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CALTECH GE 133 - FINAL STAGES OF PLANET FORMATION

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FINAL STAGES OF PLANET FORMATIONPeter Goldreich,1, 2Yoram Lithwick,3and Re’em Sari2Receivved 2004 April 12; accepted 2004 June 22ABSTRACTWe address three questions regarding solar system planets: What determined their number? Why a re their orbitsnearly circular and coplanar? How long did they take to form?Runaway accretion in a disk of small bo dies resulted in a tiny fraction of the bodies growing much larger than allthe others. These big bodies dominated the viscous stir ring of all bodies. Dynamical friction by small bodiescooled the random velocities of the big ones. Random velocities of small bodies were cooled by mutual collisionsand/or gas drag. Runaway accretion terminated when the orbital separations of the big bodies became as wide astheir feeding zones. This was followed by oligarchic growth dur ing which the big bodies maintained similarmasses and uniformly spaced semimajor axe s. As the oligarchs grew, their number density decreased, b ut theirsurface mass density increased. We depart f rom standard treatments of planet formation by assuming that as t hebig bodies got bigger, the small ones got smaller a s the result of undergoing a collisional fragmentation cascade. Itfollows that oligarchy w as a brief stage in solar system evolution.When the oligarchs’ surface mass density matched that of the small bodies, dynamical friction was no longerable to balance viscous stirring, so their velocity dispersion increased to the extent that their orbits cro ssed. Thismarked the e nd of oligarchy. What happened next differed in the inner and outer parts of the planetary sy stem. Inthe inner part, where the ratios of the escape velocities from the surfaces of the planets to the escape velocities fromtheir orbits are smaller than unity, big bodies collided and coalesced after their random velocities became com-parable to their escape velocities. In the outer part, where these ratios are larger than unity, the random velocities ofsome of the big bodies continued to rise until they were ejected. In both parts, the number d ensity of the bigbodies eventually decreased to the extent that gravitational interactions among them no longer produced large-scale chaos. A fter that their orbital eccentricities and inclinations were damped by dynamical friction from theremaining small bodies.The last and longest stage in plane t formation w as the clea nup of small bodies. Our understand ing of this stageis fraught with uncertainty. The surviving protoplanet s cleared wide gaps around their orbits that inhibited theirability to accrete small bodies. Nevertheless, in the inner planet system, all of the material in the small bodiesended up inside planets. Small bodies in the oute r planet system probably could not have been accreted in the ageof the solar system. A se cond gene ration of planetesimals may have formed in the disk of small bodies, by eithercollisional coagulation or gravitational instability. In the outer planet system, bodies of kilometer size or largerwould 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 importantdistinction is t hat growth of the in ner planets continued through cleanup, whereas assembly of the outer planetswas essentially complete by the end of oligarchy. These co nclusions imply that the surface density of theprotoplanetary disk was that of the minimum solar mass nebula in the inner planet region but a few times largerin the outer planet region . The timescale through cleanup was set by the accretion rate at the geometrical crosssection in the inner planet region and by the ejection rate at the gravitationally enhanced cross section in the outerplanet region. It was a few hundred million y ears in the former and a few billion years in the latter. However,since Uranus and Neptune a cquired most of their mass by the end of oligarchy, they may have formed beforeEar th!A few implications of the above scenario a re worth noting. Impacts among protoplanets of comparable sizewere common in the inner planet system but not in the o uter. Ejections from the outer planet system includedseveral bodies with mas ses in excess of Earth after oligarchy and an adequ ate number of kilometer-size bodies topopulate the Oort comet cloud during cleanup. Except at the very end o f cleanup, collisions preve nted Uranusand Neptune from ejecting kilometer-size objects. Only Jupiter and, to a much lesser extent, Saturn were capableof populating the Oort Cloud with comets of kilometer size.Subject headinggs: planetary systems: protoplanetary disks — solar system: formation1Institute for Advanced Study, School of Natural Sciences , Einstein Drive, Princeton, NJ 08540; [email protected] tical Astrophysics, California Institute of Technology, MS 130-33, Pasadena, CA 91125; [email protected] ch.edu.3Department of Astronomy, University of Califor nia, 601 Campbell Hall, Berkeley, CA 94720; [email protected] eley.edu.497The Astrophysical Journal, 614:497–507, 2004 October 10# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.1. INTRODUCTIONModern scenarios for planet formation may be broken downinto several s tages. The growth of the smallest gravitationallyactive bodies, planetesimals, is mired in controversy (Lissauer1993; Youdin & Shu 200 2). Orderly growth by the mergingof planetesimals is followed by ru naway accre tion in which asmall fraction of the bodies grow much larger than all theothers (Safronov 1972; Wetherill & Stewart 1989). When the sebig bodies are sparse enough so that each domina tes viscousstirring in its feeding zone, runaway growth gives way tooligarchic growth during which th e big bodies grow in lock-step, maintaining similar masses and uniformly spaced orbits(Kokubo & Ida 1998). As oligarchs grow, their orbital spacingincreases and their number decreases. We investigate how oli-garchy ends and what happens after it does. The plan of ourpaper is as follows. We describe the conditions that pertain atthe end of oligarchy in x 2. We show in x 3thatatthisstagedynamical friction from the small bodies is no longer able tobalance the mutual stirring of the big bodies. In x 4wetreatthe regularization of the orbits of the big bodies and the cleanupof small bodies. We summarize our findings in x 5.1.A few definitions are in order. For simplicity, we considertwo classes of bodies, big ones


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CALTECH GE 133 - FINAL STAGES OF PLANET FORMATION

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