Protoplanets develop via collisions between planetesimals and planetary embryos in the final assembly stage of planet formation. The efficiency of the planet formation can be defined by the mass ratio between formed protoplanets and the initial mass of embryos and planetesimals. In final assembly planet formation models, the gravitational interactions between planetesimals are usually neglected due to computational difficulties, namely, computations require fewer resources in this way. We investigated the effect of this simplification via modeling the planet formation efficiency in a circumstellar belt of embryos and self-interacting or non-self-interacting planetesimals. We used our own developed GPU-based direct N-body integrator, HIPERION, for the simulations. We found that planet formation efficiency is higher if the planetesimal self-interaction is taken into account in models that contain the commonly used 100 embryos. The observed effect can be explained by the damping of planetesimal eccentricities by their self-gravity. The non-self-interacting and self-interacting models show qualitatively the same results if the initial number of embryos is above 200.
We investigate planetary accretion that starts from equal-mass planetesimals using an analytic theory and numerical simulations. We particularly focus on how the planetary mass $M_{\rm oli}$ at the onset of oligarchic growth depends on the initial mass $m_0$ of a planetesimal. Oligarchic growth commences when the velocity dispersion relative to the Hill velocity of the protoplanet takes its minimum. We find that if $m_0$ is small enough, this normalized velocity dispersion becomes as low as unity during the intermediate stage between the runaway and oligarchic growth stages. In this case, $M_{…
Accretion among macroscopic bodies of ~km size or larger is enhanced significantly due to gravitational focusing. Two regimes can be distinguished. Initially, the system experiences runaway growth, in which the gravitational focusing factors increase, and bodies at the high-mass tail of the distribution grow fastest. However, at some point the runaway body dynamically heats its environment, gravitational focusing factors decrease, and runaway growth passes into oligarchic growth. Based on the results of recent simulations, we reconsider the runaway growth-oligarchy transition. In contrast to o…
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle librating and/or with a two-body resonant angle librating for each pair. Here we investigate whether close-in super-Earths and mini-Neptunes forming in situ can lock into resonant chains due to dissipation from a depleted gas disk. We simulate the giant impact phase of planet formation, including eccentricity damping from a gaseous disk, followed by subsequen…
We present N-body simulations of planetary system formation in thermally-evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion onto planetary cores, and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the init…
Dauphas and Pourmand (2011) [Nature 473, 489--492] estimated the accretion timescale of Mars to be 1.8 $^{+0.9}_{-1.0}$ Myr from the W isotopes of martian meteorites. This timescale was derived assuming perfect metal-silicate equilibration between the impactor and the target's mantle. However, in the case of a small impactor most likely only a fraction of the target's mantle is involved in the equilibration, while only a small part of the impactor's core equilibrates in the case of a giant impact. We examined the effects of imperfect equilibration using results of high-resolution $N$-body simu…
Inside-Out Planet Formation (IOPF) is a theory addressing the origin of Systems of Tightly-Packed Inner Planets (STIPs) via {\it in situ} formation and growth of the planets. It predicts that a pebble ring is established at the pressure maximum associated with the dead zone inner boundary (DZIB) with an inner disk magnetorotational instability (MRI)-active region. Using direct $N$-body simulations, we study the collisional evolution of planetesimals formed from such a pebble ring, in particular examining whether a single dominant planet emerges. We consider a variety of models, including some …
According to the sequential accretion model, giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. In order to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. We compute the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more dif…
The discovery of short-period Neptune-mass objects, now including the remarkable system HD69830 (Lovis et al. 2006) with three Neptune analogues, raises difficult questions about current formation models which may require a global treatment of the protoplanetary disc. Several formation scenarios have been proposed, where most combine the canonical oligarchic picture of core accretion with type I migration (e.g. Terquem & Papaloizou 2007) and planetary atmosphere physics (e.g. Alibert et al. 2006). To date, published studies have considered only a small number of progenitors at late times. This…
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…
(Abridged) We present the results of N-body simulations of planetary systems formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly-used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas acc…
In this Thesis I studied the formation of the four giant planets of the Solar System in the framework of the nucleated instability hypothesis. The model considers that solids and gas accretion are coupled in an interactive fashion, taking into account detailed constitutive physics for the envelope. The accretion rate of the core corresponds to the oligarchic growth regime. I also considered that accreted planetesimals follow a size distribution. One of the main results of this Thesis is that I was able to compute the formation of Jupiter, Saturn, Uranus and Neptune in less than 10 million year…
Chondrules are millimeter-sized spherules that dominate primitive meteorites (chondrites) originating from the asteroid belt. The incorporation of chondrules into asteroidal bodies must be an important step in planet formation, but the mechanism is not understood. We show that the main growth of asteroids can result from gas-drag-assisted accretion of chondrules. The largest planetesimals of a population with a characteristic radius of 100 km undergo run-away accretion of chondrules within ~3 Myr, forming planetary embryos up to Mars sizes along with smaller asteroids whose size distribution m…
The Grand Tack model of terrestrial planet formation has emerged in recent years as the premier scenario used to account for several observed features of the inner solar system. It relies on early migration of the giant planets to gravitationally sculpt and mix the planetesimal disc down to ~1 AU, after which the terrestrial planets accrete from material left in a narrow circum-solar annulus. Here we have investigated how the model fares under a range of initial conditions and migration course-change (`tack') locations. We have run a large number of N-body simulations with a tack location of 1…
When planetesimals grow via collisions in a turbulent disk, stirring through density fluctuation caused by turbulence effectively increases the relative velocities between planetesimals, which suppresses the onset of runaway growth. We investigate the onset of runaway growth in a turbulent disk through simulations that calculate the mass and velocity evolution of planetesimals. When planetesimals are small, the average relative velocity between planetesimals, $v_{\rm r}$, is much greater than their surface escape velocity, $v_{\rm esc}$, so that runaway growth does not occur. As planetesimals …
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…
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 present a new numerical framework to model the formation and evolution of giant planets. The code is based on the further development of the stellar evolution toolkit Modules for Experiments in Stellar Astrophysics (MESA). The model includes the dissolution of the accreted planetesimals/pebbles, which are assumed to be made of water ice, in the planetary gaseous envelope, and the effect of envelope enrichment on the planetary growth and internal structure is computed self-consistently. We apply our simulations to Jupiter and investigate the impact of different heavy-element and gas accretio…
In the standard model of core accretion, the formation of giant planets occurs by two main processes: first, a massive core is formed by the accretion of solid material; then, when this core exceeds a critical value (typically greater than 10 Earth masses) a gaseous runaway growth is triggered and the planet accretes big quantities of gas in a short period of time until the planet achieves its final mass. Thus, the formation of a massive core has to occur when the nebular gas is still available in the disk. This phenomenon imposes a strong time-scale constraint in giant planet formation due to…
The core accretion mechanism is presently the most widely accepted cause of the formation of giant planets. For simplicity, most models presently assume that the growth of planetary embryos occurs in isolation. We explore how the simultaneous growth of two embryos at the present locations of Jupiter and Saturn affects the outcome of planetary formation. We model planet formation on the basis of the core accretion scenario and include several key physical ingredients. We consider a protoplanetary gas disk that exponentially decays with time. For planetesimals, we allow for a distribution of siz…
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 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…
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…
We investigate pathways for the formation of icy super-Earth mass planets orbiting at 125-250 AU around a 1 solar mass star. An extensive suite of coagulation calculations demonstrates that swarms of 1 cm to 10 m planetesimals can form super-Earth mass planets on time scales of 1-3 Gyr. Collisional damping of 0.01-100 cm particles during oligarchic growth is a highlight of these simulations. In some situations, damping initiates a second runaway growth phase where 100-3000 km protoplanets grow to super-Earth sizes. Our results establish the initial conditions and physical processes required fo…
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…
In the last few years, the so-called "Nice model" has got a significant importance in the study of the formation and evolution of the solar system. According to this model, the initial orbital configuration of the giant planets was much more compact than the one we observe today. We study the formation of the giant planets in connection with some parameters that describe the protoplanetary disk. The aim of this study is to establish the conditions that favor their simultaneous formation in line with the initial configuration proposed by the Nice model. We focus in the conditions that lead to t…
We develop a simple model of planetary formation, focusing our attention on those planets with masses less than 10 Earth masses and studying particularly the primordial spin parameters of planets resulting from the accretion of planetesimals and produced by the collisions between the embryos. As initial conditions, we adopt the oligarchic growth regime of protoplanets in a disc where several embryos are allowed to form. We take different initial planetary system parameters and for each initial condition, we consider an evolution of 20 millon of years of the system. We perform simulations for 1…
The Earth appears non-chondritic in its abundances of refractory lithophile elements, posing a significant problem for our understanding of its formation and evolution. It has been suggested that this non-chondritic composition may be explained by collisional erosion of differentiated planetesimals of originally chondritic composition. In this work, we present N-body simulations of terrestrial planet formation that track the growth of planetary embryos from planetesimals. We simulate evolution through the runaway and oligarchic growth phases under the Grand Tack model and in the absence of gia…
We investigate the formation of multiple-planet systems in the presence of a hot Jupiter using extended N-body simulations that are performed simultaneously with semi-analytic calculations. Our primary aims are to describe the planet formation process starting from planetesimals using high-resolution simulations, and to examine the dependences of the architecture of planetary systems on input parameters (e.g., disk mass, disk viscosity). We observe that protoplanets that arise from oligarchic growth and undergo type I migration stop migrating when they join a chain of resonant planets outside …
In order to explain the main characteristics of the observed population of extrasolar planets and the giant planets in the Solar System, we need to get a clear understanding of which are the initial conditions that allowed their formation. To this end we develop a semi-analytical model for computing planetary systems formation based on the core instability model for the gas accretion of the embryos and the oligarchic growth regime for the accretion of the solid cores. With this model we explore not only different initial discs profiles motivated by similarity solutions for viscous accretion di…
