Context. In the core-accretion model, the typical size of solids that are accreted to form planetary embryos and planetary cores is debated. First, models assumed that the main part of planetary ...cores came from large-sized planetesimals, but other more recent models are based on the accretion of small-sized pebbles. Aims. The goal of this paper is to compute the maximum mass a growing planetary embryo can reach depending on the size of accreted planetesimals or pebbles, and to infer the possibility of growing the cores of giant planets and giant planets themselves. Methods. We computed the internal structure of the gas envelope of planetary embryos to determine the core mass that is necessary to bind an envelope large enough to destroy planetesimals or pebbles while they are gravitationally captured. We also considered the effect of the advection wind originating from the protoplanetary disk, following the results of Ormel et al. (2015, MNRAS, 447, 3512). Results. We show that for low-mass pebbles the envelope is large enough to destroy and vaporize pebbles completely before they can reach the core once the planetary embryo is larger than a fraction of the Earth mass. The material constituting pebbles is therefore released in the planetary envelope and is later on dispersed in the protoplanetary disk if the advection wind is strong enough. As a consequence, the growth of the planetary embryo is stopped at a mass that is so low that Kelvin-Helmholtz accretion cannot lead to the accretion of significant amounts of gas. For larger planetesimals, a similar process occurs but at much higher mass, on the order of ten Earth masses, and it is followed by rapid accretion of gas. Conclusions. If the effect of the advection wind is as efficient as described in Ormel et al. (2015), the combined effect of the vaporization of accreted solids in the envelope of forming planetary embryos and of this advection wind prevents the growth of the planets at masses lower than or similar to the Earth mass in the case of formation by pebble accretion, up to a distance on the order of 10 AU. In the case of formation by accretion of high-mass planetesimals, the growth of the planetary core is limited at masses on the order of ten Earth masses. However, in contrast to the case of pebble accretion, further growth is still possible and proceeds either through the accretion of gas or through the accretion of solids that are destroyed in the planetary envelope when the effect of the advection wind has ceased and the planetary Hill radius becomes comparable to the disk scale height.
Context. The formation stage of planetesimals represents a major gap in our understanding of the planet formation process. Late-stage planet accretion models typically make arbitrary assumptions ...about planetesimal and pebble distribution, while dust evolution models predict that planetesimal formation is only possible at some orbital distances. Aims. We wish to test the importance of the water snow line in triggering the formation of the first planetesimals during the gas-rich phase of a protoplanetary disk, when cores of giant planets have to form. Methods. We connected prescriptions for gas disk evolution, dust growth and fragmentation, water ice evaporation and recondensation, the transport of both solids and water vapor, and planetesimal formation via streaming instability into a single one-dimensional model for protoplanetary disk evolution. Results. We find that processes taking place around the snow line facilitate planetesimal formation in two ways. First, because the sticking properties between wet and dry aggregates change, a “traffic jam” inside of the snow line slows the fall of solids onto the star. Second, ice evaporation and outward diffusion of water followed by its recondensation increases the abundance of icy pebbles that trigger planetesimal formation via streaming instability just outside of the snow line. Conclusions. Planetesimal formation is hindered by growth barriers and radial drift and thus requires particular conditions to take place. The snow line is a favorable location where planetesimal formation is possible for a wide range of conditions, but not in every protoplanetary disk model, however. This process is particularly promoted in large cool disks with low intrinsic turbulence and an increased initial dust-to-gas ratio.
Context. The conditions that a planet must fulfill to be habitable are not precisely known. However, it is comparatively easier to define conditions under which a planet is very likely not habitable. ...Finding such conditions is important as it can help select, in an ensemble of potentially observable planets, which ones should be observed in greater detail for characterization studies. Aims. Assuming, as in the Earth, that the presence of a C-cycle is a necessary condition for long-term habitability, we derive, as a function of the planetary mass, a radius above which a planet is likely not habitable. We compute the maximum radius a planet can have to fulfill two constraints: surface conditions compatible with the existence of liquid water, and no ice layer at the bottom of a putative global ocean. We demonstrate that, above a given radius, these two constraints cannot be met. Methods. We compute internal structure models of planets, using a five-layer model (core, inner mantle, outer mantle, ocean, and atmosphere), for different masses and composition of the planets (in particular, the Fe/Si ratio of the planet). Results. Our results show that for planets in the super-Earth mass range (1–12 M⊕), the maximum that a planet, with a composition similar to that of the Earth, can have varies between 1.7 and 2.2 R⊕. This radius is reduced when considering planets with higher Fe/Si ratios and taking radiation into account when computing the gas envelope structure. Conclusions. These results can be used to infer, from radius and mass determinations using high-precision transit observations like those that will soon be performed by the CHaracterizing ExOPlanet Satellite (CHEOPS), which planets are very likely not habitable, and therefore which ones should be considered as best targets for further habitability studies.
Context. When a planet becomes massive enough, it gradually carves a partial gap around its orbit in the protoplanetary disk. A pressure maximum can be formed outside the gap where solids that are ...loosely coupled to the gas, typically in the pebble size range, can be trapped. The minimum planet mass for building such a trap, which is called the pebble isolation mass (PIM), is important for two reasons: it marks the end of planetary growth by pebble accretion, and the trapped dust forms a ring that may be observed with millimetre observations. Aims. We study the effect of disk turbulence on the PIM and find its dependence on the gas turbulent viscosity, aspect ratio, and particles Stokes number. Methods. By means of 2D gas hydrodynamical simulations, we found the minimum planet mass to form a radial pressure maximum beyond the orbit of the planet, which is the necessary condition to trap pebbles. We then carried out 2D gas plus dust hydrodynamical simulations to examine how dust turbulent diffusion impacts particles trapping at the pressure maximum. We finally provide a semi-analytical calculation of the PIM based on comparing the radial drift velocity of solids and the root mean square turbulent velocity fluctuations around the pressure maximum. Results. From our results of gas simulations, we provide an expression for the PIM vs. disk aspect ratio and turbulent viscosity. Our gas plus dust simulations show that the effective PIM can be nearly an order of magnitude larger in high-viscosity disks because turbulence diffuse particles out of the pressure maximum. This is quantified by our semi-analytical calculation, which gives an explicit dependence of the PIM with Stokes number of particles. Conclusions. Disk turbulence can significantly alter the PIM, depending on the level of turbulence in regions of planet formation.
Context. The consistency of planet formation models suffers from the disconnection between the regime of small and large bodies. This is primarily caused by so-called growth barriers: the direct ...growth of larger bodies is halted at centimetre-sized objects and particular conditions are required for the formation of larger, gravitationally bound planetesimals. Aims. We aim to connect models of dust evolution and planetesimal formation to identify regions of protoplanetary discs that are favourable for the formation of kilometre-sized bodies and the first planetary embryos. Methods. We combine semi-analytical models of viscous protoplanetary disc evolution, dust growth and drift including backreaction of the dust particles on the gas, and planetesimal formation via the streaming instability into one numerical code. We investigate how planetesimal formation is affected by the mass of the protoplanetary disc, its initial dust content, and the stickiness of dust aggregates. Results. We find that the dust growth and drift leads to a global redistribution of solids. The pile-up of pebbles in the inner disc provides local conditions where the streaming instability is effective. Planetesimals form in an annulus with its inner edge lying between 0.3 AU and 1 AU and its width ranging from 0.3 AU to 3 AU. The resulting surface density of planetesimals follows a radial profile that is much steeper than the initial disc profile. These results support formation of terrestrial planets in the solar system from a narrow annulus of planetesimals, which reproduces their peculiar mass ratios.
Context. The determination of the abundance of volatiles in extrasolar planets is very important as it can provide constraints on transport in protoplanetary disks and on the formation location of ...planets. However, constraining the internal structure of low-mass planets from transit measurements is known to be a degenerate problem. Aims. Using planetary structure and evolution models, we show how observations of transiting planets can be used to constrain their internal composition, in particular the amount of volatiles in the planetary interior, and consequently the amount of gas (defined in this paper to be only H and He) that the planet harbors. We first explore planets that are located close enough to their star to have lost their gas envelope. We then concentrate on planets at larger distances and show that the observation of transiting planets at different evolutionary ages can provide statistical information on their internal composition, in particular on their volatile fraction. Methods. We computed the evolution of low-mass planets (super-Earths to Neptune-like) for different fractions of volatiles and gas. We used a four-layer model (core, silicate mantle, icy mantle, and gas envelope) and computed the internal structure of planets for different luminosities. With this internal structure model, we computed the internal and gravitational energy of planets, which was then used to derive the time evolution of the planet. Since the total energy of a planet depends on its heat capacity and density distribution and therefore on its composition, planets with different ice fractions have different evolution tracks. Results. We show for low-mass gas-poor planets that are located close to their central star that assuming evaporation has efficiently removed the entire gas envelope, it is possible to constrain the volatile fraction of close-in transiting planets. We illustrate this method on the example of 55 Cnc e and show that under the assumption of the absence of gas, the measured mass and radius imply at least 20% of volatiles in the interior. For planets at larger distances, we show that the observation of transiting planets at different evolutionary ages can be used to set statistical constraints on the volatile content of planets. Conclusions. These results can be used in the context of future missions like PLATO to better understand the internal composition of planets, and based on this, their formation process and potential habitability.
We present a study into the formation of planetary systems around low mass stars similar to Trappist-1, through the accretion of either planetesimals or pebbles. The aim is to determine if the ...currently observed systems around low mass stars could favour one scenario over the other. To determine these differences, we ran numerous N-body simulations, coupled to a thermally evolving viscous 1D disc model, and including prescriptions for planet migration, photoevaporation, and pebble and planetesimal dynamics. We mainly examine the differences between the pebble and planetesimal accretion scenarios, but we also look at the influences of disc mass, size of planetesimals, and the percentage of solids locked up within pebbles. When comparing the resulting planetary systems to Trappist-1, we find that a wide range of initial conditions for both the pebble and planetesimal accretion scenarios can form planetary systems similar to Trappist-1, in terms of planet mass, periods, and resonant configurations. Typically these planets formed exterior to the water iceline and migrated in resonant convoys into the inner region close to the central star. When comparing the planetary systems formed through pebble accretion to those formed through planetesimal accretion, we find a large number of similarities, including average planet masses, eccentricities, inclinations, and period ratios. One major difference between the two scenarios was that of the water content of the planets. When including the effects of ablation and full recycling of the planets’ envelope with the disc, the planets formed through pebble accretion were extremely dry, whilst those formed through planetesimal accretion were extremely wet. If the water content is not fully recycled and instead falls to the planets’ core, or if ablation of the water is neglected, then the planets formed through pebble accretion are extremely wet, similar to those formed through planetesimal accretion. Should the water content of the Trappist-1 planets be determined accurately, this could point to a preferred formation pathway for planetary systems, or to specific physics that may be at play.
Context. This is the fourth paper in a series showing the results of planet population synthesis calculations. In Paper I, we presented our methods. In Paper II, we compared the synthetic and the ...observed planetary population statistically. Paper III addressed the influences of the stellar mass on the population.Aims. Our goal in this fourth paper is to systematically study the effects of important disk properties, namely disk metallicity, mass, and lifetime on fundamental properties of planets like mass and semimajor axis.Methods. For a large number of protoplanetary disks that have properties following distributions derived from observations, we calculated a population of planets with our formation model. The model is based on the classical core accretion paradigm but self-consistently includes planet migration and disk evolution.Results. We find a very large number of correlations. Regarding the planetary initial mass function, metallicity, Mdisk, and τdisk play different roles. For high metallicities, giant planets are more frequent. For high Mdisk, giant planets are more massive. For long τdisk, giant planets are both more frequent and massive. At low metallicities, very massive giant planets cannot form, but otherwise giant planet mass and metallicity are nearly uncorrelated. In contrast, (maximum) planet masses and disk gas masses are correlated. The formation of giant planets is possible for initial planetesimal surface densities ΣS of at least 6 g/cm2 at 5.2 AU. The best spot for giant planet formation is at ~5 AU. In- and outside this distance, higher ΣS are necessary. Low metallicities can be compensated for by high Mdisk, and vice versa, but not ad infinitum. At low metallicities, giant planets only form outside the ice line, while giant planet formation occurs throughout the disk at high metallicities. The extent of migration increases with Mdisk and τdisk and usually decreases with metallicity. No clear correlation of metallicity and the semimajor axis distribution of giant planets exists because in low-metallicity disks, planets start farther out, but migrate more, while the contrary applies to high metallicities. The final semimajor axis distribution contains an imprint of the ice line. Close-in low mass planets have a lower mean metallicity than hot Jupiters. The frequency of giant planets varies approximately as Mdisk1.2 and τdisk2.Conclusions. The properties of protoplanetary disks – the initial and boundary conditions for planet formation – are decisive for the properties of planets, and leave many imprints on the population.
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