Gas Disk Dispersal Research Articles

Accretion and Uneven Depletion of the Main Asteroid Belt

The main asteroid belt (MAB) is known to be primarily composed of objects from two distinct taxonomic classes, generically defined here as S- and C-complex. The former probably originated from the inner solar system (interior to Jupiter’s orbit), while the latter probably originated from the outer solar system. Following this definition, (4) Vesta, a V-type residing in the inner MAB (a < 2.5 au), is the sole D > 500 km object akin to the S-complex that potentially formed in situ. This provides a useful constraint on the number of D > 500 km bodies that could have formed, or grown, within the primordial MAB. In this work, we numerically simulate the accretion of objects in the MAB region during the time when gas in the protoplanetary disk still existed while assuming different MAB primordial masses. We then account for the depletion of that population happening after gas disk dispersal. In our analysis, we subdivided the MAB into five subregions and showed that the depletion factor varies throughout the MAB. This results in uneven radial- and size-dependent depletion of the MAB. We show that the MAB primordial mass has to be ≲2.14 × 10−3 M ⊕. Larger primordial masses would lead to the accretion of tens to thousands of S-complex objects with D > 500 km in the MAB. Such large objects would survive depletion even in the outer subregions (a > 2.5 au), thus being inconsistent with observations. Our results also indicate that S-complex objects with D > 200–300 km, including (4) Vesta, are likely to be terrestrial planetesimals implanted into the MAB rather than formed in situ.

Crash Chronicles: Relative contribution from comets and carbonaceous asteroids to Earth’s volatile budget in the context of an Early Instability

Recent models of solar system formation suggest that a dynamical instability among the giant planets happened within the first 100 Myr after disk dispersal, perhaps before the Moon-forming impact. As a direct consequence, a bombardment of volatile-rich impactors may have taken place on Earth before internal and atmospheric reservoirs were decoupled. However, such a timing has been interpreted to potentially be at odds with the disparate inventories of Xe isotopes in Earth’s mantle compared to its atmosphere. This study aims to assess the dynamical effects of an Early Instability on the delivery of carbonaceous asteroids and comets to Earth, and address the implications for the Earth’s volatile budget. We perform 20 high-resolution dynamical simulations of solar system formation from the time of gas disk dispersal, each starting with 1600 carbonaceous asteroids and 10000 comets, taking into account the dynamical perturbations from an early giant planet instability. Before the Moon-forming impact, the cumulative collision rate of comets with Earth is about 4 orders of magnitude lower than that of carbonaceous asteroids. After the Moon-forming impact, this ratio either decreases or increases, often by orders of magnitude, depending on the dynamics of individual simulations. An increase in the relative contribution of comets happens in 30% of our simulations. In these cases, the delivery of noble gases from each source is comparable, given that the abundance of 132Xe is 3 orders of magnitude greater in comets than in carbonaceous chondrites. The increase in cometary flux relative to carbonaceous asteroids at late times may thus offer an explanation for the Xe signature dichotomy between the Earth’s mantle and atmosphere. Our current model falls short in simultaneously reproducing a 4%–10% carbonaceous contribution to Earth and late accretion dominated by non-carbonaceous material. In future work, it is worth exploring the possibility that a large fraction of Earth’s carbonaceous material was accreted prior to gas disk dispersal. If that were the case, it would strengthen our dynamical explanation for the Xe signature dichotomy, because the contribution of cometary relative to carbonaceous material would strongly increase at later times.

Forming rocky exoplanets around K-dwarf stars

Context. New space telescopes, such as the upcoming PLATO mission, aim to detect and study thousands of exoplanets, especially terrestrial planets around main-sequence stars. This motivates us to study how these planets formed. How multiple close-in super-Earths form around stars with masses lower than that of the Sun is still an open issue. Several recent modeling studies have focused on planet formation around M-dwarf stars, but so far no studies have focused specifically on K dwarfs, which are of particular interest in the search for extraterrestrial life. Aims. We aim to reproduce the currently known population of close-in super-Earths observed around K-dwarf stars and their system characteristics. Additionally, we investigate whether the planetary systems that we form allow us to decide which initial conditions are the most favorable. Methods. We performed 48 high-resolution N-body simulations of planet formation via planetesimal accretion using the existing GENGA software running on GPUs. In the simulations we varied the initial protoplanetary disk mass and the solid and gas surface density profiles. Each simulation began with 12 000 bodies with radii of between 200 and 2000 km around two different stars, with masses of 0.6 and 0.8 M⊙. Most simulations ran for 20 Myr, with several simulations extended to 40 or 100 Myr. Results. The mass distributions for the planets with masses between 2 and 12 M⊕ show a strong preference for planets with masses Mp &lt; 6 M⊕ and a lesser preference for planets with larger masses, whereas the mass distribution for the observed sample increases almost linearly. However, we managed to reproduce the main characteristics and architectures of the known planetary systems and produce mostly long-term angular-momentum-deficit-stable, nonresonant systems, but we require an initial disk mass of 15 M⊕ or higher and a gas surface density value at 1 AU of 1500 g cm−2 or higher. Our simulations also produce many low-mass planets with M &lt; 2 M⊕, which are not yet found in the observed population, probably due to the observational biases. Earth-mass planets form quickly (usually within a few million years), mostly before the gas disk dispersal. The final systems contain only a small number of planets with masses Mp &gt; 10 M⊕, which could possibly accrete substantial amounts of gas, and these formed after the gas had mostly dissipated. Conclusions. We mostly manage to reproduce observed K-dwarf exoplanetary systems from our GPU simulations.

Early bombardment of the moon: Connecting the lunar crater record to the terrestrial planet formation

The lunar crater record features ∼50 basins. The radiometric dating of Apollo samples indicates that the Imbrium basin formed relatively late — from the planet formation perspective — some ≃3.9 Ga. Here we develop a dynamical model for impactors in the inner solar system to provide context for the interpretation of the lunar crater record. The contribution of cometary impactors is found to be insignificant. Asteroids produced most large impacts on the terrestrial worlds in the last ≃3 Gyr. The great majority of early impactors were rocky planetesimals left behind at ∼0.5–1.5 au after the terrestrial planet accretion. The population of terrestrial planetesimals was reduced by disruptive collisions in the first t∼20 Myr after the gas disk dispersal. We estimate that there were ∼4×105 diameter d>10 km bodies when the Moon formed (total planetesimal mass ∼0.015MEarth at t∼50 Myr). The early bombardment of the Moon was intense. To accommodate ∼50 known basins, the lunar basins that formed before ≃4.35–4.41 Ga must have been erased. The late formation of Imbrium occurs with a ∼15–35% probability in our model. About 20 d>10-km bodies were expected to hit the Earth between 2.5 and 3.5 Ga, which is comparable to the number of known spherule beds in the late Archean. We discuss implications of our model for the lunar/Martian crater chronologies, Late Veneer, and noble gases in the Earth atmosphere.

Assessing the spin–orbit obliquity of low-mass planets in the breaking the chain formation model: a story of misalignment

ABSTRACT The spin–orbit obliquity of a planetary system constraints its formation history. A large obliquity may either indicate a primordial misalignment between the star and its gaseous disc or reflect the effect of different mechanisms tilting planetary systems after formation. Observations and statistical analysis suggest that system of planets with sizes between 1 and 4 R⊕ has a wide range of obliquities (∼0–30○), and that single- and multiplanet transiting have statistically indistinguishable obliquity distributions. Here, we revisit the ‘breaking the chains’ formation model with focus in understanding the origin of spin–orbit obliquities. This model suggests that super-Earths and mini-Neptunes migrate close to their host stars via planet–disc gravitational interactions, forming chain of planets locked in mean-motion resonances. After gas-disc dispersal, about 90–99 per cent of these planetary systems experience dynamical instabilities, which spread the systems out. Using synthetic transit observations, we show that if planets are born in discs where the disc angular momentum is virtually aligned with the star’s rotation spin, their final obliquity distributions peak at ∼5° or less, and the obliquity distributions of single- and multiplanet transiting systems are statistically distinct. By treating the star-disc alignment as a free-parameter, we show that the obliquity distributions of single- and multiplanet transiting systems only become statistically indistinguishable if planets are assumed to form in primordially misaligned natal discs with a tilt’ distribution peaking at ≳10–20°. We discuss the origin of these misalignments in the context of star formation and potential implications of this scenario for formation models.

The Exoplanet Radius Valley from Gas-driven Planet Migration and Breaking of Resonant Chains

The size frequency distribution of exoplanet radii between 1 and 4R ⊕ 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.

Near-infrared Accretion Signatures from the Circumbinary Planetary-mass Companion Delorme 1 (AB)b* * Based on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministério da Ciência, Tecnologia e Inovações (MCTI/LNA) do Brasil, the US National Science Foundation's NOIRLab, the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU).

Accretion signatures from bound brown dwarf and protoplanetary companions provide evidence for ongoing planet formation, and accreting substellar objects have enabled new avenues to study the astrophysical mechanisms controlling the formation and accretion processes. Delorme 1 (AB)b, a ∼30–45 Myr circumbinary planetary-mass companion, was recently discovered to exhibit strong Hα emission. This suggests ongoing accretion from a circumplanetary disk, somewhat surprising given canonical gas disk dispersal timescales of 5–10 Myr. Here, we present the first NIR detection of accretion from the companion in Paβ, Paγ, and Brγ emission lines from SOAR/TripleSpec 4.1, confirming and further informing its accreting nature. The companion shows strong line emission, with L line ≈ 1–6 × 10−8 L ⊙ across lines and epochs, while the binary host system shows no NIR hydrogen line emission (L line < 0.32–11 × 10−7 L ⊙). Observed NIR hydrogen line ratios are more consistent with a planetary accretion shock than with local line excitation models commonly used to interpret stellar magnetospheric accretion. Using planetary accretion shock models, we derive mass accretion rate estimates of –4 × 10−8 M J yr−1, somewhat higher than expected under the standard star formation paradigm. Delorme 1 (AB)b’s high accretion rate is perhaps more consistent with formation via disk fragmentation. Delorme 1 (AB)b is the first protoplanet candidate with clear (signal-to-noise ratio ∼5) NIR hydrogen line emission.

The ‘breaking the chains’ migration model for super-Earth formation: the effect of collisional fragmentation

ABSTRACT Planets between 1 and 4 R⊕ (Earth radius) with orbital periods &amp;lt;100 d are strikingly common. The migration model proposes that super-Earths migrate inwards and pile up at the disc inner edge in chains of mean motion resonances. After gas disc dispersal, simulations show that super-Earth’s gravitational interactions can naturally break their resonant configuration leading to a late phase of giant impacts. The instability phase is key to matching the orbital spacing of observed systems. Yet, most previous simulations have modelled collisions as perfect accretion events, ignoring fragmentation. In this work, we investigate the impact of imperfect accretion on the ‘breaking the chains’ scenario. We performed N-body simulations starting from distributions of planetary embryos and modelling the effects of pebble accretion and migration in the gas disc. Our simulations also follow the long-term dynamical evolution of super-Earths after the gas disc dissipation. We compared the results of simulations where collisions are treated as perfect merging events with those where imperfect accretion and fragmentation are allowed. We concluded that the perfect accretion is a suitable approximation in this regime, from a dynamical point of view. Although fragmentation events are common, only ∼10 per cent of the system mass is fragmented during a typical ‘late instability phase’, with fragments being mostly reacreted by surviving planets. This limited total mass in fragments proved to be insufficient to alter qualitatively the final system dynamical configuration – e.g. promote strong dynamical friction or residual migration – compared to simulations where fragmentation is neglected.

Formation of planetary systems by pebble accretion and migration

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 useN-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 (≲15M⊕) and super-massive planetary cores potentially able to become gas giant planets (≳15M⊕). 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.

The Role of Early Giant-planet Instability in Terrestrial Planet Formation

Abstract The terrestrial planets are believed to have formed by violent collisions of tens of lunar- to Mars-size protoplanets at time t &lt; 200 Myr after the protoplanetary gas disk dispersal (t 0). The solar system giant planets rapidly formed during the protoplanetary disk stage and, after t 0, radially migrated by interacting with outer disk planetesimals. An early (t &lt; 100 Myr) dynamical instability is thought to have occurred with Jupiter having gravitational encounters with a planetary-size body, jumping inward by ∼0.2–0.5 au, and landing on its current, mildly eccentric orbit. Here we investigate how the giant-planet instability affected the formation of the terrestrial planets. We study several instability cases that were previously shown to match many solar system constraints. We find that resonances with giant planets help to remove solids available for accretion near ∼1.5 au, thus stalling the growth of Mars. It does not matter, however, whether the giant planets are placed on their current orbits at t 0 or whether they realistically evolve in one of our instability models; the results are practically the same. The tight orbital spacing of Venus and Earth is difficult to reproduce in our simulations, including cases where bodies grow from a narrow annulus at 0.7–1 au, because protoplanets tend to spread radially during accretion. The best results are obtained in the narrow-annulus model when protoplanets emerging from the dispersing gas nebula are assumed to have (at least) the mass of Mars. This suggests efficient accretion of the terrestrial protoplanets during the first ∼10 Myr of the solar system.

The eccentricity distribution of giant planets and their relation to super-Earths in the pebble accretion scenario

Observations of the population of cold Jupiter planets (r &gt;1 AU) show that nearly all of these planets orbit their host star on eccentric orbits. For planets up to a few Jupiter masses, eccentric orbits are thought to be the outcome of planet–planet scattering events taking place after gas dispersal. We simulated the growth of planets via pebble and gas accretion as well as the migration of multiple planetary embryos in their gas disc. We then followed the long-term dynamical evolution of our formed planetary system up to 100 Myr after gas disc dispersal. We investigated the importance of the initial number of protoplanetary embryos and different damping rates of eccentricity and inclination during the gas phase for the final configuration of our planetary systems. We constrained our model by comparing the final dynamical structure of our simulated planetary systems to that of observed exoplanet systems. Our results show that the initial number of planetary embryos has only a minor impact on the final orbital eccentricity distribution of the giant planets, as long as the damping of eccentricity and inclination is efficient. If the damping is inefficient (slow), systems with a larger initial number of embryos harbour larger average eccentricities. In addition, for slow damping rates, we observe that scattering events are already common during the gas disc phase and that the giant planets that formed in these simulations match the observed giant planet eccentricity distribution best. These simulations also show that massive giant planets (above Jupiter mass) on eccentric orbits are less likely to host inner super-Earths as they get lost during the scattering phase, while systems with less massive giant planets on nearly circular orbits should harbour systems of inner super-Earths. Finally, our simulations predict that giant planets are not single, on average, but they live in multi-planet systems.

Effects of photoevaporation on protoplanetary disc ‘isochrones’

ABSTRACT Protoplanetary discs are the site of star and planet formation, and their evolution and consequent dispersal deeply affect the formation of planetary systems. In the standard scenario they evolve on time-scales ∼Myr due to the viscous transport of angular momentum. The analytical self-similar solution for their evolution predicts specific disc isochrones in the accretion rate–disc mass plane. However, photoevaporation by radiation emitted by the central star is likely to dominate the gas disc dispersal of the innermost region, introducing another (shorter) time-scale for this process. In this paper, we include the effect of internal (X and EUV) photoevaporation on the disc evolution, finding numerical solutions for a population of protoplanetary discs. Our models naturally reproduce the expected quick dispersal of the inner region of discs when their accretion rates match the rate of photoevaporative mass loss, in line with previous studies. We find that photoevaporation preferentially removes the lightest discs in the sample. The net result is that, counter-intuitively, photoevaporation increases the average disc mass in the sample, by dispersing the lightest discs. At the same time, photoevaporation also reduces the mass accretion rate by cutting the supply of material from the outer to the inner disc. In a purely viscous framework, this would be interpreted as the result of a longer viscous evolution, leading to an overestimate of the disc age. Our results thus show that photoevaporation is a necessary ingredient to include when interpreting observations of large disc samples with measured mass accretion rates and disc masses. Photoevaporation leaves a characteristic imprint on the shape of the isochrone. Accurate data of the accretion rate–disc mass plane in the low disc mass region therefore give clues on the typical photoevaporation rate.

Dynamical rearrangement of super-Earths during disk dispersal

The Kepler mission has discovered that multiple close-in super-Earth planets are common around solar-type stars, but their period ratios do not show strong pile-ups near mean motion resonances (MMRs). One scenario is that super-Earths form in a gas-rich disk, and they interact gravitationally with the surrounding gas, inducing their orbital migration. Disk migration theory predicts, however, that planets would end up at resonant orbits due to their differential migration speed. Motivated by the discrepancy between observation and theory, we seek for a mechanism that moves planets out of resonances. We examine the orbital evolution of planet pairs near the magnetospheric cavity during the gas disk dispersal phase. Our study determines the conditions under which planets can escape resonances. We perform two-planet N-body simulations, varying the planet masses, stellar magnetic field strengths, disk accretion rates and gas disk depletion timescales. As planets migrate outward with the expanding magnetospheric cavity, their dynamical configurations can be rearranged. Migration of planets is substantial (minor) in a massive (light) disk. When the outer planet is more massive than the inner planet, the period ratio of two planets increases through outward migration. On the other hand, when the inner planet is more massive, the final period ratio tends to remain similar to the initial one. Larger stellar magnetic field strengths result in planets stopping their migration at longer periods. We highlight \textit{magnetospheric rebound} as an important ingredient able to reconcile disk migration theory with observations. Even when planets are trapped into MMR during the early gas-rich stage, subsequent cavity expansion would induce substantial changes to their orbits, moving them out of resonance.

THE IMPACT OF DUST EVOLUTION AND PHOTOEVAPORATION ON DISK DISPERSAL

Protoplanetary disks are dispersed by viscous evolution and photoevaporation in a few million years; in the interim small, sub-micron sized dust grains must grow and form planets. The time-varying abundance of small grains in an evolving disk directly affects gas heating by far-ultraviolet photons, while dust evolution affects photoevaporation by changing the disk opacity and resulting penetration of FUV photons in the disk. Photoevaporative flows, in turn, selectively carry small dust grains leaving the larger particles---which decouple from the gas---behind in the disk. We study these effects by investigating the evolution of a disk subject to viscosity, photoevaporation by EUV, FUV and X-rays, dust evolution, and radial drift using a 1-D multi-fluid approach (gas + different dust grain sizes) to solve for the evolving surface density distributions. The 1-D evolution is augmented by 1+1D models constructed at each epoch to obtain the instantaneous disk structure and determine photoevaporation rates. The implementation of a dust coagulation/fragmentation model results in a marginal decrease in disk lifetimes when compared to models with no dust evolution; the disk lifetime is thus found to be relatively insensitive to the evolving dust opacity. We find that photoevaporation can cause significant reductions in the gas/dust mass ratio in the planet-forming regions of the disk as it evolves, and may result in a corresponding increase in heavy element abundances relative to hydrogen. We discuss implications for theories of planetesimal formation and giant planet formation, including the formation of gas-poor giants. After gas disk dispersal, $\sim 3\times 10^{-4}$ \ms\ of mass in solids typically remain, comparable to the solids inventory of our solar system.

On the formation of planetary systems via oligarchic growth in thermally evolving viscous discs

We present N-body simulations of planetary system formation in thermally-evolving, viscous disc models. The simulations incorporate type I migration (including corotation torques and their saturation), gap formation, type II migration, gas accretion onto planetary cores, and gas disc dispersal through photoevaporation. The aim is to examine whether or not the oligarchic growth scenario, when combined with self-consistent disc models and up-to-date prescriptions for disc-driven migration, can produce planetary systems similar to those that have been observed. The results correlate with the initial disc mass. Low mass discs form close-packed systems of terrestrial-mass planets and super-Earths. Higher mass discs form multiple generations of planets, with masses in the range 10 < mp < 45M_Earth. These planets generally type I migrate into the inner disc, because of corotation torque saturation, where they open gaps and type II migrate into the central star. Occasionally, a final generation of low-to-intermediate mass planets forms and survives due to gas disc dispersal. No surviving gas giants were formed in our simulations. Analysis shows that these planets can only survive migration if a core forms and experiences runaway gas accretion at orbital radii r > 10 au prior to the onset of type II migration. We conclude that planet growth above masses mp > 10M_Earth during the gas disc life time leads to corotation torque saturation and rapid inward migration, preventing the formation and survival of gas giants. This result is in contrast to the success in forming gas giant planets displayed by some population synthesis models. This discrepancy arises, in part, because the type II migration prescription adopted in the population synthesis models causes too large a reduction in the migration speed when in the planet dominated regime.

Early dynamical instabilities in the giant planet systems

The observed wide eccentricity distribution of extrasolar giant planets is thought to be the result of dynamical instabilities and gravitational scattering among planets. Previously, it has been assumed that the orbits in giant planet systems become gravitationally unstable after the gas nebula dispersal. It was not well understood, however, how these unstable conditions were established in the first place. In this work we numerically simulate the evolution of systems of three planets as the planets sequentially grow to Jupiter's mass, and dynamically interact among themselves and with the gas disk. We use the hydro-dynamical code FARGO that we modified by implementing the $N$-body integrator SyMBA. The new code can handle close encounters and collisions between planets. To test their stability, the planetary systems were followed with SyMBA for up to $10^8$ yr after the gas disk dispersal. We find that dynamics of the growing planets is complex, because migration and resonances raise their orbital eccentricities, and cause dynamical instabilities when gas is still around. If the dynamical instabilities occur early, planets can be removed by collisions and ejections, and the system rearranges into a new, more stable configuration. In this case, the planetary systems emerging from the gas disks are expected to be stable, and would need to be destabilized by other means (low-mass planets, planetesimal disks, etc.). Alternatively, for the giant planet system to be intrinsically unstable upon the gas disk dispersal, a special timing would be required with the growth of (at least some of) the giant planets having to occur near the end of the gas disk lifetime.

Global models of planetary system formation in radiatively-inefficient protoplanetary discs

We present the results of N-body simulations of planetary system formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low-mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas accretion on to forming planetary cores, and gas disc dispersal. We perform a suite of simulations for a variety of disc models with power-law surface density and temperature profiles, with a focus on models in which unsaturated corotation torques can drive outward migration of protoplanets. In some models, we account for the quenching of corotation torques which arises when planetary orbits become eccentric. Approximately half of our simulations lead to the successful formation of gas giant planets with a broad range of masses and semimajor-axes. Giant planetary masses range from being approximately equal to that of Saturn up to approximately twice that of Jupiter. The semimajor-axes of these range from being ∼0.2 au up to ∼75 au, with disc models that drive stronger outward migration favouring the formation of longer period giant planets. Out of a total of 20 giant planets being formed in our simulation suite, we obtain three systems that contain two giants. No super-Earth or Neptune-mass planets were present in the final stages of our simulations, in contrast to the large abundance of such objects being discovered in observation surveys. This result arises because of rapid inward migration suffered by massive planetary cores that form early in the disc lifetime (for which the corotation torques saturate), combined with gas accretion on to massive cores which leads them to become gas giants. Numerous low-mass planets are formed and survive in the simulations, with masses ranging from a few tenths of an Earth mass up to ∼3 Earth masses. Simulations in which the quenching of corotation torques for planets on modestly eccentric orbits was included failed to produce any giant planets, apparently because Lindblad torques induce rapid inward migration of planetary cores in these systems. We conclude that convergent migration induced by corotation torques operating during planetary formation can enhance the growth rate of planetary cores, but these often migrate into the central star because corotation torques saturate. Outward migration of planetary cores of modest mass can lead to the formation of gas giant planets at large distances from the central star, similar to those observed recently through direct imaging surveys. The excitation of planetary eccentricities through planet–planet scattering during oligarchic growth may quench the effects of corotation torques, however, such that inward migration is driven by Lindblad torques.

YOUNG SOLAR SYSTEM's FIFTH GIANT PLANET?

Recent studies of solar system formation suggest that the solar system's giant planets formed and migrated in the protoplanetary disk to reach resonant orbits with all planets inside 15 AU from the Sun. After the gas disk's dispersal, Uranus and Neptune were likely scattered by gas giants, and approached their current orbits while dispersing the transplanetary disk of planetesimals, whose remains survived to this time in the region known as the Kuiper belt. Here we performed N-body integrations of the scattering phase between giant planets in an attempt to determine which initial states are plausible. We found that the dynamical simulations starting with a resonant system of four giant planets have a low success rate in matching the present orbits of giant planets, and various other constraints (e.g., survival of the terrestrial planets). The dynamical evolution is typically too violent, if Jupiter and Saturn start in the 3:2 resonance, and leads to final systems with fewer than four planets. Several initial states stand out in that they show a relatively large likelihood of success in matching the constraints. Some of the statistically best results were obtained when assuming that the solar system initially had five giant planets and one ice giant, with the mass comparable to that of Uranus and Neptune, was ejected to interstellar space by Jupiter. This possibility appears to be conceivable in view of the recent discovery of a large number free-floating planets in interstellar space, which indicates that planet ejection should be common.

Terrestrial planet formation in low-eccentricity warm-Jupiter systems

<i>Context. <i/>Extrasolar giant planets are found to orbit their host stars with a broad range of semi-major axes 0.02 <i>≤<i/> <i>a<i/> <i>≤<i/> 6 AU. Current theories suggest that giant planets orbiting at distances between AU probably formed at larger distances and migrated to their current locations via type II migration, disturbing any inner system of forming terrestrial planets along the way. Migration probably halts because of fortuitously-timed gas disk dispersal.<i>Aims. <i/>The aim of this paper is to examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13-1.7 AU due to gas disk dispersal, and examine the effect of including or neglecting type I migration forces on the forming terrestrial system.<i>Methods. <i/>We employ an <i>N<i/>-body code that is linked to a viscous gas disk algorithm capable of simulating gas loss via accretion onto the central star and photoevaporation, gap formation by the giant planet, type II migration of the giant, optional type I migration of protoplanets, and gas drag on planetesimals.<i>Results. <i/>Most of the inner system planetary building blocks survive the passage of the giant planet, either by being shepherded inward or scattered into exterior orbits. Systems of one or more hot-Earths are predicted to form and remain interior to the giant planet, especially if type II migration has been limited, or where type I migration has affected protoplanetary dynamics. Habitable planets in low-eccentricity warm-Jupiter systems appear possible if the giant planet makes a limited incursion into the outer regions of the habitable zone (HZ), or traverses its entire width and ceases migrating at a radial distance of less than half that of the HZ's inner edge.<i>Conclusions. <i/>Type II migration does not prevent terrestrial planet formation. A wide variety of planetary system architectures exists that can potentially host habitable planets.

On the growth and stability of Trojan planets

Aims. We investigate the stability of those low-mass Trojan planets that form in a protoplanetary disc and subsequently accrete gas to become gas giants.Methods. We calculate their evolution before, during, and after gas disc dispersal. A two-dimensional hydrodynamics code combined with an N -body solver is used to evolve the system of disc and planets. Gas disc dispersal is simulated in a simple manner by assuming global exponential decay of the disc mass, leading to the stalling of migration after semi-major axes have approximately halved from their initial values. We consider Trojan pairs with different initial masses and gas accretion rates and gas disc models with different masses and viscosities. An N -body code, adapted to model disc forces, is used to examine large-scale migration and the formation of very short period Trojan planets.Results. For each combination of planetary pair and disc model that we consider in our hydrodynamic simulations, each Trojan system remains stable before, during, and after disc dispersal. The long-term stability of these systems in the absence of gas is tested using N -body simulations, and all systems remain stable for those evolution times equal to 109 years. Eccentricities remain low () in all cases. Increases in the amplitude of libration about the L 4 /L 5 Lagrange points accompany the inward migration, and during very large-scale migration Trojan systems may be disrupted prior to the onset of disc dispersal.Conclusions. The stability of Trojan pairs during rapid type I migration, during the transition to type II migration with the accompanying gap formation in the gas disc, and during gas loss when the disc disperses, indicates that isolated Trojan planet systems are very stable. If a common mechanism exists for their formation, we suggest they may be readily observed in nature.