Final Stages of Planet Formation

By Peter Goldreich, Y. Lithwick, R. Sari. 2004

186 citations recorded by the source corpus.

We address three questions regarding solar system planets: What determined their number? Why are their orbits nearly circular and coplanar? How long did they take to form? Runaway accretion in a disk of small bodies resulted in a tiny fraction of the bodies growing much larger than all the others. These big bodies dominated the viscous stirring of all bodies. Dynamical friction by small bodies cooled the random velocities of the big ones. Random velocities of small bodies were cooled by mutual collisions and/or gas drag. Runaway accretion terminated when the orbital separations of the big bodies became as wide as their feeding zones. This was followed by oligarchic growth during which the big bodies maintained similar masses and uniformly spaced semimajor axes. As the oligarchs grew, their number density decreased, but their surface mass density increased. We depart from standard treatments of planet formation by assuming that as the big bodies got bigger, the small ones got smaller as the result of undergoing a collisional fragmentation cascade. It follows that oligarchy was a brief stage in solar system evolution. When the oligarchs' surface mass density matched that of the small bodies, dynamical friction was no longer able to balance viscous stirring, so their velocity dispersion increased to the extent that their orbits crossed. This marked the end of oligarchy. What happened next differed in the inner and outer parts of the planetary system. In the inner part, where the ratios of the escape velocities from the surfaces of the planets to the escape velocities from their orbits are smaller than unity, big bodies collided and coalesced after their random velocities became comparable to their escape velocities. In the outer part, where these ratios are larger than unity, the random velocities of some of the big bodies continued to rise until they were ejected. In both parts, the number density of the big bodies eventually decreased to the extent that gravitational interactions among them no longer produced large-scale chaos. After that their orbital eccentricities and inclinations were damped by dynamical friction from the remaining small bodies. The last and longest stage in planet formation was the cleanup of small bodies. Our understanding of this stage is fraught with uncertainty. The surviving protoplanets cleared wide gaps around their orbits that inhibited their ability to accrete small bodies. Nevertheless, in the inner planet system, all of the material in the small bodies ended up inside planets. Small bodies in the outer planet system probably could not have been accreted in the age of the solar system. A second generation of planetesimals may have formed in the disk of small bodies, by either collisional coagulation or gravitational instability. In the outer planet system, bodies of kilometer size or larger would have had their random velocities excited until their orbits crossed those of neighboring protoplanets. Ultimately they would have either escaped from the Sun or become residents of the Oort Cloud. An important distinction is that growth of the inner planets continued through cleanup, whereas assembly of the outer planets was essentially complete by the end of oligarchy. These conclusions imply that the surface density of the protoplanetary disk was that of the minimum solar mass nebula in the inner planet region but a few times larger in the outer planet region. The timescale through cleanup was set by the accretion rate at the geometrical cross section in the inner planet region and by the ejection rate at the gravitationally enhanced cross section in the outer planet region. It was a few hundred million years in the former and a few billion years in the latter. However, since Uranus and Neptune acquired most of their mass by the end of oligarchy, they may have formed before Earth! A few implications of the above scenario are worth noting. Impacts among protoplanets of comparable size were common in the inner planet system but not in the outer. Ejections from the outer planet system included several bodies with masses in excess of Earth after oligarchy and an adequate number of kilometer-size bodies to populate the Oort comet cloud during cleanup. Except at the very end of cleanup, collisions prevented Uranus and Neptune from ejecting kilometer-size objects. Only Jupiter and, to a much lesser extent, Saturn were capable of populating the Oort Cloud with comets of kilometer size.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/6570c627eba7f079dbfc00e6d4cd14e57503c777

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Citations in the corpus

High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics (2005, unknown): “This effect certainly plays an important role in the final assembly of ter restrial planets ( Goldreich et al. , 2004 ).”
Streaming Instabilities in Protoplanetary Disks (2004, background): “Forming planetesimals via gravitational instabilities would be trivial in a gas-free disk, since collisional damping dominates viscous stirring in the absence of protoplanets (Goldreich et al. 2004a).”
Atmospheres of Protoplanetary Cores: Critical Mass for Nucleated Instability (2004, background): “This ‘‘slow accretion’’ regimemay take place after cores have reached the isolation mass by oligarchic growth (Chambers 2001; Goldreich et al. 2004).”
Debris disks as signposts of terrestrial planet formation (2011, methodology): “…quantity Θ2, the ratio of the escape speed from the planet’s surface to the escape speed from the planetary system at that location (Safronov 1969; Goldreich et al. 2004): Θ2 = Mp M Rp a , (11) where Mp and M are the planetary and stellar mass, respectively, Rp is the planetary radius and a is…”
Atmospheric mass loss during planet formation: The importance of planetesimal impacts (2014, unknown): “…stirring rates of the protoplanets with the damping rates due to dynamical friction by the planetesimal population and numerical simulations find that giant impacts set in when the total mass in protoplanets is comparable to the mass in planetesimals (Goldreich et al. 2004; Kenyon & Bromley 2006).”
A Perspective from Extinct Radionuclides on a Young Stellar Object: The Sun and Its Accretion Disk (2011, background): “Orderly, runaway, and oligarchic growth of planetesimals formed several Moon- to Mars-sized embryos at regular heliocentric distances (Goldreich et al. 2004, Kokubo & Ida 1998, Safronov 1969, Wetherill & Stewart 1989); these embryos later collided to form terrestrial planets (Chambers & Wetherill…”
Debris disc stirring by secular perturbations from giant planets (2009, background): “…in the context of debris disc evolution include planet formation proceeding more rapidly when a gap-opening giant planet has formed (Bryden et al. 2000; Thommes 2005), or an outer disc being stirred by planetesimal that have been scattered out from the inner system (Goldreich et al. 2004a).”
COLLISIONS BETWEEN GRAVITY-DOMINATED BODIES. II. THE DIVERSITY OF IMPACT OUTCOMES DURING THE END STAGE OF PLANET FORMATION (2011, background): “When the total mass in planetary embryos is equal to the total mass in smaller planetesimals, viscous stirring by the embryos cannot be damped by dynamical friction from the planetesimals, which marks the end of oligarchic growth (Kokubo & Ida 1998; Goldreich et al. 2004).”
Planet Formation around Stars of Various Masses: The Snow Line and the Frequency of Giant Planets (2007, background): “(6) The normalisation of equation (6) depends on the size of the small objects (e.g. Goldreich et al. 2004; Chambers 2006).”
Extrasolar planet population synthesis I: Method, formation tracks and mass-distance distribution (2009, background): “…to the concurrent growth of many planets, see below), inside the iceline, for disks similar to the MMSN, growth from Miso ∼ 0.01 − 0.1 M⊕ to the final masses occurs through giant impacts on timescales that exceed by roughly one order of magnitude typical gas disk lifetimes (Goldreich et al. 2004a).”
Extrasolar planet population synthesis - II. Statistical comparison with observations (2009, background): “If all originally present solids are incorporated into the planets, and their final relative spacing is of the order of ∆a ∼ a/3 as in the solar system (Goldreich et al. 2004), then planets as massive as 10 Earth masses could form at 0.1 AU in the most metal rich disk which would fill up at least…”
Asteroids Were Born Big (2009, background): “In the outer Solar System, beyond the so-called snowline (Podolak and Zucker, 2004), it is generally expected that the end result is the formation of a few super-Earth cores (Thommes et al., 2003; Goldreich et al., 2004; Chambers, 2006) that, by accretion of a massive gaseous atmosphere from the dis”
Can Giant Planets Form by Direct Gravitational Instability? (2004, background): “However, recent work by Rafikov (2003) and Goldreich et al. (2004) has found core formation time to be actually quite short, essentially removing the timescale issue from the core instability scenario.”
Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations (2012, background): “…∼10 Earth masses (ME) form beyond the so-called snowline (the orbital radius beyond which temperature is cold enough that water condenses into ice; Podolak & Zucker 2004), as required in the core-accretion model for giant planet formation (Thommes et al. 2003; Goldreich et al. 2004; Chambers 2006).”
Dynamical Outcomes of Planet-Planet Scattering (2007, methodology): “According to the model of oligarchic growth, planetesimals form in a nearly maximally packed configuration in the protoplanetary disk, followed by gas accretion (Goldreich et al. 2004; Ida & Lin 2004b; Kokubo & Ida 2002).”