Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as "oligarchic growth." Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼ 10× minimum-mass) is required to produce giant planet core-sized bodies (∼ 10 M ⊕ ) within the lifetime of the nebular gas ( ∼ < 10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of non-interacting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System's two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas, and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.-2 -

Planets are believed to have formed through the accumulation of a large number of small bodies. In the case of the gas-giant planets Jupiter and Saturn, they accreted a significant amount of gas directly from the protosolar nebula after accumulating solid cores of about 5-15 Earth masses. Such models, however, have been unable to produce the smaller ice giants Uranus and Neptune at their present locations, because in that region of the Solar System the small planetary bodies will have been more widely spaced, and less tightly bound gravitationally to the Sun. When applied to the current Jupiter-Saturn zone, a recent theory predicts that, in addition to the solid cores of Jupiter and Saturn, two or three other solid bodies of comparable mass are likely to have formed. Here we report the results of model calculations that demonstrate that such cores will have been gravitationally scattered outwards as Jupiter, and perhaps Saturn, accreted nebular gas. The orbits of these cores then evolve into orbits that resemble those of Uranus and Neptune, as a result of gravitational interactions with the small bodies in the outer disk of the protosolar nebula.

The ensemble of now more than 250 discovered planetary systems displays a wide range of masses, orbits and in multiple systems, dynamical interactions.These represent the endpoint of a complex sequence of events, wherein an entire protostellar disk converts itself into a small number of planetary bodies.Here we present self-consistent numerical simulations of this process, which produce results in agreement with some of the key trends observed in the properties of the exoplanets. Analogues to our own Solar System do not appear to be common, originating from disks near the boundary between barren and (giant) planet-forming.Gas giant planets form within 1-10 million years (Myrs), during the time that their parent star possesses a gas disk (1). Two-and three-dimensional hydrodynamic simulations of planets embedded in protostellar disks are, due to their computational cost, limited to following a maximum of 10 3 − 10 4 orbits; even for a planet as far out as Jupiter (orbital period 11 years), this amounts to at most a tenth of a protostellar disk's total lifetime. For this reason, 1

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the solar nebula dispersed. The most popular model of giant planet formation is the so-called core accretion model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study, we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments, we have included a large number of physical processes that might enhance accretion. In particular, we have included (1) aerodynamic gas drag, (2) collisional damping between planetesimals, (3) enhanced embryo cross sections due to their atmospheres, (4) planetesimal fragmentation, and (5) planetesimaldriven migration. We find that the gravitational interaction between the embryos and the planetesimals leads to the wholesale redistribution of material-regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near those embryos is cleared of planetesimals before much growth can occur. Thus, the widely used assumption that the surface density distribution of planetesimals is smooth can lead to misleading results. In the remaining 10% of our simulations, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ∼10 5 years, the outer embryo can migrate ∼6 AU and grow to roughly 30 M ⊕ . This represents a largely unexplored mode of core formation. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth except for a narrow range of fragment migration rates.