THE FORMATION OF URANUS AND NEPTUNE AMONG JUPITER AND SATURNE. W. ThommesDepartment of Astronomy, University of California at Berkeley, Berkeley, CA 94720; [email protected]. J. DuncanDepartment of Physics, Queen’s University, Kingston, ON K7L 3N6, Canada; [email protected]. F. LevisonSouthwest Research Institute, 1050 Walnut Street, Boulder, CO 80302; [email protected] 2001 November 14; accepted 2002 January 30ABSTRACTThe outer giant planets, Uranus and Neptune, pose a challenge to theories of planet formation. They existin a region of the solar system where long dynamical timescales and a low primordial density of materialwould have conspired to make the formation of such large bodies (15 and 17 times as massive as Earth,respectively) very difficult. Previously, we proposed a model that addressed this problem: Instead of formingin the trans-Saturnian region, Uranus and Neptune underwent most of their growth among proto-Jupiterand proto-Saturn, were scattered outward when Jupiter acquired its massive gas envelope, and subsequentlyevolved toward their present orbits. We present the results of additional numerical simulations, which furtherdemonstrate that the model readily produces analogs to our solar system for a wide range of initial condi-tions. We also find that this mechanism may partly account for the high orbital inclinations observed in theKuiper belt.Key words: celestial mechanics — Kuiper belt — planets and satellites: formation —solar system: formation1. INTRODUCTIONThe growth of Uranus and Neptune in the outer solar sys-tem is not readily accounted for by conventional models ofplanet formation. A low primo rdial density of planetesimalsand weak solar gravity would have made the proc ess ofaccretion slow and inefficient. In direct N-body simulationsof accretion among (approximately) Earth-mass bodiesbeyond 10 AU, performed with three different computercodes, little accretion is found to take place over timescalesof 108yr and, by extrapolation, over the age of the solar sys-tem (Levison & Stewart 2001). Earlier simulations by Bru-nini & Fernandez (1999) showed accretion of the ice giantsin several times 107yr with the same initial conditions, butlater simulations, performed with an improved integrator,required that bodies be enhanced in radius by a factor of atleast 10 relative to bodies having the density of Uranus andNeptune in order to recover the previous result (Brunini2000). Therefore, Uranus and Neptune are unlikely to haveformed from a late stage of mergers among large protopla-nets, analogous to the putative final phase of planet forma-tion in the terrestrial zone (e.g., Wetherill 1996; Cham bers& Wetherill 1998). The oligarchic growth model, in whichthe principal growth mode is accretion of small planetesi-mals by a protoplanet, also produces timescales that are toolong (Kokubo & Ida 2000; Thommes 2000), unless the feed-ing zones of Uranus and Neptune can be replenishedquickly enough with low random velocity planetesimalsfrom elsewhere in the nebula (Bryden, Lin, & Ida 2000).Thommes, Duncan, & Levison (1999, hereafter TDL99)develop an alternative model to in situ formation for the ori-gin of Uranus and Neptune . Beginning with four or moreplanetary embryos of 10–15 Min the Jup iter-Saturnregion, they explore through N-body simulation the evolu-tion of the system after one of these bodies (and in one case,two at the same time) accretes a massive gas envelope tobecome a gas giant. They find that the remaining giant pro-toplanets are predomi nantly scattered outward. Dynamicalfriction with the planetesimal disk subsequently recircular-izes their orbits, which leads in about half the simulationsperformed to a configuration quite similar to the presentouter solar system, with the scattered giant protopl anetstaking the roles of Uranus, Neptune, and Saturn. Theseresults suggest that Uranus and Neptune are actually poten-tial gas giant cores that formed in the same region as Jupiterand Saturn but lost the race to reach runaway gas accretion.Here we explore this model in more detail and performfurther simulations: xx 2 and 3 motivate our choice of initialconditions for the simulations; x 4 discusses the mechanismfor transporting a proto-Uranus and proto-Neptune to theouter solar system. N-body simulation results are presentedin x 5. The effect on the asteroid and Kuiper belts is dis-cussed in x 6. We summarize and discuss our findings in x 7.2. AVAILABLE MATERIAL IN THEJUPITER-SATURN REGIONHayashi (1981) estimated the minimum primordial sur-face density of solids in the outer solar system to beminðaÞ¼2:7a5AU 3=2gcm 2: ð1ÞThe requirement that the cores of Jupiter and Saturn bemassive enough to ha ve initiated runaway gas accretion sug-gests that they are 10 Min mass (Mizuno, Nakazawa, &Hayashi 1978; Pollack et al. 1996). Interior models are con-sistent with such a core mass but also allow a coreless Jupi-ter (Gui llot 1999). We assume in this work that both Jupiterand Saturn began as 10 Mbodies; putting gas giant coresThe Astronomical Journal, 123:2862–2883, 2002 May# 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.2862and ice giant cores on the same footing is necessary in the‘‘ strong ’’ version of our model, although it is not essentialto the basic mechanism; we discuss variations on the modelin x 7.A surface density of 2.7 g cm 2was likely too low to forman 10 Mbody at 5 AU before the gas was removed fromthe protoplanetary disk. Lissauer (1987) finds that a surfa cedensity of 15–30 g cm 2is needed to allow formation ofJupiter’s core on a timescale of 5 105–5 106yr, while themodel of Pollack et al. (1996), which includes co ncurrentaccretion of solids and gas, produces Jupiter in less than 107yr with 10 g cm 2. The formation of giant planet cores mayhave been triggered at least in part by the enhancement inthe solids surface density beyond the ‘‘ snow line,’’ wherewater goes from being a gaseous to a solid constituent of theprotoplanetary disk. In fact, outward diffusion and subse-quent freezing of water vapor from the inner solar systemmay have resulted in a large local density enhancementaround 5 AU, perhaps yielding a surface density even higherthan 30 g cm 2(Stevenson & Lunine 1988). Here we assumea power-law surface density,ðaÞ¼0a5AU : ð2ÞThe above discussion suggests 10–30
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