Solid Surface Density Research Articles

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 < 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 < 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 > 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.

Inner edges of planetesimal belts: collisionally eroded or truncated?

ABSTRACT The radial structure of debris discs can encode important information about their dynamical and collisional history. In this paper, we present a three-phase analytical model to analyse the collisional evolution of solids in debris discs, focusing on their joint radial and temporal dependence. Consistent with previous models, we find that as the largest planetesimals reach collisional equilibrium in the inner regions, the surface density of dust and solids becomes proportional to ∼r2 within a certain critical radius. We present simple equations to estimate the critical radius and surface density of dust as a function of the maximum planetesimal size and initial surface density in solids (and vice versa). We apply this model to Atacama Large Millimeter/submillimeter Array observations of seven wide debris discs. We use both parametric and non-parametric modelling to test if their inner edges are shallow and consistent with collisional evolution. We find that four out of seven have inner edges consistent with collisional evolution. Three of these would require small maximum planetesimal sizes below 10 km, with HR 8799’s disc potentially lacking solids larger than a few centimetres. The remaining systems have inner edges that are much sharper, which requires maximum planetesimal sizes ≳ 10 km. Their sharp inner edges suggest they could have been truncated by planets, which JWST could detect. In the context of our model, we find that the seven discs require surface densities below a Minimum Mass Solar Nebula, avoiding the so-called disc mass problem. Finally, during the modelling of HD 107146 we discover that its wide gap is split into two narrower ones, which could be due to two low-mass planets formed within the disc.

Solid Accretion onto Neptune-mass Planets. I. In Situ Accretion and Constraints from the Metallicity of Uranus and Neptune

The currently available, detailed properties (e.g., isotopic ratios) of solar system planets may provide guides for constructing better approaches to exoplanet characterization. With this motivation, we explore how the measured values of the deuterium-to-hydrogen (D/H) ratio of Uranus and Neptune can constrain their formation mechanisms. Under the assumption of in situ formation, we investigate three solid accretion modes: a dominant accretion mode switches from pebble accretion to drag-enhanced three-body accretion and to canonical planetesimal accretion, as the solid radius increases. We consider a wide radius range of solids that are accreted onto (proto)Neptune-mass planets and compute the resulting accretion rate as a function of both the solid size and the solid surface density. We find that for small-sized solids, the rate becomes high enough to halt concurrent gas accretion if all the solids have the same size. For large-sized solids, the solid surface density needs to be enhanced to accrete enough amounts of solids within the gas disk lifetime. We apply these accretion modes to the formation of Uranus and Neptune and show that if the minimum-mass solar nebula model is adopted, solids with a radius of ∼1 m to ∼10 km should have contributed mainly to their deuterium enrichment; a tighter constraint can be derived if the full solid size distribution is determined. This work therefore demonstrates that the D/H ratio can be used as a tracer of solid accretion onto Neptune-mass planets. Similar efforts can be made for other atomic elements that serve as metallicity indicators.

Generalized Peas in a Pod: Extending Intra-system Mass Uniformity to Non-TTV Systems via the Gini Index

It has been demonstrated that planets belonging to the same close-in, compact multiple-planet system tend to exhibit a striking degree of uniformity in their sizes. A similar trend has also been found to hold for the masses of such planets, but considerations of such intra-system mass uniformity have generally been limited to statistical samples wherein a majority of systems have constituent planetary mass measurements obtained via analysis of transit timing variations (TTVs). Since systems with strong TTV signals typically lie in or near mean motion resonance, it remains to be seen whether intra-system mass uniformity is still readily emergent for nonresonant systems with non-TTV mass provenance. We thus present in this work a mass uniformity analysis of 17 non-TTV systems with masses measured via radial velocity measurements. Using the Gini index, a common statistic for economic inequality, as our primary metric for uniformity, we find that our sample of 17 non-TTV systems displays intra-system mass uniformity at a level of ∼2.5σ confidence. We provide additional discussion of possible statistical and astrophysical underpinnings for this result. We also demonstrate the existence of a correlation (r = 0.25) between characteristic solid surface density (Σ0) of the minimum-mass extrasolar nebula and system mass Gini index, suggesting that more-massive disks may generally form systems with more-unequal planetary masses.

Rapid formation of super-Earths around low-mass stars

ABSTRACT NASA’s TESS mission is expected to discover hundreds of M dwarf planets. However, few studies focus on how planets form around low-mass stars. We aim to better characterize the formation process of M dwarf planets to fill this gap and aid in the interpretation of TESS results. We use ten sets of N-body planet formation simulations that vary in whether a gas disc is present, initial range of embryo semimajor axes, and initial solid surface density profile. Each simulation begins with 147 equal-mass embryos around a 0.2 solar mass star and runs for 100 Myr. We find that planets form rapidly, with most collisions occurring within the first 1 Myr. The presence of a gas disc reduces the final number of planets relative to a gas-free environment and causes planets to migrate inward. We find that roughly a quarter of planetary systems experience their final giant impact inside the gas disc, suggesting that some super-Earths may be able to reaccrete an extended gaseous envelope after their final giant impact, though these may be affected by additional processes such as photoevaporation. In addition, we find that the final distribution of planets does not retain a memory of the slope of the initial surface density profile, regardless of whether or not a gas disc is present. Thus, our results suggest that present-day observations are unlikely to provide sufficient information to accurately reverse-engineer the initial distribution of solids.

Antifungal Polyvinyl Alcohol Coatings Incorporating Carvacrol for the Postharvest Preservation of Golden Delicious Apple

Different polyvinyl alcohol (PVA) coating formulations incorporating starch (S) and carvacrol (C) as the active agent were applied to Golden Delicious apples to evaluate their effectiveness at controlling weight loss, respiration rate, fruit firmness, and fungal decay against B. cinerea and P. expansum throughout storage time. Moreover, the impact of these coatings on the sensory attributes of the fruit was also analyzed. The application of the coatings did not notably affect the weight loss, firmness changes, or respiration pathway of apples, probably due to the low solid surface density of the coatings. Nevertheless, they exhibited a highly efficient disease control against both black and green mold growths, as a function of the carvacrol content and distribution in the films. The sensory analysis revealed the great persistence of the carvacrol aroma and flavor in the coated samples, which negatively impact the acceptability of the coated products.

California-Kepler Survey. IX. Revisiting the Minimum-mass Extrasolar Nebula with Precise Stellar Parameters

Abstract We investigate a possible correlation between the solid surface density Σ of the minimum-mass extrasolar nebula (MMEN) and the host star mass M ⋆ and metallicity [Fe/H]. Leveraging on the precise host star properties from the California-Kepler Survey (CKS), we found that (a/1 au)−1.75±0.07 (M ⋆/M ⊙)1.04±0.22 100.22±0.05[Fe/H] for Kepler-like systems (1–4R ⊕; a < 1 au). The strong M ⋆ dependence is reminiscent of previous dust continuum results that the solid disk mass scales with M ⋆. The weaker [Fe/H] dependence shows that sub-Neptune planets, unlike giant planets, form readily in lower metallicity environment. The innermost region (a < 0.1 au) of an MMEN maintains a smooth profile despite a steep decline of planet occurrence rate: a result that favors the truncation of disks by corotating magnetospheres with a range of rotation periods, rather than the sublimation of dust. The Σ of Kepler multitransiting systems shows a much stronger correlation with M ⋆ and [Fe/H] than singles. This suggests that the dynamically hot evolution that produced single systems also partially removed the memory of formation in disks. Radial-velocity planets yielded a MMEN very similar to CKS planets; transit-timing-variation planets’ postulated convergent migration history is supported by their poorly constrained MMEN. We found that lower mass stars have a higher efficiency of forming/retaining planets: for Sun-like stars, about 20% of the solid mass within ∼1 au are converted/preserved as sub-Neptunes, compared to 70% for late-K to early-M stars. This may be due to the lower binary fraction, lower giant-planet occurrence, or the longer disk lifetime of lower mass stars.

Capture of solids by growing proto-gas giants: effects of gap formation and supply limited growth

Studies of internal structure of gas giant planets suggest that their envelopes are enriched with heavier elements than hydrogen and helium relative to their central stars. Such enrichment likely occurred by solid accretion during late formation stages of gas giant planets in which gas accretion dominates protoplanetary growth. Some previous studies performed orbital integration of planetesimals around a growing protoplanet with the assumption of an uniform circumstellar disc to investigate how efficiently the protoplanet captures planetesimals. However, not only planetesimals but also disc gas are gravitationally perturbed by the protoplanet in its late formation stages, resulting in gap opening in the circumstellar disc. In this study, we investigate the effects of such gap formation on the capture of planetesimals by performing dynamical simulations of planetesimals around a growing proto-gas giant planet. Gap formation reduces the surface density of disc gas, makes a steep pressure gradient and limits the growth rate of the protoplanet. We find that the first effect enhances the capture of planetesimals, while the others reduce it. Consequently the amount of planetesimals captured during the gas accretion is estimated to be at most ~3 Mearth. We conclude that the in-situ capture of planetesimals needs the initial solid surface density more than five times higher than that of the minimum mass solar nebula for explaining the inferred large amount of heavy element in Jupiter. For highly dense warm Jupiters, we would need additional processes enhancing the capture and/or supply of planetesimals.

On the use of carrageenan matrices for the development of antiviral edible coatings of interest in berries

Different film-forming dispersions (FFD) based on κ−, ι− and λ− carrageenans and green tea extract (GTE) have been developed as an innovative strategy to guarantee the food safety of blueberries and raspberries. First, the FFD were characterized (surface tension and viscosity) and the physicochemical properties (water vapour permeability-WVP-, water sorption, contact angle, mechanical properties) of the stand-alone films were evaluated. Then, the FFD were applied to refrigerated-stored raspberries and blueberries, and the antiviral activity against murine norovirus (MNV), a cultivable norovirus surrogate, and hepatitis A virus (HAV) of coated fruits was determined at refrigerated (10 °C) and ambient conditions (25 °C). The type of carrageenan used significantly affected the WVP and the mechanical properties of the stand-alone films, being k-carrageenan films more rigid and less permeable. The incorporation of GTE resulted in less ductile and deformable films and slightly more permeable than their counterparts prepared without the extract. All the coatings were effective in extending the shelf life of raspberries and blueberries under refrigeration, preserving their firmness to a greater extent and promoting better appearance. In general, FFD with similar viscosity (κ− and λ− carrageenans) showed higher antiviral activity as the gelling capacity of the carrageenan increased (κ− carrageenan) because of the formation of a more cohesive polymer matrix and the higher solid surface density (SSD) deposited onto the berry surfaces. Adding GTE enhanced the carrageenan antiviral activity at both refrigerated and ambient temperatures in blueberries and raspberries, being slightly more effective in the case of MNV.

New Formation Models for the Kepler-36 System

Abstract Formation of the planets in the Kepler-36 system is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. The standard model is updated to include the dissolution of accreting rocky planetesimals in the gaseous envelope of the planet, leading to substantial enrichment of the envelope mass in heavy elements and a non-uniform composition with depth. For Kepler-36 c, models involving in situ formation and models involving orbital migration are considered. The results are compared with standard formation models. The calculations include the formation (accretion) phase as well as the subsequent cooling phase, up to the age of Kepler-36 (7 Gyr). During the latter phase, mass loss induced by stellar XUV radiation is included. In all cases, the results fit the measured mass, 7.84 M ⊕, and radius, 3.68 R ⊕, of Kepler-36 c. Two parameters are varied to obtain these fits: the disk solid surface density at the formation location and the “efficiency” factor in the XUV mass-loss rate. The updated models are hotter and therefore less dense in the silicate portion of the planet and in the overlying layers of H/He, as compared with standard models. The lower densities mean that only about half as much H/He is needed to be accreted to fit the present-day mass and radius constraints. For Kepler-36 b, an updated in situ calculation shows that the entire H/He envelope is lost, early in the cooling phase, in agreement with observation.

A balanced budget view on forming giant planets by pebble accretion

Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose Stokes numbers approach unity. While fast, pebble accretion is also lossy. Gas drag brings pebbles to protocores but also sweeps them past; those particles with the largest accretion cross-sections also have the fastest radial drift speeds and are the most easily drained out of discs. We present a global model of planet formation by pebble accretion that keeps track of the disc's mass budget. Cores, each initialized with a lunar mass, grow from discs whose finite stores of mm-cm sized pebbles drift inward across all radii in viscously accreting gas. For every 1 $M_\oplus$ netted by a core, at least 10 $M_\oplus$ and possibly much more are lost to radial drift. Core growth rates are typically exponentially sensitive to particle Stokes number, turbulent Mach number, and solid surface density. This exponential sensitivity, when combined with disc migration, tends to generate binary outcomes from 0.1-30 AU: either sub-Earth cores remain sub-Earth, or explode into Jupiters, with the latter migrating inward to varying degrees. When Jupiter-breeding cores assemble from mm-cm sized pebbles, they do so in discs where such particles drain out in $\sim$10$^5$ yr or less; such fast-draining discs do not fit mm-wave observations.

From Planetesimal to Planet in Turbulent Disks. II. Formation of Gas Giant Planets

Abstract In the core accretion scenario, gas giant planets are formed form solid cores with several Earth masses via gas accretion. We investigate the formation of such cores via collisional growth from kilometer-sized planetesimals in turbulent disks. The stirring by forming cores induces collisional fragmentation, and surrounding planetesimals are ground down until radial drift. The core growth is therefore stalled by the depletion of surrounding planetesimals due to collisional fragmentation and radial drift. The collisional strength of planetesimals determines the planetesimal-depletion timescale, which is prolonged for large planetesimals. The size of planetesimals around growing cores is determined by the planetesimal size distribution at the onset of runaway growth. Strong turbulence delays the onset of runaway growth, resulting in large planetesimals. Therefore, the core mass evolution depends on the turbulent parameter α; the formation of cores massive enough without significant depletion of surrounding planetesimals needs a strong turbulence of α ≳ 10−3. However, strong turbulence with α ≳ 10−3 leads to a significant delay of the onset of runaway growth and prevents the formation of massive cores within the disk lifetime. The formation of cores massive enough within several million years therefore requires that solid surface densities are several times higher, which is achieved in the inner disk ≲10 au due to pile-up of drifting dust aggregates. In addition, the collisional strength even for kilometer-sized or smaller bodies affects the growth of cores; for bodies ≲1 km is likely for this gas giant formation.

The Fuzziness of Giant Planets’ Cores

Abstract Giant planets are thought to have cores in their deep interiors, and the division into a heavy-element core and hydrogen–helium envelope is applied in both formation and structure models. We show that the primordial internal structure depends on the planetary growth rate, in particular, the ratio of heavy elements accretion to gas accretion. For a wide range of likely conditions, this ratio is in one-to-one correspondence with the resulting post-accretion profile of heavy elements within the planet. This flux ratio depends sensitively on the assumed solid-surface density in the surrounding nebula. We suggest that giant planets’ cores might not be distinct from the envelope and includes some hydrogen and helium, and the deep interior can have a gradual heavy-element structure. Accordingly, Jupiter’s core may not be well defined. Accurate measurements of Jupiter’s gravitational field by Juno could put constraints on Jupiter’s core mass. However, as we suggest here, the definition of Jupiter’s core is complex, and the core’s physical properties (mass, density) depend on the actual definition of the core and on the planet’s growth history.

The abundance and thermal history of water ice in the disk surrounding HD 142527 from the DIGITHerschelKey Program

The presence or absence of ice in protoplanetary disks is of great importance for the formation of planets. By enhancing the solid surface density and increasing the sticking efficiency, ice catalyzes the rapid formation of planetesimals and decreases the time scale for giant planet core accretion. Aims: In this paper we analyse the composition of the outer disk around the Herbig star HD~142527. We focus on the composition of the water ice, but also analyse the abundances of previously proposed minerals. Methods: We present new Herschel far infrared spectra and a re-reduction of archival data from the Infrared Space Observatory (ISO). We model the disk using full 3D radiative transfer to obtain the disk structure. Also, we use an optically thin analysis of the outer disk spectrum to obtain firm constraints on the composition of the dust component. Results: The water ice in the disk around HD~142527 contains a large reservoir of crystalline water ice. We determine the local abundance of water ice in the outer disk (i.e. beyond 130\,AU). The re-reduced ISO spectrum differs significantly from that previously published, but matches the new Herschel spectrum at their common wavelength range. In particular, we do not detect any significant contribution from carbonates or hydrous silicates, in contrast to earlier claims. Conclusions: The amount of water ice detected in the outer disk requires $\sim80\,$\% of the oxygen atoms. This is comparable to the water ice abundance in the outer solar system, in comets and in dense interstellar clouds. The water ice is highly crystalline while the temperatures where we detect it are too low to crystallize the water on relevant time scales. We discuss the implications of this finding.

IN SITU AND EX SITU FORMATION MODELS OF KEPLER 11 PLANETS

ABSTRACT We present formation simulations of the six Kepler 11 planets. Models assume either in situ or ex situ assembly, the latter with migration, and are evolved to the estimated age of the system, . Models combine detailed calculations of both the gaseous envelope and the condensed core structures, including accretion of gas and solids, of the disk’s viscous and thermal evolution, including photo-evaporation and disk-planet interactions, and of the planet’s evaporative mass loss after disk dispersal. Planet–planet interactions are neglected. Both sets of simulations successfully reproduce measured radii, masses, and orbital distances of the planets, except for the radius of Kepler 11b, which loses its entire gaseous envelope shortly after formation. Gaseous (H+He) envelopes account for % of the planet masses, and between and % of the planet radii. In situ models predict a very massive inner disk, whose solid surface density ( ) varies from over 104 to at stellocentric distances . Initial gas densities would be in excess of if solids formed locally. Given the high disk temperatures ( ), planetary interiors can only be composed of metals and highly refractory materials. Sequestration of hydrogen by the core and subsequent outgassing is required to account for the observed radius of Kepler 11b. Ex situ models predict a relatively low-mass disk, whose initial varies from to at and whose initial gas density ranges from to . All planetary interiors are expected to be rich in H2O, as core assembly mostly occurs exterior to the ice condensation front. Kepler 11b is expected to have a steam atmosphere, and H2O is likely mixed with H+He in the envelopes of the other planets. Results indicate that Kepler 11g may not be more massive than Kepler 11e.

Onset of oligarchic growth and implication for accretion histories of dwarf planets

We investigate planetary accretion that starts from equal-mass planetesimals using an analytic theory and numerical simulations. We particularly focus on how the planetary mass Moli at the onset of oligarchic growth depends on the initial mass m0 of a planetesimal. Oligarchic growth commences when the velocity dispersion relative to the Hill velocity of the protoplanet takes its minimum. We find that if m0 is small enough, this normalized velocity dispersion becomes as low as unity during the intermediate stage between the runaway and oligarchic growth stages. In this case, Moli is independent of m0. If m0 is large, on the other hand, oligarchic growth commences directly after runaway growth, and Moli∝m03/7. The planetary mass Moli for the solid surface density of the Minimum Mass Solar Nebula is close to the masses of the dwarf planets in a reasonable range of m0. This indicates that they are likely to be the largest remnant planetesimals that failed to become planets. The power-law exponent q of the differential mass distribution of remnant planetesimals is typically −2.0 and −2.7 to −2.5 for small and large m0. The slope, q≃−2.7, and the bump at 1021 g (or 50 km in radius) for the mass distribution of hot Kuiper belt objects are reproduced if m0 is the bump mass. On the other hand, small initial planetesimals with m0 ∼ 1013 g or less are favored to explain the slope of large asteroids, q≃−2.0, while the bump at 1021 g can be reproduced by introducing a small number of asteroid seeds each with mass of 1019 g.

CORRELATIONS BETWEEN COMPOSITIONS AND ORBITS ESTABLISHED BY THE GIANT IMPACT ERA OF PLANET FORMATION

ABSTRACT The giant impact phase of terrestrial planet formation establishes connections between super-Earths’ orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by residual disk gas plays a critical role in regulating mergers and in damping inclinations and eccentricities. Systems with moderate gas damping and high solid surface density spawn gas-enveloped super-Earths with tight spacings, small eccentricities, and small inclinations. Systems in which super-Earths coagulate without as much ambient gas, in disks with low solid surface density, produce rocky planets with wider spacings, larger eccentricities, and larger mutual inclinations. A combination of both populations can reproduce the observed distributions of spacings, period ratios, transiting planet multiplicities, and transit duration ratios exhibited by Kepler super-Earths. The two populations, both formed in situ, also help to explain observed trends of eccentricity versus planet size, and bulk density versus method of mass measurement (radial velocities versus transit timing variations). Simplifications made in this study—including the limited time span of the simulations, and the approximate treatments of gas dynamical friction and gas depletion history—should be improved on in future work to enable a detailed quantitative comparison to the observations.

A metallicity recipe for rocky planets

Planets with sizes between those of Earth and Neptune divide into two populations: purely rocky bodies whose atmospheres contribute negligibly to their sizes, and larger gas-enveloped planets possessing voluminous and optically thick atmospheres. We show that whether a planet forms rocky or gas-enveloped depends on the solid surface density of its parent disk. Assembly times for rocky cores are sensitive to disk solid surface density. Lower surface densities spawn smaller planetary embryos; to assemble a core of given mass, smaller embryos require more mergers between bodies farther apart and therefore exponentially longer formation times. Gas accretion simulations yield a rule of thumb that a rocky core must be at least 2$M_\oplus$ before it can acquire a volumetrically significant atmosphere from its parent nebula. In disks of low solid surface density, cores of such mass appear only after the gas disk has dissipated, and so remain purely rocky. Higher surface density disks breed massive cores more quickly, within the gas disk lifetime, and so produce gas-enveloped planets. We test model predictions against observations, using planet radius as an observational proxy for gas-to-rock content and host star metallicity as a proxy for disk solid surface density. Theory can explain the observation that metal-rich stars host predominantly gas-enveloped planets.

The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores

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.

Time evolution of snow regions and planet traps in an evolving protoplanetary disk

Aims. We track the time evolution of planet traps and snowlines in a viscously evolving protoplanetary disk using an opacity table that accounts for the composition of the dust material. Methods. We coupled a dynamical and thermodynamical disk model with a temperature-dependent opacity table (that accounts for the sublimation of the main dust components) to investigate the formation and evolution of snowlines and planet traps during the first million years of disk evolution. Results. Starting from a minimum mass solar nebula (MMSN), we find that the disk mid-plane temperature profile shows several plateaux (0.1-1 AU wide) at the different sublimation temperatures of the species that make up the dust. For water ice, the correspond- ing plateau can be larger than 1 AU, which means that this is a snow "region" rather than a snow "line". As a consequence, the surface density of solids in the snow region may increase gradually, not abruptly. Several planet traps and desert regions appear naturally as a result of abrupt local changes in the temperature and density profiles over the disk lifetime. These structures are mostly located at the edges of the temperature plateaux (surrounding the dust sublimation lines) and at the heat-transition barrier where the disk stellar heating and viscous heating are of the same magnitude (around 10 AU after 1 Myr). Conclusions. Several traps are identified: although a few appear to be transient, most of them slowly migrate along with the heat- transition barrier or the dust sublimation lines. These planet traps may temporarily favor the growth of planetary cores.