Constraining the primordial orbits of the terrestrial planets (original) (raw)
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Formation of Earth‐like Planets During and After Giant Planet Migration
The Astrophysical Journal, 2007
Close-in giant planets are thought to have formed in the cold outer regions of planetary systems and migrated inward, passing through the orbital parameter space occupied by the terrestrial planets in our own Solar System. We present dynamical simulations of the effects of a migrating giant planet on a disk of protoplanetary material and the subsequent evolution of the planetary system. We numerically investigate the dynamics of post-migration planetary systems over 200 million years using models with a single migrating giant planet, one migrating and one non-migrating giant planet, and excluding the effects of a gas disk. Material that is shepherded in front of the migrating giant planet by moving mean motion resonances accretes into "hot Earths", but survival of these bodies is strongly dependent on dynamical damping. Furthermore, a significant amount of material scattered outward by the giant planet survives in highly excited orbits; the orbits of these scattered bodies are then damped by gas drag and dynamical friction over the remaining accretion time. In all simulations Earth-mass planets accrete on approximately 100 Myr timescales, often with orbits in the Habitable Zone. These planets range in mass and water content, with both quantities increasing with the presence of a gas disk and decreasing with the presence of an outer giant planet. We use scaling arguments and previous results to derive a simple recipe that constrains which giant planet systems are able to form and harbor Earth-like planets in the Habitable Zone, demonstrating that roughly one third of the known planetary systems are potentially habitable.
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.
STATISTICAL STUDY OF THE EARLY SOLAR SYSTEM'S INSTABILITY WITH FOUR, FIVE, AND SIX GIANT PLANETS
The Astronomical Journal, 2012
Several properties of the solar system, including the wide radial spacing and orbital eccentricities of giant planets, can be explained if the early solar system evolved through a dynamical instability followed by migration of planets in the planetesimal disk. Here we report the results of a statistical study, in which we performed nearly 10 4 numerical simulations of planetary instability starting from hundreds of different initial conditions. We found that the dynamical evolution is typically too violent, if Jupiter and Saturn start in the 3:2 resonance, leading to ejection of at least one ice giant from the solar system. Planet ejection can be avoided if the mass of the transplanetary disk of planetesimals was large (M disk 50 M Earth ), but we found that a massive disk would lead to excessive dynamical damping (e.g., final e 55 0.01 compared to present e 55 = 0.044, where e 55 is the amplitude of the fifth eccentric mode in the Jupiter's orbit), and to smooth migration that violates constraints from the survival of the terrestrial planets. Better results were obtained when the solar system was assumed to have five giant planets initially, and one ice giant, with mass comparable to that of Uranus and Neptune, was ejected into interstellar space by Jupiter. The best results were obtained when the ejected planet was placed into the external 3:2 or 4:3 resonance with Saturn and M disk 20 M Earth . The range of possible outcomes is rather broad in this case, indicating that the present solar system is neither a typical nor expected result for a given initial state, and occurs, in best cases, with only a 5% probability (as defined by the success criteria described in the main text). The case with six giant planets shows interesting dynamics but does offer significant advantages relative to the five-planet case.
The Astrophysical Journal, 2012
We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. Using a modified secular model we have identified six secular resonances between the ν 5 frequency of Jupiter and Saturn and the four apsidal eigenfrequencies of the terrestrial planets (g 1-4). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. Because of the small amplitudes of the j = 2, 3 terrestrial eigenmodes the g 2 −ν 5 and g 3 −ν 5 resonances provide the strongest constraints on giant planet migration. If Jupiter and Saturn migrated with eccentricities comparable to their present-day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (τ ∼ 5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g., τ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j = 2, 3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Results of orbital integrations show that very short migration timescales (τ < 0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9 ± 0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.
Survival of terrestrial planets in the presence of giant planet migration
The Astrophysical Journal Letters, 2003
The presence of hot Jupiters, Jovian-mass planets with very short orbital periods orbiting nearby main-sequence stars, has been proposed to be primarily due to the orbital migration of planets formed in orbits initially much farther from the parent star. This migration affects ...
A low mass for Mars from Jupiter/'s early gas-driven migration
Nature, 2011
1 were susceptible to disk-driven migration on timescales of only ∼100 Kyr. 2 Hydrodynamical simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration. 3-5 The terrestrial planets finished accreting much later, 6 and their characteristics, including Mars' small mass, are best reproduced starting from a planetesimal disk with an outer edge at ∼1 AU. 7, 8 Here we present simulations of the early Solar System that show how the inward migration of Jupiter to 1.5 AU, and its subsequent outward migration, leads to a planetesimal disk truncated at 1 AU, from which the terrestrial planets form over the next 30-50 million years, with a correct Earth/Mars mass ratio. Scattering by Jupiter initially empties, but then repopulates the asteroid belt, with inner-belt bodies originating between 1-3 AU and outer belt bodies originating between and beyond the giant planets. This explains the significant compositional differences across the asteroid belt. The key aspect missing from previous models of terrestrial planet formation is an inward, and subsequent outward, migration of Jupiter. We conclude that the behaviour of our giant planets, characterized by substantial radial migration, is more similar to that inferred for extra-solar planets than previously thought.
Towards an initial mass function for giant planets
Monthly Notices of the Royal Astronomical Society
The distribution of exoplanet masses is not primordial. After the initial stage of planet formation is complete, the gravitational interactions between planets can lead to the physical collision of two planets, or the ejection of one or more planets from the system. When this occurs, the remaining planets are typically left in more eccentric orbits. Here we use present-day eccentricities of the observed exoplanet population to reconstruct the initial mass function of exoplanets before the onset of dynamical instability. We developed a Bayesian framework that combines data from N-body simulations with present-day observations to compute a probability distribution for the planets that were ejected or collided in the past. Integrating across the exoplanet population, we obtained an estimate of the initial mass function of exoplanets. We find that the ejected planets are primarily sub-Saturn type planets. While the presentday distribution appears to be bimodal, with peaks around ∼ 1M J and ∼ 20M ⊕ , this bimodality does not seem to be primordial. Instead, planets around ∼ 60M ⊕ appear to be preferentially removed by dynamical instabilities. Attempts to reproduce exoplanet populations using population synthesis codes should be mindful of the fact that the present population has been depleted of intermediate-mass planets. Future work should explore how the system architecture and multiplicity might alter our results.
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.
The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk
Icarus, 2007
We study the possibility that the mutual interactions between Jupiter and Saturn prevented Type II migration from driving these planets much closer to the Sun. Our work extends previous results by , by exploring a wider set of initial conditions and disk parameters, and by using a new hydrodynamical code that properly describes for the global viscous evolution of the disk. Initially both planets migrate towards the Sun, and Saturn's migration tends to be faster. As a consequence, they eventually end up locked in a mean motion resonance. If this happens in the 2:3 resonance, the resonant motion is particularly stable, and the gaps opened by the planets in the disk may overlap.