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Dynamical Simulations of Terrestrial Planet Formation and Water Delivery Icarus 168 (2004) 1–17 www.elsevier.com/locate/icarus Making other earths: dynamical simulations of terrestrial planet formation and water delivery Sean N. Raymond,a,∗ Thomas Quinn,a and Jonathan I. Lunine b a Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA b Lunar and Planetary Laboratory, The University of Arizona, Tucson, AZ 85287, USA Received 6 August 2003; revised 12 November 2003 Abstract We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial 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 and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1–4 terrestrial planets inside 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 × 1024 g), and vary in mass between 0.23M⊕ and 3.85M⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1–2M⊕ protoplanets which can serve as the accretion seeds for 2 + M⊕ planets with large water contents. 2003 Elsevier Inc. All rights reserved. Keywords: Planetary formation; Extrasolar planets; Origin, Solar System; Cosmochemistry; Exobiology 1. Introduction implications for the abundance of habitable planets available for Terrestrial Planet Finder (TPF) to discover. There is a paradox in the definition of the habitable zone In the current paradigm of planet formation four dynam- with respect to the presence of liquid water. Imagine a planet ically distinct stages are envisioned (Lissauer, 1993): at the right distance from a star to have stable liquid wa- ter on its surface, supported by a modest greenhouse effect. Initial stage: Grains condense and grow in the hot nebular Nebular models and meteorite data suggest that the local disk, gradual settling to the mid-plane. The com- environment during the early formation of this planet was position of the grains is determined by the local sufficiently hot to prevent hydration of the planetesimals and temperature of the nebula. Gravitational instability protoplanets out of which the planet was formed (Morbidelli among the grains is resisted owing to continuous et al., 2000). That is, the local building blocks of this “hab- stirring by convective and turbulent motions. itable” planet were devoid of water. How, then, could this Early stage: Growth of grains to km-sized planetesimals occurs via pairwise accretion in the turbulent disk, planet acquire water and become truly habitable? Delivery of or possibly via gravitational instability under cer- water-laden planetesimals from colder regions of the disk is tain nebular conditions (Goldreich and Ward, 1973; one solution, but it implies that the habitability of extrasolar Youdin and Shu, 2002). Planetesimals initially have planets depends on the details of their final assembly, with low eccentricities (e) and inclinations (i) due to gas drag. * Corresponding author. Middle stage—oligarchic growth: “Focused merging”— E-mail address: [email protected] (S.N. Raymond). accretion with gravitationally augmented cross 0019-1035/$ – see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2003.11.019 2 S.N. Raymond et al. / Icarus 168 (2004) 1–17 sections—leads to agglomeration of planetesimals embryos from outside its local region, including a few from into Moon-to Mars-sized “planetary embryos.” past 2.5 AU, which delivered the bulk of the Earth’s water. Possible runaway accretion and subsequent energy In this model the Earth accreted water since its formation, in equipartition (dynamical friction) may lead to po- the form of an early bombardment of asteroids and comets, larization of the mass distribution: a few large bod- a few large “wet” planetary embryos, and continual impacts ies with low e and i in a swarm of much smaller of small bodies over long timescales. This scenario explains planetesimals with high e and i. The timescale the D/H ratio of Earth’s water in the context of late-stage for this process correlates inversely with heliocen- planetary accretion. tric distance. Simulations of oligarchic growth by Morbidelli et al. (2000) assumed that oligarchic growth Kokubo and Ida (2000) suggest that planetary em- took place throughout the inner Solar System, with plane- bryos form in < 1Myrat1AU,in∼ 40 Myr at 5 tary embryos out to 4 AU. If the timescale for the formation AU, and in > 300 Myr past 10 AU. Since the gi- of Jupiter is less than that for planetary embryos in the outer ant planets are constrained to have formed within asteroid belt (past 2.5 AU), these initial conditions neglect 10 Myr from inferred lifetimes of gaseous disks Jupiter’s strong gravitational influence on the oligarchic around young stars (Briceño et al., 2001), embryos growth process in the asteroid belt, as well as planetesimal– could only have formed in the innermost Solar Sys- embryo interactions. Several other authors (e.g., Chambers, tem within that time. Thus, we expect that at the 2001; Chambers and Cassen, 2002) subsequently have nu- time of the formation of Jupiter, the inner terres- merically formed terrestrial planets, including both planetary trial region was dominated by ∼ 30–50 planetary embryos and planetesimals in their simulations. Their ini- embryos while the asteroid belt consisted of a large tial conditions often seem ad hoc, and not based on the state number of ∼ 1 km planetesimals. of the protoplanetary disk at the end of oligarchic growth, Note that this scenario is based on a relatively in particular the radial dependence of the planetary embryo low surface density model, and is somewhat in- formation timescale, which depends in turn on the surface consistent with the “core accretion” model for the density of the disk (Kokubo and Ida, 2002). formation of giant planets (Pollack et al., 1996), Chambers (2003) used a statistical Öpik–Arnold method which requires solid accretion cores of several to test planet formation in a number of scenarios, including Earth masses to form between 5 and 10 AU in less some which are similar to those we present in this paper. than 10 Myr, presumably by oligarchic growth. The The advantage of his statistical method is its low computa- formation timescale and masses of planetary em- tional expense relative to N-body simulations, allowing the bryos are sensitive to the surface density (Kokubo quick exploration of a large parameter space. Its drawback and Ida, 2002), and the detailed mass distribution in is the difficulty of implementing realistic dynamics. There- the disk at the time of Jupiter’s formation is unclear. fore, N-body simulations like those we present here may be Late Stage: Once runaway accretion has terminated due to used to “calibrate,” and thereby complement the statistical lack of slow moving material, planetary embryos simulations. and planetesimals gradually evolve into crossing In this paper, we characterize the process of terrestrial orbits as a result of cumulative gravitational per- planet formation and volatile delivery as a function of several turbations. This leads to radial mixing and giant parameters of the protoplanetary system. Our initial condi- impacts until only a few survivors remain. The tions attempt to realistically describe the protoplanetary disk timescale for this process is ∼ 108 yr. at the beginning of late-stage accretion, assuming a relatively low density protoplanetary disk in which oligarchic growth Until recently, a leading hypothesis for the origin of proceeds as described above. We do not limit ourselves to Earth’s water was the “late veneer” scenario, in which our own Solar System, and focus on the formation of planets the Earth formed primarily from local material, and ac- within the habitable zone of their parent stars. The parame- quired its water at later times from a large number of ters we vary in our simulations are cometary impacts. These impacts resulted in a hot water vapor atmosphere which condensed into oceans (Matsui (i) Jupiter’s mass, and Abe, 1986). However, the D/H ratio of three comets (ii) eccentricity, has been measured to be 12 times higher than the pro- (iii) semimajor axis, and tosolar value (Balsiger et al., 1995; Meier et al., 1998; (iv) time of formation, Bockelee-Morvan et al., 1998), and roughly twice the ter- (v) the density in solids of the protoplanetary disk, and restrial oceanic (roughly the chondritic) value. This implies (vi) the location of the snow line. that at most 10% of the Earth’s water came from a cometary source (Morbidelli et al., 2000). Section 2 describes our initial conditions and numerical Morbidelli et al. (2000) proposed that the bulk of the methods. Section 3 presents our results, which are discussed Earth’s water may have come from the asteroid belt in the in Section 4, including application to the NASA’s Terrestrial form of planetary embryos.
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