Pebble Accretion Research Articles

Evolution of gas envelopes and outgassed atmospheres of rocky planets that formed via pebble accretion

In this work, we present results of numerical simulations of the formation and early evolution of rocky planets through pebble accretion, with an emphasis on hydrogen envelope longevity and the composition of the outgassed atmosphere. We modelled planets with a range in mass from 0.1 to 5 Earth masses that orbit between 0.7 and 1.7 AU. The composition of the outgassed atmosphere was calculated with the partial pressure of free oxygen fit to geophysical models of magma ocean self-oxidation. The combined X-ray and UV (XUV) radiation-powered photoevaporation is considered as the main driver of atmospheric escape. We modelled planets that remain below the pebble isolation mass and hence accrete tenuous envelopes only. We considered slow, medium, or fast initial stellar rotation for the temporal evolution of the XUV flux. The loss of the envelope is a key event that allows the magma ocean to crystallise and outgas its bulk volatiles. The atmospheric composition of the majority of our simulated planets is dominated by CO$_2$. Our planets accrete a total of 11.6 Earth oceans of water, the majority of which enters the core. The hydrospheres of planets lighter than the Earth reach several times the mass of the Earth's modern oceans, while the hydrospheres of planets ranging from 1 to 3.5 Earth masses are comparable to those of our planet. However, planets of 4-5 Earth masses have smaller hydrospheres due to the trapping of volatiles in their massive mantles. Overall, our simulations demonstrate that hydrogen envelopes are easily lost from rocky planets and that this envelope loss triggers the most primordial partitioning of volatiles between the solid mantle and the atmosphere.

Origin of transition disk cavities: Pebble-accreting protoplanets vs super-Jupiters

Protoplanetary disks surrounding young stars are the birth places of planets. Among them, transition disks with inner dust cavities of tens of au are sometimes suggested to host massive companions. Yet, such companions are often not detected. Some transition disks exhibit a large amount of gas inside the dust cavity and relatively high stellar accretion rates, which contradicts typical models of gas-giant-hosting systems. Therefore, we investigate whether a sequence of low-mass planets can create the appearance of cavities in the dust disk. We evolve the disks with low-mass growing embryos in combination with 1D dust transport and 3D pebble accretion, to investigate the reduction of the pebble flux at the embryos' orbits. We vary the planet and disk properties to understand the resulting dust profile. We find that multiple pebble-accreting planets can efficiently decrease the dust surface density, resulting in dust cavities consistent with transition disks. The number of low-mass planets necessary to sweep up all pebbles decreases with decreasing turbulent strength and is preferred when the dust Stokes number is $10^ $. Compared to dust rings caused by pressure bumps, those by efficient pebble accretion exhibit more extended outer edges. We also highlight the observational reflections: the transition disks with rings featuring extended outer edges tend to have a large gas content in the dust cavities and rather high stellar accretion rates. We propose that planet-hosting transition disks consist of two groups. In Group A disks, planets have evolved into gas giants, opening deep gaps in the gas disk. Pebbles concentrate in pressure maxima, forming dust rings. In Group B, multiple Neptunes (unable to open deep gas gaps) accrete incoming pebbles, causing the appearance of inner dust cavities and distinct ring-like structures near planet orbits. The morphological discrepancy of these rings may aid in distinguishing between the two groups using high-resolution ALMA observations.

Dust Growth and Evolution in Protoplanetary Disks

Over the past decade, advancement of observational capabilities, specifically the Atacama Large Millimeter/submillimeter Array (ALMA) and Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instruments, alongside theoretical innovations like pebble accretion, have reshaped our understanding of planet formation and the physics of protoplanetary disks. Despite this progress, mysteries persist along the winded path of micrometer-sized dust, from the interstellar medium, through transport and growth in the protoplanetary disk, to becoming gravitationally bound bodies. This review outlines our current knowledge of dust evolution in circumstellar disks, yielding the following insights: ▪Theoretical and laboratory studies have accurately predicted the growth of dust particles to sizes that are susceptible to accumulation through transport processes like radial drift and settling.▪Critical uncertainties in that process remain the level of turbulence, the threshold collision velocities at which dust growth stalls, and the evolution of dust porosity.▪Symmetric and asymmetric substructures are widespread. Dust traps appear to be solving several long-standing issues in planet formation models, and they are observationally consistent with being sites of active planetesimal formation.▪In some instances, planets have been identified as the causes behind substructures. This underlines the need to study earlier stages of disks to understand how planets can form so rapidly. In the future, better probes of the physical conditions in optically thick regions, including densities, turbulence strength, kinematics, and particle properties, will be essential for unraveling the physical processes at play.

Suppression of giant planet formation around low-mass stars in clustered environments

Context. Current exoplanet formation studies tend to overlook the birth environment of stars in clustered environments. However, the effects of this environment on the planet formation process are important, especially in the earliest stage. Aims. We investigate the differences in planet populations forming in star-cluster environments through pebble accretion and compare these results with planet formation around isolated stars. We strive to provide potential signatures of the young planetary systems to guide future observations. Methods. We present a new planet population synthesis code designed for clustered environments. This planet formation model is based on pebble accretion and includes migration in the circumstellar disk. The disk’s gas and dust have been evolved via 1D simulations, while considering the effects of photo-evaporation of the nearby stars. Results. Planetary systems in a clustered environment are different than those born in isolation; the environmental effects are important for a wide range of observable parameters and the eventual architecture of the planetary systems. Planetary systems born in a clustered environment lack cold Jupiters, as compared to isolated planetary systems. This effect is more pronounced for low-mass stars (≲0.2 M⊙). On the other hand, planetary systems born in clusters show an excess of cold Neptune around these low-mass stars. Conclusions. In future observations, finding an excess of cold Neptunes and a lack of cold Jupiters could be used to constrain the birth environments of these planetary systems. Exploring the dependence of cold Jupiter’s intrinsic occurrence rate on stellar mass offers insights into the birth environment of their proto-embryos.

Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion

Pebbles drifting past a disk-embedded low-mass planet develop asymmetries in their distribution and exert a substantial gravitational torque on the planet, thus modifying its migration rate. Our aim is to assess how the distribution of pebbles and the resulting torque change in the presence of pebble accretion, focusing on its 2D regime. First, we performed 2D high-resolution multi-fluid simulations with Fargo3D but found that they are impractical for resolving pebble accretion due to the smoothing of the planetary gravitational potential. To remove the smoothing and directly trace pebbles accreted by the planet, we developed a new code Deneb which evolves an ensemble of pebbles, represented by Lagrangian superparticles, in a steady-state gaseous background. For small and moderate Stokes numbers, $ St pebble accretion creates two underdense regions with a front-rear asymmetry with respect to the planet. The underdensity trailing the planet is more extended. The resulting excess of pebble mass in front of the planet then makes the pebble torque positive and capable of outperforming the negative gas torque. Pebble accretion thus enables outward migration (previously thought to occur mainly for $ St in a larger portion of the parameter space. It occurs for the planet mass pl oplus $ and for all the Stokes numbers considered in our study, $ St $, assuming a pebble-to-gas mass ratio of $Z=0.01$. If some of the observed planets underwent outward pebble-driven migration during their accretion, the formation sites of their progenitor embryos could have differed greatly from the usual predictions of planet formation models. To enable an update of the respective models, we provide a scaling law for the pebble torque that can be readily incorporated in N-body simulations.

Rocky planet formation in compact disks around M dwarfs

Due to the improvements in radial velocity and transit techniques, we know that rocky or rocky-icy planets, in particular close-in super-Earths in compact configurations, are the most common ones around M dwarfs. On the other hand, thanks to the high angular resolution of ALMA we know that many disks around very low-mass stars (between 0.1 and 0.5 M$_ are rather compact and small (without observable substructures and radius less than 20 au), which favors the idea of an efficient radial drift that could enhance planet formation in the terrestrial zone. Our aim was to investigate the potential formation paths of the observed close-in rocky exoplanet population around M dwarfs, especially close-in super-Earths, assuming that planet formation could take place in compact disks with an efficient dust radial drift. We developed N-body simulations that include a sample of embryos growing by pebble accretion exposed to planet-disk interactions, star-planet tidal interactions, and general relativistic corrections that include the evolution of the luminosity, radius, and rotational period of the star. For a star of 0.1 M$_ we considered different gas disk viscosities and initial embryo distributions. We also explored planet formation by pebble accretion around stars of 0.3 M$_ and 0.5 M$_ Lastly, for each stellar mass, we ran simulations that include a sample of embryos growing by planetesimal accretion instead of pebble accretion. Our main result is that the sample of simulated planets that grow by pebble accretion in a gas disk with low viscosity ($ $) can reproduce the close-in low-mass exoplanet population around M dwarfs in terms of multiplicity, mass, and semi-major axis. Furthermore, we found that a gas disk with high viscosity ($ $), and thus lower pebble accretion rates, cannot reproduce the observed planet masses as no planet more massive than 0.5 M$_ could be formed in our simulations. In addition, we show that planetesimal accretion favors the formation of smaller planets than pebble accretion does. Whether this planet population truly exists remains unknown with the current instrumental sensitivity. Rocky planet formation around M dwarfs can take place in compact and small dust disks driven by an efficient radial drift in a gas disk with low viscosity ($ $). This result points toward a new approach in the direction of the disk conditions needed for rocky planet formation around very low-mass stars.

Giant planet formation in the Solar System

The formation history of Jupiter has been of interest due to its ability to shape the solar system’s history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here we explore through N-body simulations the implications of the simplest disc and pebble accretion model with steady-state accretion and an assumed ring structure in the disc at 5 AU on the formation of the giant planets in the solar system. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter to control the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in logr, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets indicating that systems with more massive planets are more violent. We compute the average formation time for proto-Jupiter to reach 10 Earth masses to be 〈tc,J〉=1.1±0.3 Myr and for proto-Saturn 〈tc,S〉=3.3±0.4 Myr, while for the ice giants this increases to 〈tc,I〉=4.9±0.1 Myr. The formation timescales of the cores of the gas giants are distinct at >95% confidence, suggesting that they formed sequentially.

Sequential giant planet formation initiated by disc substructure

Context. Planet formation models are necessary to understand the origins of diverse planetary systems. Circumstellar disc substructures have been proposed as preferred locations of planet formation, but a complete formation scenario has not been covered by a single model so far. Aims. We aim to study the formation of giant planets facilitated by disc substructure and starting with sub-micron-sized dust. Methods. We connect dust coagulation and drift, planetesimal formation, N-body gravity, pebble accretion, planet migration, planetary gas accretion, and gap opening in one consistent modelling framework. Results. We find rapid formation of multiple gas giants from the initial disc substructure. The migration trap near the substructure allows for the formation of cold gas giants. A new pressure maximum is created at the outer edge of the planetary gap, which triggers the next generation of planet formation resulting in a compact chain of giant planets. A high planet formation efficiency is achieved, as the first gas giants are effective at preventing dust from drifting further inwards, which preserves material for planet formation. Conclusions. Sequential planet formation is a promising framework to explain the formation of chains of gas and ice giants.

Formation of Giant Planets by Gas Disk Gravitational Instability on Wide Orbits around Protostars with Varied Masses. II. Quadrupled Spatial Resolution and Beta Cooling

Exoplanet demographics are sufficiently advanced to provide important constraints on theories of planet formation. While core and pebble accretion are preferred for rocky and icy planets, there appears to be a need for gas disk gravitational instability (GDGI) to play a role in the formation of M-dwarf gas giants and those orbiting at large distances. Here we present GDGI models that go beyond those presented by Boss (2011) dealing with the formation of wide-orbit gas giants. The new models use quadrupled spatial resolution, in both the radial and azimuthal directions, to reduce the effects of finite spatial resolution. The new models also employ the β cooling approximation, instead of the diffusion approximation used by Boss (2011), in order to push the models further in time. As in Boss (2011), the central protostars have masses of 0.1, 0.5, 1.0, 1.5, or 2.0 M ⊙, surrounded by disks with masses ranging from 0.019 M ⊙ to 0.21 M ⊙. For each case, two models are computed, one with an initial minimum Toomre Q stability value ranging from 1.1 to 1.7, and one with a higher initial disk temperature, resulting in the initial minimum Q ranging from 2.2 to 3.4. These new models continue to show that GDGI can explain the formation of gas giants at distances of ∼30 to ∼50 au on eccentric orbits (e less than ∼0.2), though the number formed drops to 0 as the protostar mass decreases to 0.1 M ⊙.

Probing Dust and Gas Properties Using Ringed Disks

How rapidly a planet grows in mass and how far it may park from the host star depend sensitively on two nondimensional parameters: Stokes number St and turbulent α. Yet these parameters remain highly uncertain, being difficult or impossible to measure directly. Here, we demonstrate how the ringed disks can be leveraged to obtain St and α separately by constructing a simple toy model that combines the dust radial equation of motion under aerodynamic drag and coupling to gas motion with the measured distribution of dust masses in Class 0/I disks. Focusing on known systems with well-resolved dust rings, we find that the ranges of St and α that are consistent with the measured properties of the rings are small: 10−4 ≲ St ≲ 10−2 and 10−5 ≲ α ≲ 10−3. These low St and α ensure the observed rings are stable against clumping. Even in one marginal case where the formation of bound clumps is possible, further mass growth by pebble accretion is inhibited. Furthermore, the derived low α is consistent with the nearly inviscid regime where type I migration can be prematurely halted. Our analysis predicts a minimal planet population beyond ∼tens of au, where we observe dust rings and significantly more vigorous planet formation inside ∼10 au, consistent with current exo-giant statistics. We close with discussions on the implications of our results on small planet statistics at large orbital distances.

C/O Ratios and the Formation of Wide-separation Exoplanets

The gas and solid-state C/O ratios provide context to potentially link the atmospheric composition of planets to that of the natal disk. We provide a synthesis of extant estimates of the gaseous C/O and C/H ratios in planet-forming disks obtained primarily through analysis of Atacama Large Millimeter/submillimeter Array observations. These estimates are compared to atmospheric abundances of wide-separation (>10 au) gas giants. The resolved disk gas C/O ratios, from seven systems, generally exhibit C/O ≥ 1 with subsolar, or depleted, carbon content. In contrast, wide-separation gas giants have atmospheric C/O ratios that cluster near or slightly above the presumed stellar value with a range of elemental C/H. From the existing disk composition, we infer that the solid-state millimeter/centimeter-sized pebbles have a total C/O ratio (solid cores and ices) that is solar (stellar) in content. We explore simple models that reconstruct the exoplanet atmospheric composition from the disk, while accounting for silicate cloud formation in the planet atmosphere. If wide-separation planets formed via the core-accretion mechanism, they must acquire their metals from pebble or planetesimal accretion. Further, the dispersion in giant planet C/H content is best matched by a disk composition with modest and variable factors of carbon depletion. An origin of the wide-separation gas giants via gravitational instability cannot be ruled out, as stellar C/O ratios should natively form in this scenario. However, the variation in planet metallicity with a stellar C/O ratio potentially presents challenges to these models.

Rapid Protoplanet Formation in Vortices: Three-dimensional Local Simulations with Self-gravity

Disk vortices, seen in numerical simulations of protoplanetary disks and found observationally in Atacama Large Millimeter/submillimeter Array and Very Large Array images of these objects, are promising sites for planet formation given their pebble trapping abilities. Previous works have shown a strong concentration of pebbles in vortices, but gravitational collapse has only been shown in low-resolution, two-dimensional, global models. In this Letter, we aim to study the pebble concentration and gravitational collapse of pebble clouds in vortices via high-resolution, three-dimensional, local models. We performed simulations of the dynamics of gas and solids in a local shearing box where the gas is subject to convective overstability, generating a persistent giant vortex. We find that the vortex produces objects of Moon and Mars mass, with a mass function of power-law dlnN/dlnM=−1.6±0.3 . The protoplanets grow rapidly, doubling in mass in about five orbits, following pebble accretion rates. The mass range and mass doubling rate are in broad agreement with previous low-resolution global models. We conclude that Mars-mass planetary embryos are the natural outcome of planet formation inside the disk vortices seen in millimeter and radio images of protoplanetary disks.

How planets grow by pebble accretion

The characterization of super-Earth- to Neptune-sized exoplanets relies heavily on our understanding of their formation and evolution. In this study, we link a model of planet formation by pebble accretion to the planets’ long-term observational properties by calculating the interior evolution, starting from the dissipation of the protoplanetary disk. We investigate the evolution of the interior structure in 5–20 M⊕ planets, accounting for silicate redistribution caused by convective mixing, rainout (condensation and settling), and mass loss. Specifically, we have followed the fate of the hot silicate vapor that remained in the planet’s envelope after planet formation as the planet cools. We find that disk dissipation is followed by a rapid contraction of the envelope from the Hill or Bondi radius to about one-tenth of that size within 10 Myr. Subsequent cooling leads to substantial growth of the planetary core through silicate rainout accompanied by inflated radii, in comparison to the standard models of planets that formed with core-envelope structure. We examined the dependence of rainout on the planet’s envelope mass, on the distance from its host star, on its silicate mass, and on the atmospheric opacity. We find that the population of planets that formed with polluted envelopes can be roughly divided into three groups based on the mass of their gas envelopes: bare rocky cores that have shed their envelopes, super-Earth planets with a core-envelope structure, and Neptune-like planets with diluted cores that undergo gradual rainout. For polluted planets that formed with envelope masses below 0.4 M⊕, we anticipate that the inflation of the planet’s radius caused by rainout will enhance the mass loss by a factor of 2–8 compared to planets with unpolluted envelopes. Our model bridges the gap between the predicted composition gradients in massive planets and the core-envelope structure in smaller planets.

A formation pathway for terrestrial planets with moderate water content involving atmospheric-volatile recycling

Of the many recently discovered terrestrial exoplanets, some are expected to harbor moderate water mass fractions of a few percent. The formation pathways that can produce planets with these water mass fractions are not fully understood. Here, we use the code chemcomp which consists of a semi-analytical 1D protoplanetary disk model harboring a migrating and accreting planet, to model the growth and composition of planets with moderate water mass fractions by pebble accretion in a protoplanetary disk around a TRAPPIST-1 analog star. This star is accompanied by seven terrestrial planets, of which the outer four planets likely contain water mass fractions of between 1<!PCT!> and 10<!PCT!>. We adopt a published model that considers the evaporation of pebbles in the planetary envelope, from where recycling flows can transport the volatile vapor back into the disk. We find that with this model, the planetary water content depends on the influx rate of pebbles onto the planet. A decreasing pebble influx with time reduces the envelope temperature and consequently allows the formation of planets with moderate water mass fractions as inferred for the outer TRAPPIST-1 planets for a number of different simulation configurations. This is further evidence that the recycling of vapor is an important component of planet formation needed to explain the vast and diverse population of exoplanets.

Thermal structure of circumbinary discs: Circumbinary planets should be icy, not rocky

The process of forming a circumbinary planet is thought to be intimately related to the structure of the nascent circumbinary disc. It has been shown that the structure of a circumbinary disc depends strongly on three-dimensional effects and on detailed modelling of the thermodynamics. Here, we employ three-dimensional hydrodynamical simulations, combined with a proper treatment of the thermal physics using the RADMC-3D radiation transport code, to examine the location of the snow line in circumbinary discs. The models have application to the circumbinary planets that have been discovered in recent years by the Kepler and TESS transit surveys. We find that the snow line is located in a narrow region of the circumbinary disc, close to the inner cavity that is carved out by the central binary, at typical orbital distances of ~ 1.5–2 au for the system parameters considered. In this region, previous work has shown that both grain growth and pebble accretion are likely to be inefficient because of the presence of hydrodynamical turbulence. Hence, in situ planet formation interior to the snow line is unlikely to occur and circumbinary planets should preferentially be icy, not rocky.

A fading radius valley towards M dwarfs, a persistent density valley across stellar types

The radius valley separating super-Earths from mini-Neptunes is a fundamental benchmark for theories of planet formation and evolution. Observations show that the location of the radius valley decreases with decreasing stellar mass and with increasing orbital period. Here, we build on our previous pebble-based formation model. Combined with photoevaporation after disc dispersal, it has allowed us to unveil the radius valley as a separator between rocky and water-worlds. In this study, we expand our model for a range of stellar masses spanning from 0.1 to 1.5 M⊙. We find that the location of the radius valley is well described by a power-law in stellar mass as Rvalley = 1.8197 M⋆0.14(+0.02/−0.01), which is in excellent agreement with observations. We also find very good agreement with the dependence of the radius valley on orbital period, both for FGK and M dwarfs. Additionally, we note that the radius valley gets filled towards low stellar masses, particularly at 0.1–0.4 M⊙, yielding a rather flat slope in Rvalley − Porb. This is the result of orbital migration occurring at lower planet mass for less massive stars, which allows for low-mass water-worlds to reach the inner regions of the system, blurring the separation in mass (and size) between rocky and water worlds. Furthermore, we find that for planetary equilibrium temperatures above 400 K, the water in the volatile layer exists fully in the form of steam, puffing the planet radius up (as compared to the radii of condensed-water worlds). This produces an increase in planet radii of ∼30% at 1 M⊕ and of ∼15% at 5 M⊕ compared to condensed-water worlds. As with Sun-like stars, we find that pebble accretion leaves its imprint on the overall exoplanet population as a depletion of planets with intermediate compositions (i.e. water mass fractions of ∼0 − 20%), carving an planet-depleted diagonal band in the mass-radius (MR) diagrams. This band is better visualised when plotting the planet’s mean density in terms of an Earth-like composition. This change in coordinates causes the valley to emerge for all the stellar mass cases.

The metal-poor atmosphere of a potential sub-Neptune progenitor

Young transiting exoplanets offer a unique opportunity to characterize the atmospheres of freshly formed and evolving planets. We present the transmission spectrum of V1298 Tau b, a 23-Myr-old warm Jupiter-sized (0.91 ± 0.05 RJ, where RJ is the radius of Jupiter) planet orbiting a pre-main-sequence star. We detect a mostly clear primordial atmosphere with an exceptionally large atmospheric scale height, and a water vapour absorption at a 5σ level of significance, from which we estimate a planetary mass upper limit (23 Earth masses, 0.12 g cm−3 at a 3σ level). This is one of the lowest-density planets discovered so far. We retrieve a low atmospheric metallicity (logZ=−0.7−0.7+0.8solar\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\log{Z}=-0.{7}_{-0.7}^{+0.8}\\,{\\mathrm{solar}}$$\\end{document}), consistent with solar/sub-solar values. Our findings challenge the expected mass–metallicity relation from core-accretion theory. Our observations can instead be explained by in situ formation via pebble accretion together with ongoing evolutionary mechanisms. We do not detect methane, which hints at a hotter-than-expected interior from just the formation entropy of this planet. Our observations suggest that V1298 Tau b is likely to evolve into a sub-Neptune.

Relative Occurrence Rate between Hot and Cold Jupiters as an Indicator to Probe Planet Migration

We propose a second-order statistic parameter ε, the relative occurrence rate between hot Jupiters (HJs) and cold Jupiters (CJs) (ε = η HJ/η CJ), to probe the migration of gas giants. Since the planet occurrence rate is the combined outcome of the formation and migration processes, a joint analysis of HJ and CJ frequency may shed light on the dynamical evolution of giant planet systems. We first investigate the behavior of ε as the stellar mass changes observationally. Based on the occurrence rate measurements of HJs (η HJ) from the Transiting Exoplanet Survey Satellite survey and CJs (η CJ) from the California Legacy Survey, we find a tentative trend (97% confidence) that ε drops when the stellar mass rises from 0.8 to 1.4 M ⊙, which can be explained by different giant planet growth and disk migration timescales around different stars. We carry out planetesimal and pebble accretion simulations, both of which can reproduce the results of η HJ, η CJ, and ε. Our findings indicate that the classical core accretion + disk migration model can explain the observed decreasing trend of ε. We propose two ways to increase the significance of the trend and verify the anticorrelation. Future works are required to better constrain ε, especially for M dwarfs and for more massive stars.

Dust-gas coupling in turbulence- and MHD wind-driven protoplanetary disks: Implications for rocky planet formation

The degree of coupling between dust particles and their surrounding gas in protoplanetary disks is quantified by the dimensionless Stokes number. The Stokes number (St) governs particle size and spatial distributions, in turn establishing the dominant mode of planetary accretion in different disk regions. In this paper, we model the characteristic St of particles across time in disks evolving under both turbulent viscosity and magnetohydrodynamic (MHD) disk winds. In both turbulence- and wind-dominated disks, we find that collisional fragmentation is the limiting mechanism of particle growth. The water-ice sublimation line constitutes a critical transition point in dust settling, drift, and size regimes. For a fiducial disk evolution parameter α̃≃10−3, silicate particles inteior to the ice-line are characterized by low St (≲10−2) and sizes in the sub-mm- to 1cm-scale. Icy particles/boulders beyond the ice-line are characterized by high St (≳10−2) and sizes in the cm to dm size range. Hence, icy particles settle into a thin layer at the outer disk midplane and drift inward at velocities exceeding the gaseous accretionary flow due to substantial headwind drag. Silicate particles in the inner disk remain relatively well dispersed and are to a large extent advected inward with their surrounding gas.The St dichotomy across the ice-line translates to distinct planet formation pathways between the inner and outer disk. While pebble accretion proceeds slowly for rocky embryos within the ice-line (across most of parameter space), it does so rapidly for volatile-rich embryos beyond it, allowing for the growth of giant planet cores before disk dissipation. Through simulations of rocky planet growth, we evaluate the competition between pebble accretion and classical pairwise collisions between planetesimals. We conclude that the dominance of pebble accretion can only be realized in disks that are driven by MHD winds, slow-evolving (α̃≲10−3.5), and devoid of pressure maxima that may concentrate solids and give rise of planetesimal rings in which classical growth is enhanced. Such disks are extremely quiescent, with Shakura-Sunyaev turbulence parameters αν≲10−4. We conclude that for most of parameter space corresponding to values of αν reflected in observations of protoplanetary disks (≳10−4), pairwise planetesimal collisions constitute the dominant pathway of rocky planet accretion. Our results are discussed in the context of super-Earth origins, and lend support to the emerging view that they formed in planetesimal rings. Moreover, these results argue against a significant contribution (≳ 10%) of outer disk, carbonaceous material to the proto-Earth in the form of pebbles, in agreement with chemical and isotopic investigations of Earth’s accretion history.

Growth and evolution of low-mass planets in pressure bumps

Observations of protoplanetary disks have revealed dust rings that are likely due to the presence of pressure bumps in the disk. Because these structures tend to trap drifting pebbles, it has been proposed that pressure bumps may play an important role in the planet formation process. In this paper, we investigate the orbital evolution of a 0.1 M⊕ protoplanet embedded in a pressure bump using 2D hydrodynamical simulations of protoplanetary disks consisting of gas and pebbles. We examine the role of thermal forces generated by the pebble accretion-induced heat release, taking into account the feedback between the luminosity and the eccentricity. We also study the effect of the pebble-scattered flow on the planet’s orbital evolution. Due to the accumulation of pebbles at the pressure bump, the planet’s accretion luminosity is high enough to induce significant eccentricity growth through thermal forces. Accretion luminosity is also responsible for vortex formation at the planet’s position through baroclinic effects, which cause the planet to escape from the dust ring if dust feedback on the gas is neglected. Including the effect of the dust feedback leads to weaker vortices, which enable the planet to remain close to the pressure maximum on an eccentric orbit. Simulations in which the planet mass is allowed to increase as a consequence of pebble accretion result in the formation of giant planet cores with masses in the range of 5–20 M⊕ over ~2 × 104 yr. This occurs for moderate values of the Stokes number, St ≈ 0.01, such that the pebble drift velocity is not too high and the dust ring mass not too small. Our results suggest that pressure bumps mays be preferred locations for the formation of giant planets, but this requires a moderate level of grain growth within the disk.