for the terrestrial planets to survive, which is one of the major problems in the planet formation scenario. Although the linear theory assumes a protoplanet being in a gas disk alone, Kominami et al. [Kominami, J., Tanaka, H., Ida, S., 2005. Icarus 167, 231-243] showed that the effect of the interaction with the planetesimal disk and the neighboring protoplanets on type-I migration is negligible. The migration becomes pronounced before the planet's mass reaches the isolation mass, and decreases the solid component in the disk. Runaway protoplanets form again in the planetesimal disk with decreased surface density. In this paper, we present the analytical formulas that describe the evolution of the solid surface density of the disk as a function of gas-to-dust ratio, gas depletion time scale and semimajor axis, which agree well with our results of N-body simulations. In general, significant depletion of solid material is likely to take place in inner regions of disks. This might be responsible for the fact that there is no planet inside Mercury's orbit in our Solar System. Our most important result is that the final surface density of solid components (Σd) and mass of surviving planets depend on gas surface density (Σg) and its depletion time scale (τdep) but not on initial Σd; they decrease with increase in Σg and τdep. For a fixed gas-to-dust ratio and τdep, larger initial Σd results in smaller final Σd and smaller surviving planets, because of larger Σg. To retain a specific amount of Σd, the efficient disk condition is not an initially large Σd but the initial Σd as small as the specified final one and a smaller gas-to-dust ratio. To retain Σd comparable to that of the minimum mass solar nebula (MMSN), a disk must have the same Σd and a gas-to-dust ratio that is smaller than that of MMSN by a factor of 1.3×(τdep/1 Myr) at ∼1 AU. (Equivalently, type-I migration speed is slower than that predicted by the linear theory by the same factor.) The surviving planets are Mars-sized ones in this case; in order to form Earth-sized planets, their eccentricities must be pumped up to start orbit crossing and coagulation among them. At ∼5 AU, Σd of MMSN is retained under the same condition, but to form a core massive enough to start runaway gas accretion, a gas-to-dust ratio must be smaller than that of MMSN by a factor of 3×τdep/1 Myr.     

High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics

The final stage in the formation of terrestrial planets consists of the accumulation of ∼1000-km “planetary embryos” and a swarm of billions of 1-10 km “planetesimals.” During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000-2000 embryos and planetesimals, roughly 5-10 times more particles than in previous simulations. Each simulation formed 2-4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ∼0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earth's current water budget. We demonstrate several new aspects of the accretion process: (1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. (2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. (3) If planetary embryos form relatively slowly, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. (4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation.     

The thermal structure and the location of the snow line in the protosolar nebula: Axisymmetric models with full 3-D radiative transfer

The precise location of the water ice condensation front (‘snow line’) in the protosolar nebula has been a debate for a long time. Its importance stems from the expected substantial jump in the abundance of solids beyond the snow line, which is conducive to planet formation, and from the higher ‘stickiness’ in collisions of ice-coated dust grains, which may help the process of coagulation of dust and the formation of planetesimals. In an optically thin nebula, the location of the snow line is easily calculated to be around 3 AU, subject to brightness variations of the young Sun. However, in its first 5-10 myr, the solar nebula was optically thick, implying a smaller snowline radius due to shielding from direct sunlight, but also a larger radius because of viscous heating. Several models have attempted to treat these opposing effects. However, until recently treatments beyond an approximate 1 + 1D radiative transfer were unfeasible. We revisit the problem with a fully self-consistent 3D treatment in an axisymmetric disk model, including a density-dependent treatment of the dust and ice sublimation. We find that the location of the snow line is very sensitive to the opacities of the dust grains and the mass accretion rate of the disk. We show that previous approximate treatments are quite efficient at determining the location of the snow line if the energy budget is locally dominated by viscous accretion. Using this result we derive an analytic estimate of the location of the snow line that compares very well with results from this and previous studies. Using solar abundances of the elements we compute the abundance of dust and ice and find that the expected jump in solid surface density at the snow line is smaller than previously assumed. We further show that in the inner few AU the refractory species are also partly evaporated, leading to a significantly smaller solid state surface density in the regions where the rocky planets were formed.     

Building the terrestrial planets: Constrained accretion in the inner Solar System

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.     

Meteoritical and dynamical constraints on the growth mechanisms and formation times of asteroids and Jupiter

Thermal models and radiometric ages for meteorites show that the peak temperatures inside their parent bodies were closely linked to their accretion times. Most iron meteorites come from bodies that accreted <0.5 Myr after CAIs formed and were melted by ²⁶Al and ⁶⁰Fe, probably inside 2 AU. Rare carbon-rich differentiated meteorites like ureilites probably also come from bodies that formed <1 Myr after CAIs, but in the outer part of the asteroid belt. Chondrite groups accreted intermittently from diverse batches of chondrules and other materials over a 4 Myr period starting 1 Myr after CAI formation when planetary embryos may already have formed at ∼1 AU. Meteorite evidence precludes accretion of late-forming chondrites on the surface of early-formed bodies; instead chondritic and non-chondritic meteorites probably formed in separate planetesimals. Maximum metamorphic temperatures in chondrite groups are correlated with mean chondrule age, as expected if ²⁶Al and ⁶⁰Fe were the predominant heat sources. Because late-forming bodies could not accrete close to large, early-formed bodies, planetesimal formation may have spread across the nebula from regions where the differentiated bodies formed. Dynamical models suggest that the asteroids could not have accreted in the main belt if Jupiter formed before the asteroids. Therefore Jupiter probably reached its current mass >3-5 Myr after CAIs formed. This precludes formation of Jupiter via a gravitational instability <1 Myr after the solar nebula formed, and strongly favors core accretion. Jupiter probably formed too late to make chondrules by generating shocks directly, or indirectly by scattering Ceres-sized bodies across the belt. Nevertheless, shocks formed by gravitational instabilities or Ceres-sized bodies scattered by planetary embryos may have produced some chondrules. The minimum lifetime for the solar nebula of 3-5 Myr inferred from the total spread of CAI and chondrule ages may exceed the median lifetime of 3 Myr for protoplanetary disks, but is well within the 1-10 Myr observed range. Shorter formation times for extrasolar planets may help to explain their unusual orbits compared to those of solar giant planets.     

On the stability of a planet between Mars and the asteroid belt: Implications for the Planet V hypothesis

The stability of an additional planet between the orbit of Mars and the asteroid belt is examined in the context of the Planet V hypothesis. In this model, the Solar System initially contained a fifth terrestrial planet, “Planet V,” which was removed after ∼700 Myr, a possible trigger for the late heavy bombardment on the inner planets. The model is investigated using 96 N-body integrations of the 8 major planets with an additional body between Mars and the asteroid belt. In more than 1/4 of simulations, Planet V survives for 1000 Myr. In most other cases, Planet V collides with the Sun or hits another planet after several hundred Myr, leaving 4 surviving terrestrial planets. In 24/96 simulations, Planet V is lost by ejection or collision with the Sun while the other four terrestrial planets survive without undergoing a collision. In 18 cases, Planet V is removed at least 200 Myr after the beginning of the simulation. The endstate depends sensitively on the mass of Planet V. Collision with the Sun is likely when Planet V's mass is 0.25 Mars masses or less. When Planet V is more massive than this, collisions involving it and/or other terrestrial planets become commonplace. In unstable systems, the times of first encounter and first collision/ejection depend on the initial aphelion distance of Mars. Reducing Mars's aphelion distance increases these times and also increases the fraction of systems surviving for 1000 Myr. When Mars's current orbit is used, the stability of Planet V increases when these two planets are widely separated initially. Planet V's aphelion distance Q typically begins to cross the asteroid belt within a few tens to a few hundred Myr, and its orbit last leaves the belt several hundred Myr later in most cases. The total time spent with Q>2.1 AU is typically less than 200 Myr.     

Making other earths: dynamical simulations of terrestrial planet formation and water delivery

We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals, assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter's mass, position and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1-4 terrestrial planets inside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11 “habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100+oceans of water (1 ocean=1.5×10²⁴ g), and vary in mass between 0.23M_⊕ and 3.85M_⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1-2M_⊕ protoplanets which can serve as the accretion seeds for 2+M_⊕ planets with large water contents.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.     

From discs to planetesimals: Evolution of gas and dust discs

I review the processes that shape the evolution of protoplanetary discs around young, solar-mass stars. I first discuss observations of protoplanetary discs, and note in particular the constraints these observations place on models of disc evolution. The processes that affect the evolution of gas discs are then discussed, with the focus in particular on viscous accretion and photoevaporation, and recent models which combine the two. I then discuss the dynamics and growth of dust grains in discs, considering models of grain growth, the gas–grain interaction and planetesimal formation, and review recent research in this area. Lastly, I consider the so-called “transitional” discs, which are thought to be observed during disc dispersal. Recent observations and models of these systems are reviewed, and prospects for using statistical surveys to distinguish between the various proposed models are discussed.     

How rapidly did Mars accrete? Uncertainties in the Hf-W timing of core formation

Estimates for the martian core formation timescale based on the hafnium-tungsten (Hf-W) isotopic system have varied by almost an order of magnitude, because of uncertainties in the martian mantle Hf/W ratio. Here we argue that the Hf/W ratio is ∼4 but is uncertain by ∼25%, resulting in (instantaneous) martian core formation timescales ranging from 0 to 10 Myr; accordingly, Hf-W isotope observations currently have limited utility in distinguishing between scenarios in which Mars formed as a stranded embryo and scenarios in which Mars suffered a prolonged accretion history.     

Response of sandstone to atmospheric heating during the STONE 5 experiment: Implications for the palaeofluid record in meteorites

A 1 cm thick sandstone disk exposed to atmospheric re-entry on the heat shield of a spacecraft (the STONE 5 experiment) shows alteration of fluid inclusions compared to a control sample. The sandstone contained inclusions in quartz grains, feldspar grains and calcite cement before flight. After flight, inclusions in the feldspar were all decrepitated, few inclusions in calcite survived intact and they yielded widely varying microthermometric data, and the quartz inclusions also yielded disturbed microthermometric data. The quartz becomes less affected with depth below the surface, and extrapolation suggests would be unaffected at a depth of about 2 cm. These data show that fluid inclusion data from meteorites must be treated with caution, but that a genuine fluid record may survive in the interior portions. The possibility of thermal sterilization to 2 cm depth also implies that small meteorites may be unsuitable vehicles for the transfer of microbial life from one planetary body to another. As the interiors of larger meteorites tend to have very low porosity and permeability, microbial colonization would be difficult, and the potential for panspermia is accordingly low.     

Magnitude of global contraction on Mars from analysis of surface faults: Implications for martian thermal history

Faults provide a record of a planet’s crustal stress state and interior dynamics, including volumetric changes related to long-term cooling. Previous work has suggested that Mars experienced a pulse of large-scale global contraction during Hesperian time. Here we evaluate the evidence for martian global contraction using a recent compilation of thrust faults. Fault-related strains were calculated for wrinkle ridges and lobate scarps to provide lower and upper bounds, respectively, on the magnitude of global contraction from contractional structures observed on the surface of Mars. During the hypothesized pulse of global contraction, contractional strain of −0.007% to −0.13% is indicated by the structures, corresponding to decreases in planetary radius of 112 m to 2.24 km, respectively. By contrast, consideration of all recognized thrust faults regardless of age produces a globally averaged contractional strain of −0.011% to −0.22%, corresponding to a radius decrease of 188 m to 3.77 km since the Early Noachian. The amount of global contraction predicted by thermal models is larger than what is recorded by the faults at the surface, paralleling similar studies for Mercury and the Moon, which suggests that observations of fault populations at the surface may provide tighter bounds on planetary thermal evolution than models alone.     

The evolution of the water distribution in a viscous protoplanetary disk

Astronomical observations have shown that protoplanetary disks are dynamic objects through which mass is transported and accreted by the central star. This transport causes the disks to decrease in mass and cool over time, and such evolution is expected to have occurred in our own solar nebula. Age dating of meteorite constituents shows that their creation, evolution, and accumulation occupied several Myr, and over this time disk properties would evolve significantly. Moreover, on this timescale, solid particles decouple from the gas in the disk and their evolution follows a different path. It is in this context that we must understand how our own solar nebula evolved and what effects this evolution had on the primitive materials contained within it. Here we present a model which tracks how the distribution of water changes in an evolving disk as the water-bearing species experience condensation, accretion, transport, collisional destruction, and vaporization. Because solids are transported in a disk at different rates depending on their sizes, the motions will lead to water being concentrated in some regions of a disk and depleted in others. These enhancements and depletions are consistent with the conditions needed to explain some aspects of the chemistry of chondritic meteorites and formation of giant planets. The levels of concentration and depletion, as well as their locations, depend strongly on the combined effects of the gaseous disk evolution, the formation of rapidly migrating rubble, and the growth of immobile planetesimals. Understanding how these processes operate simultaneously is critical to developing our models for meteorite parent body formation in the Solar System and giant planet formation throughout the galaxy. We present examples of evolution under a range of plausible assumptions and demonstrate how the chemical evolution of the inner region of a protoplanetary disk is intimately connected to the physical processes which occur in the outer regions.     

Implications of large elastic thicknesses for the composition and current thermal state of Mars

The martian elastic lithosphere thickness Te has recently been constrained by modeling the geodynamical response to loading at the martian polar caps and Te was found to exceed 300 km at the north pole today. Geological evidence suggests that Mars has been volcanically active in the recent past and we have reinvestigated the martian thermal evolution, identifying models which are consistent with Te>300 km and the observed recent magmatic activity. We find that although models satisfying both constraints can be constructed, special assumptions regarding the concentration and distribution of radioactive elements, the style of mantle convection and/or the mantle's volatile content need to be made. If a dry mantle rheology is assumed, strong plumes caused by, e.g., a strongly pressure dependent mantle viscosity or endothermic phase transitions near the core-mantle boundary are required to allow for decompression melting in the heads of mantle plumes. For a wet mantle, large mantle water contents of the order of 1000 ppm are required to allow for partial mantle melting. Also, for a moderate crustal enrichment of heat producing, elements the planet's bulk composition needs to be 25 and 50% sub-chondritic for dry and wet mantle rheologies, respectively. Even then, models resulting in a globally averaged elastic thicknesses of Te>300 km are difficult to reconcile with most elastic thickness estimates available for the Hesperian and Amazonian periods. It therefore seems likely that large elastic thicknesses in excess of 300 km are not representative for the bulk of the planet and that Te possibly shows a large degree of spatial heterogeneity.     

Detection of sporadic impact flashes on the Moon: Implications for the luminous efficiency of hypervelocity impacts and derived terrestrial impact rates

We present the first redundant detection of sporadic impact flashes on the Moon from a systematic survey performed between 2001 and 2004. Our wide-field lunar monitoring allows us to estimate the impact rate of large meteoroids on the Moon as a function of the luminous energy received on Earth. It also shows that some historical well-documented mysterious lunar events fit in a clear impact context. Using these data and traditional values of the luminous efficiency for this kind of event we obtain that the impact rate on Earth of large meteoroids (0.1-10 m) would be at least one order of magnitude larger than currently thought. This discrepancy indicates that the luminous efficiency of the hypervelocity impacts is higher than 10⁻², much larger than the common belief, or the latest impact fluxes are somewhat too low, or, most likely, a combination of both. Our nominal analysis implies that on Earth, collisions of bodies with masses larger than 1 kg can be as frequent as 80,000 per year and blasts larger than 15-kton could be as frequent as one per year, but this is highly dependent on the exact choice of the luminous efficiency value. As a direct application of our results, we expect that the impact flash of the SMART-1 spacecraft should be detectable from Earth with medium-sized telescopes.