•We explain why Mars-mass embryos formed in the inner Solar System and massive cores in the outer System.•Accretion of planetesimals cannot explain this mass difference.•The scenario of formation of ...embryos and cores can explain this mass difference.
The basic structure of the Solar System is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance r<rice and r>rice, where rice is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to ∼20 Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.
Abstract
The evolution of protoplanetary discs embedded in stellar clusters depends on the age and the stellar density in which they are embedded. Stellar clusters of young age and high stellar ...surface density destroy protoplanetary discs by external photoevaporation and stellar encounters. Here, we consider the effect of background heating from newly formed stellar clusters on the structure of protoplanetary discs and how it affects the formation of planets in these discs. Our planet formation model is built on the core accretion scenario, where we take the reduction of the core growth time-scale due to pebble accretion into account. We synthesize planet populations that we compare to observations obtained by radial velocity measurements. The giant planets in our simulations migrate over large distances due to the fast type-II migration regime induced by a high disc viscosity (α = 5.4 × 10−3). Cold Jupiters (rp > 1 au) originate preferably from the outer disc, due to the large-scale planetary migration, while hot Jupiters (rp < 0.1 au) preferably form in the inner disc. We find that the formation of gas giants via pebble accretion is in agreement with the metallicity correlation, meaning that more gas giants are formed at larger metallicity. However, our synthetic population of isolated stars host a significant amount of giant planets even at low metallicity, in contradiction to observations where giant planets are preferably found around high metallicity stars, indicating that pebble accretion is very efficient in the standard pebble accretion framework. On the other hand, discs around stars embedded in cluster environments hardly form any giant planets at low metallicity in agreement with observations, where these changes originate from the increased temperature in the outer parts of the disc, which prolongs the core accretion time-scale of the planet. We therefore conclude that the outer disc structure and the planet's formation location determines the giant planet occurrence rate and the formation efficiency of cold and hot Jupiters.
The full spatial structure and temporal evolution of the accretion flow into the envelopes of growing gas giants in their nascent discs is only accessible in simulations. Such simulations are ...constrained in their approach of computing the formation of gas giants by dimensionality, resolution, consideration of self-gravity, energy treatment and the adopted opacity law. Our study explores how a number of these parameters affect the measured accretion rate of a Saturn-mass planet. We present a global 3D radiative hydrodynamics framework using the FARGOCA-code. The planet is represented by a gravitational potential with a smoothing length at the location of the planet. No mass or energy sink is used; instead luminosity and gas accretion rates are self-consistently computed. We find that the gravitational smoothing length must be resolved by at least ten grid cells to obtain converged measurements of the gas accretion rates. Secondly, we find gas accretion rates into planetary envelopes that are compatible with previous studies, and continue to explain those via the structure of our planetary envelopes and their luminosities. Our measured gas accretion rates are formally in the stage of Kelvin–Helmholtz contraction due to the modest entropy loss that can be obtained over the simulation timescale, but our accretion rates are compatible with those expected during late run-away accretion. Our detailed simulations of the gas flow into the envelope of a Saturn-mass planet provide a framework for understanding the general problem of gas accretion during planet formation and highlight circulation features that develop inside the planetary envelopes. Those circulation features feedback into the envelope energetics and can have further implications for transporting dust into the inner regions of the envelope.
Growing planets interact with their natal protoplanetary disc, which exerts a torque onto them allowing them to migrate in the disc. Small mass planets do not affect the gas profile and migrate in ...the fast type-I migration. Although type-I migration can be directed outwards for planets smaller than 20−30M⊕ in some regions of the disc, planets above this mass should be lost into the central star long before the disc disperses. Massive planets push away material from their orbit and open a gap. They subsequently migrate in the slower, type II migration, which could save them from migrating all the way to the star. Hence, growing giant planets can be saved if and only if they can reach the gap opening mass, because this extends their migration timescale, allowing them to eventually survive at large orbits until the disc itself disperses.
However, most of the previous studies only measured the torques on planets with fixed masses and orbits to determine the migration rate. Additionally, the transition between type-I and type-II migration itself is not well studied, especially when taking the growth mechanism of rapid gas accretion from the surrounding disc into account. Here we use isothermal 2D disc simulations with FARGO-2D1D to study the migration behaviour of gas accreting protoplanets in discs. We find that migrating giant planets always open gaps in the disc. We further show analytically and numerically that in the runaway gas accretion regime, the growth time-scale is comparable to the type-I migration time-scale, indicating that growing planets will reach gap opening masses before migrating all the way to the central star in type-I migration if the disc is not extremely viscous and/or thick. An accretion rate limited to the radial gas flow in the disc, in contrast, is not fast enough. When gas accretion by the planet is taken into account, the gap opening process is accelerated because the planet accretes material originating from its horseshoe region. This allows an accreting planet to transition to type-II migration before being lost even if gas fails to be provided for a rapid enough growth and the classical gap opening mass is not reached.
Context. With an average eccentricity of about 0.29, the eccentricity distribution of extrasolar planets is markedly different from the solar system. Among other scenarios considered, it has been ...proposed that eccentricity may grow through planet-disc interaction. Recently, it has been noticed that the thermodynamical state of the disc can significantly influence the migration properties of growing protoplanets. However, the evolution of planetary eccentricity in radiative discs has not been considered yet. Aims. In this paper we study the evolution of planets on eccentric orbits that are embedded in a three-dimensional viscous disc and analyse the disc’s effect on the orbital evolution of the planet. Methods. We use the three-dimensional hydrodynamical code NIRVANA that includes full tensor viscosity and implicit radiation transport in the flux-limited diffusion approximation. The code uses the FARGO-algorithm to speed up the simulations. First we measure the torque and power exerted on the planet by the disc for fixed orbits, and then we let the planet start with initial eccentricity and evolve it in the disc. Results. For locally isothermal discs we confirm previous results and find eccentricity damping and inward migration for planetary cores. For low eccentricity (e ≲ 2H/r) the damping is exponential, while for higher e it follows ė ∝ e-2. In the case of radiative discs, the planets experience an inward migration as long as its eccentricity lies above a certain threshold. After the damping of eccentricity cores with masses below 33 MEarth begin to migrate outward in radiative discs, while higher mass cores always migrate inward. For all planetary masses studied (up to 200 MEarth) we find eccentricity damping. Conclusions. In viscous discs the orbital eccentricity of embedded planets is damped during the evolution independent of the mass. Hence, planet-disc interaction does not seem to be a viable mechanism to explain the observed high eccentricity of exoplanets.
ABSTRACT
Recent detailed observations of protoplanetary discs revealed a lot of substructures that are mostly ring like. One interpretation is that these rings are caused by growing planets. These ...potential planets are not yet opening very deep gaps in their discs. These planets instead form small gaps in the discs to generate small pressure bumps exterior to their orbits that stop the inflow of the largest dust particles. In the pebble accretion paradigm, this planetary mass corresponds to the pebble isolation mass, where pebble accretion stops and efficient gas accretion starts. We perform planet population synthesis via pebble and gas accretion including type-I and type-II migration. In the first stage of our simulations, we investigate the conditions necessary for planets to reach the pebble isolation mass and compare their position to the observed gaps. We find that in order to match the gap structures 2000ME in pebbles is needed, which would be only available for the most metal-rich stars. We then follow the evolution of these planets for a few Myr to compare the resulting population with the observed exoplanet populations. Planet formation in discs with these large amounts of pebbles results in mostly forming gas giants and only very little super-Earths, contradicting observations. This leads to the conclusions that either (i) the observed discs are exceptions, (ii) not all gaps in observed discs are caused by planets, or (iii) that we miss some important ingredients in planet formation related to gas accretion and/or planet migration.
Pebble accretion is an efficient mechanism that is able to build up the core of the giant planets within the lifetime of the protoplanetary disc gas-phase. The core grows via this process until the ...protoplanet reaches its pebble isolation mass and starts to accrete gas. During the growth, the protoplanet undergoes a rapid, large-scale, inward migration due to the interactions with the gaseous protoplanetary disc. In this work, we have investigated how this early migration would have affected the minor body populations in our solar system. In particular, we focus on the Jupiter Trojan asteroids (bodies in the coorbital resonance 1:1 with Jupiter, librating around the L4 and L5 Lagrangian points called, respectively, the leading and the trailing swarm) and the Hilda asteroids. We characterised their orbital parameter distributions after the disc dispersal and their formation location and compare them to the same populations produced in a classical in situ growth model. We find that a massive and eccentric Hilda group is captured during the migration from a region between 5 and 8 au and subsequently depleted during the late instability of the giant planets. Our simulations also show that inward migration of the giant planets always produces a Jupiter Trojans’ leading swarm more populated than the trailing one, with a ratio comparable to the current observed Trojan asymmetry ratio. The in situ formation of Jupiter, on the other hand, produces symmetric swarms. The reason for the asymmetry is the relative drift between the migrating planet and the particles in the coorbital resonance. The capture happens during the growth of Jupiter’s core and Trojan asteroids are afterwards carried along during the giant planet’s migration to their final orbits. The asymmetry and eccentricity of the captured Trojans correspond well to observations, but their inclinations are near zero and their total mass is three to four orders of magnitude higher than the current population. Future modelling will be needed to understand whether the dynamical evolution of the Trojans over billions of years will raise the inclinations and deplete the masses to observed values.
One of the current challenges of planet formation theory is to explain the enrichment of observed exoplanetary atmospheres. While past studies have focused on scenarios where either pebbles or ...planetesimals are the main drivers of heavy element enrichment, here we combine the two approaches to understand whether the composition of a planet can constrain its formation pathway. We study three different formation scenarios: pebble accretion, pebble accretion with planetesimal formation inside the disc, and combined pebble and planetesimal accretion. We used the
CHEMCOMP
code to perform semi-analytical 1D simulations of protoplanetary discs, including viscous evolution, pebble drift, and simple chemistry to simulate the growth of planets from planetary embryos to gas giants as they migrate through the disc, while simultaneously tracking their composition. Our simulations confirm that the composition of the planetary atmosphere is dominated by the accretion of gas vapour enriched by inward-drifting and evaporating pebbles. Including planetesimal formation hinders this enrichment because many pebbles are locked into planetesimals and cannot evaporate and enrich the disc. This results in a dramatic drop in accreted heavy elements in the cases of planetesimal formation and accretion, demonstrating that planetesimal formation needs to be inefficient in order to explain planets with high heavy element content. On the other hand, accretion of planetesimals enhances the refractory component of the atmosphere, leading to low volatile-to-refractory ratios in the atmosphere, in contrast to the majority of pure pebble simulations. However, low volatile-to-refractory ratios can also be achieved in the pure pebble accretion scenario if the planet migrates all the way into the inner disc and accretes gas that is enriched in evaporated refractories. Distinguishing these two scenarios requires knowledge about the planet’s atmospheric C/H and O/H ratios, which are much higher in the pure pebble scenario compared to the planetesimal formation and accretion scenario. This implies that a detailed knowledge of the composition of planetary atmospheres could help to distinguish between the different formation scenarios.
In this paper, we address the migration of small-mass planets in 3D radiative discs. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, ...thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydrodynamical code fargo to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs' parameters for which outward migration has been shown in the range of 5, 35 Earth masses, we find that the transition to inward migration occurs for masses in the range 3, 5 Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modelling of the energy equation.
ABSTRACT
The final orbital position of growing planets is determined by their migration speed, which is essentially set by the planetary mass. Small mass planets migrate in type-I migration, while ...more massive planets migrate in type-II migration, which is thought to depend mostly on the viscous evolution rate of the disc. A planet is most vulnerable to inward migration before it reaches type-II migration and can lose a significant fraction of its semimajor axis at this stage. We investigated the influence of different disc viscosities, the dynamical torque, and gas accretion from within the horseshoe region as mechanisms for slowing down planet migration. Our study confirms that planets growing in low viscosity environments migrate less, due to the earlier gap opening and slower type-II migration rate. We find that taking the gas accretion from the horseshoe region into account allows an earlier gap opening and this results in less inward migration of growing planets. Furthermore, this effect increases the planetary mass compared to simulations that do not take the effect of gas accretion from the horseshoe region. Moreover, combining the effect of the dynamical torque with the effect of gas accretion from the horseshoe region, significantly slows down inward migration. Taking these effects into account could allow the formation of cold Jupiters (a > 1 au) closer to the water ice line region compared to previous simulations that did not take these effects into account. We, thus, conclude that gas accretion from within the horseshoe region and the dynamical torque play crucial roles in shaping planetary systems.
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