Pebble Flux Research Articles

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.

Thermal processing of primordial pebbles in evolving protoplanetary disks

During protoplanetary disk formation, dust grains located in the outer disk retain their pristine icy composition, while solids in the inner stellar-heated disk undergo volatile loss. This process may have left a fossil record in Solar System material, showing different nucleosynthetic imprints that have been attributed to different degrees of thermal processing. However, it remains unclear how a large mass fraction of thermally processed inner-disk pebbles is produced and how these grains are subsequently transported throughout the disk. In this work, we numerically investigate the evolution in time of a two-component pebble disk consisting of both pristine pebbles and those that underwent ice sublimation. We find that stellar outbursts exceeding 1000 times the solar luminosity are efficient in thermally altering, through ice sublimation, a large mass fraction of pebbles (around 80%). After the establishment of this initial radial dust composition gradient throughout the disk, the subsequent mixing and inward drift of pristine outer-disk pebbles alter the inner disk bulk composition from processed to more unprocessed in time. Therefore, if processed pebbles without ice mantles have an isotopic composition similar to ureilite meteorites from the inner Solar System, inner-disk minor bodies forming from the early pebble flux (<1 Myr) will be isotopically ureilite-like, while later-formed bodies will be increasingly admixed with the signature of the lateincoming, CI chondrite-like unprocessed pebbles. This appears to be largely consistent with the trend seen between the accretion age of different meteoric classes and their different stable isotope composition anomalies (in μ54Cr, μ48Ca, μ30Si, and μ58Ni), but further work may be needed to explain the role of isotopically anomalous refractory inclusions and anomaly trends in other elements. Our findings further support an early thermal processing of ice mantles via stellar outbursts that are common around young Sun-like stars.

Which stars can form planets: Planetesimal formation at low metallicities

The diversity of exoplanets has been linked to the disc environment in which they form, where the host star metallicity and the formation pathways play a crucial role. In the context of the core accretion paradigm, the initial stages of planet formation require the growth of dust material from micrometre-sized to planetesimal-sized bodies before core accretion can kick in. Although numerous studies have been conducted on planetesimal formation, it is still poorly understood how this process takes place in low-metallicity stellar environments. In this work, we explore how planetesimals are formed in stellar environments with primarily low metallicities. We performed global 1D viscous disc evolution simulations, including the growth of dust particles and the evaporation and condensation of chemical species at ice lines. We followed the formation of planetesimals during disc evolution and tested different metallicities, disc sizes, and turbulent viscosity strengths. We find that at solar and sub-solar metallicities, there is a significant increase in the midplane dust-to-gas mass ratios at the ice lines, but this leads to planetesimal formation only at the water--ice line. In our simulations Fe/H $= -0.6$ is the lower limit of metallicity for planetesimal formation where a few Earth masses of planetesimals can form. Our results further show that for such extreme disc environments, large discs are more conducive than small discs for forming large amounts of planetesimals at a fixed metallicity because the pebble flux can be maintained for a longer time, resulting in a longer and more efficient planetesimal formation phase. At lower metallicities, planetesimal formation is less supported in quiescent discs compared to turbulent discs, which produce larger amounts of planetesimals, because the pebble flux can be maintained for a longer time. The amount of planetesimals formed at sub-solar metallicities in our simulations places a limit on core sizes that could potentially result only in the formation of super-Earths.

Formation of wide-orbit giant planets in protoplanetary disks with a decreasing pebble flux

The presence of distant protoplanets may explain the observed gaps in the dust emission of protoplanetary disks. Here, we derive a novel analytical model to describe the temporal decay of the pebble flux through a protoplanetary disk as the result of radial drift. This has allowed us to investigate the growth and migration of distant protoplanets throughout the lifespan of the disk. We find that Moon-mass protoplanets that formed early on can grow to their pebble isolation mass, between approximately 20 and 80 M⊕, within less than 1 Myr, in the 20–80 AU region around solar-like stars. The subsequent fast migration in the early stages of gas accretion, after pebble accretion ends, transports these giant planets into their final orbits at <10 AU. However, our pebble decay model allows us to include a new pathway that may trigger the transition from pebble accretion to gas accretion after the pebble flux has decayed substantially. With this pebble decay pathway, we show that it is also possible to form gas giants beyond 10 AU. The occurrence of these wide-orbit gas giants should be relatively low, since their core must attain sufficient mass to accrete gas before the pebble flux decays, while avoiding excessive migration. Since these gas giants do not reach the pebble isolation mass, their heavy element content is typically less than 10M⊕. Our results imply that the observed gaps in protoplanetary disks could be caused by distant protoplanets that reached the pebble isolation mass and then migrated, while gas giants in wide orbits, such as PDS 70 b and c, accreted their gas after the decay in the pebble flux.

How to make giant planets via pebble accretion

Planet formation is directly linked to the birthing environment that protoplanetary disks provide. The disk properties determine whether a giant planet will form and how it evolves. The number of exoplanet and disk observations is consistently rising, however, it is not yet possible to directly link these two populations. Therefore, a deep theoretical understanding of how planets form is crucial. Giant planets are not the most common exoplanets, but their presence in a disk can have significant consequences for the evolution of the disk itself and the planetary system undergoing formation. Their presence also offers more chances of spotting observational features in the disk structure. We performed numerical simulations of planet formation via pebble and gas accretion, while including migration, in a viscously evolving protoplanetary disk, with dust growing, drifting, and evaporating at the ice lines. In our investigation of the most favorable conditions for giant planet formation, we find that these are high disk masses, early formation, and a large enough disk to host a long-lasting pebble flux, so that efficient core growth can take place before the pebble flux decays over time. Specifically, core growth needs to start before 0.9 Myr to form a giant, with an initial disk mass of 0.04 M⊙ (or higher) and the disk radius needs to be larger than 50 AU. However, small disks with the same mass allow more efficient gas accretion onto already formed planetary cores, leading to more massive gas giants. Given the right conditions, high viscosity (α = 10−3) leads to more massive cores (compared to α = 10−4) and it also enhances gas accretion. At the same time, it causes faster type II migration rates, so the giants have a decreasing final position for increasing viscosity. Intermediate dust fragmentation velocities, between 4 and 7 m s−1, provide the necessary pebble sizes and radial drift velocities for maximized pebble accretion with optimal pebble flux. The starting location of a planetary embryo defines whether a giant planet will form, with the highest fraction of giants originating between 5 and 25 AU. Finally, a dust-to-gas ratio of 0.03 can compensate for lower disk masses with fDG ≤ 0.015, but early formation is still important in order to form giant planets. We conclude that there is no specific initial parameter that leads to giant planet formation; rather, it is the outcome of a combination of complementary factors. This also implies that the diversity of the exoplanet systems is the product of the intrinsic diversity of the protoplanetary disks and it is crucial to take advantage of the increasing number and quality of observations to constrain the disk population properties and ultimately devise planet formation theories.

Enriching inner discs and giant planets with heavy elements

Giant exoplanets seem to have on average a much higher heavy-element content than the Solar System giants. Past attempts to explain this heavy-element content include collisions between planets, accretion of volatile rich gas, and accretion of gas enriched in micrometre-sized solids. However, these different theories individually could not explain the heavy-element content of giants and the volatile-to-refractory ratios in the atmospheres of giant planets at the same time. Here we combine the approaches of gas accretion enhanced with vapour and small micrometre-sized dust grains within one model. To this end, we present detailed models of inward-drifting and evaporating pebbles, and describe how these pebbles influence the dust-to-gas ratio and the heavy-element content of the disc. As pebbles drift inwards, the volatile component evaporates and enriches the disc. At the same time, the smaller silicate core of the pebble continues to move inwards. As the silicate pebbles are presumably smaller than the ice grains, they drift more slowly, leading to a pile-up of material inside of the water-ice line, increasing the dust-to-gas ratio in this region. Under the assumption that these small dust grains follow the motion of the gas even through the pressure bumps generated by the gaps between planets, gas accreting giants can accrete large fractions of small solids in addition to the volatile vapour. We find that the effectiveness of the solid enrichment requires a large disc radius to maintain the pebble flux for a long time and a high viscosity that reduces the size and inward drift of the small dust grains. However, this process depends crucially on the debated size difference of the pebbles that are inside and outside of the water-ice line. On the other hand, the volatile component released by the inward-drifting pebbles can lead to a high enrichment with heavy-element vapour, independently of a size difference of pebbles inside and outside the water-ice line. Our model emphasises the importance of the disc’s radius and viscosity to the enrichment of dust and vapour. Consequently, we show how our model could explain the heavy-element content of the majority of giant planets by using combined estimates of dust and vapour enrichment.

Atmospheric recycling of volatiles by pebble-accreting planets

ABSTRACT Planets, embedded in their natal discs, harbour hot envelopes. When pebbles are accreted by these planets, the contained volatile components may sublimate, enriching the envelope and potentially changing its thermodynamical properties. However, the envelopes of embedded planets actively exchange material with the disc, which would limit the buildup of a vapour-rich atmosphere. To properly investigate these processes, we have developed a new phase change module to treat the sublimation process with hydrodynamical simulations. Combined with the recently developed multidust fluid approach, we conduct 2D self-consistent hydrodynamic simulations to study how pebble sublimation influences the water content of super-Earths and sub-Neptunes. We find the extent and the amount of vapour that a planet is able to hold on to is determined by the relative size of the sublimation front and the atmosphere. When the sublimation front lies far inside the atmosphere, vapour tends to be locked deep in the atmosphere and keeps accumulating through a positive feedback mechanism. On the other hand, when the sublimation front exceeds the (bound) atmosphere, the ice component of incoming pebbles can be fully recycled and the vapour content reaches a low, steady value. Low disc temperature, small planet mass, and high pebble flux (omitting accretion heating by pebbles) render the planet atmosphere vapour-rich while the reverse changes render it vapour-poor. The phase change module introduced here can in future studies also be employed to model the chemical composition of the gas in the vicinity of accreting planets and around snowlines.

Planetesimal Growth in Evolving Protoplanetary Disks: Constraints from the Pebble Supply

In the core accretion model, planetesimals grow by mutual collisions and engulfing millimeter-to-centimeter particles, i.e., pebbles. Pebble accretion can significantly increase the accretion efficiency and help explain the presence of planets on wide orbits. However, the pebble supply is typically parameterized as a coherent pebble mass flux, sometimes being constant in space and time. Here we solve the dust advection and diffusion within viciously evolving protoplanetary disks to determine the pebble supply self-consistently. The pebbles are then accreted by planetesimals interacting with the gas disk via gas drag and gravitational torque. The pebble supply is variable with space and decays with time quickly, with a pebble flux below 10 M ⊕ Myr−1 after 1 Myr in our models. As a result, only when massive planetesimals (>0.01 M ⊕) are luckily produced by the streaming instability or the disk has low viscosity (α ∼ 0.0001) can the herd of planetesimals grow over a Mars mass within 2 Myr. By then, planetesimals only capture pebbles about 50 times their mass and as little as 10 times beyond 20 au due to limited pebble supply. Further studies considering multiple dust species in various disk conditions are warranted to fully assess the realistic pebble supply and its influence on planetesimal growth.

Planet formation via pebble accretion in externally photoevaporating discs

ABSTRACT We demonstrate that planet formation via pebble accretion is sensitive to external photoevaporation of the outer disc. In pebble accretion, planets grow by accreting from a flux of solids (pebbles) that radially drift inwards from the pebble production front. If external photoevaporation truncates the outer disc fast enough, it can shorten the time before the pebble production front reaches the disc outer edge, cutting off the supply of pebble flux for accretion, hence limiting the pebble mass reservoir for planet growth. Conversely, cloud shielding can protect the disc from strong external photoevaporation and preserve the pebble reservoir. Because grain growth and drift can occur quickly, shielding even on a short time-scale (<1 Myr) can have a non-linear impact on the properties of planets growing by pebble accretion. For example, a $10^{-3}\, \mathrm{ M}_{\oplus }$ planetary seed at 25 au stays at 25 au with a lunar mass if the disc is immediately irradiated by a 103 G0 field, but grows and migrates to be approximately Earth-like in both mass and orbital radius if the disc is shielded for just 1 Myr. In NGC 2024, external photoevaporation is thought to happen to discs that are <0.5 Myr old, which coupled with the results here suggests that the exact planetary parameters can be very sensitive to the star-forming environment. Universal shielding for time-scales of at least ${\sim} 1.5\,$ Myr would be required to completely nullify the environmental impact on planetary architectures.

Nonlinear Outcome of Coagulation Instability in Protoplanetary Disks. II. Dust-ring Formation Mediated by Backreaction and Fragmentation

In our previous work (Paper I), we demonstrated that coagulation instability results in dust concentration against depletion due to the radial drift and accelerates dust growth locally. In this work (Paper II), we perform numerical simulations of coagulation instability taking into account effects of backreaction to gas and collisional fragmentation of dust grains. We find that the slowdown of the dust drift due to backreaction regulates dust concentration in the nonlinear growth phase of coagulation instability. The dust-to-gas surface density ratio increases from 10−3 up to ∼10−2. Each resulting dust ring tends to have a mass of ≃0.5 M ⊕ − 1.5 M ⊕ in our disk model. In contrast to Paper I, the dust surface density profile shows a local plateau structure at each dust ring. In spite of the regulation at the nonlinear growth, the efficient dust concentration reduces their collision velocity. As a result, dust grains can grow beyond the fragmentation barrier, and the dimensionless stopping time reaches unity, as in Paper I. The necessary condition for the efficient dust growth is (1) weak turbulence of α < 1 × 10−3 and (2) a large critical velocity for dust fragmentation (>1 m s−1). The efficient dust concentration in outer regions will reduce the inward pebble flux and is expected to decelerate the planet formation via the pebble accretion. We also find that the resulting rings can be unstable to secular gravitational instability (GI). The subsequent secular GI promotes planetesimal formation. We thus expect that a combination of these instabilities is a promising mechanism for dust-ring and planetesimal formation.

On the evolution of pebble-accreting planets in evolving protoplanetary discs

ABSTRACTWe examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot{M}= 2\times 10^{-8}\, \mathrm{ M}_\odot$ yr−1 and pebble flux $\dot{M}_{\mathrm{ peb}}=170\, \mathrm{ M}_\oplus$ Myr−1, we find that embryo eccentricities attain values comparable to the disc aspect ratio. The planet radial excursion in the disc, however, causes the torque exerted by inflowing pebbles to cancel on average and migration to transition from outward to inward. This is found to arise because the magnitude of thermal torques decreases exponentially with increasing eccentricity, and we provide a fitting formula for the thermal torque attenuation as a function of eccentricity. As the disc evolves, the accretion luminosity becomes at some point too small to make the core eccentricity grow such that the solid component can exert a non-zero torque on the planet. This torque is positive and for gas accretion rates $\dot{M} \lesssim 5\times 10^{-9}$M⊙ yr−1 and pebble fluxes $\dot{M}_{\rm {peb}} \lesssim 120\, \mathrm{ M}_\oplus $ Myr−1, it is found to overcome the gas torque exerted on cores with mass $m_\mathrm{ p}\lesssim \, 1\,\mathrm{ {M}}_\oplus$, resulting in outward migration.

Growth after the streaming instability: The radial distance dependence of the planetary growth

Streaming instability is hypothesized to be triggered at particular protoplanetary disk locations where the volume density of the solid particles is enriched comparable to that of the gas. A ring of planetesimals thus forms when this condition is fulfilled locally. These planetesimals collide with each other and accrete inward drifting pebbles from the outer disk to further increase masses. We investigate the growth of the planetesimals that form in a ring-belt at various disk radii. Their initial mass distributions are calculated based on the formula summarized from the streaming instability simulations. We simulate the subsequent dynamical evolution of the planetesimals with a protoplanetary disk model based either on the minimum mass solar nebula (MMSN) or on the Toomre stability criterion. For the MMSN model, both pebble accretion and planetesimal accretion are efficient at a close-in orbit of 0.3 AU, resulting in the emergence of several super-Earth mass planets after 1 Myr. For comparison, only the most massive planetesimals undergo substantial mass growth when they are born at r = 3 AU, while the planetesimals at r = 30 AU experience little or no growth. On the other hand, in the denser Toomre disk, the most massive forming planets can reach Earth mass at t = 1 Myr and reach a mass between that of Neptune and that of Saturn within 3 Myr at 30 AU and 100 AU. Both the pebble and planetesimal accretion rate decrease with disk radial distance. Nevertheless, planetesimal accretion is less pronounced than pebble accretion at more distant disk regions. Taken together, the planets acquire higher masses when the disk has a higher gas density, a higher pebble flux, and/or a lower Stokes number of pebbles.

Monte Carlo Simulation of Dust Particles in a Protoplanetary Disk: Crystalline to Amorphous Silicate Ratio in Comets

Abstract The observationally inferred crystalline abundance in silicates in comets, which should have been formed in the outer region of a protoplanetary disk, is relatively high (∼10%–60%), although crystalline silicates would be formed by the annealing of amorphous precursors in the inner disk region. In order to quantitatively address this puzzle, we performed a Monte Carlo simulation of the advection/diffusion of silicate particles in a turbulent disk in a setting based on the pebble accretion model: pebbles consisting of many small amorphous silicates embedded in an icy mantle are formed in the outer disk region, silicate particles are released at the snow line, crystalline silicate particles are produced at the annealing line, silicate particles diffuse beyond the snow line, and they eventually stick to drifting pebbles to return to the snow line. In the simple case without sticking and with steady pebble flux, we show through the simulations and analytical arguments that the crystalline components in silicate materials beyond the snow line are robustly and uniformly ≃5%. On the other hand, in a more realistic case with sticking and with a decaying pebble flux, the crystalline abundance increases to ∼20%–25%, depending on the ratio of the decay to diffusion timescales. This abundance is consistent with the observations. In this investigation, we assume a simple steady-accretion disk. The simulations coupled with the disk evolution are needed for a more detailed comparison with observed data.

Resilience of Planetesimal Formation in Weakly Reinforced Pressure Bumps

Abstract The discovery that axisymmetric dust rings are ubiquitous in protoplanetary disks has provoked a flurry of research on the role of pressure bumps in planet formation. High-resolution simulations by our group have shown that even a modest bump can collect enough dust to trigger planetesimal formation by the streaming instability. In this work, we probe the limits of planetesimal formation when the external source of pressure bump reinforcement is extremely weak. We conduct simulations of radially elongated shearing boxes to capture the entire bump, which is generated and maintained over some timescale t reinf by a Newtonian relaxation scheme. We find that planetesimal formation is extremely resilient for centimeter-sized grains. We reduced the strength of reinforcement by up to a factor of 100 and the location and initial masses of planetesimals were essentially unaffected. However, we do find that strong reinforcement causes much faster pebble drift compared to the standard pebble drift rates. The resulting larger pebble flux enhances the planetesimal growth rate by pebble accretion. We hypothesize that, to sustain the bump, our code has to extract angular momentum (the strength of this negative torque depends on t reinf ), and some of this torque is transferred to the particles, causing them to drift faster for a stronger torque (i.e., smaller t reinf ). Since any physical process that sustains a pressure bump must do so by torquing the gas, we conjecture that the effect on pebble drift is a real phenomenon, motivating further work with physically realistic sources to generate the bump.

Linking Outer Disk Pebble Dynamics and Gaps to Inner Disk Water Enrichment

Abstract Millimeter continuum imaging of protoplanetary disks reveals the distribution of solid particles and the presence of substructures (gaps and rings) beyond 5–10 au, while infrared (IR) spectra provide access to abundances of gaseous species at smaller disk radii. Building on recent observational findings of an anti-correlation between the inner disk water luminosity and outer dust disk radius, we aim here at investigating the dynamics of icy solids that drift from the outer disk and sublimate their ice inside the snow line, enriching the water vapor that is observed in the IR. We use a volatile-inclusive disk evolution model to explore a range of conditions (gap location, particle size, disk mass, and α viscosity) under which gaps in the outer disk efficiently block the inward drift of icy solids. We find that inner disk vapor enrichment is highly sensitive to the location of a disk gap, yielding for each particle size a radial “sweet spot” that reduces the inner disk vapor enrichment to a minimum. For pebbles of 1–10 mm in size, which carry the most mass, this sweet spot is at 7–15 au, suggesting that inner gaps may have a key role in reducing ice delivery to the inner disk and may not allow the formation of Earths and super-Earths. This highlights the importance of observationally determining the presence and properties of inner gaps in disks. Finally, we argue that the inner water vapor abundance can be used as a proxy for estimating the pebble drift efficiency and mass flux entering the inner disk.

How planets grow by pebble accretion

Context. In the theory of pebble accretion, planets form by the subsequent accretion of solids (micron-sized dust and larger pebbles) and gas. The amount of nebular gas that a planet can bind is limited by its cooling rate, which is set by the opacity of its envelope. Accreting dust and pebbles contribute to the envelope opacity and, thus, influence the outcome of planet formation. Aims. Our aim is to model the size evolution and opacity contribution of solids inside planetary envelopes. We then use the resultant opacity relations to study emergent trends in planet formation. Methods. We design a model for the opacity of solids in planetary envelopes that accounts for the growth, fragmentation, and erosion of pebbles during their sedimentation. It also includes a separate dust component, which can be both replenished and swept up by encounters with pebbles, depending on the relative velocities. We formulate analytical expressions for the opacity of pebbles and dust and map out their trends as a function of depth, planet mass, distance, and accretion rate. Results. The accretion of pebbles rather than planetesimals can produce fully convective envelopes, but only in lower-mass planets that reside in the outer disk or in those that are accreting pebbles at a high rate. In these conditions, pebble sizes are limited by fragmentation and erosion, allowing them to pile up in the envelope. At higher planetary masses or reduced accretion rates, a different regime applies, where the sizes of sedimenting pebbles are only limited by their rate of growth. The opacity in this growth-limited regime is much lower and declines steeply with depth and planet mass but is invariant with the pebble mass flux. Our results imply that the opacity of a forming planet’s envelope cannot be approximated by a value that is constant with either depth or planet mass. Applying these results to the Solar System, we argue that Uranus and Neptune could not have maintained a sufficiently high opacity to avoid runaway gas accretion unless they both experienced sufficiently rapid accretion of solids and formed late.

Forming pressure traps at the snow line to isolate isotopic reservoirs in the absence of a planet

Context.Pressure maxima are regions in protoplanetary disks in which pebbles can be trapped because the regions have no local pressure gradient. These regions could be ideal places in which planetesimals might be formed or to isotopic reservoirs might be isolated. Observations of protoplanetary disks show that dusty ring structures are common, and pressure maxima are sometimes invoked as a possible explanation. In our Solar System, pressure bumps have been suggested as a possible mechanism for separating reservoirs with different nucleosynthetic compositions that are identified among chondrites and iron meteorites. In this paper, we detail a mechanism by which pressure maxima form just inward of the snow line in stratified disks (with a dead zone and an active layer). This mechanism does not require the presence of a planet.Aims.We investigate the conditions for the formation of pressure maxima using a vertically averagedαviscosity model and release of water vapor at the snow line.Methods.We considered a 1Dαdisk model. Using a combination of analytical and numerical investigations, we explored the range of conditions for a pressure maximum to form inside the dead zone and just inward of the snow line.Results.When the vertically averagedαis a decreasing function of the surface density, then the release of water vapor at the snow line decreases the sound velocity, and a pressure bump appears in turn. This requires a constant inflow of icy pebbles with a ratio of the pebble influx to gas influx &gt;0.6 for a power-law disk with a 1% ice-to-gas ratio, and &gt;1.8 for a disk with an ice-to-gas ratio ~0.3%. If these conditions are met, then a pressure maximum appears just inward of the snow line due to a process that couples the dead and active layers at the evaporation front. The pressure bump survives as long as the icy pebble flux is high enough. The formation of the pressure bump is triggered by the decrease in sound velocity inward of the snow line through the release of water vapor.Conclusions.This mechanism is promising for isolating early reservoirs carrying different isotopic signatures in the Solar System and for promoting dry planetesimal formation inward of the snow line, provided the vertically averaged description of a dead zone is valid.

Streaming instability in a global patch simulation of protoplanetary disks

Aims. In recent years, sub-millimeter (mm) observations of protoplanetary disks have revealed an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to that of the gas, increasing the importance of the interaction between the two components there. Methods. We use numerical 2.5D simulations to study the interaction between gas and dust in fully globally stratified disks. To this end, we employ the recently developed dust grain module of the PLUTO code. Our model focuses on a typical T Tauri disk model, simulating a short patch of the disk at 10 au which includes grains of a constant Stokes number of St = 0.01 and St = 0.1, corresponding to grains with sizes of 0.9 cm and 0.9 mm, respectively, for the given disk model. Results. By injecting a constant pebble flux at the outer domain, the system reaches a quasi-steady state of turbulence and dust concentrations driven by the streaming instability. For our given setup, and using resolutions up to 2500 cells per scale height, we resolve the streaming instability that leads to local dust clumping and concentrations. Our results show dust density values of around 10–100 times the gas density with a steady-state pebble flux of between 3.5 × 10−4 and 2.5 × 10−3 MEarth yr−1 for the models with St = 0.01 and St = 0.1. Conclusions. Grain size and pebble flux for model St = 0.01 compare well with dust evolution models of the first million years of disk evolution. For those grains, the scatter opacity dominates the extinction coefficient at mm wavelengths. These types of global dust and gas simulations are a promising tool for studies of the gas and dust evolution at pressure bumps in protoplanetary disks.

Formation of planetary systems by pebble accretion and migration

At least 30% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We useN-body simulations including a model for gas-assisted pebble accretion and disk–planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes (≲15M⊕) and super-massive planetary cores potentially able to become gas giant planets (≳15M⊕). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to ~95% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction (≳95%) of unstable systems with a sprinkling (≲5%) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (N≥ 2) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet–planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths are systematically ice rich. This contrasts with the interpretation that most super-Earths are rocky based on bulk-density measurements of super-Earths and photo-evaporation modeling of their bimodal radius distribution. We investigate the conditions needed to form rocky super-Earths. The formation of rocky super-Earths requires special circumstances, such as far more efficient planetesimal formation well inside the snow line, or much faster planetary growth by pebble accretion in the inner disk. Intriguingly, the necessary conditions to match the bulk of hot super-Earths are at odds with the conditions needed to match the Solar System.

Building the Galilean moons system via pebble accretion and migration: a primordial resonant chain

ABSTRACT The origins of the Galilean satellites – namely Io, Europa, Ganymede, and Callisto – is not fully understood yet. Here we use N-body numerical simulations to study the formation of Galilean satellites in a gaseous circumplanetary disc around Jupiter. Our model includes the effects of pebble accretion, gas-driven migration, and gas tidal damping and drag. Satellitesimals in our simulations first grow via pebble accretion and start to migrate inwards. When they reach the trap at the disc inner edge, scattering events and collisions take place promoting additional growth. Growing satellites eventually reach a multiresonant configuration anchored at the disc inner edge. Our results show that an integrated pebble flux of ≥2 × 10−3 MJ results in the formation of satellites with masses typically larger than those of the Galilean satellites. Our best match to the masses of the Galilean satellites is produced in simulations where the integrated pebble flux is ∼10−3 MJ. These simulations typically produce between three and five satellites. In our best analogues, adjacent satellite pairs are all locked in 2:1 mean motion resonances. However, they have also moderately eccentric orbits (∼0.1), unlike the current real satellites. We propose that the Galilean satellites system is a primordial resonant chain, similar to exoplanet systems as TRAPPIST-1, Kepler-223, and TOI-178. Callisto was probably in resonance with Ganymede in the past but left this configuration – without breaking the Laplacian resonance – via divergent migration due to tidal planet–satellite interactions. These same effects further damped the orbital eccentricities of these satellites down to their current values (∼0.001). Our results support the hypothesis that Io and Europa were born with water-ice rich compositions and lost all/most of their water afterwards. Firmer constraints on the primordial compositions of the Galilean satellites are crucial to distinguish formation models.