We present results from a suite of N-body simulations that follow the 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--4.0 AU and the collisional growth is followed until the completion of planetary accretion (> 100 Myr). 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, and orbits of Jupiter and Saturn. We end up with one to five 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.
When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are…
The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early …
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 growth time scales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. We quantify the timescales and spatial distribution of planetary embryos via collisional growth and fragmentation of dynamically forming 100km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. We connect a on…
In this paper we extend our numerical method for simulating terrestrial planet formation from Leinhardt and Richardson (2005) to include dynamical friction from the unresolved debris component. In the previous work we implemented a rubble pile planetesimal collision model into direct N-body simulations of terrestrial planet formation. The new collision model treated both accretion and erosion of planetesimals but did not include dynamical friction from debris particles smaller than the resolution limit for the simulation. By extending our numerical model to include dynamical friction from the …
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…
According to the core accretion theory, circumbinary embryos can form only beyond a critical semimajor axis (CSMA). However, due to the relatively high density of solid materials in the inner disk, significant amount of small planetesimals must exist in the inner zone when embryos were forming outside this CSMA. So embryos migration induced by the planetesimal swarm is possible after the gas disk depletion. Through numerical simulations, we found (i) the scattering-driven inward migration of embryos is robust, planets can form in the habitable zone if we adopt a mass distribution of MMSN-like …
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…
Using the Cosmic Origins Spectrograph onboard the Hubble Space Telescope, we have obtained high-resolution ultraviolet observations of GD 362 and PG 1225-079, two helium-dominated, externally-polluted white dwarfs. We determined or placed useful upper limits on the abundances of two key volatile elements, carbon and sulfur, in both stars; we also constrained the zinc abundance in PG 1225-079. In combination with previous optical data, we find strong evidence that each of these two white dwarfs has accreted a parent body that has evolved beyond primitive nebular condensation. The planetesimal a…
No planets exist inside the orbit of Mercury and the terrestrial planets of the solar system exhibit a localized configuration. According to thermal structure calculation of protoplanetary disks, a silicate condensation line (~ 1300 K) is located around 0.1 au from the Sun except for the early phase of disk evolution, and planetesimals could have formed inside the orbit of Mercury. A recent study of disk evolution that includes magnetically driven disk winds showed that the gas disk obtains a positive surface density slope inside ~ 1 au from the central star. In a region with positive midplane…
The composition of planets is largely determined by the chemical and dynamical evolution of the disk during planetesimal formation and growth. To predict the diversity of exoplanet compositions, previous works modeled planetesimal composition as the equilibrium chemical composition of a proto- planetary disk at a single time. However, planetesimals form over an extended period of time, during which, elements sequentially condense out of the gas as the disk cools and are accreted onto planetesi- mals. To account for the evolution of the disk during planetesimal formation, we couple models of di…
The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolut…
We present numerical simulations of terrestrial planet formation that examine the growth continuously from planetesimals to planets in the inner Solar System. Previous studies show that the growth will be inside-out, but it is still common practice to assume that the entire inner disk will eventually reach a bi-modal distribution of embryos and planetesimals. For the combinations of disk mass, initial planetesimal radius and gas disk lifetime explored in this work the entire disk never reaches a simple bi-modal mass distribution. We find that the inside-out growth is amplified by the combined …
We investigate planetesimal accretion via a direct N-body simulation of an annulus at 1 AU orbiting a 1 $M_{\odot}$ star. The planetesimal ring, which initially contains N = $10^6$ bodies is evolved into the oligarchic growth phase. Unlike previous lower resolution studies, we find that the mass distribution of planetesimals develops a bump at intermediate mass after the oligarchs form. This feature marks a boundary between growth modes. The smallest planetesimals are packed tightly enough together to populate mean motion resonances with the oligarchs, which heats the small bodies, enhancing t…
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…
We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about 60% - 80%. In each simulation, 3 - 4 terrestrial planets are formed inside "Jupiter" with m…
The intermediate phases of planet formation are not directly observable due to lack of emission from planetesimals. Planet formation is, however, a dynamically active process resulting in collisions between the evolving planetesimals and the production of dust. Thus, indirect observation of planet formation may indeed be possible in the near future. In this paper we present synthetic observations based on numerical N-body simulations of the intermediate phase of planet formation including a state-of-the-art collision model, EDACM, which allows multiple collision outcomes, such as, accretion, e…
Outgassing Composition of the Murchison Meteorite: Implications for Volatile Depletion of Planetesimals and Interior-atmosphere Connections for Terrestrial Exoplanets
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…
In their model for the origin of the parent bodies of iron meteorites, Bottke et al proposed differentiated planetesimals that were formed in the region of 1-2 AU during the first 1.5 Myr, as the parent bodies, and suggested that these objects and their fragments were scattered into the asteroid belt as a result of interactions with planetary embryos. Although viable, this model does not include the effect of a giant planet that might have existed or been growing in the outer regions. We present the results of a concept study where we have examined the effect of a planetary body in the orbit o…
We investigate the formation of terrestrial planets in the late stage of planetary formation using two-planet model. At that time, the protostar has formed for about 3 Myr and the gas disk has dissipated. In the model, the perturbations from Jupiter and Saturn are considered. We also consider variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals. Our results show that, terrestrial planets are formed in 50 Myr, and the accretion rate is about $60% - 80%$. In each simulation, 3 - 4 terrestrial planets are formed inside "Jupiter" with…
Recent detection of exoplanets with Earth-like insolation attracts growing interest in how common Earth-like aqua planets are beyond the solar system. While terrestrial planets are often assumed to capture icy or water-rich planetesimals, a primordial atmosphere of nebular origin itself can produce water through oxidation of the atmospheric hydrogen with oxidising minerals from incoming planetesimals or the magma ocean. Thermodynamically, normal oxygen buffers produce water comparable in mole number to or more than hydrogen. Thus, the primordial atmosphere would likely be highly enriched with …
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…
The past decade has seen major progress in our understanding of terrestrial planet formation. Yet key questions remain. In this review we first address the growth of 100 km-scale planetesimals as a consequence of dust coagulation and concentration, with current models favoring the streaming instability. Planetesimals grow into Mars-sized (or larger) planetary embryos by a combination of pebble- and planetesimal accretion. Models for the final assembly of the inner Solar System must match constraints related to the terrestrial planets and asteroids including their orbital and compositional dist…
In the standard model of core accretion, the cores of the giant planets form by the accretion of planetesimals. In this scenario, the evolution of the planetesimal population plays an important role in the formation of massive cores. Recently, we studied the role of planetesimal fragmentation in the in situ formation of a giant planet. However, the exchange of angular momentum between the planet and the gaseous disk causes the migration of the planet in the disk. In this new work, we incorporate the migration of the planet and globally study the role of planet migration in the formation of a m…
It has been long proposed that, if all the terrestrial planets form within a tiny ring of solid material at around 1 AU, the concentrated mass-distance distribution of the current system can be reproduced. Recent planetesimal formation models also support this idea. In this study, we revisit the ring model by performing a number of high-resolution N-body simulations for 10 Myr of a ring of self-interacting planetesimals, with various radial distributions of the gas disc. We found that even if all the planetesimals form at ~1 AU in a minimum mass solar nebula-like disc, the system tends to spre…
As to April 2010, 48 TNO (trans-Neptunian Object) binaries have been found. This is about 6% of known TNOs. However, in previous theoretical studies of planetary formation in the TNO region, the effect of binary formation has been neglected. TNO binaries can be formed through a variety of mechanisms, such as three-body process, dynamical friction on two massive bodies, inelastic collisions between two bodies etc. Most of these mechanisms become more effective as the distance from the Sun increases. In this paper, we studied three-body process using direct N-body simulations. We systematically …
Modern models of terrestrial planet formation require solids depletion interior to 0.5-0.7 au in the planetesimal disk to explain the small mass of Mercury. Earth and Venus analogues emerge after ~100 Myr collisional growth while Mercury form in the diffusive tails of the planetesimal disk. We carried out 250 N-body simulations of planetesimal disks with mass confined to 0.7-1.0 au to study the statistics of close encounters which were recently proposed as an explanation for the high iron mass fraction in Mercury by Deng (2020). We formed 39 Mercury analogues in total and all proto-Mercury ana…
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 …
Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We simulate planetary system evolution around Sun-like stars from initial conditions that comprise: an inner disk of planetesimals and planetary embryos, three giant planets at Jupiter-Saturn distances, and a massive outer planetesimal disk. We then calculate dust production rates and debris disk SEDs assuming that each planetesimal particle represents an ensemble…
We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow kee…
To study the terrestrial-type planet formation during the post oligarchic growth, the initial distributions of planetary embryos and planetesimals used in N-body simulations play an important role. Most of these studies typically use ad hoc initial distributions based on theoretical and numerical studies. We analyze the formation of planetary systems without gas giants around solar-type stars focusing on the sensitivity of the results to the particular initial distributions of planetesimals and embryos. The formation of terrestrial planets in the habitable zone (HZ) and their final water conte…
Recent work has shown that aside from the classical view of collisions by increasingly massive planetesimals, the accretion of mm- to m-sized 'pebbles' can also reproduce the mass-orbit distribution of the terrestrial planets. Here, we perform N-body simulations to study the effects of pebble accretion onto growing planetesimals of different diameters located in the inner Solar System. The simulations are run to occur during the lifetime of the gas disc while also simultaneously taking Jupiter's growth into account. We find that pebble accretion can increase the mass in the solid disc by at le…
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…
Transit surveys combined with Doppler data have revealed a class of gas giant planets that are massive and highly enriched in heavy elements (e.g., HD149026b, GJ436b, and HAT-P-20b). It is tempting to consider these planets as validation of core accretion plus gas capture because it is often assumed that disk instability planets should be of nebular composition. We show in this paper, to the contrary, that gas giants that form by disk instability can have a variety of heavy element compositions, ranging from sub- to super-nebular values. High levels of enrichment can be achieved through one or…
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 …
We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these …
We present preliminary results of terrestrial planet formation using on the one hand classical numerical integration of hundreds of small bodies on CPUs and on the other hand -- for comparison reasons -- the results of our GPU code with thousands of small bodies which then merge to larger ones. To be able to determine the outcome of collision events we use our smooth particle hydrodynamics (SPH) code which tracks how water is lost during such events.
Super-Earths with orbital periods less than 100 days are extremely abundant around Sun-like stars. It is unlikely that these planets formed at their current locations. Rather, they likely formed at large distances from the star and subsequently migrated inward. Here we use N-body simulations to study the effect of super-Earths on the accretion of rocky planets. In our simulations, one or more super-Earths migrates inward through a disk of planetary embryos and planetesimals embedded in a gaseous disk. We tested a wide range of migration speeds and configurations. Fast-migrating super-Earths ($…
The New Horizons flyby of the cold classical Kuiper Belt object MU69 showed it to be a contact binary. The existence of other contact binaries in the 1-10km range raises the question of how common these bodies are and how they evolved into contact. Here we consider that the lobes of MU69 formed as a binary in the Solar nebula, and calculate its orbital evolution in the presence of gas. We find that the sub-Keplerian wind of the disk brings the drag timescales for 10km bodies under 1 Myr for quadratic-velocity drag. In the Kuiper belt, however, the drag is linear with velocity and the effect of…
Chondrites, the building blocks of the terrestrial planets, have mass and atomic proportions of oxygen, iron, magnesium, and silicon totaling $\geq$90\% and variable Mg/Si ($\sim$25\%), Fe/Si (factor of $\geq$2), and Fe/O (factor of $\geq$3). The Earth and terrestrial planets (Mercury, Venus, and Mars) are differentiated into three layers: a metallic core, a silicate shell (mantle and crust), and a volatile envelope of gases, ices, and, for the Earth, liquid water. Each layer has different dominant elements (e.g., increasing Fe content with depth and increasing oxygen content to the surface). …
Planetesimals form in gas-rich protoplanetary disks around young stars. However, protoplanetary disks fade in about 10 Myr. The planetesimals (and also many of the planets) left behind are too dim to study directly. Fortunately, collisions between planetesimals produce dusty debris disks. These debris disks trace the processes of terrestrial planet formation for 100 Myr and of exoplanetary system evolution out to 10 Gyr. This chapter begins with a summary of planetesimal formation as a prelude to the epoch of planetesimal destruction. Our review of debris disks covers the key issues, including…
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…
Recent observations started revealing the compositions of protostellar discs and planets beyond the Solar System. In this paper, we explore how the compositions of terrestrial planets are affected by dynamical evolution of giant planets. We estimate the initial compositions of building blocks of these rocky planets by using a simple condensation model, and numerically study the compositions of planets formed in a few different formation models of the Solar System. We find that the abundances of refractory and moderately volatile elements are nearly independent of formation models, and that all…
Many massive objects have been found in the outer region of the Solar system. How they were formed and evolved has not been well understood, although there have been intensive studies on accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner…
A high fraction of carbon bound in solid carbonaceous material is observed to exist in bodies formed in the cold outskirts of the solar nebula, while bodies in the terrestrial planets region contain nearly none. We study the fate of the carbonaceous material during the spiral-in of matter as the sun accretes matter from the solar nebula. From observational data on the composition of the dust component in comets and interplanetary dust particles, and from data on pyrolysis experiments, we construct a model for the composition of the pristine carbonaceous material in the outer parts of the solar…
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…
