Lunar and terrestrial planet formation in the Grand (original) (raw)
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Dynamical models of terrestrial planet formation
Advanced Science …, 2011
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 Marsmass 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 7 − 10 8 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 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. 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.
Numerical simulation of the final stages of terrestrial planet formation
Icarus, 1980
Four representative numerical simulations of the growth of the terrestrial planets by accretion of large protoplanets are presented. The mass and relative velocity distributions of the bodies in these simulations are free to evolve simultaneously in response to close gravitational encounters and occasional collisions between bodies. The collisions between bodies, therefore, arise in a natural way and the assumption of expressions for the relative velocity distribution and the gravitational collision cross-section is unnecessary. The relation of the present work to scenarios given by Safronov (1969), Goldreich and Ward (1973), and Greenberg et al. (1977) for the early stages of solar system evolution is discussed. A comparison of predictions of the commonly employed two-body gravitational model with integrations of the equations of motion which include the influence of the Sun indicate that the twobody model is inadequate for the treatment of encounters between large protoplanets, particularly when they move along low eccentricity orbits resulting in encounters with low relative velocities. A new model is, therefore, proposed for single close encounters between two small masses, m I and m 2 , which orbit a much larger mass, M. Comparisons of predictions of the model with integrations of the three-body equations of motion indicate that the model is an adequate approximation
Proceedings of the National Academy of Sciences, 2011
Advances in our understanding of terrestrial planet formation have come from a multidisciplinary approach. Studies of the ages and compositions of primitive meteorites with compositions similar to the Sun have helped to constrain the nature of the building blocks of planets. This information helps to guide numerical models for the three stages of planet formation from dust to planetesimals (∼10 6 y), followed by planetesimals to embryos (lunar to Mars-sized objects; few × 10 6 y), and finally embryos to planets (10 7 –10 8 y). Defining the role of turbulence in the early nebula is a key to understanding the growth of solids larger than meter size. The initiation of runaway growth of embryos from planetesimals ultimately leads to the growth of large terrestrial planets via large impacts. Dynamical models can produce inner Solar System configurations that closely resemble our Solar System, especially when the orbital effects of large planets (Jupiter and Saturn) and damping mechani...
Formation of the terrestrial planets
2019
Probabilities of Collisions of Planetesimals from Different Regions of the Feeding Zone of the Terrestrial Planets with the Forming Planets and the MoonS. I. IpatovISSN 0038-0946, Solar System Research, 2019, Vol. 53, No. 5, pp. 332–361. © Pleiades Publishing, Inc., 2019.Russian Text © The Author(s), 2019, published in Astronomicheskii Vestnik, 2019, Vol. 53, No. 5, pp. 349–379.<br>
The Role of Giant Planets in Terrestrial Planet Formation
The Astronomical Journal, 2003
We present the results of simulations of the late stages of terrestrial planet formation under the gravitational influence of 6 different outer giant planetary systems with a wide range of dynamical characteristics. Our goal is to determine the role that the giant planets play in determining the number, mass and orbital characteristics of the resulting terrestrial planets and their general potential for habitability. Each of the giant planet systems affects the embryos in its own unique way. However, we find that the most profound effects are secular in nature. We also discovered that dynamical excitation of the embryos by the giant planets in one region can be transferred into another on short timescales via what we call secular conduction. Despite large differences in the behaviors of our systems, we have found general trends that seem to apply. The number, mass, and the location of the terrestrial planets are directly related to the amount of dynamical excitation experienced by the planetary embryos near 1 AU. In general, if the embryos' eccentricities are large each is crossing the orbits of a larger fraction of its cohorts, which leads to a fewer number of more massive planets. In addition, embryos tend to collide with objects near their periastron. Thus, in systems where the embryos' eccentricities are large, planets tend to form close to the central star.
Theory of planet formation and comparison with observation
EPJ Web of Conferences, 2011
The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows us to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic M − R diagram. This shape can be understood with basic concepts of the core accretion model.
Planet formation: The case for large efforts on the computational side
arXiv: Earth and Planetary Astrophysics, 2019
Modern astronomy has finally been able to observe protoplanetary disks in reasonable resolution and detail, unveiling the processes happening during planet formation. These observed processes are understood under the framework of disk-planet interaction, a process studied analytically and modeled numerically for over 40 years. Long a theoreticians' game, the wealth of observational data has been allowing for increasingly stringent tests of the theoretical models. Modeling efforts are crucial to support the interpretation of direct imaging analyses, not just for potential detections but also to put meaningful upper limits on mass accretion rates and other physical quantities in current and future large-scale surveys. This white paper addresses the questions of what efforts on the computational side are required in the next decade to advance our theoretical understanding, explain the observational data, and guide new observations. We identified the nature of accretion, ab initio p...
Arxiv preprint arXiv: …, 2010
We review the current theoretical understanding how growth from micrometer sized dust to massive giant planets occurs in disks around young stars. After introducing a number of observational constraints from the solar system, from observed protoplanetary disks, and from the extrasolar planets, we simplify the problem by dividing it into a number of discrete stages which are assumed to occur in a sequential way. In the first stage -the growth from dust to kilometer sized planetesimals -the aerodynamics of the bodies are of central importance. We discuss both a purely coagulative growth mode, as well as a gravoturbulent mode involving a gravitational instability of the dust. In the next stage, planetesimals grow to protoplanets of roughly 1000 km in size. Gravity is now the dominant force. The mass accretion can be strongly non-linear, leading to the detachment of a few big bodies from the remaining planetesimals. In the outer planetary system (outside a few AU), some of these bodies can become so massive that they eventually accrete a large gaseous envelope. This is the stage of giant planet formation, as understood within the core accretiongas capture paradigm. We also discuss the direct gravitational collapse model where giant planets are thought to form directly via a gravitational fragmentation of the gas disk. In the inner system, protoplanets collide in the last stage -probably after the dispersal of the gaseous disk -in giant impacts until the separations between the remaining terrestrial planets become large enough to allow long term stability. We finish the review with some selected questions.
Planet formation models: the interplay with the planetesimal disc
Astronomy & Astrophysics, 2012
Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims. We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods. We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results. We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M ⊕ or above several Jupiter masses. Conclusions. To form giant planets before the dissipation of the disc, small planetesimals (∼0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.
Astronomy & Astrophysics, 2015
Context. Recent three-dimensional magnetohydrodynamical simulations have identified a disk wind by which gas materials are lost from the surface of a protoplanetary disk, which can significantly alter the evolution of the inner disk and the formation of terrestrial planets. A simultaneous description of the realistic evolution of the gaseous and solid components in a disk may provide a clue for solving the problem of the mass concentration of the terrestrial planets in the solar system. Aims. We simulate the formation of terrestrial planets from planetary embryos in a disk that evolves via magnetorotational instability and a disk wind. The aim is to examine the effects of a disk wind on the orbital evolution and final configuration of planetary systems. Methods. We perform N-body simulations of sixty 0.1 Earth-mass embryos in an evolving disk. The evolution of the gas surface density of the disk is tracked by solving a one-dimensional diffusion equation with a sink term that accounts for the disk wind. Results. We find that even in the case of a weak disk wind, the radial slope of the gas surface density of the inner disk becomes shallower, which slows or halts the type I migration of embryos. If the effect of the disk wind is strong, the disk profile is significantly altered (e.g., positive surface density gradient, inside-out evacuation), leading to outward migration of embryos inside ∼ 1AU. Conclusions. Disk winds play an essential role in terrestrial planet formation inside a few AU by changing the disk profile. In addition, embryos can undergo convergent migration to ∼ 1AU in certainly probable conditions. In such a case, the characteristic features of the solar system's terrestrial planets (e.g., mass concentration around 1 AU, late giant impact) may be reproduced.