Abstract
Mass-independent isotopic anomalies of carbonaceous and noncarbonaceous meteorites show a clear dichotomy suggesting an efficient separation of the inner and outer solar system. Observations ...show that ring-like structures in the distribution of millimeter-sized pebbles in protoplanetary disks are common. These structures are often associated with drifting pebbles being trapped by local pressure maxima in the gas disk. Similar structures may also have existed in the Sun’s natal disk, which could naturally explain the meteorite/planetary isotopic dichotomy. Here, we test the effects of a strong pressure bump in the outer disk (e.g., ∼5 au) on the formation of the inner solar system. We model dust coagulation and evolution, planetesimal formation, as well as embryo growth via planetesimal and pebble accretion. Our results show that terrestrial embryos formed via planetesimal accretion rather than pebble accretion. In our model, the radial drift of pebbles fosters planetesimal formation. However, once a pressure bump forms, pebbles in the inner disk are lost via drift before they can be efficiently accreted by embryos growing at ⪆1 au. Embryos inside ∼0.5–1.0 au grow relatively faster and can accrete pebbles more efficiently. However, these same embryos grow to larger masses so they should migrate inwards substantially, which is inconsistent with the current solar system. Therefore, terrestrial planets most likely accreted from giant impacts of Moon to roughly Mars-mass planetary embryos formed around ⪆1.0 au. Finally, our simulations produce a steep radial mass distribution of planetesimals in the terrestrial region, which is qualitatively aligned with formation models suggesting that the asteroid belt was born low mass.
Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an ...evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20–40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100–200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (rP < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5–10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50–100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.
At least 30% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use
N
-body simulations including a model for gas-assisted ...pebble accretion and disk–planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes (≲15
M
⊕
) and super-massive planetary cores potentially able to become gas giant planets (≳15
M
⊕
). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to ~95% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction (≳95%) of unstable systems with a sprinkling (≲5%) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (
N
≥ 2) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet–planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths are systematically ice rich. This contrasts with the interpretation that most super-Earths are rocky based on bulk-density measurements of super-Earths and photo-evaporation modeling of their bimodal radius distribution. We investigate the conditions needed to form rocky super-Earths. The formation of rocky super-Earths requires special circumstances, such as far more efficient planetesimal formation well inside the snow line, or much faster planetary growth by pebble accretion in the inner disk. Intriguingly, the necessary conditions to match the bulk of hot super-Earths are at odds with the conditions needed to match the Solar System.
Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disc between 1 and 3 au. The Grand Tack model invokes a specific migration history of ...the giant planets to remove most of the mass initially beyond 1 au and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas drag, as has been proposed to explain the formation of close-in super-Earths. Here we show that the asteroid belt’s orbital excitation provides a crucial constraint against this scenario for the Solar system. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from discs of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Discs with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogues significantly more massive than the real planet. In contrast, a disc with a surface density gradient proportional to r(exp −5.5) reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disc profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.
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.
The main asteroid belt (MB) is low in mass but dynamically excited. Here we propose a new mechanism to excite the MB during the giant planet (the "Nice model") instability, which is expected to ...feature repeated close encounters between Jupiter and one or more ice giants ("jumping Jupiter" or JJ). We show that, when Jupiter temporarily reaches a high-enough level of excitation, both in eccentricity and inclination, it induces strong forced vectors of eccentricity and inclination across the MB region. Because during the JJ instability Jupiter's orbit "jumps" around, the forced vectors keep changing both in magnitude and phase throughout the whole MB region. The entire cold primordial MB is thus excited as a natural outcome of the JJ instability. The level of such an excitation, however, is typically larger than the current orbital excitation observed in the MB. We show that the subsequent evolution of the solar system is capable of reshaping the resultant overexcited MB to its present-day orbital state, and that a strong mass depletion (∼90%) is associated with the JJ instability phase and its subsequent evolution throughout the age of the solar system.
ABSTRACT The orbital structure of the asteroid belt holds a record of the solar system's dynamical history. The current belt only contains ∼10−3 Earth masses yet the asteroids' orbits are dynamically ...excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter's orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth's orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter's and Saturn's early orbits were chaotic. Stochastic variations in the gas giants' orbits cause resonances to continually jump across the main belt and excite the asteroids' orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants' current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.
Super-Earths with orbital periods less than 100 days are extremely abundant around Sun-like stars. It is unlikely that these planets formed at their current locations. Rather, they likely formed at ...large distances from the star and subsequently migrated inward. Here we use N-body simulations to study the effect of super-Earths on the accretion of rocky planets. In our simulations, one or more super-Earths migrate inward through a disk of planetary embryos and planetesimals embedded in a gaseous disk. We tested a wide range of migration speeds and configurations. Fast-migrating super-Earths (tau sub(mig) ~ 0.01-0.1 Myr) only have a modest effect on the protoplanetary embryos and planetesimals. Sufficient material survives to form rocky, Earth-like planets on orbits exterior to the super-Earths'. In contrast, slowly migrating super-Earths shepherd rocky material interior to their orbits and strongly deplete the terrestrial planet-forming zone. In this situation any Earth-sized planets in the habitable zone are extremely volatile-rich and are therefore probably not Earth-like.
Abstract
The size frequency distribution of exoplanet radii between 1 and 4
R
⊕
is bimodal with peaks at ∼1.4
R
⊕
and ∼2.4
R
⊕
, and a valley at ∼1.8
R
⊕
. This radius valley separates two classes of ...planets—usually referred to as “super-Earths” and “mini-Neptunes”—and its origin remains debated. One model proposes that super-Earths are the outcome of photoevaporation or core-powered mass loss stripping the primordial atmospheres of the mini-Neptunes. A contrasting model interprets the radius valley as a dichotomy in the bulk compositions, where super-Earths are rocky planets and mini-Neptunes are water-ice-rich worlds. In this work, we test whether the migration model is consistent with the radius valley and how it distinguishes these views. In the migration model, planets migrate toward the disk’s inner edge, forming a chain of planets locked in resonant configurations. After the gas disk dispersal, orbital instabilities “break the chains” and promote late collisions. This model broadly matches the period-ratio and planet-multiplicity distributions of Kepler planets and accounts for resonant chains such as TRAPPIST-1, Kepler-223, and TOI-178. Here, by combining the outcome of planet formation simulations with compositional mass–radius relationships and assuming the complete loss of primordial H-rich atmospheres in late giant impacts, we show that the migration model accounts for the exoplanet radius valley and the intrasystem uniformity (“peas in a pod”) of Kepler planets. Our results suggest that planets with sizes of ∼1.4
R
⊕
are mostly rocky, whereas those with sizes of ∼2.4
R
⊕
are mostly water-ice-rich worlds. Our results do not support an exclusively rocky composition for the cores of mini-Neptunes.
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