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.
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 …
The terrestrial planets are believed to have formed by violent collisions of tens of lunar- to Mars-size protoplanets at time t<200 Myr after the protoplanetary gas disk dispersal (t_0). The solar system giant planets rapidly formed during the protoplanetary disk stage and, after t_0, radially migrated by interacting with outer disk planetesimals. An early (t<100 Myr) dynamical instability is thought to have occurred with Jupiter having gravitational encounters with a planetary-size body, jumping inward by ~0.2-0.5 au, and landing on its current, mildly eccentric orbit. Here we investigate how…
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 …
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 fi…
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 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…
Chondrules are primitive materials in the Solar System. They are formed in the first about 3 Myr of the Solar System's history. This timescale is longer than that of Mars formation, and it is conceivable that protoplanets, planetesimals and chondrules might have existed simultaneously in the solar nebula. Due to protoplanets perturbation on the planetesimal dynamics and chondrule accretion on them, all the formed chondrules are unlikely to be accreted by planetesimals. We investigate the amount of chondrules accreted by planetesimals in such a condition. We assume that a protoplanet is in olig…
We perform hydrodynamical simulations of the accretion of pebbles and rocks onto protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the protoplanetary disc gas. Particle streams interacting with the gas far out within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted onto the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10%-50% of their mass from pe…
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…
Recent observations of protoplanets embedded in circumstellar disks have shed light on the planet formation process. In particular, detection of hydrogen Balmer-line (Hα) emission gives direct constraints on late-stage accretion onto gas giants. Very recently Haffert et al. (2019) measured the spectral line-widths, in addition to intensities, of Hα emission from the two protoplanets orbiting PDS 70. Here, we study these protoplanets by applying radiation-hydrodynamic models of the shock-heated accretion flow onto protoplanets that Aoyama et al. (2018) has recently developed. As a result, we de…
We investigate the properties of circumplanetary discs formed in three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities. We find that the analytical prediction of circumplanetary disc radii in an evacuated gap (R_Hill/3) from Quillen & Trilling (1998) yields a good estimate for discs formed by high mass protoplanets. The radial density profiles of the circumplanetary discs may be described by p…
Pebbles of millimeter sizes are abundant in protoplanetary discs around young stars. Chondrules inside primitive meteorites - formed by melting of dust aggregate pebbles or in impacts between planetesimals - have similar sizes. The role of pebble accretion for terrestrial planet formation is nevertheless unclear. Here we present a model where inwards-drifting pebbles feed the growth of terrestrial planets. The masses and orbits of Venus, Earth, Theia (which later collided with the Earth to form the Moon) and Mars are all consistent with pebble accretion onto protoplanets that formed around Mar…
The formation of planets depends on the underlying protoplanetary disc structure, which influences both the accretion and migration rates of embedded planets. The disc itself evolves on time-scales of several Myr during which both temperature and density profiles change as matter accretes onto the central star. Here we use a detailed model of an evolving disc to determine the growth of planets by pebble accretion and their migration through the disc. Cores that reach their pebble isolation mass accrete gas to finally form giant planets with extensive gas envelopes, while planets that do not re…
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplaneta…
Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in s…
Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by accreting particles of size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximatio…
Planets grow via the collisional accretion of small bodies in a protoplanetary disk. Such small bodies feel strong gas drag and their orbits are significantly affected by the gas flow and atmospheric structure around the planet. We investigate the gas flow in the protoplanetary disk perturbed by the gravity of the planet by three-dimensional hydrodynamic simulation. We then calculate the orbital evolutions of particles in the gas structure obtained from the hydrodynamic simulation. Based on the orbital calculations, we obtain the collision rate between the planet and centimeter to kilometer si…
Axisymmetric dust rings containing tens to hundreds of Earth masses of solids have been observed in protoplanetary discs with (sub-)millimetre imaging. Here, we investigate the growth of a planetary embryo in a massive (150M$_\oplus$) axisymmetric dust trap through dust and gas hydrodynamics simulations. When accounting for the accretion luminosity of the planetary embryo from pebble accretion, the thermal feedback on the surrounding gas leads to the formation of an anticyclonic vortex. Since the vortex forms at the location of the planet, this has significant consequences for the planet's gro…
Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, …
We study the three-dimensional evolution of a viscous protoplanetary disc which accretes gas material from a second protoplanetary disc during a close encounter in an embedded star cluster. The aim is to investigate the capability of the mass accretion scenario to generate strongly inclined gaseous discs which could later form misaligned planets. We use smoothed particle hydrodynamics to study mass transfer and disc inclination for passing stars and circumstellar discs with different masses. We explore different orbital configurations to find the parameter space which allows significant disc i…
We investigate gas accretion onto a protoplanet, by considering the thermal effect of gas in three-dimensional hydrodynamical simulations, in which the wide region from a protoplanetary gas disk to a Jovian radius planet is resolved using the nested-grid method. We estimate the mass accretion rate and growth timescale of gas giant planets. The mass accretion rate increases with protoplanet mass for M_p < M_cri, while it becomes saturated or decreases for M_p > M_cri, where M_cri = 0.036 M_Jup (a_p/1AU)^0.75, and M_Jup and a_p are the Jovian mass and the orbital radius, respectively. The growth…
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). …
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 known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary disks provides one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure and physical processes that drive the evolution of the protoplanetary disk. In this review we focus on how disk-planet interactions drive the migration of planets when different assumptions are ma…
It is widely known that giant planets have the capacity to open deep gaps in their natal gaseous protoplanetary discs. It is unclear, however, how gas accretion onto growing planets influences the shape and depth of their growing gaps. We performed isothermal hydrodynamical simulations with the Fargo-2D1D code, which assumes planets accreting gas within full discs that range from 0.1 to 260 AU. The gas accretion routine uses a sink cell approach, in which different accretion rates are used to cope with the broad range of gas accretion rates cited in the literature. We find that the planetary g…
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…
Combining isotopic constraints from meteorite data with dynamical models of planet formation proves to be advantageous in identifying the best model for terrestrial planet formation. Prior studies have shown that the probability of reproducing the distinct isotopic compositions of the Earth and Mars for both classical and Grand Tack models is very low. In the framework of the Grand Tack model, for Mars to be isotopically different from the Earth, it had to form under very specific conditions. Here, we subjected a fairly new and unexplored model--the depleted disc model--to the test. It presupp…
In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favor the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. We aim to study the radial drift of pebbles and planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of…
Recent ALMA molecular line observations have revealed 3-D gas velocity structure in protoplanetary disks, shedding light on mechanisms of disk accretion and structure formation. 1) By carrying out viscous simulations, we confirm that the disk's velocity structure differs dramatically using vertical stress profiles from different accretion mechanisms. Thus, kinematic observations tracing flows at different disk heights can potentially distinguish different accretion mechanisms. On the other hand, the disk surface density evolution is mostly determined by the vertically integrated stress. The sh…
We examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13 - 1.7 AU due to gas disk dispersal. An N-body code is employed that is linked to a viscous gas disk algorithm capable of simulating: gas loss via accretion onto the central star and photoevaporation; gap formation by the giant planet; type II migration of the giant; optional type I migration of protoplanets; gas drag on planetesimals. We find that most of the inner system planetary building bl…
We used chemical equilibrium and chemical kinetic calculations to model chemistry of the volatiles released by heating different types of carbonaceous, ordinary and enstatite chondritic material as a function of temperature and pressure. Our results predict the composition of atmospheres formed by outgassing during accretion of the Earth and other terrestrial planets. Outgassing of CI and CM carbonaceous chondritic material produces H2O-rich (steam) atmospheres in agreement with the results of impact experiments. However, outgassing of other types of chondritic material produces atmospheres do…
This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical models with geochemical, cosmochemical and chronological constraints, in order to outline a comprehensive scenario of the early evolution of our Solar System. Given that the giant planets formed first in the protoplanetary disk, we stress the sensitive dependence of the terrestrial planet accretion process on the orbital architecture of the giant planets and on t…
Final water inventories of newly formed terrestrial planets are shaped by their collision history. A setting where volatiles are transported from beyond the snowline to habitable-zone planets suggests collisions of very dry with water-rich bodies. By means of smooth particle hydrodynamics (SPH) simulations we study water delivery in scenarios where a dry target is hit by a water-rich projectile, focusing on hit-and-run encounters with two large surviving bodies, which probably comprise about half of all similar-sized collisions.
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…
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…
The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range $0.1-10\rm au$. Additionally, we determine the long-term …
In our solar system, Mars-sized protoplanets frequently collided with each other during the last stage of terrestrial planet formation called the giant impact stage. Giant impacts eject a large amount of material from the colliding protoplanets into the terrestrial planet region, which may form debris disks with observable infrared excesses. Indeed, tens of warm debris disks around young solar-type stars have been observed. Here, we quantitatively estimate the total mass of ejected materials during the giant impact stages. We found that $\sim$0.4 times the Earth's mass is ejected in total thro…
Pebble accretion is one of the major theories in planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous study, Paper I, we focused on the shear regime of pebble accretion, and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that in the unperturbed flow, in particular when ${\rm St}\lesssim10^{-3}$, where St is the…
Core accretion and disk instability require giant protoplanets to form in the presence of disk gas. Protoplanet migration models generally assume disk masses low enough that the disk's self-gravity can be neglected. However, disk instability requires a disk massive enough to be marginally gravitationally unstable (MGU). Even for core accretion, a FU Orionis outburst may require a brief MGU disk phase. We present a new set of three dimensional, gravitational radiation hydrodynamics models of MGU disks with multiple protoplanets, which interact gravitationally with the disk and with each other, …
We present global hydrodynamic and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic resistivity that depends on the overlying mass column, leading to turbulent surface layers and a dead zone near the midplane. The main results are: (i) The accretion flow in the Hill sphere is intrinsically 3D for hydrodynamic and MHD models. Net inflow toward the planet is dominated by high latitude flows. A circumplanetary disk (CPD) forms. Its midplane flows outward in a pattern whose details differ bet…
In general, most of the studies of terrestrial-type planet formation typically use ad hoc initial conditions. In this work we improved the initial conditions described in Ronco & de Elía (2014) starting with a semi-analytical model wich simulates the evolution of the protoplanetary disk during the gas phase. The results of the semi-analytical model are then used as initial conditions for the N-body simulations. We show that the planetary systems considered are not sensitive to the particular initial distribution of embryos and planetesimals and thus, the results are globally similar to those f…
Recent observations have detected excess H$α$ emission from young stellar systems with an age of several Myr such as PDS 70. One-dimensional radiation-hydrodynamic models of shock-heated flows that we developed previously demonstrate that planetary accretion flows of $>$ a few ten km s$^{-1}$ can produce H$α$ emission. It is, however, a challenge to understand the accretion process of proto-giant planets from observations of such shock-originated emission because of a huge gap in scale between the circumplanetary disk (CPD) and the microscopic accretion shock. To overcome the scale gap problem…
We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot M= 2\times 10^{-8}$ $M_\odot/$yr and pebble flux $\dot M_{peb}=170$ $M_\oplus$/Myr, we find that embryo eccentricitie…
We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos that grow rapidly experience radiogenic ingrowth of mantle $^{182}$W that is inconsistent with the measured terrestrial composition, unless much of the tungsten is removed by an impactor core that m…
Hydrodynamical instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable regions for the Vertical Shear Instability (VSI), the Convective OverStability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady state accretion disk models, including stellar irradiation, accretion heating and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, in dependence …
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
