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 origin of the particular shape of comet 67P/Churyumov-Gerasimenko (67P) is a topic of active research. How and when it acquired its peculiar characteristics has distinct implications on ...the origin of the solar system and its dynamics. Aims. We investigate how shapes such as that of comet 67P can result from a new type of low-energy, sub-catastrophic impact involving elongated, rotating bodies. We focus on parameters potentially leading to bi-lobed structures. We also estimate the probability of such structures surviving subsequent impacts. Methods. We used a smooth particle hydrodynamics (SPH) shock physics code to model the impacts, the subsequent re-accumulation of material and the reconfiguration into a stable final shape. The energy increase as well as the degree of compaction of the resulting bodies were tracked in the simulations. Results. Our modelling results suggest that the formation of bi-lobed structures like 67P is a natural outcome of the low-energy, sub-catastrophic collisions considered here. Conclusions. Sub-catastrophic impacts have the potential to alter the shape of a small body significantly, without leading to major heating or compaction. The currently observed shapes of cometary nuclei, such as 67P, may be a result of such a major shape forming impact.
Context. The recent detection of planets around very low mass stars raises the question of the formation, composition, and potential habitability of these objects. Aims. We use planetary system ...formation models to infer the properties, in particular their radius distribution and water content, of planets that may form around stars ten times less massive than the Sun. Methods. Our planetary system formation and composition models take into account the structure and evolution of the protoplanetary disk, the planetary mass growth by accretion of solids and gas, as well as planet-planet, planet-star, and planet-disk interactions. Results. We show that planets can form at small orbital period in orbit about low-mass stars. We show that the radius of the planets is peaked at about 1 R⊕ and that they are, in general, volatile rich especially if proto-planetary disks orbiting this type of stars are long lived. Conclusions. Close-in planets orbiting low-mass stars similar in terms of mass and radius to those recently detected can be formed within the framework of the core-accretion paradigm as modeled here. The properties of protoplanetary disks, and their correlation with the stellar type, are key to understand their composition.
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.
Context. One of the main scenarios of planet formation is the core accretion model where a massive core forms first and then accretes a gaseous envelope. This core forms by accreting solids, either ...planetesimals or pebbles. A key constraint in this model is that the accretion of gas must proceed before the dissipation of the gas disc. Classical planetesimal accretion scenarios predict that the time needed to form a giant planet’s core is much longer than the time needed to dissipate the disc. This difficulty led to the development of another accretion scenario, in which cores grow by accretion of pebbles, which are much smaller and thus more easily accreted, leading to more rapid formation. Aims. The aim of this paper is to compare our updated pebble-based planet formation model with observations, in particular the well-studied metallicity effect. Methods. We adopt the Bitsch et al. (2015a, A&A, 575, A28) disc model and the Bitsch et al. (2015b, A&A, 582, A112) pebble model and use a population synthesis approach to compare the formed planets with observations. Results. We find that keeping the same parameters as in Bitsch et al. (2015b, A&A, 582, A112) leads to no planet growth due to a computation mistake in the pebble flux (2018b). Indeed a large fraction of the heavy elements should be put into pebbles (Zpeb∕Ztot = 0.9) in order to form massive planets using this approach. The resulting mass functions show a huge amount of giants and a lack of Neptune-mass planets, which are abundant according to observations. To overcome this issue we include the computation of the internal structure for the planetary atmosphere in our model. This leads to the formation of Neptune-mass planets but no observable giants. Furthermore, reducing the opacity of the planetary envelope more closely matches observations. Conclusions. We conclude that modelling the internal structure for the planetary atmosphere is necessary to reproduce observations.
Context. This is the second paper in a series of papers showing the results of extrasolar planet population synthesis calculations using our extended core accretion model. In the companion paper ...(Paper I), we presented in detail the methods we use. In subsequent papers, we shall discuss the effect of the host star's mass on the planetary population and the influence of various properties of protoplanetary disks.Aims. In this second paper, we focus on planets orbiting solar-like stars. The goal is to use the main characteristics of the actually observed extrasolar planet population to derive in a statistical manner constraints on the planet formation models.Methods. Drawing initial conditions for our models at random from probability distributions derived as closely as possible from observations, we synthesize a number of planetary populations. By applying an observational detection bias appropriate for radial velocity surveys, we identify the potentially detectable synthetic planets. The properties of these planets are compared in quantitative statistical tests with the properties of a carefully selected sub-population of actually observed extrasolar planets.Results. We use a two dimensional Kolmogorov-Smirnov test to compare the mass-distance distributions of synthetic and observed planets, as well as the one dimensional version of the test to compare the $M \sin i$, the semimajor axis and the Fe/H distribution. We find that while many combinations of parameters lead to unacceptable distributions, a number of models can account to a reasonable degree of statistical significance for most of the properties of the observed sample. We concurrently account for many other observed features, e.g. the ``metallicity effect''. This gives us confidence that our model captures several essential features of giant planet formation. In addition, the fact that many parameter combinations could be rejected indicates that planet population synthesis is indeed a promising approach to constrain formation models. Our simulations allow us also to extract a number of properties of the underlying exoplanet population that are not yet directly detectable. For example, we have derived the planetary initial mass function (PIMF) and have been led to conclude that the planets detected so far represent only the tip of the iceberg (9%) of all the existing planets. The PIMF can also be used to predict how the detectable extrasolar planet population will change as the instrumental precision of radial velocity surveys improves from $\sim $10 m/s to $\sim $1 m/s, or even to an extreme precision of 0.1 m/s.
Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have ...partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods. We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results. We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.
Context. One of the most challenging steps in planet formation theory is the one leading to the formation of planetesimals of kilometre size. A promising scenario involves the existence of vortices ...able to concentrate a large amount of dust and grains in their centres. Up to now this scenario has mostly been studied in 2D razor thin disks. A 3D study including, simultaneously, the formation and resulting dust concentration of the vortices with vertical settling, is still missing. Aims. The Rossby wave instability self-consistently forms 3D vortices, which have the unique quality of presenting a large-scale vertical velocity in their centre. Here we aim to study how this newly discovered effect can alter the dynamic evolution of the dust. Methods. We performed global 3D simulations of the RWI in a radially and vertically stratified disk using the code MPI-AMRVAC. After the growth phase of the instability, the gas and solid phases are modelled by a bi-fluid approach, where the dust is considered as a fluid without pressure. Both the drag force of the gas on the dust and the back reaction of the dust on the gas are included. Multiple grain sizes from 1 mm to 5 cm are used with a constant density distribution. Results. We obtain in a short timescale a high concentration of the largest grains in the vortices. Indeed, in 3 rotations the dust-to-gas density ratio grows from 10-2 to unity leading to a concentration of mass up to that of Mars in one vortex. The presence of the radial drift is also at the origin of a dust pile-up at the radius of the vortices. Lastly, the vertical velocity of the gas in the vortex causes the sedimentation process to be reversed, the mm size dust is lifted and higher concentrations are obtained in the upper layer than in the midplane. Conclusions. The Rossby wave instability is a promising mechanism for planetesimal formation, and the results presented here can be of particular interest in the context of future observations of protoplanetary disks.
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