Recent high precision meteoritic data improve constraints on the formation timescale and bulk composition of the terrestrial planets. High resolution N-body simulations allow direct comparison of embryo growth timescale and accretion zones to these constraints. In this paper, we present results of high resolution simulations for embryo formation from a disc of up to 41,000 fully-self gravitating planetesimals with the GPU-based N-body code GENGA. Our results indicate that the growth of embryos are highly dependent on the initial conditions. More massive initial planetesimals, a shorter gas disc decay timescale and initially eccentric Jupiter and Saturn (EJS) all lead to faster growth of embryos. Asteroid belt material can thereby be implanted into the terrestrial planet region via sweeping secular resonances. This could possibly explain the rapid growth of Mars within 10 Myr inferred from its Hf-W chronology. The sweeping secular resonance almost completely clears the asteroid belt and deposits this material in the Mercury-Venus region, altering the composition of embryos there. This could result in embryos in the Mercury-Venus region accreting an unexpectedly high mass fraction from beyond 2 AU. Changing the initial orbits of Jupiter and Saturn to more circular (CJS) or assuming embryos formed in a gas free environment removes the sweeping secular resonance effect and thus greatly decreases material accreted from beyond 2 AU for Mercury-Venus region embryos. We therefore propose that rock samples from Mercury and Venus could aid greatly in deducing the condition and lifetime of the initial protoplanetary gas disc during planetesimal and embryo formation, as well as the initial architecture of the giant planets.
Mars is likely to be a planetary embryo formed through collisions with planetesimals, which can explain its small mass and rapid formation timescale obtained from 182Hf-182$W chronometry. In the classical theory of planet formation, the final embryo mass is determined only by the solid surface density. However, embryos can stir surrounding planetesimals, leading to fragmentation through erosive (cratering) collisions. We find that radial drift of small fragments can drastically reduce the solid surface density. On the other hand, embryo growth is accelerated by fragment accretion. Since collis…
Recent high precision meteoritic data infers that Mars finished its accretion rapidly within 10 Myr of the beginning of the Solar system and had an accretion zone that did not entirely overlap with the Earth's. Here we present a detailed study of the accretion zone of planetary embryos from high resolution simulations of planetesimals in a disc. We found that all simulations with Jupiter and Saturn on their current eccentric orbits (EJS) result in a similar accretion zone between fast-forming Mars and Earth region embryos. Assuming more circular orbits for Jupiter and Saturn (CJS), on the othe…
The solar system's terrestrial planets are thought to have accreted over millions of years out of a sea of smaller embryos and planetesimals. Because it is impossible to know the surface density profile for solids and size frequency distribution in the primordial solar nebula, distinguishing between the various proposed evolutionary schemes has been historically difficult. Nearly all previous simulations of terrestrial planet formation assume that Moon to Mars massed embryos formed throughout the inner solar system during the primordial gas-disk phase. However, validating this assumption throu…
Here we discuss the current state of knowledge on how atmospheric escape processes can fractionate noble gas isotopes and moderately volatile rock-forming elements that populate primordial atmospheres, magma ocean related environments, and catastrophically outgassed steam atmospheres. Variations of isotopes and volatile elements in different planetary reservoirs keep information about atmospheric escape, composition and even the source of accreting material. We summarize our knowledge on atmospheric isotope ratios and discuss the latest evidence that proto-Venus and Earth captured small H$_2$-…
Planetary embryos form protoplanets via mutual collisions, which can lead to the development of magma oceans. During their solidification, large amounts of the mantles' volatile contents may be outgassed. The resulting H$_2$O/CO$_2$ dominated steam atmospheres may be lost efficiently via hydrodynamic escape due to the low gravity and the high stellar EUV luminosities. Protoplanets forming later from such degassed building blocks could therefore be drier than previously expected. We model the outgassing and subsequent hydrodynamic escape of steam atmospheres from such embryos. The efficient out…
Many dynamical aspects of the solar system can be explained by the outer planets experiencing a period of orbital instability sometimes called the Nice Model. Though often correlated with a perceived delayed spike in the lunar cratering record known as the Late Heavy Bombardment (LHB), recent work suggests that this event may have occurred much earlier; perhaps during the epoch of terrestrial planet formation. While current simulations of terrestrial accretion can reproduce many observed qualities of the solar system, replicating the small mass of Mars requires modification to standard planet …
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…
Chondrules are millimeter-sized spherules that dominate primitive meteorites (chondrites) originating from the asteroid belt. The incorporation of chondrules into asteroidal bodies must be an important step in planet formation, but the mechanism is not understood. We show that the main growth of asteroids can result from gas-drag-assisted accretion of chondrules. The largest planetesimals of a population with a characteristic radius of 100 km undergo run-away accretion of chondrules within ~3 Myr, forming planetary embryos up to Mars sizes along with smaller asteroids whose size distribution m…
Dauphas and Pourmand (2011) [Nature 473, 489--492] estimated the accretion timescale of Mars to be 1.8 $^{+0.9}_{-1.0}$ Myr from the W isotopes of martian meteorites. This timescale was derived assuming perfect metal-silicate equilibration between the impactor and the target's mantle. However, in the case of a small impactor most likely only a fraction of the target's mantle is involved in the equilibration, while only a small part of the impactor's core equilibrates in the case of a giant impact. We examined the effects of imperfect equilibration using results of high-resolution $N$-body simu…
It has been shown that some aspects of the terrestrial planets can be explained, particularly the Earth/Mars mass ratio, when they form from a truncated disk with an outer edge near 1.0 au (Hansen 2009). This has been previously modeled starting from an intermediate stage of growth utilizing pre-formed planetary embryos. We present simulations that were designed to test this idea by following the growth process from km-sized objects located between 0.7 to 1.0 au up to terrestrial planets. The simulations explore initial conditions where the solids in the disk are planetesimals with radii initi…
Models of terrestrial planet formation for our solar system have been successful in producing planets with masses and orbits similar to those of Venus and Earth. However, these models have generally failed to produce Mars-sized objects around 1.5 AU. The body that is usually formed around Mars' semimajor axis is, in general, much more massive than Mars. Only when Jupiter and Saturn are assumed to have initially very eccentric orbits (e $\sim$ 0.1), which seems fairly unlikely for the solar system, or alternately, if the protoplanetary disk is truncated at 1.0 AU, simulations have been able to …
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…
We use radiation hydrodynamics with direct particle integration to explore the feasibility of chondrule formation in planetary embryo bow shocks. The calculations presented here are used to explore the consequences of a Mars-size planetary embryo traveling on a moderately excited orbit through the dusty, early environment of the solar system. The embryo's eccentric orbit produces a range of supersonic relative velocities between the embryo and the circularly orbiting gas and dust, prompting the formation of bow shocks. Temporary atmospheres around these embryos, which can be created via volati…
Advances in computing power and numerical methodologies over the past several decades sparked a prolific output of dynamical investigations of the late stages of terrestrial planet formation. Among other peculiar inner solar system qualities, the ability of simulations to reproduce the small mass of Mars within the planets' geochemically inferred accretion timescale of <10 Myr after the appearance of calcium aluminum-rich inclusions (CAIs) is arguably considered the gold standard for judging evolutionary hypotheses. At present, a number of independent models are capable of consistently generat…
Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals…
Latest research in planet formation indicate that Mars formed within a few million years (Myr) and remained a planetary embryo that never grew to a more massive planet. It can also be expected from dynamical models, that most of Mars' building blocks consisted of material that formed in orbital locations just beyond the ice line which could have contained ~0.1-0.2 wt. % of H2O. By using these constraints, we estimate the nebula-captured and catastrophically outgassed volatile contents during the solidification of Mars' magma ocean and apply a hydrodynamic upper atmosphere model for the study o…
With approximately one ninth of Earth's mass, Mars is widely considered to be a stranded planetary embryo that never became a fully-grown planet. A currently popular planet formation theory predicts that Mars formed near Earth and Venus and was subsequently scattered outwards to its present location. In such a scenario, the compositions of the three planets are expected to be similar to each other. However, bulk elemental and isotopic data for martian meteorites demonstrate that key aspects of Mars' composition are markedly different from that of Earth. This suggests that Mars formed outside o…
The timescales of accretion, core formation, and magmatic differentiation in planetary bodies can be constrained using extinct radionuclide systems. Experiments have shown that Ni becomes more siderophile with decreasing pressure, which is reflected in the progressively higher Fe/Ni ratios in the mantles of Earth, Mars and Vesta. Mars formed rapidly and its mantle has a high Fe/Ni ratio, so the 60Fe-60Ni decay system (t1/2=2.62 Myr) is well suited to establish the timescale of core formation in this object. We report new measurements of 60Ni/58Ni ratios in bulk SNC/martian (Shergotty-Nakhla-Ch…
We discuss the current state of knowledge of terrestrial planet formation from the aspects of different planet formation models and isotopic data from 182Hf-182W, U-Pb, lithophile-siderophile elements, 48Ca/44Ca isotope samples from planetary building blocks, 36Ar/38Ar, 20Ne/22Ne, 36Ar/22Ne isotope ratios in Venus' and Earth's atmospheres, the expected solar 3He abundance in Earth's deep mantle and Earth's D/H sea water ratios that shed light on the accretion time of the early protoplanets. Accretion scenarios that can explain the different isotope ratios, including a Moon-forming event after …
Radiometric dating indicates that Mars accreted in the first ~4 Myr of solar system formation, which coincides with the formation and possible migration of Jupiter. While nebular gas from the protoplanetary disk was still present, Jupiter may have migrated inwards and tacked at 1.5 AU in a 3:2 resonance with Saturn. This migration excited planetary building blocks in the inner solar system, resulting in extensive mixing and planetesimal removal. Here we evaluate the plausible nature of Mars' building blocks, focusing in particular on how its growth was influenced by the formation and migration…
Protoplanets develop via collisions between planetesimals and planetary embryos in the final assembly stage of planet formation. The efficiency of the planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of embryos and planetesimals. In final assembly planet formation models, the gravitational interactions between planetesimals are usually neglected due to computational difficulties, namely, computations require fewer resources in this way. We investigated the effect of this simplification via modeling the planet formation efficiency in a circumste…
Mass-independent isotopic anomalies of carbonaceous and non-carbonaceous meteorites show a clear dichotomy suggesting an efficient separation of the inner and outer solar system. Observations show that ring-like structures in the distribution of mm-sized pebbles in protoplanetary disks are common. These structures are often associated with drifting pebbles being trapped by local pressure maxima in the gas disk. Similar structures may also have existed in the sun's natal disk, which could naturally explain the meteorite/planetary isotopic dichotomy. Here, we test the effects of a strong pressur…
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…
We model the early stages of planet formation in the Solar System, including continual planetesimal formation, and planetesimal and pebble accretion onto planetary embryos in an evolving disk driven by a disk wind. The aim is to constrain aspects of planet formation that have large uncertainties by matching key characteristics of the Solar System. The model produces a good fit to these characteristics for a narrow range of parameter space. Planetary growth beyond the ice line is dominated by pebble accretion. Planetesimal accretion is more important inside the ice line. Pebble accretion inside…
Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constrain…
Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of …
The effect of protoplanetary differentiation on the fate of life essential volatiles like nitrogen and carbon and its subsequent effect on the dynamics of planetary growth is unknown. Because the dissolution of nitrogen in magma oceans depends on its partial pressure and oxygen fugacity, it is an ideal proxy to track volatile redistribution in protoplanets as a function of their sizes and growth zones. Using high pressure and high temperature experiments in graphite undersaturated conditions, here we show that the iron loving character of nitrogen is an order of magnitude higher than previous …
The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets. We investigated the effects of the planetesimal-driven migration of Jupiter and Saturn, and the influence of their mutual 1:2 MMR crossing on terrestrial planet formation for the first time, by performing N-body simulations. These simulations considered distinct timescales of MMR crossing and planet migration. In total, 68 high-resolution simulation runs using 2000 disk planetesimals were performed, which wa…
The growth and composition of Earth is a direct consequence of planet formation throughout the Solar System. We discuss the known history of the Solar System, the proposed stages of growth and how the early stages of planet formation may be dominated by pebble growth processes. Pebbles are small bodies whose strong interactions with the nebula gas lead to remarkable new accretion mechanisms for the formation of planetesimals and the growth of planetary embryos. Many of the popular models for the later stages of planet formation are presented. The classical models with the giant planets on fixe…
To reproduce the orbits and masses of the terrestrial planets (analogs) of the solar system, most studies scrutinize simulations for success as a batch. However, there is insufficient discussion in the literature on the likelihood of forming planet analogs simultaneously in the same system (analog system). To address this issue, we performed 540 N-body simulations of protoplanetary disks representative of typical models in the literature. We identified a total of 194 analog systems containing at least three analogs, but only 17 systems simultaneously contained analogs of the four terrestrial p…
The formation of the four terrestrial planets of the solar system is one of the most fundamental problems in the planetary sciences. However, the formation of Mercury remains poorly understood. We investigated terrestrial planet formation by performing 110 high-resolution N-body simulation runs using more than 100 embryos and 6000 disk planetesimals representing a primordial protoplanetary disk. To investigate the formation of Mercury, these simulations considered an inner region of the disk at 0.2-0.5 au (the Mercury region) and disks with and without mass enhancements beyond the ice line loc…
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…
We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial pla…
Considering the huge computational resources required by smoothed particle hydrodynamics (SPH) simulations and the overestimation of post-collision materials from perfect merging, we develop a statistical method to deal with collisions during the formation of planetary systems by introducing random material loss. In this method the mass and water content lost by the sole outcome from every merger vary randomly within a range dependent on the total mass and water content of colliding bodies. The application of the random loss method to the planet formation in the solar system shows a good consi…
Minerals detection over large volume of spectra is the challenge addressed by current hyperspectral imaging spectrometer in Planetary Science. Instruments such OMEGA (Mars Express), CRISM (Mars Reconnaissance Orbiter), M^{3} (Chandrayaan-1), VIRTIS (Rosetta) and many more, have been producing very large datasets since one decade. We propose here a fast supervised detection algorithm called LinMin, in the framework of linear unmixing, with innovative arrangement in order to treat non-linear cases due to radiative transfer in both atmosphere and surface. We use reference laboratory and synthetic…
The inner solar system's modern orbital architecture provides inferences into the epoch of terrestrial planet formation; a ~100 Myr time period of planet growth via collisions with planetesimals and other proto-planets. While classic numerical simulations of this scenario adequately reproduced the correct number of terrestrial worlds, their semi-major axes and approximate formation timescales, they struggled to replicate the Earth-Mars and Venus-Mercury mass ratios. In a series of past independent investigations, we demonstrated that Mars' mass is possibly the result of Jupiter and Saturn's ea…
In spite of substantial advancements in simulating planet formation, the planet Mercury's diminutive mass, isolated orbit, and the absence of planets with shorter orbital periods in the solar system continue to befuddle numerical accretion models. Recent studies have shown that, if massive embryos (or even giant planet cores) formed early in the innermost parts of the Sun's gaseous disk, they would have migrated outward. This migration may have reshaped the surface density profile of terrestrial planet-forming material and generated conditions favorable to the formation of Mercury-like planets…
A successful solar system model must reproduce the four terrestrial planets. Here, we focus on 1) the likelihood of forming Mercury and the four terrestrial planets in the same system (a 4-P system); 2) the orbital properties and masses of each terrestrial planet; and 3) the timing of Earth's last giant impact and the mass accreted by our planet thereafter. Addressing these constraints, we performed 450 N-body simulations of terrestrial planet formation based on narrow protoplanetary disks with mass confined to 0.7-1.0 au. We identified 164 analogue systems, but only 24 systems contained Mercu…
Recent improvements to GPU hardware and the symplectic N-body code GENGA allow for unprecedented resolution in simulations of planet formation. In this paper, we report results from high-resolution N-body simulations of terrestrial planet formation that are mostly direct continuation of our previous 10 Myr simulations (Woo et al. 2021a) until 150 Myr. By assuming that Jupiter and Saturn have always maintained their current eccentric orbits (EJS), we are able to achieve a reasonably good match to the current inner solar system architecture. However, due to the strong radial mixing that occurs i…
The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. We review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, an…
