Recent high-precision measurements of the isotopic composition of lunar rocks demonstrate that the bulk silicate Earth and the Moon show an unexpectedly high degree of similarity. This is inconsistent with one of the primary results of classic dynamical simulations of the widely accepted giant impact model for the formation of the Moon, namely that most of the mass of the Moon originates from the impactor, not Earth.
Resolution of this discrepancy without changing the main premises of the giant impact model requires total isotopic homogenisation of Earth and impactor material after the impact for a wide range of elements including O, Si, K, Ti, Nd and W. Even if this process could explain the O isotope similarity, it is unlikely to work for the much heavier, refractory elements. Given the increasing uncertainty surrounding the giant impact model in light of these geochemical data, alternative hypotheses for lunar formation should be explored. In this paper, we revisit the hypothesis that the Moon was formed directly from terrestrial mantle material. We show that the dynamics of this scenario requires a large amount of energy, almost instantaneously generated additional energy. The only known source for this additional energy is nuclear fission. We show that it is feasible to form the Moon through the ejection of terrestrial silicate material triggered by a nuclear explosion at Earths core-mantle boundary (CMB), causing a shock wave propagating through the Earth. Hydrodynamic modelling of this scenario shows that a shock wave created by rapidly expanding plasma resulting from the explosion disrupts and expels overlying mantle and crust material.
The origin of Saturn's inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn's rings is debated. Charnoz et al. (2010) introduced the idea that the smallest inner moons could form from the spreading of the rings' edge while Salmon et al. (2010) showed that the rings could have been initially massive, and so was the ring's progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested in Canup (2010). However, the process driving mid-sized moons accretion from the icy debris disks has not been i…
Despite its importance to questions of lunar origin, the chemical composition of the Moon is not precisely known. In recent years, however, the isotopic composition of lunar samples has been determined to high precision and found to be indistinguishable from the terrestrial mantle despite widespread isotopic heterogeneity in the Solar System. In the context of the giant-impact hypothesis, this level of isotopic homogeneity can evolve if the proto-lunar disk and post-impact Earth undergo turbulent mixing into a single uniform reservoir while the system is extensively molten and partially vapori…
The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, n…
Among the elements exhibiting non-mass dependent isotopic variations in meteorites, chromium (Cr) has been central in arguing for an isotopic homogeneity between the Earth and the Moon. However, the 54Cr isotope composition of the Moon relies on 2 samples only, which define an average value that is slightly different from the terrestrial standard. Here, by determining the Cr isotopic composition of 17 lunar, 9 terrestrial and 5 enstatite chondrite samples, we re-assess the isotopic similarity between these different planetary bodies, and provide the first robust estimate for the Moon. In avera…
Migration of planetesimals from the feeding zone of the terrestrial planets, which was divided into seven regions depending on the distance to the Sun, was simulated. The influence of gravity of all planets was taken into account. In some cases, the embryos of the terrestrial planets rather than the planets themselves were considered; their masses were assumed to be 0.1 or 0.3 of the current masses of the planets. The arrays of orbital elements of migrated planetesimals were used to calculate the probabilities of their collisions with the planets, the Moon, or their embryos. Based on our calcu…
From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter's orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth's embryo, when its mass was smaller than the current mass of the Earth. While the Earth's embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Ju…
We present integrations of a model Solar System with five terrestrial planets (beginning ~30-50 Myr after the formation of primitive Solar System bodies) in order to determine the preferred regions of parameter space leading to a giant impact that resulted in the formation of the Moon. Our results indicate which choices of semimajor axes and eccentricities for Theia (the proto-Moon) at this epoch can produce a late Giant Impact, assuming that Mercury, Venus, and Mars are near the current orbits. We find that the likely semimajor axis of Theia, at the epoch when our simulations begin, depends o…
[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet's feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet's mass and its volatile inventory. Instead, we find that the feeding …
In the giant impact theory for lunar origin, the Moon forms from material ejected by the impact into an Earth-orbiting disk. Here we report the initial results from a silicate melt-vapor equilibrium chemistry model for such impact-generated planetary debris disks. In order to simulate the chemical behavior of a two-phase (melt+vapor) disk, we calculate the temperature-dependent pressure and chemical composition of vapor in equilibrium with molten silicate from 2000 to 4000 K. We consider the elements O, Na, K, Fe, Si, Mg, Ca, Al, Ti, and Zn for a range of bulk silicate compositions (Earth, Moo…
We study the evolution of debris created in the giant impacts expected during the final stages of terrestrial planet formation. The starting point is the debris created in a simulation of the Moon-forming impact. The dynamical evolution is followed for 10 Myr including the effects of Earth, Venus, Mars and Jupiter. The spatial distribution evolves from a clump in the first few months to an asymmetric ring for the first 10 kyr and finally becoming an axisymmetric ring by about 1 Myr after the impact. By 10 Myr after the impact 20% of the particles have been accreted onto Earth and 17% onto Venu…
Water content and the internal evolution of terrestrial planets and icy bodies are closely linked. The distribution of water in planetary systems is controlled by the temperature structure in the protoplanetary disk and dynamics and migration of planetesimals and planetary embryos. This results in the formation of planetesimals and planetary embryos with a great variety of compositions, water contents and degrees of oxidation. The internal evolution and especially the formation time of planetesimals relative to the timescale of radiogenic heating by short-lived 26Al decay may govern the amount…
The Kepler mission found hundreds of planet candidates within the habitable zones (HZ) of their host star, including over 70 candidates with radii larger than 3 Earth radii ($R_\oplus$) within the optimistic habitable zone (OHZ) (Kane et al. 2016). These giant planets are potential hosts to large terrestrial satellites (or exomoons) which would also exist in the HZ. We calculate the occurrence rates of giant planets ($R_p =$~3.0--25~$R_\oplus$) in the OHZ and find a frequency of $(6.5 \pm 1.9)\%$ for G stars, $(11.5 \pm 3.1)\%$ for K stars, and $(6 \pm 6)\%$ for M stars. We compare this with p…
Ascertaining rocky exoplanets dynamic evolution requires better understanding of key internal thermophysical processes that shaped their geological surfaces, heat fluxes, volatiles and atmospheric content. New high-pressure experiments on iron and silicates compressible, melting and transport properties are providing new constraints that demand reassessments of super-Earths thermal and magnetic evolution models. We examine the interior structure, temperature distribution, thermal states and dynamo action of these planets with masses ranging from 1-10 ME. We show that the shallow adiabaticity o…
We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such configurations was deduced from oversimplified tidal models assuming either a constant tidal torque or a torque linear in the tidal frequency. A more accurate treatment requires that the torque be decomposed into the Darwin-Kaula series over the tidal modes, and that this decomposition be combined with a realistic choice of rheological properties of the mantle. This…
We investigate the possibility that the Moon's formation impact was triggered by an early dynamical instability of the giant planets. We consider the well-studied "jumping Jupiter" hypothesis for the solar system's instability, where Jupiter and Saturn's semi-major axes evolve in step-wise manner from their primordially compact architecture to their present locations. Moreover, we test multiple different configurations for the primordial system of terrestrial planets and the Moon-forming projectile, with particular focus on the almost equal masses impact. We find that the instability/migration…
In the canonical model of Moon formation, a Mars-sized protoplanet "Theia" collides with proto-Earth at close to their mutual escape velocity $v_{\rm esc}$ and a common impact angle 45°. The "graze-and-merge" collision strands a fraction of Theia's mantle into orbit, while Earth accretes most of Theia and its momentum. Simulations show that this produces a hot, high angular momentum, silicate-dominated protolunar system, in substantial agreement with lunar geology, geochemistry, and dynamics. However, a Moon that derives mostly from Theia's mantle, as angular momentum dictates, is challenged b…
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 is 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 timescale of 100 years 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 s…
During the last stages of the terrestrial planet formation, planets grow mainly through giant-impacts with large planetary embryos. The Earth's Moon was suggested to form through one of these impacts. However, since the proto-Earth has experienced many giant-impacts, several moons are naturally expected to form through a sequence of multiple (including smaller scale) impacts. Each impact potentially forms a sub-Lunar mass moonlet that interacts gravitationally with the proto-Earth and possibly with previously-formed moonlets. Such interactions result in either moonlet-moonlet mergers, moonlet …
Current protoplanetary dust coagulation theory does not predict dry silicate planetesimals, in tension with the Earth. While remedies to this predicament have been proposed, they have generally failed numerical studies, or are in tension with the Earth's (low, volatility dependent) volatile and moderately volatile elemental abundances. Expanding on the work of Boley et al. (2014), we examine the implications of molten grain collisions and find that they may provide a solution to the dry silicate planetesimal problem. Further, the source of the heating, be it the hot inner disk or an FU Orionis…
The final stage of terrestrial planet formation consists of the cleanup of residual planetesimals after the giant impact phase. Dynamically, a residual planetesimal population is needed to damp the high eccentricities of the terrestrial planets after the giant impact stage. Geochemically, highly siderophile element (HSE) abundance patterns inferred for the terrestrial planets and the Moon suggest that a total of about 0.01 M_Earth of chondritic material was delivered as `late veneer' by planetesimals to the terrestrial planets after the end of giant impacts. Here we combine these two independe…
The Earth's comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al., 2010, where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a p…
We investigate spectra of airless rocky exoplanets with a theoretical framework that self-consistently treats reflection and thermal emission. We find that a silicate surface on an exoplanet is spectroscopically detectable via prominent Si-O features in the thermal emission bands of 7 - 13 μm and 15 - 25 μm. The variation of brightness temperature due to the silicate features can be up to 20 K for an airless Earth analog, and the silicate features are wide enough to be distinguished from atmospheric features with relatively high-resolution spectra. The surface characterization thus provides a …
Planetary rotation rate has a significant effect on atmospheric circulation, where the strength of the Coriolis effect in part determines the efficiency of latitudinal heat transport, altering cloud distributions, surface temperatures, and precipitation patterns. In this study we use the ROCKE-3D dynamic-ocean general circulation model to study the effects of slow rotations and increased insolations on the 'fractional habitability' and silicate weathering rate of an Earth-like world. Defining the fractional habitability f_h to be the percentage of a planet's surface which falls in the 0 <= T <…
We present conclusions from a large number of N-body simulations of the giant impact phase of terrestrial planet formation. We focus on new results obtained from the recently proposed Grand Tack model, which couples the gas-driven migration of giant planets to the accretion of the terrestrial planets. The giant impact phase follows the oligarchic growth phase, which builds a bi-modal mass distribution within the disc of embryos and planetesimals. By varying the ratio of the total mass in the embryo population to the total mass in the planetesimal population and the mass of the individual embry…
Terrestrial and lunar rocks share chemical and isotopic similarities in refractory elements, suggestive of a common precursor. By contrast, the marked depletion of volatile elements in lunar rocks together with their enrichment in heavy isotopes compared to Earth s mantle suggests that the Moon underwent evaporative loss of volatiles. However, whether equilibrium prevailed during evaporation, and, if so, at what conditions (temperature, pressure and oxygen fugacity) remain unconstrained. Chromium may shed light on this question, as it has several thermodynamically-stable, oxidised gas species …
The chemical compositions of Earth's core and mantle provide insight into the processes that led to their formation. N-body simulations, on the other hand, generally do not contain chemical information, and seek to only reproduce the masses and orbits of the terrestrial planets. These simulations can be grouped into four potentially viable scenarios of Solar System formation (Classical, Annulus, Grand Tack, and Early Instability) for which we compile a total of 433 N-body simulations. We relate the outputs of these simulations to the chemistry of Earth's core and mantle using a melt-scaling la…
In order to test planetary accretion and differentiation scenarios, we integrated a multistage core-mantle differentiation model with N-body accretion simulations. Impacts between embryos and planetesimals result in magma ocean formation and episodes of core formation. The core formation model combines rigorous chemical mass balance with metal-silicate element partitioning data. The primary constraint on the combined model is the composition of the Earth's primitive mantle, the composition of the Martian mantle, and the mass fractions of the metallic cores of Earth and Mars. The model is refin…
It is generally accepted that silicate-metal (`rocky') planet formation relies on coagulation from a mixture of sub-Mars sized planetary embryos and (smaller) planetesimals that dynamically emerge from the evolving circum-solar disc in the first few million years of our Solar System. Once the planets have, for the most part, assembled after a giant impact phase, they continue to be bombarded by a multitude of planetesimals left over from accretion. Here we place limits on the mass and evolution of these planetesimals based on constraints from the highly siderophile element (HSE) budget of the …
Embryos of the Moon and the Earth may have formed as a result of contraction of a common parental rarefied condensation. The required angular momentum of this condensation could largely be acquired in a collision of two rarefied condensations producing the parental condensation. With the subsequent growth of embryos of the Moon and the Earth taken into account, the total mass of as-formed embryos needed to reach the current angular momentum of the Earth-Moon system could be below 0.01 of the Earth mass. For the low lunar iron abundance to be reproduced with the growth of originally iron-deplet…
Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in Δ"17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average Δ"17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.
The distribution and isotopic composition of volatile elements in planetary materials holds a key to the characterization of the early solar system and the Moon's formation. The Moon and Earth are chemically and isotopically very similar. However, the Moon is highly depleted in volatile elements and the origin of this depletion is still debated. We present gallium isotopic and elemental measurements in a large set of lunar samples to constrain the origin of this volatile depletion. We show that while Ga has a geochemical behavior different from zinc, both elements show a systematic enrichment …
The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally …
The paper discusses a model of the bombardment of the Earth and the Moon by small bodies when these planets were formed. It is shown that the total ice mass delivered with the bodies to the Earth from the feeding zone of the giant planets and the outer asteroid belt could have been comparable to the total mass of the Earth's oceans. Objects that initially crossed Jupiter's orbit could become Earth-crossers mainly within the first one million years. Most collisions of bodies originally located at a distance of 4 to 5 AU (astronomical units) from the Sun with the Earth occurred during the first …
The classical scenario of terrestrial planet formation is characterized by a phase of giant impacts among Moon-to-Mars mass planetary embryos. While the classic model and its adaptations have produced adequate analogs of the outer three terrestrial planets, Mercury's origin remains elusive. Mercury's high-core mass fraction compared to the Earth's is particularly outstanding. Among collisional hypotheses, this feature has been long interpreted as the outcome of an energetic giant impact among two massive protoplanets. Here, we revisit the classical scenario of terrestrial planet formation with…
The problem of the formation of the Moon is still not explained satisfactorily. While it is a generally accepted scenario that the last giant impact on Earth between some 50 to 100 million years after the starting of the formation of the terrestrial planets formed our natural satellite, there are still many open questions like the isotopic composition which is identical for these two bodies. In our investigation we will not deal with these problems of chemical composition but rather undertake a purely dynamical study to find out the probability of a Mars-sized body to collide with the Earth sh…
In the giant impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however the current lunar orbital inclination of 5 degrees requires a subsequent dynamical process that is still debated. In addition, the giant impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here, we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the past lunar inclination must have been very large, defying theoretical explanations. We present a new tidal evolution model …
All 4 giant planets in the Solar System host systems of multiple moons, whereas the terrestrial planets only host up to 2 moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons could stably orbit the Earth, or an Earth-mass exoplanet. We perform a series of N-body simulations of closely-spaced equal mass moons in nested orbits around an Earth-mass planet orbiting a Sun-like star. The innermost moon begins near the host planets Roche radius, and the system is packed until the outermost moon begins near the stability limit for single mo…
The final assembly of terrestrial planets occurs via massive collisions, which can launch copious clouds of dust that are warmed by the star and glow in the infrared. We report the real-time detection of a debris-producing impact in the terrestrial planet zone around a 35-million year-old solar analog star. We observed a substantial brightening of the debris disk at 3-5 μm, followed by a decay over a year, with quasi-periodic modulations of the disk flux. The behavior is consistent with the occurrence of a violent impact that produced vapor out of which a thick cloud of silicate spherules cond…
Kaib & Cowan (2015) recently used terrestrial planet formation simulations to conclude that the moon-forming impactor (Theia) had only a ~5% or less chance of having the same oxygen isotope composition as Earth, while Mastrobuono-Battisti et al. (2015) used seemingly similar simulations and methods to arrive at a higher value of ~20% or more. Here we derive the results of both papers from a single set of simulations. Compared to Kaib & Cowan (2015), the analysis of Mastrobuono-Battisti et al. (2015) systematically yields more massive Theia analogs and imposes flatter isotopic gradients across …
A terrestrial planet is molten during formation and may remain so if subject to intense insolation or tidal forces. Observations continue to favour the detection and characterisation of hot planets, potentially with large outgassed atmospheres. We aim to determine the radius of hot Earth-like planets with large outgassed atmospheres and explore differences between molten and solid silicate planets and their influence on the mass-radius relationship and transmission and emission spectra. An interior-atmosphere model, combined with static structure calculations, tracks the evolving radius of a r…
Subsequent to the Moon's formation, late accretion to the terrestrial planets modified their silicate crusts and mantles. We combine dynamical N-body and Monte Carlo simulations to determine impact probabilities, impact velocities, and expected mass augmentation onto the terrestrial planets from three sources: planetesimals left over from primary accretion, asteroids from the E-belt, and comets arriving from the outer Solar System. We present estimates of the amount of cometary material striking the terrestrial planets in an early episode of planetesimal-driven giant planet migration (Mojzsis …
Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic composition show them to be highly similar. In contrast, the compositions of other solar system bodies are significantly different than the Earth and Moon. This poses a major challenge to the giant impact scenario since the Moon-forming impactor is then thought to al…
Given their tendency to be incorporated into the core during differentiation, the highly-siderophile elements (HSEs) in Earth's mantle are thought to have been accreted as a `late veneer' after the end of the giant impact phase. Bottke et al (2010) proposed that the large Earth-to-Moon HSE abundance ratio can be explained if the late veneer was characterized by large (D = 1000-4000km) impactors. Here we simulate the evolution of the terrestrial planets during a stochastic late veneer phase from the end of accretion until the start of the late heavy bombardment ~500 Myr later. We show that a la…
Scientific visualization tools are currently not optimized to create cinematic, production-quality representations of numerical data for the purpose of science communication. In our pipeline \texttt{Estra}, we outline a step-by-step process from a raw simulation into a finished render as a way to teach non-experts in the field of visualization how to achieve production-quality outputs on their own. We demonstrate feasibility of using the visual effects software Houdini for cinematic astrophysical data visualization, informed by machine learning clustering algorithms. To demonstrate the capabil…
Characterizing habitable exoplanets and/or their moons is of paramount importance. Here we show the results of our magnetic field topological modeling which demonstrate that terrestrial exoplanet-exomoon coupled magnetospheres work together to protect the early atmospheres of both the exoplanet and the exomoon. When exomoon magnetospheres are within the exoplanet's magnetospheric cavity, the exomoon magnetosphere acts like a protective magnetic bubble providing an additional magnetopause confronting the stellar winds when the moon is on the dayside. In addition, magnetic reconnection would cre…
The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid cores and subsurface oceans, whose dynamics then significantly differ from solid body rotation. In particular, tides in non-synchronized bodies and libration in synchronized ones are known to be capable of exciting the so-called elliptical instability, i.e. a generic instability corresponding to the destabilization of two-dimensional flows with elliptical stre…
