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«corresponding author: Alessandro Morbidelli Dep. Cassiopée, Universite’ de Nice-Sophia Antipolis, Observatoire de la Côte d'Azur, CNRS B.P.4229, ...»

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A. Morbidelli1, J.I. Lunine2, D.P. O’Brien3, S.N. Raymond4, K. J. Walsh5


Dep. Cassiopée, Universite’ de Nice-Sophia Antipolis, Observatoire de la Côte d'Azur, CNRS, B.P.4229,

06304 Nice Cedex 4, France; morby@oca.eu


Department of Astronomy, Cornell University, Ithaca, NY 14853, USA; jlunine@astro.cornell.edu


Planetary Science Institute, 1700 E. Fort Lowell, Tucson, AZ 85719, USA; obrien@psi.edu 4 Université de Bordeaux, Observatoire Aquitain des Sciences de l'Univers, CNRS, 2 rue de l'Observatoire, BP 89, F-33271 Floirac Cedex, France;rayray.sean@gmail.com 5 Department of Space Studies, Southwest Research Institute, 1050 Walnut St. Suite 400, Boulder, CO 80302, USA; kwalsh@boulder.swri.edu corresponding author: Alessandro Morbidelli Dep. Cassiopée, Universite’ de Nice-Sophia Antipolis, Observatoire de la Côte d'Azur, CNRS B.P.4229, 06304 Nice Cedex 4, France;

EMAIL: morby@oca.eu; TEL:(+33) 4 92 00 30 51

Table of Contents:

1. Introduction

2. Step I: from dust to planetesimals

3. Step II: from planetesimals to planetary embryos

4. Step III: from embryos to terrestrial planets: overview

5. From embryos to terrestrial planets: Dependence of the results on simulation and model parameters

5.1 Outcome of giant collisions

5.2 Disk mass and radial profile

5.3 Particle size distribution in the disk

5.4 Giant planet architecture

6. The Grand Tack Scenario

7. Origin of Terrestrial water

8. Summary and Future Prospects Keywords: protoplanetary disk, planetesimals, meteorites, giant impacts, giant planet migration, water Abstract This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical models with geochemical, cosmochemical and chronological constraints, in order to outline a comprehensive scenario of the early evolution of our Solar System. Given that the giant planets formed first in the protoplanetary disk, we stress the sensitive dependence of the terrestrial planet accretion process on the orbital architecture of the giant planets and on their evolution. This suggests a great diversity among the terrestrial planets populations in extrasolar systems. Issues such as the cause for the different masses and accretion timescales between Mars and the Earth and the origin of water (and other volatiles) on our planet are discussed at depth.

1. Introduction Although we have more information about the terrestrial planets than about virtually any other celestial bodies, the processes leading to their formation have long remained elusive. Only in the last few decades has there been significant progress. On one hand, geochemical and cosmo-chemical analyses performed with laboratory instruments of unprecedented precision have produced a huge amount of data on the chemical and isotopic composition of the planets and of their precursors -- meteorites -- as well as constraints on the chronology of their accretion and thermal evolution. On the other hand, the remarkable increase in computer performance has allowed modelers to undertake increasingly realistic simulations of the dynamical process of terrestrial planet accretion. The results achieved on each front have reached a sufficient level of reliability to be integrated in a comprehensive view of the early evolution of the inner solar system. This review paper will focus on the key processes as seen from an astrophysical point of view but we will make reference to geochemical, cosmochemical and astronomical constraints. Our aim is that this chapter be useful to both theorists and observers in confronting the results of the modeling with laboratory and observational constraints.

Terrestrial planet formation occurred through three distinct modes of growth that were ordered in time in the protoplanetary disk. An observer privileged to watch this process live would see a very distinct distribution of gas and solids, of particles sizes, and of orbits of solid bodies, in each of the three steps; they are potentially distinguishable from each other through disk observations by the next generation of powerful ground and space-based observatories. In step I, planetesimals are formed in a disk of gas and dust. In step II, the collisional evolution of the planetesimal population leads to the growth of a new class of objects called planetary embryos, which represent an intermediate stage between planetesimals and planets. Giant planets probably form at roughly the same time as planetary embryos. In step III, after the disappearance of gas from the proto-planetary disk, the embryos’ orbits become unstable, and their mutual collisions give birth to a small number of massive objects, the terrestrial planets. These steps are described in Sects. 2-4. Section 5 details how the results of the simulations change depending on various assumptions (eg. the mass distribution in the disk, giant planet orbits, outcome of collisions etc.). Section 6 discusses a new model that aims to link in a coherent scenario the dynamical evolution of the giant planets with the formation of the terrestrial planets, with the specific goal of explaining the small mass of Mars relative to the Earth. Section 7 discusses the origin of water on Earth and other chemical implications of the terrestrial planet accretion models, while Section 8 details future observing capabilities that might test these ideas.

We dedicate this review to G.W. Wetherill, who was the first to investigate terrestrial planet formation by combining dynamical simulations and geo/cosmo-chemical constraints. He traced the path that we are continuing to follow here.

2. Step I: from dust to planetesimals.

When a molecular cloud collapses under its own gravity to form a star, the material forms a disk-like structure in orbit around the central object, due to the conservation of angular momentum. These proto-planetary disks are now routinely observed around pre-main sequence stars (e.g., McCaughrean & O’Dell 1996, Kenyon & Hartmann 1995), while that for the Sun -- the “solar nebula” -- is understood from the physical and chemical evidence left behind in our solar system.

In proto-planetary disks, dust grains sediment into a thin layer at the mid-plane of the disks (Wedenschilling 1980). The sedimentation timescale and the volume density of grains near the mid-plane depend on the severity of turbulence in the disk gas, as strong turbulence inhibits sedimentation. Even in laminar disks, though, the volume density of grains in the mid-plane could not reach arbitrarily large values, because the sedimentation of an excessive amount of solids would itself generate turbulence in the disk via the so-called Kelvin-Helmoltz instability (Weidenschilling 1995).

The growth from these grains to kilometer-size planetesimals is still quite a mystery. In principle, one could expect that grains, once sufficiently concentrated near the mid-plane, should stick to each other to form progressively larger objects, in an ordered-growth process. But particles of cm-size are too small for gravity to be effective in particle-particle collisions, and too big to stick together through electrostatic forces. Moreover, grains are subject to gas drag, which makes them drift towards the central star (Weideschilling 1977). The drift speed is size-dependent; thus, particles of different sizes should collide with non-negligible relative velocities of the order of several cm/s. At these speeds particles should break, rather than coagulate (but see Wettlaufer 2010). Because the drift speed towards the central star is maximal for meter-size boulders, this issue is known as the “meter-size barrier problem”, even though it is likely that the fragmentation bottle-neck for accretion starts at much smaller sizes (cm or dm).

A new alternative to this ordered-growth process is that planetesimals form due to the collective gravity of massive swarms of small particles, concentrated at some locations (local maxima of the gas density distribution or inter-vortex regions, depending on particle sizes) by the turbulence of the disk (Johansen et al.

2007; Cuzzi et al. 2008). These “gravoturbulent” models can explain the formation of planetesimals of size 100 km or larger without passing through intermediate small sizes, thereby circumventing the meter-size barrier problem. The size distribution of objects in the asteroid belt and in the Kuiper belt, where most of the mass is concentrated in 100km objects, supports this scenario (Morbidelli et al. 2009; but see Weidenschilling 2010). The existence and the properties of binary Kuiper belt objects also are best explained by the gravitational collapse of massive swarms of small particles that have angular momenta too large to form single objects (Nesvorny et al. 2010). Although more work is needed to explore all the facets of this novel view of planetesimal formation, it seems to resolve many of the outstanding problems that have plagued other models.

In the gravitoturbulent models, once enough small particles are concentrated at some location, the formation of a planetesimal is extremely rapid (Johansen et al. 2007; Cuzzi et al. 2008). However, the formation of selfgravitating clumps of small particles is sporadic (Cuzzi et al. 2010; Chambers 2010), and hence planetesimal formation can in principle proceed over an extended period of time. Moreover, one should not assume that planetesimal formation starts at the same “time zero” in every region of the proto-planetary disk, where “time zero” is usually identified with the formation time of the first solids, the calcium-aluminium inclusions (CAIs, dated at 4.568 Gy ago; Bouvier et al. 2007; Burkhardt et al. 2008). Sufficient clumping of small particles to form planetesimals is possible only if the solid/gas density ratio is larger than some threshold value (Johansen et al. 2009). This ratio in principle increases with time due to the progressive removal of gas from the disk (Throop & Bally 2005). Thus, in some parts of the disk, for instance the innermost regions, this condition might have been met very early, thus leading to a first generation of planetesimals rich enough in short-lived radionuclides (principally 26Al and 60Fe; Ghosh et al 2006) to undergo melting or metamorphism of the rocky component. Farther out in the disk, this condition might have generally been met late enough that the remaining quantities of short-lived radionuclides was too small to allow thermally-driven melting or metamorphism of 100-km scale planetesimals. The threshold for differentiation of 100-km planetesimals might have been reached inward of (Bottke et al. 2006), or even within (Ghost et al. 2006), the asteroid belt.

In an idealized chemical model, planetesimals should accrete all elements and molecules that are in condensed form at their corresponding location of the disk. Since at a given time the temperature in the disk decreases with distance from the Sun, a classic condensation sequence characterized by a clear radial gradient of chemical properties should be obtained (e.g., Dodson-Robinson et al 2009). However, in gravoturbulent models, planetesimals form sporadically so that at any given location they need not have formed at the same time. This effect probably makes the radial gradient of chemical compositions in the planetesimal disk less “clean” than one would predict from a purely condensation-driven sequence.

Observational constraints are available to deduce properties and confront models of the planetesimal disk.

There are three classes of chondritic meteorites: enstatite, ordinary and carbonaceous. Their chemistry and mineralogy suggest that these three classes formed respectively at decreasing temperatures. For instance, water is essentially absent on enstatite meteorites, and quite abundant in (some subclasses of) carbonaceous chondrites, while the water-content in ordinary chondrites is intermediate between the two (Robert 2003).

Spectroscopic observations link these three classes of meteorites to asteroids of different taxonomic type (although not necessarily to specific parent bodies): enstatite chondrites can be linked with E-type asteroids (Fornasier et al. 2008), which are predominant in the Hungaria region at 1.8 Astronomical units (AU; 1 AU is the mean Sun-Earth distance); ordinary chondrites are linked to S-type asteroids (Binzel et al. 1996), which are predominant in the inner belt (2.1-2.8 AU); and carbonaceous chondrites are linked to C-type asteroids (Burbine 2000), predominant in the outer belt (beyond 2.8 AU). There is, however, substantial overlap in the radial distribution of these three types of asteroids (Gradie and Tedesco 1982). This could be the result of the formation of subsequent generations of asteroids in a cooling disk, as mentioned before. However, the analysis of the ages of the individual chondrules in meteorites does not show any clear difference in accretion age of the parent bodies of ordinary and carbonaceous chondrites (Villeneuve et al. 2009), which both seem to have formed 3-4 My after CAI formation. This supports the alternative idea that the partial overlapping of the radial distribution of asteroids of different types is due to dynamical mixing that occurred after the formation of the asteroids (see sections 4 and 6).

Comets are representative of the planetesimal disk that formed at larger distances than the asteroid belt, i.e. in between and beyond the giant planets orbits. The classical view is that, while the parent bodies of carbonaceous chondrites are rich in hydrated minerals, comets are rich in water ice and lack hydrated silicates, presumably because they formed in a colder environment. However, new discoveries are making the difference between carbonaceous chondrites (or C-type asteroids) and comets less well defined. The close flyby images of comets (e.g. Comet Borrelly) show very little surface ice and small active regions (Sunshine et al. 2006). The samples from comet Wild 2 by the Stardust Mission turned out to be quite similar to meteoritic samples (Zolensky et al. 2006). Modeling work on the origin of the dust that produces the zodiacal light (Nesvorny et al. 2010b) predicts that at least 50% of the micro-meteorites collected on Earth are cometary;

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