Making other earths: dynamical simulations of terrestrial planet formation and water deliveryIntroductionModelInitial conditionsWater contentNumerical methodResultsOne simulationDependences on system parametersPlanetesimal massSurface densityJupiter's massJupiter's eccentricityJupiter's semimajor axisThe position of the snow lineTime of Jupiter formationWater contentCharacterizing the formed terrestrial planetsDiscussionApplications to TPF/DarwinConclusionsAcknowledgmentsReferencesIcarus 168 (2004) 1–17www.elsevier.com/locate/icarusMaking other earths: dynamical simulations of terrestrial planet formationand water deliverySean N. Raymond,a,∗Thomas Quinn,aand Jonathan I. LuninebaDepartment of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USAbLunar and Planetary Laboratory, The University of Arizona, Tucson, AZ 85287, USAReceived 6 August 2003; revised 12 November 2003AbstractWe present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to theterrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals,assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter’s mass, position andeccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1–4 terrestrial planetsinside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11“habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100 + oceans of water (1 ocean =1.5 × 1024g), and vary in mass between 0.23M⊕and 3.85M⊕. There is a good deal of stochastic noise in these simulations, but the mostimportant parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in thisregion results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planetswhich form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities thana circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1–2M⊕protoplanets which can serve as the accretionseeds for 2 + M⊕planets with large water contents. 2003 Elsevier Inc. All rights reserved.Keywords: Planetary formation; Extrasolar planets; Origin, Solar System; Cosmochemistry; Exobiology1. IntroductionThere is a paradox in the definition of the habitable zonewith respect to the presence of liquid water. Imagine a planetat the right distance from a star to have stable liquid wa-ter on its surface, supported by a modest greenhouse effect.Nebular models and meteorite data suggest that the localenvironment during the early formation of this planet wassufficiently hot to preventhydration of the planetesimals andprotoplanets out of which the planet was formed (Morbidelliet al., 2000). That is, the local building blocks of this “hab-itable” planet were devoid of water. How, then, could thisplanet acquire water and become trulyhabitable?Deliveryofwater-laden planetesimals from colder regions of the disk isone solution, but it implies that the habitability of extrasolarplanets depends on the details of their final assembly, with*Corresponding author.E-mail address: [email protected] (S.N. Raymond).implications for the abundance of habitable planets availablefor Terrestrial Planet Finder (TPF) to discover.In the current paradigm of planet formation four dynam-ically distinct stages are envisioned (Lissauer, 1993):Initial stage: Grains condense and grow in the hot nebulardisk, gradual settling to the mid-plane. The com-position of the grains is determined by the localtemperature of the nebula. Gravitational instabilityamong the grains is resisted owing to continuousstirring by convective and turbulent motions.Early stage: Growth of grains to km-sized planetesimalsoccurs via pairwise accretion in the turbulent disk,or possibly via gravitational instability under cer-tain nebular conditions (Goldreich and Ward, 1973;Youdin and Shu, 2002). Planetesimals initially havelow eccentricities (e) and inclinations (i) due to gasdrag.Middle stage—oligarchic growth: “Focused merging”—accretion with gravitationally augmented cross0019-1035/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2003.11.0192 S.N. Raymond et al. / Icarus 168 (2004) 1–17sections—leads to agglomeration of planetesimalsinto Moon-to Mars-sized “planetary embryos.”Possible runaway accretion and subsequent energyequipartition (dynamical friction) may lead to po-larization of the mass distribution: a few large bod-ies with low e and i in a swarm of much smallerplanetesimals with high e and i. The timescalefor this process correlates inversely with heliocen-tric distance. Simulations of oligarchic growth byKokubo and Ida (2000) suggest that planetary em-bryos form in < 1Myrat1AU,in∼ 40 Myr at 5AU, and in > 300 Myr past 10 AU. Since the gi-ant planets are constrained to have formed within10 Myr from inferred lifetimes of gaseous disksaround young stars (Briceño et al., 2001), embryoscould only have formed in the innermost Solar Sys-tem within that time. Thus, we expect that at thetime of the formation of Jupiter, the inner terres-trial region was dominated by ∼ 30–50 planetaryembryos while the asteroid belt consisted of a largenumber of ∼ 1 km planetesimals.Note that this scenario is based on a relativelylow surface density model, and is somewhat in-consistent with the “core accretion” model for theformation of giant planets (Pollack et al., 1996),which requires solid accretion cores of severalEarth masses to form between 5 and 10 AU in lessthan 10 Myr, presumablyby oligarchic growth. Theformation timescale and masses of planetary em-bryos are sensitive to the surface density (Kokuboand Ida, 2002),and the detailed mass distribution inthe disk at the time of Jupiter’s formation is unclear.Late Stage: Once runaway accretion has terminated due tolack of slow moving material, planetary embryosand planetesimals gradually evolve into crossingorbits as a result of cumulative gravitational per-turbations. This leads to radial mixing and
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