Dynamical Models of Terrestrial Planet Formation

📝 Abstract

We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial planet formation is dominated by gravitational interactions and collisions. The earliest phase of terrestrial-planet formation involve the growth of km-sized or larger planetesimals from dust grains, followed by the accumulations of these planetesimals into ~100 lunar- to Mars-mass bodies that are initially gravitationally isolated from one-another in a swarm of smaller planetesimals, but eventually grow to the point of significantly perturbing one-another. The mutual perturbations between the embryos, combined with gravitational stirring by Jupiter, lead to orbital crossings and collisions that drive the growth to Earth-sized planets on a timescale of 10-100 million years. Numerical treatment of this process has focussed on the use of symplectic integrators which can rapidly integrate the thousands of gravitationally-interacting bodies necessary to accurately model planetary growth. While the general nature of the terrestrial planets–their sizes and orbital parameters–seem to be broadly reproduced by the models, there are still some outstanding dynamical issues. One of these is the presence of an embryo-sized body, Mars, in our system in place of the more massive objects that simulations tend to yield. [Abridged]

💡 Analysis

We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial planet formation is dominated by gravitational interactions and collisions. The earliest phase of terrestrial-planet formation involve the growth of km-sized or larger planetesimals from dust grains, followed by the accumulations of these planetesimals into ~100 lunar- to Mars-mass bodies that are initially gravitationally isolated from one-another in a swarm of smaller planetesimals, but eventually grow to the point of significantly perturbing one-another. The mutual perturbations between the embryos, combined with gravitational stirring by Jupiter, lead to orbital crossings and collisions that drive the growth to Earth-sized planets on a timescale of 10-100 million years. Numerical treatment of this process has focussed on the use of symplectic integrators which can rapidly integrate the thousands of gravitationally-interacting bodies necessary to accurately model planetary growth. While the general nature of the terrestrial planets–their sizes and orbital parameters–seem to be broadly reproduced by the models, there are still some outstanding dynamical issues. One of these is the presence of an embryo-sized body, Mars, in our system in place of the more massive objects that simulations tend to yield. [Abridged]

📄 Content

arXiv:0906.4369v1 [astro-ph.EP] 23 Jun 2009 Dynamical Models of Terrestrial Planet Formation Jonathan I. Lunine∗, Lunar and Planetary Laboratory, The University of Arizona, Tucson AZ USA, 85721. jlunine@lpl.arizona.edu David P. O’Brien, Planetary Science Institute, Tucson AZ USA 85719 Sean N. Raymond, Center for Astrophysics and Space Astronomy, UCB 389, University of Col- orado, Boulder, CO 80309-0389 and Laboratoire d’Astrophysique de Bordeaux (CNRS; Universit Bordeaux I), BP 89, F-33270 Floirac, France Alessandro Morbidelli, Obs. de la Cˆote d’Azur, Nice, F-06304 France Thomas Quinn, Department of Astronomy, University of Washington, Seattle USA 98195 Amara L. Graps, Southwest Research Institute, Boulder CO USA 80302 Accepted for publication in Advanced Science Letters June 10, 2009 ∗Corresponding author Abstract We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial planet formation is dominated by gravitational interactions and collisions. The ear- liest phase of terrestrial-planet formation involve the growth of km-sized or larger planetesimals from dust grains, followed by the accumulations of these planetesimals into ∼100 lunar- to Mars- mass bodies that are initially gravitationally isolated from one-another in a swarm of smaller plan- etesimals, but eventually grow to the point of significantly perturbing one-another. The mutual perturbations between the embryos, combined with gravitational stirring by Jupiter, lead to orbital crossings and collisions that drive the growth to Earth-sized planets on a timescale of 107 −108 years. Numerical treatment of this process has focussed on the use of symplectic integrators which can rapidy integrate the thousands of gravitationally-interacting bodies necessary to accurately model planetary growth. While the general nature of the terrestrial planets–their sizes and orbital parameters–seem to be broadly reproduced by the models, there are still some outstanding dynam- ical issues. One of these is the presence of an embryo-sized body, Mars, in our system in place of the more massive objects that simulations tend to yield. Another is the effect such impacts have on the geochemistry of the growing planets; re-equilibration of isotopic ratios of major elements during giant impacts (for example) must be considered in comparing the predicted compositions of the terrestrial planets with the geochemical data. As the dynamical models become successful in reproducing the essential aspects of our own terrestrial planet system, their utility in predicting the distribution of terrestrial planet systems around other stars, and interpreting observations of such systems, will increase. Keywords: planets, dynamics, formation, Earth, water, Moon Dedicated to George Wetherill (1925-2006), pioneer in studies of the formation of the terrestrial planets. 2 1 Introduction The formation of the terrestrial planets remains one of the enduring problems in planetary science and (in view of the expectation of large numbers of extrasolar terrestrial-type planets) astrophysics today. The complexity of terrestrial geochemistry, constraints on timescales, the presence of abun- dant water on the Earth, and the curious geochemical and dynamical relationships between the Earth and the Moon are among the problems that must be addressed by models. Pioneering studies by Safronov1 and successors such as Weidenschilling2 established the basic physics of gas-free accretion. The effects of gas on accretion were examined somewhat later, most notably by the “Kyoto” school of Hayashi and collaborators3. In the 1980’s, studies of terrestrial planet forma- tion advanced further thanks to George Wetherill4, his students and postdoctoral collaborators, who highlighted the basic problems of obtaining the correct low planetary eccentricities and incli- nations, as well as producing a diversity of sizes ranging from Earth through Mars and Mercury. Breakthroughs in the subject came through the development of special numerical approaches to the problem, as well as theoretical insights that allowed for the right starting boundary conditions. Additional geochemical considerations, including formation timescales derived from radioactive isotopic ratios, and stable isotopic constraints on source regions, continue to challenge the models today. Decades of research have established a rough timeline of events during the formation of the Solar System’s terrestrial planets. These are summa

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