Stage Of Terrestrial Planet Formation Research Articles

On the formation of the martian moons from a circum-martian accretion disk

We reconsider two scenarios for the formation of Phobos and Deimos from a circum-martian accretion disk of debris: the strong tide regime for which accretion occurs close to the planet at the Roche limit and the weak tide regime for which accretion occurs farther from the planet. We assume a disk with an initial mass of 1018kg (Craddock, R.A. [2011]. Icarus 211, 1150–1161). In the strong tide regime, the disk loses its material by viscous spreading inward to and outward from the planet. When outward moving material crosses the Roche limit, small-sized moonlets are accreted from gravitational instabilities with a shape and density similar to Phobos and Deimos. Due to the gravitational torque exerted by the disk, the moonlets migrate away from the planet, though they cannot reach the synchronous orbit (lying at 6 Mars’ radii). After the disk has lost most of its mass they rapidly fall back onto Mars due to the tidal decay of their orbits. Although, the total mass of moonlets is comparable to the mass of Phobos, their survival time does not exceed 200Ma, which is incompatible with the formation of Phobos and Deimos early in Mars’ history. In the weak tide regime, moonlets can accrete near the synchronous orbit with the mass of Deimos in a disk of up to 1018kg (similarly to planetary embryos formation in the protoplanetary disk). A Phobos-mass embryo can also be formed in the same disk but closer to Mars (at 3–4 Mars’ radii) so that it rapidly falls back onto Mars by tidal decay of its orbit. However, several embryos may accrete together in the disk (similarly to the final stage of terrestrial planet formation), and Phobos and Deimos may be the last two remnants of those bodies formed near the synchronous distance to Mars. Further investigations are still needed to understand such accretion mechanism within a circum-martian disk primarily extending below the synchronous orbit.

Giant Impacts and Debris Disks

AbstractDuring the last stage of terrestrial planet formation, Mars-sized protoplanets often collides with each other. Our high-resolution impact simulations show that such giant impacts produce a significant amount of fragments within the terrestrial planet region. These ejected fragments form a hot debris disk around the central star. We calculated the evolution of the surface density and size distribution of the debris disk using the analytical model of collision disruption, and estimated its infrared excess emission. We found that 24 μm flux from the debris disk is higher than stellar flux throughout the giant impact stage (~ 108 years), which can explain the infrared excess recently observed around the star with the age of 107 – 108 years.

Debris from terrestrial planet formation: the Moon-forming collision

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 per cent of the particles have been accreted on to Earth and 17 per cent on to Venus, with 8 per cent ejected by Jupiter and other bodies playing minor roles. However, the fate of the debris also depends strongly on how fast it is collisionally depleted, which depends on the poorly constrained size distribution of the impact debris. Assuming that the debris is made up of 30 per cent by mass mm–cm-sized vapour condensates and 70 per cent boulders up to 500 km, we find that the condensates deplete rapidly on ∼1000 yr time-scales, whereas the boulders deplete predominantly dynamically. By considering the luminosity of dust produced in collisions within the boulder–debris distribution we find that the Moon-forming impact would have been readily detectable around other stars in Spitzer 24 μm surveys for around 25 Myr after the impact, with levels of emission comparable to many known hot dust systems. The vapour condensates meanwhile produce a short-lived, optically thick, spike of emission. We use these surveys to make an estimate of the fraction of stars that form terrestrial planets, FTPF. Since current terrestrial planet formation models invoke multiple giant impacts, the low fraction of 10–100 Myr stars found to have warm (>rsim150 K) dust implies that per cent. For this number to be higher, it would require that either terrestrial planets are largely fully formed when the protoplanetary disc disperses, or that impact generated debris consists purely of sub-km objects such that its signature is short-lived.

THE LAST STAGES OF TERRESTRIAL PLANET FORMATION: DYNAMICAL FRICTION AND THE LATE VENEER

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 independent lines of evidence for a leftover population of planetesimals and show that: 1) A residual planetesimal population containing 0.01 M_Earth is able to damp the eccentricities of the terrestrial planets after giant impacts to their observed values. 2) At the same time, this planetesimal population can account for the observed relative amounts of late veneer added to the Earth, Moon and Mars provided that the majority of the late veneer was delivered by small planetesimals with radii <10m. These small planetesimal sizes are required to ensure efficient damping of the planetesimal's velocity dispersion by mutual collisions, which in turn ensures that the planets' accretion cross sections are significantly enhanced by gravitational focusing above their geometric values. Specifically we find, in the limit that the relative velocity between the terrestrial planets and the planetesimals is significantly less than the terrestrial planets' escape velocities, that gravitational focusing yields an accretion ratio Earth/Mars~17, which agrees well with the accretion ratio inferred from HSEs of 12-23. For the Earth-Moon system, we find an accretion ratio of ~200, which is consistent with estimates of 150-700 derived from HSE abundances that include the lunar crust as well as mantle component. (Abridged)

MERGING CRITERIA FOR GIANT IMPACTS OF PROTOPLANETS

At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding protoplanets always merge. However, recent impact simulations have shown that collisions among protoplanets are not always merging events, that is, two colliding protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step towards studying the effects of such imperfect accretion of protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky protoplanets. Using the smoothed particle hydrodynamic (SPH) method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of protoplanets, $\gamma$, the total mass of two protoplanets, $M_{\rm T}$, the impact angle, $\theta$, and the impact velocity, $v_{\rm imp}$. We investigated the critical impact velocity, $v_{\rm cr}$, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, $v_{\rm cr}/v_{\rm esc}$, depends on $\gamma$ and $\theta$, but does not depend on $M_{\rm T}$, where $v_{\rm esc}$ is the two-body escape velocity. We derived a simple formula for $v_{\rm cr}/v_{\rm esc}$ as a function of $\gamma$ and $\theta$, and applied it to the giant impact events obtained by \textit{N}-body calculations in the previous studies. We found that 40% of these events should not be merging events.

FORMATION OF TERRESTRIAL PLANETS FROM PROTOPLANETS UNDER A REALISTIC ACCRETION CONDITION

The final stage of terrestrial planet formation is known as the giant impact stage where protoplanets collide with one another to form planets. So far this stage has been mainly investigated by N-body simulations with an assumption of perfect accretion in which all collisions lead to accretion. However, this assumption breaks for collisions with high velocity and/or a large impact parameter. We derive an accretion condition for protoplanet collisions in terms of impact velocity and angle and masses of colliding bodies, from the results of numerical collision experiments. For the first time, we adopt this realistic accretion condition in N-body simulations of terrestrial planet formation from protoplanets. We compare the results with those with perfect accretion and show how the accretion condition affects terrestrial planet formation. We find that in the realistic accretion model, about half of collisions do not lead to accretion. However, the final number, mass, orbital elements, and even growth timescale of planets are barely affected by the accretion condition. For the standard protoplanetary disk model, typically two Earth-sized planets form in the terrestrial planet region over about 100 M years in both realistic and perfect accretion models. We also find that for the realistic accretion model, the spin angular velocity is about 30% smaller than that for the perfect accretion model that is as large as the critical spin angular velocity for rotational instability. The spin angular velocity and obliquity obey Gaussian and isotropic distributions, respectively, independently of the accretion condition.

Formation of Terrestrial Planets from Protoplanets. II. Statistics of Planetary Spin

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. The initial spin state of terrestrial planets is determined at this stage. We statistically investigate the spin parameters of terrestrial planets assembled from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We find that the spin angular velocity of the planets is well expressed by a Gaussian distribution, and their obliquity is well expressed by an isotropic distribution. The typical spin angular velocity is given by the critical spin angular velocity for rotational instability under the assumption of perfect accretion in collisions. We show the dependencies of the spin parameters on the initial protoplanet system parameters. The initial orbital separation and velocity anisotropy of protoplanets barely affect the spin parameters. The bulk density of protoplanets does not affect the obliquity distribution, while the spin angular velocity increases with the bulk density.

Habitable Planet Formation in Binary Planetary Systems

Recent radial velocity observations have indicated that Jovian-type planets can exist in moderately close binary star systems. Numerical simulations of the dynamical stability of terrestrial-class planets in such environments have shown that, in addition to their giant planets, these systems can also harbor Earth-like objects. In this paper, we study the late stage of terrestrial planet formation in such binary-planetary systems, and present the results of the simulations of the formation of Earth-like bodies in their habitable zones. We consider a circumprimary disk of Moon- to Mars-sized objects and numerically integrate the orbits of these bodies at the presence of the Jovian-type planet of the system and for different values of the mass, semimajor axis, and orbital eccentricity of the secondary star. Results indicate that, Earth-like objects, with substantial amounts of water, can form in the habitable zone of the primary star. Simulations also indicate that, by transferring angular momentum from the secondary star to protoplanetary objects, the giant planet of the system plays a key role in the radial mixing of these bodies and the water contents of the final terrestrial planets. We will discuss the results of our simulation and show that the formation of habitable planets in binary-planetary systems is more probable in binaries with moderate to large perihelia.

Terrestrial planet formation surrounding close binary stars

Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around both components of some young close binary star systems. Additionally, it has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around ‘close’ binary star systems with stellar separations 0.05 AU ⩽ a B ⩽ 0.4 AU and binary eccentricities 0 ⩽ e B ⩽ 0.8 . In each simulation, the sum of the masses of the two stars is 1 M ⊙ , and giant planets are included. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet formation within our Solar System by Chambers [Chambers, J.E., 2001. Icarus 152, 205–224], and around each individual component of the α Centauri AB binary star system by Quintana et al. [Quintana, E.V., Lissauer, J.J., Chambers, J.E., Duncan, M.J., 2002. Astrophys. J. 576, 982–996]. Multiple simulations are performed for each binary star system under study, and our results are statistically compared to a set of planet formation simulations in the Sun–Jupiter–Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances Q B ≡ a B ( 1 + e B ) ≲ 0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities.

Orbital Stability of Protoplanetary Systems in Nebular Gas and Implications for Terrestrial Planet Formation

The oligarchic growth model of planetary accretion predicts the formation of protoplanets of similar sizes, and the final stage of terrestrial planet formation involves long-term orbital instability and mutual collision of protoplanets through their gravitational interaction. However, the mass of the protoplanets formed by oligarchic growth depends on the initial surface density of the protoplanetary disk, as well as the distance from the central star. In order to better understand the final stage of terrestrial planet formation in disks with various profiles, we perform orbital integration for systems of five protoplanets and examine the dependence of the orbital instability timescale of the systems on the mass of the protoplanets, Mp, both with and without nebular gas. Previous studies have shown that the timescale for orbital instability in the absence of nebular gas increases exponentially with the initial semimajor axis difference between the protoplanets. We find that the exponential constant is independent of the mass of the protoplanets, as long as the initial separation is measured in units of ~M, which is very close to the previously derived mass dependence of the critical separation for the onset of chaotic behavior in the restricted circular three-body problem. In the presence of nebular gas, on the other hand, protoplanetary systems are stabilized by gas drag and experience no orbital instability when the initial semimajor axis difference is larger than a certain critical value. Using these results, we discuss the orbital stability of protoplanetary systems in disks with various surface densities.

The Search for Other Earths: Limits on the Giant Planet Orbits That Allow Habitable Terrestrial Planets to Form

Gas giant planets are far easier than terrestrial planets to detect around other stars, and they are thought to form much more quickly than terrestrial planets. Thus, in systems with giant planets, the late stages of terrestrial planet formation are strongly affected by the giant planets' dynamical presence. Observations of giant planet orbits may therefore constrain the systems that can harbor potentially habitable, Earth-like planets. We present results of 460 N-body simulations of terrestrial accretion from a disk of Moon- to Mars-sized planetary embryos. We systematically vary the orbital semimajor axis of a Jupiter-mass giant planet between 1.6 and 6 AU, and eccentricity between 0 and 0.4. We find that for Sun-like stars, giant planets inside roughly 2.5 AU inhibit the growth of 0.3 Earth-mass planets in the habitable zone. If planets accrete water from volatile-rich embryos past 2-2.5 AU, then water-rich habitable planets can only form in systems with giant planets beyond 3.5 AU. Giant planets with significant orbital eccentricities inhibit both accretion and water delivery. The majority of the current sample of extrasolar giant planets appears unlikely to form habitable planets.

Formation of Terrestrial Planets from Protoplanets. I. Statistics of Basic Dynamical Properties

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. As this process is stochastic, in order to clarify it, it is necessary to quantify it statistically. We investigate this final assemblage of terrestrial planets from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. We systematically change the surface density, surface density profile, and orbital separation of the initial protoplanet system, and the bulk density of protoplanets, while the initial system radial range is fixed at 0.5-1.5 AU. For each initial condition, we perform 20 runs, and from their results we derive the statistical properties of the assembled planets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We show the dependences of the masses and orbital elements of planets on the initial protoplanet system parameters and give their simple empirical fits. The number of planets slowly decreases as the surface density of the initial protoplanets increases, while the masses of individual planets increase almost linearly. For a steeper surface density profile, large planets tend to form closer to the star. For the parameter ranges that we test, the basic structure of planetary systems depends only slightly on the initial distribution of protoplanets and the bulk density as long as the total mass is fixed.

Isotopic outcomes of N-body accretion simulations: Constraints on equilibration processes during large impacts from Hf/W observations

Abstract Most estimates of planetary core formation timescales using hafnium–tungsten (Hf–W) isotopes employ analytical expressions assuming either continuous planetary growth or instantaneous core formation. In contrast, dynamical modelling of planetary accretion suggests that the final stage of terrestrial planet formation is punctuated by multiple large and stochastic impacts. Such giant impacts have significant thermal and isotopic consequences. We present a framework for calculating the Hf–W isotope evolution of individual bodies based on the results of an N-body accretion simulation and assuming constant partition coefficients. The results show that smaller bodies exhibit a larger range in isotopic values than larger bodies, because the latter have suffered more impacts. The analytical core formation timescales calculated using these isotopic values can differ very significantly from the timing of the final giant impact each planet actually experiences. Simulations in which 1) even the largest impactors undergo re-equilibration with the target's mantle, rather than the cores merging directly, and 2) the original planetary embryos possessed radially variable iron : silicate ratios, produce results which are consistent with the observed physical and isotopic characteristics of inner solar system bodies. Varying W partition coefficients (due to changing mantle oxidation state) or initial planetesimal Hf / W ratios might produce similar isotopic outcomes, and potentially permit core mergers without violating the isotopic constraints. The style of re-equilibration required suggests that magma oceans were present on Mars-sized and larger bodies; an alternative for bodies of Mars-size and smaller is that the bulk of the mass was delivered as impactors much smaller than the target. For Mars we conclude that a prolonged (∼10 Myr) accretion process is both dynamically and isotopically plausible. We also predict likely Pd–Ag isotopic anomalies for Vesta-, Mars- and Earth-size bodies.

Accretion Efficiency during Planetary Collisions

We present the results of smoothed particle hydrodynamic simulations of collisions between two 0.10 M⊕ differentiated planetary embryos with impact dynamics that are thought to be common to the late stage of terrestrial planet formation. At low impact velocities (vimp/vesc < 1.5) and for direct collisions, the impacts are largely accretionary. Inelastic bouncing between embryos with varying degrees of erosion, followed by escape to infinity, is also a common outcome. For dynamical environments typical of most late-stage accretion models, we estimate that more than half of all collisions between like-sized planetary embryos do not result in accumulation into a larger embryo.

Formation, migration, and stability of extrasolar planetary systems

This paper presents recent results concerning the planet formation, planet migration, and the long term stability of planetary systems. Most stars are found in binary systems and binary companions can disrupt both planet formation and stability. We first consider the effects of outer binary companions on the late stages of terrestrial planet formation and show how planet formation depends on the binary periastron. We then consider migration mechanisms for giant planets. In this case, planet scattering produces the full range of orbital eccentricities, but is less effective in moving planets inward (decreasing their semi-major axes). Disk torques are effective at moving planets inward, but not at increasing the eccentricities. We explore a scenario in which disk torques act in concert with planet scattering to provide the full range of orbital elements observed in extrasolar planetary systems. Finally, we consider the longer term stability of Earth-like planets in binary systems; we find that nearly 50 percent of binaries allow for Earth-like planets to remain stable over the current (4.6 Gyr) age of our solar system.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The Role of Giant Planets in Terrestrial Planet Formation

We present the results of simulations of the late stages of terrestrial planet formation under the gravitational influence of six different outer giant planetary systems with a wide range of dynamical characteristics. Our goal is to examine the role that the giant planets play in determining the number, mass, and orbital characteristics of the resulting terrestrial planets and their general potential for habitability. Each of the giant-planet systems affects the embryos in its own unique way. However, we find that the most profound effects are secular in nature. We also discovered that dynamical excitation of the embryos by the giant planets in one region can be transferred into another on short timescales via what we call secular conduction. Despite large differences in the behaviors of our systems, we have found general trends that seem to apply. The number, mass, and location of the terrestrial planets are directly related to the amount of dynamical excitation experienced by the planetary embryos near 1 AU. In general, if the embryos' eccentricities are large, each is crossing the orbits of a larger fraction of its cohorts, which leads to a lesser number of more massive planets. In addition, embryos tend to collide with objects near their periastron. Thus, in systems where the embryos' eccentricities are large, planets tend to form close to the central star.

N-body Simulations of Planet Formation

Accretion from many small planetesimals to planets is reviewed. Solid protoplanets accrete through runaway and oligarchic growth until they become isolated. The isolation mass of protoplanets in terrestrial planet region is about 0.1-0.2 Earth mass, which suggests giant impacts among the protoplanets in the final stage of terrestrial planet formation. On the other hand, the isolation mass in Jupiter's and Saturn's orbits is about a few to 5 Earth masses, which may be massive enough to trigger gas accretion onto the cores. The isolation mass in Uranus and Neptune's orbits is as large as their present cores. Extending the above arguments to extrasolar planetary systems that are formed from disks with various initial masses, we also discuss diversity of extrasolar planetary systems.

Terrestrial Planet Formation in the α Centauri System

We examine the late stages of terrestrial planet formation around each star in the α Centauri A and α Centauri B binary system. Each integration begins with a bimodal mass distribution of 14 large embryos embedded in a disk of smaller planetesimals orbiting one of the stars. These initial conditions were chosen because when they are used in simulations about a single star with giant planets, they lead to systems most closely resembling our solar system. However, it is far from certain that such a planetesimal distribution actually occurs either in single or binary star systems. We follow the evolution of the accreting bodies at various values of the inclination of the midplane of the disk relative to the binary orbit for 200 Myr to 1 Gyr. In simulations in which the midplane of the disk was inclined ≤30° relative to the binary orbital plane, three to five terrestrial planets were formed around α Cen A. When the embryos in the disk were moving retrograde relative to the binary plane, four or five terrestrial planets formed. From two to five planets formed in a disk centered around α Cen B, with α Cen A perturbing the system in the same plane. The aforementioned resulting terrestrial planetary systems are quite similar to those produced by calculations of terrestrial planet growth in the Sun-Jupiter or Sun-Jupiter-Saturn systems. In contrast, terrestrial planet growth around a star lacking both stellar and giant planet companions is slower and extends to larger semimajor axis for the same initial disk of planetary embryos. In systems with the accreting disk initially inclined at 45° relative to the binary star orbit, two to five planets formed despite the fact that more than half of the disk mass was perturbed into the central star. When the disk was inclined at 60° to the binary plane, the stability of the planetary embryos decreased dramatically because of larger variations in eccentricity caused by the Kozai resonance, and almost all of the planetary embryos and planetesimals were lost from these systems.

A short timescale for terrestrial planet formation from Hf-W chronometry of meteorites.

Determining the chronology for the assembly of planetary bodies in the early Solar System is essential for a complete understanding of star- and planet-formation processes. Various radionuclide chronometers (applied to meteorites) have been used to determine that basaltic lava flows on the surface of the asteroid Vesta formed within 3 million years (3 Myr) of the origin of the Solar System. Such rapid formation is broadly consistent with astronomical observations of young stellar objects, which suggest that formation of planetary systems occurs within a few million years after star formation. Some hafnium-tungsten isotope data, however, require that Vesta formed later (approximately 16 Myr after the formation of the Solar System) and that the formation of the terrestrial planets took a much longer time (62(-14)(+4504) Myr). Here we report measurements of tungsten isotope compositions and hafnium-tungsten ratios of several meteorites. Our measurements indicate that, contrary to previous results, the bulk of metal-silicate separation in the Solar System was completed within <30 Myr. These results are completely consistent with other evidence for rapid planetary formation, and are also in agreement with dynamic accretion models that predict a relatively short time (approximately 10 Myr) for the main growth stage of terrestrial planet formation.

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2 M⊕ and integrate the orbits for 10 7 years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1 M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2 M⊕ mass planet at 1 AU is longer than 10 8 years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10 6 years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10 6 and 10 8 years, which may correspond to a mostly depleted disk (0.01–0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10 6 years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ⋦1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10 −4–10 −3 times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.