Forming Planets via Pebble Accretion Johansen, Anders; Lambrechts, Michiel
Annual review of earth and planetary sciences,
08/2017, Volume:
45, Issue:
1
Journal Article
Peer reviewed
The detection and characterization of large populations of pebbles in protoplanetary disks have motivated the study of pebble accretion as a driver of planetary growth. This review covers all aspects ...of planet formation by pebble accretion, from dust growth over planetesimal formation to the accretion of protoplanets and fully grown planets with gaseous envelopes. Pebbles are accreted at a very high rate-orders of magnitude higher than planetesimal accretion-and the rate decreases only slowly with distance from the central star. This allows planetary cores to start their growth in much more distant positions than their final orbits. The giant planets orbiting our Sun and other stars, including systems of wide-orbit exoplanets, can therefore be formed in complete consistency with planetary migration. We demonstrate how growth tracks of planetary mass versus semimajor axis can be obtained for all the major classes of planets by integrating a relatively simple set of governing equations.
The formation of cold gas giants similar to Jupiter and Saturn in orbit and mass is a great challenge for planetesimal-driven core accretion models because the core growth rates far from the star are ...low. Here we model the growth and migration of single protoplanets that accrete planetesimals and gas. We integrated the core growth rate using fits in the literature to N-body simulations, which provide the efficiency of accreting the planetesimals that a protoplanet migrates through. We take into account three constraints from the solar system and from protoplanetary discs: (1) the masses of the terrestrial planets and the comet reservoirs in Neptune’s scattered disc and the Oort cloud are consistent with a primordial planetesimal population of a few Earth masses per AU, (2) evidence from the asteroid belt and the Kuiper belt indicates that the characteristic planetesimal diameter is 100 km, and (3) observations of protoplanetary discs indicate that the dust is stirred by weak turbulence; this gas turbulence also excites the inclinations of planetesimals. Our nominal model built on these constraints results in maximum protoplanet masses of 0.1 Earth masses. Ignoring constraint (1) above, we show that even a planetesimal population of 1000 Earth masses, corresponding to 50 Earth masses per AU, fails to produce cold gas giants (although it successfully forms hot and warm gas giants). We conclude that a massive planetesimal reservoir is in itself insufficient to produce cold gas giants. The formation of cold gas giants by planetesimal accretion additionally requires that planetesimals are small and that the turbulent stirring is very weak, thereby violating all three above constraints.
Abstract
Atmospheric chemical abundances of giant planets lead to important constraints on planetary formation and migration. Studies have shown that giant planets that migrate through the ...protoplanetary disc can accrete substantial amounts of oxygen-rich planetesimals, leading to supersolar metallicities in the envelope and solar or subsolar C/O ratios. Pebble accretion has been demonstrated to play an important role in core accretion and to have growth rates that are consistent with planetary migration. The high pebble accretion rates allow planetary cores to start their growth beyond 10 au and subsequently migrate to cold (≳1 au), warm (∼0.1–1 au) or hot (≲0.1 au) orbits. In this work we investigate how the formation of giant planets via pebble accretion influences their atmospheric chemical compositions. We find that under the standard pebble accretion scenario, where the core is isolated from the envelope, the resulting metallicities (O/H and C/H ratios) are subsolar, while the C/O ratios are supersolar. Planets that migrate through the disc to become hot Jupiters accrete substantial amounts of water vapour, but still acquire slightly subsolar O/H and supersolar C/O of 0.7–0.8. The metallicity can be substantially subsolar (∼0.2–0.5 × solar) and the C/O can even approach 1.0 if the planet accretes its envelope mostly beyond the CO2 ice line, i.e. cold Jupiters or hot Jupiters that form far out and migrate in by scattering. Allowing for core erosion yields significantly supersolar metallicities and solar or subsolar C/O, which can also be achieved by other means, e.g. photoevaporation and late-stage planetesimal accretion.
Planetary migration is a major challenge for planet-formation theories. The speed of type-I migration is proportional to the mass of a protoplanet, while the final decade of growth of a ...pebble-accreting planetary core takes place at a rate that scales with the mass to the two-thirds power. This results in planetary growth tracks (i.e., the evolution of the mass of a protoplanet versus its distance from the star) that become increasingly horizontal (migration dominated) with the rising mass of the protoplanet. It has been shown recently that the migration torque on a protoplanet is reduced proportional to the relative height of the gas gap carved by the growing planet. Here we show from 1D simulations of planet–disc interaction that the mass at which a planet carves a 50% gap is approximately 2.3 times the pebble isolation mass. Our measurements of the pebble isolation mass from 1D simulations match published 3D results relatively well, except at very low viscosities (α < 10−3) where the 3D pebble isolation mass is significantly higher, possibly due to gap edge instabilities that are not captured in 1D. The pebble isolation mass demarks the transition from pebble accretion to gas accretion. Gas accretion to form gas-giant planets therefore takes place over a few astronomical units of migration after reaching first the pebble isolation mass and, shortly after, the 50% gap mass. Our results demonstrate how planetary growth can outperform migration both during core accretion and during gas accretion, even when the Stokes number of the pebbles is small, St ~ 0.01, and the pebble-to-gas flux ratio in the protoplanetary disc is in the nominal range of 0.01–0.02. We find that planetary growth is very rapid in the first million years of the protoplanetary disc and that the probability for forming gas-giant planets increases with the initial size of the protoplanetary disc and with decreasing turbulent diffusion.
We developed a pebble-driven core accretion model to study the formation and evolution of planets around stars in the stellar mass range of 0.08 M⊙–1 M⊙. By Monte Carlo sampling of the initial ...conditions, the growth and migration of a large number of individual protoplanetary embryos were simulated in a population synthesis manner. We tested two hypotheses for the birth locations of embryos: at the water ice line or log-uniformly distributed over entire protoplanetary disks. Two types of disks with different turbulent viscous parameters αt of 10−3 and 10−4 are also investigated to shed light on the role of outward migration of protoplanets. The forming planets are compared with the observed exoplanets in terms of mass, semimajor axis, metallicity, and water content. We find that gas giant planets are likely to form when the characteristic disk sizes are larger, the disk accretion rates are higher, the disks are more metal rich, and/or their stellar hosts are more massive. Our model shows that first, the characteristic mass of super-Earth is set by the pebble isolation mass. Super-Earth masses increase linearly with the mass of its stellar host, which corresponds to one Earth mass around a late M-dwarf star and 20 Earth masses around a solar-mass star. Second, the low-mass planets, up to 20 M⊕, can form around stars with a wide range of metallicities, while massive gas giant planets are preferred to grow around metal rich stars. Third, super-Earth planets that are mainly composed of silicates, with relatively low water fractions, can form from protoplanetary embryos at the water ice line in weakly turbulent disks where outward migration is suppressed. However, if the embryos are formed over a wide range of radial distances, the super-Earths would end up having a distinctive, bimodal composition in water mass. Altogether, our model succeeds in quantitatively reproducing several important observed properties of exoplanets and correlations with their stellar hosts.
The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of ...the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τf < 0.005 can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.
The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than ~100 ...km in size. Instead, planetesimals appear to form top-down, with large 100−1000 km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We used a hydrodynamic code to model the interaction between solid particles and the gas inside a shearing box inside the disk, considering particle sizes from submillimeter-sized chondrules to meter-sized rocks. We found that particles down to millimeter sizes can form dense particle clouds through the run-away convergence of radial drift known as the streaming instability. We made a map of the range of conditions (strength of turbulence, particle mass-loading, disk mass, and distance to the star) that are prone to producing dense particle clumps. Finally, we estimate the distribution of collision speeds between mm-sized particles. We calculated the rate of sticking collisions and obtain a robust upper limit on the particle growth timescale of ~105 years. This means that mm-sized chondrule aggregates can grow on a timescale much smaller than the disk accretion timescale (~106−107 years). Our results suggest a pathway from the mm-sized grains found in primitive meteorites to fully formed asteroids. We speculate that asteroids may form from a positive feedback loop in which coagualation leads to particle clumping driven by the streaming instability. This clumping, in turn, reduces collision speeds and enhances coagulation. Future simulations should model coagulation and the streaming instability together to explore this feedback loop further.
We perform hydrodynamical simulations of the accretion of pebbles and rocks on to protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the ...protoplanetary disc gas. Particle streams interacting with the gas within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted on to the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10–50 per cent of their mass from pebbles and rocks during the gaseous solar nebula phase. Our model also offers a possible explanation for the narrow range of spin periods observed among the largest bodies in the asteroid and trans-Neptunian belts, and predicts that 1000-km-scale Kuiper Belt objects that have not experienced giant impacts should preferentially spin in the prograde direction.
We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs in the (sub)stellar mass range between 0.01
M
⊙
and ...0.1
M
⊙
. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial mass of the protoplanet (largest body from the planetesimal populations), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary disk evolution. We find that the initial protoplanets form with masses that increase with host mass and orbital distance, and decrease with age. Around late M-dwarfs of 0.1
M
⊙
, these protoplanets can grow up to Earth-mass planets by pebble accretion. However, around brown dwarfs of 0.01
M
⊙
, planets do not grow to the masses that are greater than Mars when the initial protoplanets are born early in self-gravitating disks, and their growth stalls at around 0.01 Earth-mass when they are born late in non-self-gravitating disks. Around these low-mass stars and brown dwarfs we find no channel for gas giant planet formation because the solid cores remain too small. When the initial protoplanets form only at the water-ice line, the final planets typically have ≳15% water mass fraction. Alternatively, when the initial protoplanets form log-uniformly distributed over the entire protoplanetary disk, the final planets are either very water rich (water mass fraction ≳15%) or entirely rocky (water mass fraction ≲5%).
Recent years have seen growing interest in the streaming instability as a candidate mechanism to produce planetesimals. However, these investigations have been limited to small-scale simulations. We ...now present the results of a global protoplanetary disk evolution model that incorporates planetesimal formation by the streaming instability, along with viscous accretion, photoevaporation by EUV, FUV, and X-ray photons, dust evolution, the water ice line, and stratified turbulence. Our simulations produce massive (60-130 M⊕) planetesimal belts beyond 100 au and up to ∼20 M⊕ of planetesimals in the middle regions (3-100 au). Our most comprehensive model forms 8 M⊕ of planetesimals inside 3 au, where they can give rise to terrestrial planets. The planetesimal mass formed in the inner disk depends critically on the timing of the formation of an inner cavity in the disk by high-energy photons. Our results show that the combination of photoevaporation and the streaming instability are efficient at converting the solid component of protoplanetary disks into planetesimals. Our model, however, does not form enough early planetesimals in the inner and middle regions of the disk to give rise to giant planets and super-Earths with gaseous envelopes. Additional processes such as particle pileups and mass loss driven by MHD winds may be needed to drive the formation of early planetesimal generations in the planet-forming regions of protoplanetary disks.
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