Reproducing Uranus and Neptune remains a challenge for simulations of solar system formation. The ice giants’ peculiar obliquities suggest that they both suffered giant collisions during their formation. Thus, there must have been an epoch of accretion dominated by collisions among large planetary embryos in the primordial outer solar system. We test this idea using N-body numerical simulations including the effects of a gaseous protoplanetary disk. One strong constraint is that the masses of the ice giants are very similar – the Neptune and Uranus mass ratio is ~1.18. We show that similar-sized ice giants do indeed form by collisions between planetary embryos beyond Saturn. The fraction of successful simulations varies depending on the initial number of planetary embryos in the system, their individual and total masses. Similar-sized ice giants are consistently reproduced in simulations starting with five to ten planetary embryos with initial masses of ~3–6 M⊕. We conclude that accretion from a population of planetary embryos is a plausible scenario for the origin of Uranus and Neptune.
Most of the properties of the Earth–Moon system can be explained by a collision between a planetary embryo (giant impactor) and the growing Earth late in the accretion process1,2,3. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor1,4,5. However, analysis of the terrestrial and lunar isotopic compositions show them to be highly similar6,7,8,9,10,11. In contrast, the compositions of other Solar System bodies are significantly different from those of the Earth and Moon12,13,14, suggesting that different Solar System bodies have distinct compositions. This challenges the giant impact scenario, because the Moon-forming impactor must then also be thought to have a composition different from that of the proto-Earth. Here we track the feeding zones of growing planets in a suite of simulations of planetary accretion15, to measure the composition of Moon-forming impactors. We find that different planets formed in the same simulation have distinct compositions, but the compositions of giant impactors are statistically more similar to the planets they impact. A large fraction of planet–impactor pairs have almost identical compositions. Thus, the similarity in composition between the Earth and Moon could be a natural consequence of a late giant impact.
Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model. However, previous hydrodynamical simulations were restricted to isothermal disks, with moderate aspect ratio and viscosity. Here we simulate the orbital evolution of the gas giants in disks with viscous heating and radiative cooling. We find that Jupiter and Saturn migrate outward in 3:2 resonance in modest-mass (M disk ≈ M MMSN, where MMSN is the “minimum-mass solar nebula”) disks with viscous stress parameter α between 10–3 and 10–2. In disks with relatively low-mass (M disk lesssim M MMSN), Jupiter and Saturn get captured in 2:1 resonance and can even migrate outward in low-viscosity disks (α ≤ 10–4). Such disks have a very small aspect ratio (h ~ 0.02-0.03) that favors outward migration after capture in 2:1 resonance, as confirmed by isothermal runs which resulted in a similar outcome for h ~ 0.02 and α ≤ 10–4. We also performed N-body runs of the outer solar system starting from the results of our hydrodynamical simulations and including 2-3 ice giants. After dispersal of the gaseous disk, a Nice model instability starting with Jupiter and Saturn in 2:1 resonance results in good solar systems analogs. We conclude that in a cold solar nebula, the 2:1 resonance between Jupiter and Saturn can lead to outward migration of the system, and this may represent an alternative scenario for the evolution of the solar system.
We study the evolution of multiple protoplanets of a few Earth masses embedded in a non-isothermal protoplanetary disc. The protoplanets are located in the vicinity of a convergence zone located at the transition between two different opacity regimes. Inside the convergence zone, Type I migration is directed outward and outside the zone migration is directed inward.
The field of exoplanetary science has experienced a recent surge of new systems that is largely due to the precision photometry provided by the Kepler mission. The latest discoveries have included compact planetary systems in which the orbits of the planets all lie relatively close to the host star, which presents interesting challenges in terms of formation and dynamical evolution. The compact exoplanetary systems are analogous to the moons orbiting the giant planets in our solar system, in terms of their relative sizes and semimajor axes. We present a study that quantifies the scaled sizes and separations of the solar system moons with respect to their hosts. We perform a similar study for a large sample of confirmed Kepler planets in multi-planet systems. We show that a comparison between the two samples leads to a similar correlation between their scaled sizes and separation distributions. The different gradients of the correlations may be indicative of differences in the formation and/or long-term dynamics of moon and planetary systems.
If mutual gravitational scattering among exoplanets occurs, then it may produce unique orbital properties. For example, two-planet systems that lie near the boundary between circulation and libration of their periapses could result if planet-planet scattering ejected a former third planet quickly, leaving one planet on an eccentric orbit and the other on a circular orbit. We first improve upon previous work that examined the apsidal behavior of known multiplanet systems by doubling the sample size and including observational uncertainties. This analysis recovers previous results that demonstrated that many systems lay on the apsidal boundary between libration and circulation. We then performed over 12,000 three-dimensional N-body simulations of hypothetical three-body systems that are unstable, but stabilize to two-body systems after an ejection. Using these synthetic two-planet systems, we test the planet-planet scattering hypothesis by comparing their apsidal behavior, over a range of viewing angles, to that of the observed systems and find that they are statistically consistent regardless of the multiplicity of the observed systems. Finally, we combine our results with previous studies to show that, from the sampled cases, the most likely planetary mass function prior to planet-planet scattering follows a power law with index -1.1. We find that this pre-scattering mass function predicts a mutual inclination frequency distribution that follows an exponential function with an index between -0.06 and -0.1.
Excess emission, associated with warm, dust belts, commonly known as exozodis, has been observed around a third of nearby stars. The high levels of dust required to explain the observations are not generally consistent with steady-state evolution. A common suggestion is that the dust results from the aftermath of a dynamical instability, an event akin to the Solar system’s Late Heavy Bombardment. In this work, we use a data base of N-body simulations to investigate the aftermath of dynamical instabilities between giant planets in systems with outer planetesimal belts. We find that, whilst there is a significant increase in the mass of material scattered into the inner regions of the planetary system following an instability, this is a short-lived effect. Using the maximum lifetime of this material, we determine that even if every star has a planetary system that goes unstable, there is a very low probability that we observe more than a maximum of 1 per cent of sun-like stars in the aftermath of an instability, and that the fraction of planetary systems currently in the aftermath of an instability is more likely to be limited to ≤0.06 per cent. This probability increases marginally for younger or higher mass stars. We conclude that the production of warm dust in the aftermath of dynamical instabilities is too short-lived to be the dominant source of the abundantly observed exozodiacal dust.
Given their tendency to be incorporated into the core during differentiation, the highly-siderophile elements (HSEs) in Earth’s mantle are thought to have been accreted as a “late veneer” after the end of the giant impact phase. Bottke et al. (Bottke, W.F., Walker, R.J., Day, J.M.D., Nesvorny, D., Elkins-Tanton, L. [2010]. Science 330, 1527) proposed that the large Earth-to-Moon HSE abundance ratio can be explained if the late veneer was characterized by large (D = 1000–4000 km) impactors. Here we simulate the evolution of the terrestrial planets during a stochastic late veneer phase from the end of accretion until the start of the late heavy bombardment ∼500 Myr later. We show that a late veneer population of 0.05M⊕ dominated by large (D > 1000 km) bodies naturally delivers a ∼0.01M⊕ veneer to Earth, consistent with geochemical constraints.
Earth-mass planets embedded in gaseous protoplanetary disks undergo Type I orbital migration. In radiative disks an additional component of the corotation torque scaling with the entropy gradient across the horseshoe region can counteract the general inward migration, Type I migration can then be directed either inward or outward depending on the local disk properties. Thus, special locations exist in the disk toward which planets migrate in a convergent way. Here we present N-body simulations of the convergent migration of systems of low-mass (M = 1−10M⊕) planets. We show that planets do not actually converge in convergence zones.
Nearly half the exoplanets found within binary star systems reside1 in very wide binaries with average stellar separations greater than 1,000 astronomical units (one astronomical unit (AU) being the Earth–Sun distance), yet the influence of such distant binary companions on planetary evolution remains largely unstudied. Unlike their tighter counterparts, the stellar orbits of wide binaries continually change under the influence of the Milky Way’s tidal field and impulses from other passing stars. Here we report numerical simulations demonstrating that the variable nature of wide binary star orbits dramatically reshapes the planetary systems they host, typically billions of years after formation. Contrary to previous understanding2, wide binary companions may often strongly perturb planetary systems, triggering planetary ejections and increasing the orbital eccentricities of surviving planets. Although hitherto not recognized, orbits of giant exoplanets within wide binaries are statistically more eccentric than those around isolated stars. Both eccentricity distributions are well reproduced when we assume that isolated stars and wide binaries host similar planetary systems whose outermost giant planets are scattered beyond about 10 AU from their parent stars by early internal instabilities. Consequently, our results suggest that although wide binaries eventually remove the most distant planets from many planetary systems, most isolated giant exoplanet systems harbour additional distant, still undetected planets.
It is commonly assumed that the building blocks of the terrestrial planets were derived from a cosmochemical reservoir that is best represented by chondrites, the so-called chondritic Earth model. This view is possibly a good approximation for refractory elements (although it has been recently questioned; e.g., Caro et al. 2008), but for volatile elements, other cosmochemical reservoirs might have contributed to Earth, such as the solar nebula gas and/or cometary matter (Owen et al. 1992; Dauphas 2003; Pepin 2006). Hence, in order to get insights into the origin of the carbon in Earth, it is…
Starting from planetary systems with three giant planets and an outer disc of planetesimals, we use dynamical simulations to show how dynamical instabilities can transform planetesimal discs into 102–103 au-scale isotropic clouds. The instabilities involve a phase of planet–planet scattering that concludes with the ejection of one or more planets and the inward-scattering of the surviving gas giant(s) to remove them from direct dynamical contact with the planetesimals. ‘Mini-Oort clouds’ are thus formed from scattered planetesimals whose orbits are frozen by the abrupt disappearance of the perturbing giant planet. Although the planetesimal orbits are virtually isotropic, the surviving giant planets tend to have modest inclinations (typically ∼10°) with respect to the initial orbital plane. The collisional lifetimes of mini-Oort clouds are long (10 Myr to >10 Gyr) and there is a window of ∼100 Myr or longer during which they produce spherical clouds of potentially observable dust at 70 μm. If the formation channel for hot Jupiters commonly involves planetary close encounters, we predict a correlation between this subset of extrasolar planetary systems and mini-Oort clouds.
We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple marginally unstable gas giants. We previously showed that in such systems, the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and cold dust, i.e., debris disks, which is particularly pronounced at λ ~ 70 μm. Here we present new simulations that show that this connection is qualitatively robust to a range of parameters: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk when the giant planets become unstable. We discuss how variations in these parameters affect the evolution. We find that systems with equal-mass giant planets undergo the most violent instabilities, and that these destroy both terrestrial planets and the outer planetesimal disks that produce debris disks.
We used a standard equilibrium tidal model to compute the orbital evolution of a large ensemble of planet-BD systems. We tested the effect of numerous parameters such as the initial semi-major axis and eccentricity, the rotation period of the BD, the masses of both the BD and planet, and the tidal dissipation factors.
Jupiter and Saturn formed in a few million years (ref. 1) from a gas-dominated protoplanetary disk, and were susceptible to gas-driven migration of their orbits on timescales of only ∼100,000 years (ref. 2). Hydrodynamic simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration3,4,5. The terrestrial planets finished accreting much later6, and their characteristics, including Mars’ small mass, are best reproduced by starting from a planetesimal disk with an outer edge at about one astronomical unit from the Sun7,8 (1 AU is the Earth–Sun distance). Here we report simulations of the early Solar System that show how the inward migration of Jupiter to 1.5 AU, and its subsequent outward migration, lead to a planetesimal disk truncated at 1 AU; the terrestrial planets then form from this disk over the next 30–50 million years, with an Earth/Mars mass ratio consistent with observations. Scattering by Jupiter initially empties but then repopulates the asteroid belt, with inner-belt bodies originating between 1 and 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 the substantial radial migration of the giant planets, which suggests that their behaviour is more similar to that inferred for extrasolar planets than previously thought.
The habitable zones (HZs) of main-sequence stars have traditionally been defined as the range of orbits that intercept the appropriate amount of stellar flux to permit surface water on a planet. Terrestrial exoplanets discovered to orbit M stars in these zones, which are close-in due to decreased stellar luminosity, may also undergo significant tidal heating. Tidal heating may span a wide range for terrestrial exoplanets and may significantly affect conditions near the surface. For example, if heating rates on an exoplanet are near or greater than that on Io (where tides drive volcanism that resurfaces the planet at least every 1 Myr) and produce similar surface conditions, then the development of life seems unlikely. On the other hand, if the tidal heating rate is less than the minimum to initiate plate tectonics, then CO2 may not be recycled through subduction, leading to a runaway greenhouse that sterilizes the planet. These two cases represent potential boundaries to habitability and are presented along with the range of the traditional HZ for main-sequence, low-mass stars. We propose a revised HZ that incorporates both stellar insolation and tidal heating. We apply these criteria to GJ 581 d and find that it is in the traditional HZ, but its tidal heating alone may be insufficient for plate tectonics.
To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets – Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000–2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury.
The known extrasolar multiple-planet systems share a surprising dynamical attribute: they cluster just beyond the Hill stability boundary. Here we show that the planet-planet scattering model, which naturally explains the observed exoplanet eccentricity distribution, can reproduce the observed distribution of dynamical configurations. We calculated how each of our scattered systems would appear over an appropriate range of viewing geometries; as Hill stability is weakly dependent on the masses, the mass-inclination degeneracy does not significantly affect our results. We consider a wide range of initial planetary mass distributions and find that some are poor fits to the observed systems. In fact, many of our scattering experiments overproduce systems very close to the stability boundary. The distribution of dynamical configurations of two-planet systems may provide better discrimination between scattering models than the distribution of eccentricity. Our results imply that, at least in their inner regions which are weakly affected by gas or planetesimal disks, planetary systems should be “packed,” with no large gaps between planets.
Three planets with minimum masses less than 10 M⊕ orbit the star HD 40307, suggesting these planets may be rocky. However, with only radial velocity data, it is impossible to determine if these planets are rocky or gaseous. Here we exploit various dynamical features of the system in order to assess the physical properties of the planets. Observations allow for circular orbits, but a numerical integration shows that the eccentricities must be at least 10–4. Also, planets b and c are so close to the star that tidal effects are significant. If planet b has tidal parameters similar to the terrestrial planets in the solar system and a remnant eccentricity larger than 10–3, then, going back in time, the system would have been unstable within the lifetime of the star (which we estimate to be 6.1 ± 1.6 Gyr). Moreover, if the eccentricities are that large and the inner planet is rocky, then its tidal heating may be an order of magnitude greater than extremely volcanic Io, on a per unit surface area basis. If planet b is not terrestrial, e.g., Neptune-like, these physical constraints would not apply. This analysis suggests the planets are not terrestrial-like, and are more like our giant planets. In either case, we find that the planets probably formed at larger radii and migrated early-on (via disk interactions) into their current orbits. This study demonstrates how the orbital and dynamical properties of exoplanet systems may be used to constrain the planets’ physical properties.
We study the dynamical stability of an additional, potentially habitable planet in the HD 47186 planetary system. Two planets are currently known in this system: a “hot Neptune” with a period of 4.08 days and a Saturn-mass planet with a period of 3.7 years. Here we consider the possibility that one or more undetected planets exist between the two known planets and possibly within the habitable zone (HZ) in this system. Given the relatively low masses of the known planets, additional planets could have masses $ \rlap{<}{\lower1.0ex\hbox{$\sim $}}10 {\,M_\oplus }$, and hence be terrestrial-like and further improving potential habitability. We perform N-body simulations to identify the stable zone between planets b and c and find that much of the inner HZ can harbor a 10 M ⊕ planet. With the current radial velocity threshold of ~1 m s–1, an additional planet should be detectable if it lies at the inner edge of the habitable zone at 0.8 AU. We also show that the stable zone could contain two additional planets of 10 M ⊕ each if their eccentricities are lower than ~0.3.
Tides raised on a planet by the gravity of its host star can reduce the planet’s orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars (≲0.35 M⊙). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, ∼5 M⊕ planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable. Astrobiology 8, 557–568.
To date, two planetary systems have been discovered with close-in, terrestrial-mass planets forumla. Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form ‘hot Earths’ and their observable predictions. Models include: (1) in situ accretion; (2) formation at larger orbital distance followed by inward ‘type 1’ migration; (3) formation from material being ‘shepherded’ inward by a migrating gas giant planet; (4) formation from material being shepherded by moving secular resonances during dispersal of the protoplanetary disc; (5) tidal circularization of eccentric terrestrial planets with close-in perihelion distances and (6) photoevaporative mass-loss of a close-in giant planet. Models 1–4 have been validated in previous work. We show that tidal circularization can form hot Earths, but only for relatively massive planets forumla with very close-in perihelion distances (≲0.025 au), and even then the net inward movement in orbital distance is at most only 0.1–0.15 au. For planets of less than forumla, photoevaporation can remove the planet’s envelope and leave behind the solid core on a Gyr time-scale, but only for planets inside 0.025–0.05 au. Using two quantities that are observable by current and upcoming missions, we show that these models each produce unique signatures, and can be observationally distinguished. These observables are the planetary system architecture (detectable with radial velocities, transits and transit timing) and the bulk composition of transiting close-in terrestrial planets (measured by transits via the planet’s radius).
The water content and habitability of terrestrial planets are determined during their final assembly, from perhaps 100 1,000-km “planetary embryos” and a swarm of billions of 1–10-km “planetesimals.” During this process, we assume that water-rich material is accreted by terrestrial planets via impacts of water-rich bodies that originate in the outer asteroid region. We present analysis of water delivery and planetary habitability in five high-resolution simulations containing about 10 times more particles than in previous simulations. These simulations formed 15 terrestrial planets from 0.4 to 2.6 Earth masses, including five planets in the habitable zone. Every planet from each simulation accreted at least the Earth’s current water budget; most accreted several times that amount (assuming no impact depletion). Each planet accreted at least five water-rich embryos and planetesimals from the past 2.5 astronomical units; most accreted 10–20 water-rich bodies. We present a new model for water delivery to terrestrial planets in dynamically calm systems, with low-eccentricity or low-mass giant planets—such systems may be very common in the Galaxy. We suggest that water is accreted in comparable amounts from a few planetary embryos in a “hit or miss” way and from millions of planetesimals in a statistically robust process. Variations in water content are likely to be caused by fluctuations in the number of water-rich embryos accreted, as well as from systematic effects, such as planetary mass and location, and giant planet properties. Key Words: Planetary formation—Water delivery—Extrasolar planets—Cosmochemistry. Astrobiology 7(1), 66–84.
Close-in giant planets (e.g., “hot Jupiters”) are thought to form far from their host stars and migrate inward, through the terrestrial planet zone, via torques with a massive gaseous disk. Here we simulate terrestrial planet growth during and after giant planet migration. Several-Earth-mass planets also form interior to the migrating jovian planet, analogous to recently discovered “hot Earths.” Very-water-rich, Earth-mass planets form from surviving material outside the giant planet’s orbit, often in the habitable zone and with low orbital eccentricities. More than a third of the known systems of giant planets may harbor Earth-like planets.
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.