The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions

Collisions are a fundamental process in the creation of asteroid families and in satellite formation. For this reason, understanding the outcome of impacts is fundamental to the accurate modeling of the formation and evolution of such systems. Smoothed-Particle Hydrodynamics/N-body codes have become the techniques of choice to study large-scale impact outcomes, including both the fragmentation of the parent body and the gravitational interactions between fragments. It is now possible to apply this technique to targets with either monolithic or rubble-pile internal structures. In this paper we apply these numerical techniques to rubble-pile targets, extending previous investigations by Durda et al. (Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M. [2004]. Icarus 170, 243–257; Durda, D.D., Bottke, W.F., Nesvorný, D., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C. [2007]. Icarus 186, 498–516). The goals are to study asteroid–satellite formation and the morphology of the size–frequency distributions (SFDs) from 175 impact simulations covering a range of collision speeds, impact angles, and impactor sizes. Our results show that low-energy impacts into rubble-pile and monolithic targets produce different features in the resulting SFDs and that these are potentially diagnostic of the initial conditions for the impact and the internal structure of the parent bodies of asteroid families. In contrast, super-catastrophic events (i.e., high-energy impacts with large specific impact energy) result in SFDs that are similar to each other. We also find that rubble-pile targets are less efficient in producing satellites than their monolithic counterparts. However, some features, such as the secondary-to-primary diameter ratio and the relative separation of components in binary systems, are similar for these two different internal structures of parent bodies.     

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.     

Collisional history of asteroids: Evidence from Vesta and the Hirayama families

Collisional evolution studies of asteroids indicate that the initial asteroid population at the time mean collisional velocities were pumped up to ～5 km/sec was only modestly larger than it is today; i.e., the asteroid belt was already depleted relative to the mean surface density elsewhere in the planetary region. Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run, subject to three constraints: they must (a) evolve to the present observed asteroid size distribution, (b) preserve Vesta's basaltic crust, and (c) produce at least the observed number of major Hirayama families. A “runaway growth” initial asteroid population distribution is found to best satisfy these constraints. A new model is presented for calculating the fragmental size distribution for the disruption of large, gravitationally bound bodies in which the material strength is increased by hydrostatic self-compression. This model predicts that large asteroid behave as intrinsically strong bodies, even if they have had a history of being collisionally fractured. This model, when applied to the breakup of the Themis and Eos family parent bodies, gives size distributions in reasonably good agreement with those observed.     

The influence of gravitational acceleration on the supernova-driven Parker instability

Within a framework of 2D magnetohydrodynamic (MHD) simulations, we explore the dynamical regimes initiated by a supernova explosion in a magnetized stratified interstellar medium (ISM). We concentrate on the formation of large-scale magnetic structures and outflows connected with the Parker instability. For the sake of simplicity we only show models with a fixed explosion energy corresponding to a single supernova (SN) occurring in host galaxies with different fixed values of the gravitational acceleration g and different ratios of specific heats. We show that in general, depending on these two parameters, three different regimes are possible: a slowly growing Parker instability on time-scales much longer than the galactic rotation period for small g; the Parker instability growing at roughly the rotation period, which for ratios of specific heats larger than one is accompanied by an outflow resulting from the explosion for intermediate g; and a rapidly growing instability and a strong blow-out flow for large g . By means of numerical simulations and analytical estimates we show that the explosion energy and gravitational acceleration which separate the three regimes scale as Eg ²∼constant in the 2D case. We expect that in the 3D case this scaling law is Eg ³∼constant . Our simulations demonstrate furthermore that a single SN explosion can lead to the growth of multiple Parker loops in the disc and large-scale magnetic field loops in the halo, extending over 2–3 kpc horizontally and up to 3 kpc vertically above the mid-plane of the disc.     

Karin cluster formation by asteroid impact

Insights into collisional physics may be obtained by studying the asteroid belt, where large-scale collisions produced groups of asteroid fragments with similar orbits and spectra known as the asteroid families. Here we describe our initial study of the Karin cluster, a small asteroid family that formed 5.8±0.2 Myr ago in the outer main belt. The Karin cluster is an ideal ‘natural laboratory’ for testing the codes used to simulate large-scale collisions because the observed fragments produced by the 5.8-Ma collision suffered apparently only limited dynamical and collisional erosion. To date, we have performed more than 100 hydrocode simulations of impacts with non-rotating monolithic parent bodies. We found good fits to the size-frequency distribution of the observed fragments in the Karin cluster and to the ejection speeds inferred from their orbits. These results suggest that the Karin cluster was formed by a disruption of an ≈33-km-diameter asteroid, which represents a much larger parent body mass than previously estimated. The mass ratio between the parent body and the largest surviving fragment, (832) Karin, is ≈0.15-0.2, corresponding to a highly catastrophic event. Most of the parent body material was ejected as fragments ranging in size from yet-to-be-discovered sub-km members of the Karin cluster to dust grains. The impactor was ≈5.8 km across. We found that the ejections speeds of smaller fragments produced by the collision were larger than those of the larger fragments. The mean ejection speeds of >3-km-diameter fragments were . The model and observed ejection velocity fields have different morphologies perhaps pointing to a problem with our modeling and/or assumptions. We estimate that ∼5% of the large asteroid fragments created by the collision should have satellites detectable by direct imaging (separations larger than 0.1 arcsec). We also predict a large number of ejecta binary systems with tight orbits. These binaries, located in the outer main belt, could potentially be detected by lightcurve observations. Hydrocode modeling provides important constraints on the interior structure of asteroids. Our current work suggests that the parent asteroid of the Karin cluster may have been an unfractured (or perhaps only lightly fractured) monolithic object. Simulations of impacts into fractured/rubble pile targets were so far unable to produce the observed large gap between the first and second largest fragment in the Karin cluster, and the steep slope at small sizes (≈6.3 differential index). On the other hand, the parent asteroid of the Karin cluster was produced by an earlier disruptive collision that created the much larger, Koronis family some 2-3 Gyr ago. Standard interpretation of hydrocode modeling then suggests that the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. We discuss several solutions to this apparent paradox.     

Asteroid Models from the Pan-STARRS Photometry

We present simulations on the asteroid photometric data that will be provided by the Pan-STARRS (Panoramic Survey Telescope and Rapid Response System). The simulations were performed using realistic shape and light-scattering models, random orientation of spin axes, and rotation periods in the range 2–24 h. We show that physical models of asteroids can be reconstructed from this data with some limitations (possible multiple pole solutions). We emphasize the potential of sparse photometric data to produce models of a large number of asteroids within the next decade and we outline further tests with fast and slow rotators, tumblers, and binary asteroids.     

Addition of water and ammonia cloud microphysics to the EPIC model

An active hydrological cycle has been added to the EPIC general circulation model (GCM) for planetary applications, with a special emphasis on Jupiter. Scientists have suspected for decades that clouds, and in particular latent heating, strongly influence Jupiter's atmospheric dynamics and this research provides a tool to investigate this phenomenon. Components of the model have been adapted for the planetary setting from recently published Earth microphysics schemes. The behavior of the cloud model is investigated in two steps. First, we explore in detail the runtime properties of a nominal model, and second, through sensitivity tests we determine how the full microphysics and selected components of the scheme affect the formation and evolution of clouds and precipitation. Results from our one-dimensional (vertical) simulations match expectations based on thermochemical models about the vertical positioning of ammonia and water clouds, and the nature of precipitation. Using (two-dimensional) meridional plane simulations, we investigate the latitudinal variation of clouds. We conclude that the zonal-wind structure under the visible cloud deck strongly affects the position of the cloud bases, also that the atmospheric dynamics modifies the resulting cloud structure that we can determine in 1D models. We describe in detail an equatorial storm system observed in our 2D simulations. We also show that simplification of our microphysics scheme would improperly simulate large-scale weather phenomena on Jupiter. We support future laboratory tests and in situ measurements that would improve the cloud parameterization scheme and would also add more constraints on the global distribution of condensibles and on the zonal wind-structure. The complete computer program resulting from this research can be downloaded as open-source software from NASA's Planetary Data System (PDS) Atmospheres node.     

The fossilized size distribution of the main asteroid belt

Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9-4.5 Ga. These results suggest the main belt's wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter D?120 km asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near D∼100-120 km are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of D<1000 km bodies) was 150-250 times larger than it is today, in agreement with recent dynamical simulations.     

Surface Expressions of Structural Features on Eros

NEAR Shoemaker imaging of the asteroid Eros has revealed a variety of surface forms that probably reflect underlying structures. They range from global to local in scale. The most prominent positive topographic feature is a long ridge, Rahe Dorsum, which extends over 18 km and has the morphology of a thrust fault. Two large, ancient trough systems are also present. Grooves are ubiquitous, commonly occur in suborthogonal sets, and have linear or scalloped outlines. The grooves on Eros are similar in morphology and scale to those on other small bodies such as Gaspra, Ida, and Phobos and are likely to have a similar mode of origin, namely drainage of regolith into underlying fractures. Models that use groove dimensions as indicators of regolith thickness imply depths of up to several tens of meters. Many craters have been subjected to structural control, resulting in squared outlines. We find no evidence that specific groove sets are associated with individual impact events; however, evidence exists that preexisting structures have been reactivated by later impact activity. The large scale of Rahe Dorsum and many grooves on Eros's surface suggests that the asteroid is a largely coherent, but fractured body.     

Size-frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families

We investigate the morphology of size-frequency distributions (SFDs) resulting from impacts into 100-km-diameter parent asteroids, represented by a suite of 161 SPH/N-body simulations conducted to study asteroid satellite formation [Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M., 2004. Icarus 170, 243-257]. The spherical basalt projectiles range in diameter from 10 to 46 km (in equally spaced mass increments in logarithmic space, covering six discrete sizes), impact speeds range from 2.5 to 7 km/s (generally in 1 km/s increments), and impact angles range from 15° to 75° (nearly head-on to very oblique) in 15° increments. These modeled SFD morphologies match very well the observed SFDs of many known asteroid families. We use these modeled SFDs to scale to targets both larger and smaller than 100 km in order to gain insights into the circumstances of the impacts that formed these families. Some discrepancies occur for families with parent bodies smaller than a few tens of kilometers in diameter (e.g., 832 Karin), however, so due caution should be used in applying our results to such small families. We find that ∼20 observed main-belt asteroid families are produced by the catastrophic disruption of D>100 km parent bodies. Using these data as constraints, collisional modeling work [Bottke Jr., W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H.F., 2005b. Icarus 179, 63-94] suggests that the threshold specific energy, , needed to eject 50% of the target body's mass is very close to that predicted by Benz and Asphaug [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20].     

Simulations of impact ejecta and regolith accumulation on Asteroid Eros

We have carried out a set of Monte Carlo simulations of the placement of impact ejecta on Asteroid 433 Eros, with the aim of understanding the distribution and accumulation of regolith. The simulations consisted of two stages: (1) random distribution of primary impact sites derived from a uniform isotropic flux of impactors, and (2) integration of the orbits of test particle ejecta launched from primary impact points until their re-impact or escape. We integrated the orbits of a large number of test particles (typically 10⁶ per individual case). For those particles that did not escape we collected the location of their re-impact points to build up a distribution on the asteroid surface. We find that secondary impact density is mostly controlled by the overall topography of the asteroid. A gray-scale image of the density of secondary ejecta impact points looks, in general, like a reduced-scale negative of the topography of the asteroid's surface. In other words, regolith migration tends to fill in the topography of Eros over time, whereas topographic highs are denuded of free material. Thus, the irregular shape of Eros is not a steady-state configuration, but the result of larger stochastic events.     

Earth impact probability of the Asteroid (25143) Itokawa to be sampled by the spacecraft Hayabusa

The Japanese spacecraft Hayabusa is planed to reach the Asteroid Itokawa in September 2005, and to bring back some samples of its surface to Earth in 2007. We have studied the future possible evolution of this asteroid by integrating numerically over 100 Myr a set of 39 initially indistinguishable orbits (clones), obtained either by small variations of the nominal initial conditions, or by using different computers (introducing different round-off errors). The results indicate that an Earth impact of this 500-m-size asteroid is likely within a million years, which is only a factor of four larger than the average impact frequency of asteroids of this size. The mission Hayabusa may thus sample a good candidate for being among the next 500-m-size Earth impactors.     

Empirical and theoretical comparisons of the Chicxulub and Sudbury impact structures

Abstract— Chicxulub and Sudbury are 2 of the largest impact structures on Earth. Research at the buried but well‐preserved Chicxulub crater in Mexico has identified 6 concentric structural rings. In an analysis of the preserved structural elements in the eroded and tectonically deformed Sudbury structure in Canada, we identified ring‐like structures corresponding in both radius and nature to 5 out of the 6 rings at Chicxulub. At Sudbury, the inner topographic peak ring is missing, which if it existed, has been eroded. Reconstructions of the transient cavities for each crater produce the same range of possible diameters: 80–110 km. The close correspondence of structural elements between Chicxulub and Sudbury suggests that these 2 impact structures are approximately the same size, both having a main structural basin diameter of ?150 km and outer ring diameters of ?200 km and ?260 km. This similarity in size and structure allows us to combine information from the 2 structures to assess the production of shock melt (melt produced directly upon decompression from high pressure impact) and impact melt (shock melt and melt derived from the digestion of entrained clasts and erosion of the crater wall) in large impacts. Our empirical comparisons suggest that Sudbury has ?70% more impact melt than does Chicxulub (?31,000 versus ?18,000 km³) and 85% more shock melt (27,000 km³ versus 14,500 km³). To examine possible causes for this difference, we develop an empirical method for estimating the amount of shock melt at each crater and then model the formation of shock melt in both comet and asteroid impacts. We use an analytical model that gives energy scaling of shock melt production in close agreement with more computationally intense numerical models. The results demonstrate that the differences in melt volumes can be readily explained if Chicxulub was an asteroid impact and Sudbury was a comet impact. The estimated 70% difference in melt volumes can be explained by crater size differences only if the extremes in the possible range of melt volumes and crater sizes are invoked. Preheating of the target rocks at Sudbury by the Penokean Orogeny cannot explain the excess melt at Sudbury, the majority of which resides in the suevite. The greater amount of suevite at Sudbury compared to Chicxulub may be due to the dispersal of shock melt by cometary volatiles at Sudbury.     

Magnetic fields and the dynamics of spiral galaxies

We investigate the dynamics of magnetic fields in spiral galaxies by performing 3D magnetohydrodynamics simulations of galactic discs subject to a spiral potential using cold gas, warm gas and a two-phase mixture of both. Recent hydrodynamic simulations have demonstrated the formation of interarm spurs as well as spiral arm molecular clouds, provided the interstellar medium model includes a cold H  i phase. We find that the main effect of adding a magnetic field to these calculations is to inhibit the formation of structure in the disc. However, provided a cold phase is included, spurs and spiral arm clumps are still present if β≳ 0.1 in the cold gas. A caveat to the two-phase calculations though is that by assuming a uniform initial distribution, β≳ 10 in the warm gas, emphasizing that models with more consistent initial conditions and thermodynamics are required. Our simulations with only warm gas do not show such structure, irrespective of the magnetic field strength.
Furthermore, we find that the introduction of a cold H  i phase naturally produces the observed degree of disorder in the magnetic field, which is again absent from simulations using only warm gas. Whilst the global magnetic field follows the large-scale gas flow, the magnetic field also contains a substantial random component that is produced by the velocity dispersion induced in the cold gas during the passage through a spiral shock. Without any cold gas, the magnetic field in the warm phase remains relatively well ordered apart from becoming compressed in the spiral shocks. Our results provide a natural explanation for the observed high proportions of disordered magnetic field in spiral galaxies and we thus predict that the relative strengths of the random and ordered components of the magnetic field observed in spiral galaxies will depend on the dynamics of spiral shocks.     

A plausible cause of the late heavy bombardment

Abstract— We show that at the end of the main accretional period of the terrestrial planets, a few percent of the initial planetesimal population in the 1–2 AU zone is left on highly‐inclined orbits in the inner solar system. The final depletion of this leftover population would cause an extended bombardment of all of the terrestrial planets, slowly decaying with a timescale on the order of 60 Ma. Because of the large impact velocities dictated by the high inclinations, these projectiles would produce craters much larger than those formed by asteroids of equal size on typical current near‐Earth asteroid orbits: on the Moon, basins could have been formed by bodies as small as 20 km in diameter, and 10 km craters could be produced by 400 m impactors. To account for the observed lunar crater record, the initial population of highly‐inclined leftovers would need to be a few times that presently in the main asteroid belt, at all sizes, in agreement with the simulations of the primordial sculpting of both these populations. If a terminal lunar cataclysm (a spike in the crater record ～3.9 Ga ago) really occurred on the Moon, it was not caused by the highly‐inclined leftover population, because of the monotonic decay of the latter.     

Grazing Impacts Upon Earth’s Surface: Towards an Understanding of the Rio Cuarto Crater Field

The origin of the Rio Cuarto crater field, Argentina has been widely debated since the early 1990s when it was first brought to public attention. In a binary on–off sense, however, the craters are either of a terrestrial origin or they formed via a large asteroid impact. While there are distinct arguments in favour of the former option being the correct interpretation, it is the latter possibility that is principally investigated here, and five distinct impact formation models are described. Of the impact scenarios it is found that the most workable model, although based upon a set of fine-tuned initial conditions, is that in which a large, 100–150-m initial diameter asteroid, entered Earth’s atmosphere on a shallow angle path that resulted in temporary capture. In this specific situation a multiple-thousand kilometer long flight path enables the asteroid to survive atmospheric passage, without suffering significant fragmentation, and to impact the ground as a largely coherent mass. Although the odds against such an impact occurring are extremely small, the crater field may nonetheless be interpreted as having potentially formed via a very low-angle, smaller than 5° to the horizon, impact with a ground contact speed of order 5 km/s. Under this scenario, as originally suggested by Schultz and Lianza (Nature 355:234, 1992), the largest of the craters (crater A) in the Rio Cuarto structure was produced in the initial ground impact, and the additional, smaller craters are interpreted as being formed through the down-range transport of decapitated impactor material and crater A ejecta.     

Thermal evolution of the early Moon

The early thermal evolution of Moon has been numerically simulated to understand the magnitude of the impact-induced heating and the initially stored thermal energy of the accreting moonlets. The main objective of the present study was to understand the nature of processes leading to core–mantle differentiation and the production and cooling of the initial convective magma ocean. The accretion of Moon was commenced over a time scale of 100 yr after the giant impact event around 30–100 million years in the early solar system. We studied the dependence of the planetary processes on the impact scenarios, the initial average temperature of the accreting moonlets, and the size of the protomoon that accreted rapidly beyond the Roche limit within the initial 1 yr after the giant impact. The simulations indicate that the accreting moonlets should have a minimum initial averaged temperature around 1600 K. The impacts would provide additional thermal energy. The initial thermal state of the moonlets depends upon the environment prevailing within the Roche limit that experienced episodes of extensive vaporization and recondensation of silicates. The initial convective magma ocean of depth more than 1000 km is produced in the majority of simulations along with the global core–mantle differentiation in case the melt percolation of the molten metal through porous flow from bulk silicates was not the major mode of core–mantle differentiation. The possibility of shallow magma oceans cannot be ruled out in the presence of the porous flow. Our simulations indicate the core–mantle differentiation within the initial 10² to 10³ yr of the Moon accretion. The majority of the convective magma ocean cooled down for crystallization within the initial 10³ to 10⁴ yr.     

Accretion of the asteroids: Implications for their thermal evolution

Thermal models of asteroids generally assume that they accreted either instantaneously or over an extended interval with a prescribed growth rate. It is conventionally assumed that the onset of accretion of chondrite parent bodies was delayed until a substantial fraction of the initial ²⁶Al had decayed. However, this interval is not consistent with the early melting, and differentiation of parent bodies of iron meteorites. Formation time scales are tested by dynamical simulations of accretion from small primary planetesimals. Gravitational accretion yields rapid runaway growth of large planetary embryos until most smaller bodies are depleted. In a given simulation, all asteroid‐sized bodies have comparable growth times, regardless of size. For plausible parameters, growth times are shorter than the lifetime of ²⁶Al, consistent with thermal models that assume instantaneous accretion. Rapid growth after planetesimal formation is consistent with differentiation of parent bodies of iron meteorites, but not with the assumed delay in formation of chondritic bodies. After the initial growth stage, there is an interval of slower evolution until the belt is stirred and the embryos are dynamically removed. During this interval, a fraction of asteroid‐sized bodies experience large accretional impacts, allowing bodies of the same final size to have very different histories of radius versus time. Accretion from small primary planetesimals leaves some fraction of material in bodies small enough to preserve CAIs while avoiding heating by ²⁶Al. Unheated material can be a significant fraction of the mass that remains after large embryos are removed from the Main Belt.