We study the effect of a migrating planet ($10<M_p<20$ Earth mass) on the dynamics of pebbles in a radiative disk using 2D two-fluid simulations carried out with the RoSSBi code. The combined action of the waves induced by the migrating planet and drag back-reaction on the gas produces a complex evolution of the flux of pebbles. The waves excite zonal flows which act as dust traps, and accumulate pebbles. Owing to drag back-reaction, a Kelvin-Helmholtz instability develops, generating turbulent dust rings containing several Earth masses of solids, where planetesimal formation is likely. The more massive the planet, the faster the dust rings develop. In competition with planet migration, this process triggers several dust rings, with a radial separation scaling as $1/M_p$. We discover a transition around $13$ Earth masses. Below that, pebbles are stopped at the inner side of the planet's orbit, but pebble accretion on the planet is sustained. Above that, drag back-reaction in the dust ring region flattens the pressure profile while the planet migrates, which limits further growth by pebble accretion. This new {\it pebble isolation mass} is about a factor of 2 lower than often reported in the literature. This reduces the overall formation timescale of Super-Earth planets, while favoring their survival after the disk's dissipation because further accretion is stifled. Finally, our results support an hybrid model for the formation of Jupiter via both pebbles and planetesimals accretion.
Understanding the growth of the cores of giant planets is a difficult problem. Recently, Lambrechts and Johansen (2012; LJ12) proposed a new model in which the cores grow by the accretion of pebble-size objects, as the latter drift towards the star due to gas drag. Here, we investigate the dynamics of pebble-size objects in the vicinity of planetary embryos of 1 and 5 Earth masses and the resulting accretion rates. We use hydrodynamical simulations, in which the embryo influences the dynamics of the gas and the pebbles suffer gas drag according to the local gas density and velocities. The pebb…
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 …
Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a dead zone. In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism. We improve upon the previous study of the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. We performed 1D diffusion-advection simulations of drifting pebbles…
The discovery of over 50 planets around evolved stars and more than 35 debris discs orbiting white dwarfs highlight the increasing need to understand small body evolution around both early and asymptotic giant branch (GB) stars. Pebbles and asteroids are susceptible to strong accelerations from the intense luminosity and winds of GB stars. Here, we establish equations that can model time-varying GB stellar radiation, wind drag and mass loss. We derive the complete three-dimensional equations of motion in orbital elements due to (1) the Epstein and Stokes regimes of stellar wind drag, (2) Poynt…
We perform hydrodynamical simulations of the accretion of pebbles and rocks onto protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the protoplanetary disc gas. Particle streams interacting with the gas far out within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted onto the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10%-50% of their mass from pe…
Coagulation theory predicts that micron-sized dust grains grow into pebbles which drift inward towards the star, when they reach sizes of mm-cm. When they cross the orbit of a planet, a fraction of these drifting pebbles will be accreted. In the pebble accretion mechanism, the combined effects of the planet's gravitational attraction and gas drag greatly increase the accretion rate. We calculate the pebble accretion efficiency $\varepsilon_{2D}$ -- the probability a pebble is accreted by the planet -- in the 2D limit (pebbles reside in the midplane). In particular, we investigate the dependenc…
Despite the fact that the observed gradient in water content among the Galilean satellites is globally consistent with a formation in a circum-Jovian disk on both sides of the snowline, the mechanisms that led to a low water mass fraction in Europa ($\sim$$8\%$) are not yet understood. Here, we present new modeling results of solids transport in the circum-Jovian disk accounting for aerodynamic drag, turbulent diffusion, surface temperature evolution and sublimation of water ice. We find that the water mass fraction of pebbles (e.g., solids with sizes of 10$^{-2}$ -- 1 m) as they drift inward …
Context. The classical "planetesimal" accretion scenario for the formation of planets has recently evolved with the idea that "pebbles", centimeter- to meter-sized icy grains migrating in protoplanetary disks, can control planetesimal and/or planetary growth. Aims. We investigate how pebble accretion depends on disk properties and affects the formation of planetary systems Methods. We construct analytical models of pebble accretion onto planetary embryos that consistently account for the mass and orbital evolution of the pebble flow and reflect disk structure. Results. We derive simple formula…
Pebble accretion is a new mechanism to quickly grow the cores of planets. In pebble accretion, gravity and gas drag conspire to yield large collisional cross sections for small particles in protoplanetary disks. However, before pebble accretion commences, aerodynamical deflection may act to prevent planetesimals from becoming large, because particles tend to follow gas streamlines. We derive the planetesimal radius where pebble accretion is initiated and determine the growth timescales of planetesimals by sweepup of small particles. We obtain the collision efficiency factor as the ratio of the…
It is widely held that the first step in forming the gas giant planets, such as Jupiter and Saturn, is to form solid `cores' of roughly 10 M$_\oplus$. Getting the cores to form before the solar nebula dissipates ($\sim\!1-10\,$Myr) has been a major challenge for planet formation models. Recently models have emerged in which `pebbles' (centimeter- to meter-size objects) are first concentrated by aerodynamic drag and then gravitationally collapse to form 100 --- 1000 km objects. These `planetesimals' can then efficiently accrete leftover pebbles and directly form the cores of giant planets. This…
Content: For up to a few millions of years, pebbles must provide a quasi-steady inflow of solids from the outer parts of protoplanetary disks to their inner regions. Aims: We wish to understand how a significant fraction of the pebbles grows into planetesimals instead of being lost to the host star. Methods:We examined analytically how the inward flow of pebbles is affected by the snow line and under which conditions dust-rich (rocky) planetesimals form. When calculating the inward drift of solids that is due to gas drag, we included the back-reaction of the gas to the motion of the solids. Re…
In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. MHD disc models also suggest the existence of a dead-zone at $R\lesssim 10$ AU, where the regions close to the midplane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet ($\sim 1.7 \;{\rm M_\oplus}$) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio $ε\ge 0.5$. For pebbles with Stokes numbers St=0.1, 0.5, multiple dusty …
Recently, seven Earth-sized planets were discovered around the M-dwarf star TRAPPIST-1. Thanks to transit-timing variations, the masses and therefore the bulk densities of the planets have been constrained, suggesting that all TRAPPIST-1 planets are consistent with water mass fractions on the order of 10%. These water fractions, as well as the similar planet masses within the system, constitute strong constraints on the origins of the TRAPPIST-1 system. In a previous work, we outlined a pebble-driven formation scenario. In this paper we investigate this formation scenario in more detail. We us…
Most major planetary bodies in the solar system rotate in the same direction as their orbital motion: their spin is prograde. Theoretical studies to explain the direction as well as the magnitude of the spin vector have had mixed success. When the accreting building blocks are $\sim$ km-size planetesimals -- as predicted by the classical model -- the accretion process is so symmetric that it cancels out prograde with retrograde spin contributions, rendering the net spin minute. For this reason, the currently-favored model for the origin of planetary rotation is the giant impact model, in which…
The formation of gas-giant planets within the lifetime of a protoplanetary disk is challenging especially far from a star. A promising model for the rapid formation of giant-planet cores is pebble accretion in which gas drag during encounters leads to high accretion rates. Most models of pebble accretion consider disks with a monotonic, radial pressure profile. This causes a continuous inward flux of pebbles and inefficient growth. Here we examine planet formation in a disk with multiple, intrinsic pressure bumps. In the outer disk, pebbles become trapped near these bumps allowing rapid growth…
The four major satellites of Jupiter, known as the Galilean moons, and Saturn's most massive satellite, Titan, are believed to have formed in a predominantly gaseous circum-planetary disk, during the last stages of formation of their parent planet. Pebbles from the protoplanetary disk are blocked from flowing into the circumplanetary disk by the positive pressure gradient at the outer edge of the planetary gap, so the gas drag assisted capture of planetesimals should be the main contributor to the delivery of solids onto circum-planetary disks. However, a consistent framework for the subsequen…
Aims. Dust plays a crucial role in the evolution of protoplanetary disks. We study the dynamics and growth of initially sub-$μm$ dust particles in self-gravitating young protoplanetary disks with various strengths of turbulent viscosity. We aim to understand the physical conditions that determine the formation and spatial distribution of pebbles when both disk self-gravity and turbulent viscosity can be concurrently at work. Methods. We perform the thin-disk hydrodynamics simulations of self-gravitating protoplanetary disks over an initial time period of 0.5 Myr using the FEOSAD code. Turbulen…
The growth and migration of planetesimals in a young protoplanetary disc are fundamental to planet formation. In all models of early growth, there are several processes that can inhibit grains from reaching larger sizes. Nevertheless, observations suggest that growth of planetesimals must be rapid. If a small number of 100 km sized planetesimals do manage to form in the disc, then gas drag effects could enable them to efficiently accrete small solids from beyond their gravitationally focused cross-section. This gas drag-enhanced accretion can allow planetesimals to grow at rapid rates, in prin…
Volatile molecules containing hydrogen, carbon, and nitrogen are key components of planetary atmospheres. In the pebble accretion model for rocky planet formation, these volatile species are accreted during the main planetary formation phase. For this study, we modelled the partitioning of volatiles within a growing planet and the outgassing to the surface. The core stores more than 90\% of the hydrogen and carbon budgets of Earth for realistic values of the partition coefficients of H and C between metal and silicate melts. The magma oceans of Earth and Venus are sufficiently deep to undergo …
The compact multi-transiting planet systems discovered by Kepler challenge planet formation theories. Formation in situ from disks with radial mass surface density, $Σ$, profiles similar to the minimum mass solar nebula (MMSN) but boosted in normalization by factors $\gtrsim 10$ has been suggested. We propose that a more natural way to create these planets in the inner disk is formation sequentially from the inside-out via creation of successive gravitationally unstable rings fed from a continuous stream of small (~cm--m size) "pebbles", drifting inwards via gas drag. Pebbles collect at the pr…
The Kepler-discovered Systems with Tightly-packed Inner Planets (STIPs), typically with several planets of Earth to super-Earth masses on well-aligned, sub-AU orbits may host the most common type of planets, including habitable planets, in the Galaxy. They pose a great challenge for planet formation theories, which fall into two broad classes: (1) formation further out followed by inward migration; (2) formation in situ, in the very inner regions of the protoplanetary disk. We review the pros and cons of these classes, before focusing on a new theory of sequential in situ formation from the in…
Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals…
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 disk 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 disk inner edge, scattering events and collisions take place promoting additional growth. Growing satellites event…
We present the results of planet formation N-body simulations based on a comprehensive physical model that includes planetary mass growth through mutual embryo collisions and planetesimal/boulder accretion, viscous disc evolution, planetary migration and gas accretion onto planetary cores. The main aim of this study is to determine which set of model parameters leads to the formation of planetary systems that are similar to the compact low mass multi-planet systems that have been discovered by radial velocity surveys and the Kepler mission. We vary the initial disc mass, solids-to-gas ratio an…
We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalising the approach developed in Laibe & Price (2014a). A generalisation for continuous dust distributions as well as analytic approximations for strong drag regimes are also provided. This formalism lays the foundation for numeri- cal simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, nam…
Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff, particularly because of small particles and/or strong local solid concentration, that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite th…
Dust is a major component of protoplanetary and debris disks as it is the main observable signature of planetary formation. However, since dust dynamics is size-dependent (because of gas-drag or radiation pressure) any attempt to understand the full dynamical evolution of circumstellar dusty-disks that neglect the coupling of collisional evolution with dynamical evolution is thwarted because of the feedback between these two processes. Here, a new hybrid lagrangian/eulerian code is presented that overcomes some of these difficulties. The particles representing "dust-clouds" are tracked individ…
The growth process of proto-planets can be sped-up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent discs. Here, we investigate the accretion of pebbles in turbulent discs that are driven by the purely hydrodynamical vertical shear instability (VSI). For this purpose, we perform global three-dimensional simulations of locally isothermal, VSI turbulent discs with embedded protoplanetary cores from 5 to 100 $M_\oplus$ that are placed at 5.2 au dista…
Sticking properties rule the early phases of pebble growth in protoplanetary discs in which grains regularly travel from cold, water-rich regions to the warm inner part. This drift affects composition, grain size, morphology, and water content as grains experience ever higher temperatures. In this study we tempered chondritic dust under vacuum up to 1400 K. Afterwards, we measured the splitting tensile strength of millimetre-sized dust aggregates. The deduced effective surface energy starts out as $γ_e = 0.07\,\rm J/m^2$. This value is dominated by abundant iron-oxides as measured by Mössbauer…
Millimeter astronomy provides valuable information on the birthplaces of planetary systems. In order to compare theoretical models with observations, the dust component has to be carefully calculated. Here, we aim to study the effects of dust entrainment in photoevaporative winds and the ejection and drag of dust due to effects caused by radiation from the central star. We improved and extended the existing implementation of a two-population dust and pebble description in the global Bern/Heidelberg planet formation and evolution model. Modern prescriptions for photoevaporative winds were used …
Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We perform a series of…
Gravitating bodies significantly alter the flow pattern (density and velocity) of the gas that attempts to stream past. Still, small protoplanets in the Mars--super-Earth range can only bind limited amounts of nebular gas; until the so-called critical core mass has been reached (~1-10 Earth masses) this gas is in near hydrostatic equilibrium with the nebula. Here we aim for a general description of the flow pattern surrounding these low-mass, embedded planets. Using various simplifying assumptions (subsonic, 2D, inviscid flow, etc), we reduce the problem to a partial differential equation that…
Active Galactic Nucleus Tori: Potential Birthplace to Millions of Planets
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；New Mexico State University（新墨西哥州立大学）；CUNY Borough of Manhattan Community College（纽约市立大学曼哈顿社区学院）；American Museum of Natural History（美国自然历史博物馆）
In planetary science, accretion is the process in which solids agglomerate to form larger and larger objects and eventually planets are produced. The initial conditions are a disc of gas and microscopic solid particles, with a total mass of about 1% of the gas mass. Accretion has to be effective and fast. Effective, because the original total mass in solids in the solar protoplanetary disk was probably of the order of ~ 300 Earth masses, and the mass incorporated into the planets is ~100 Earth masses. Fast, because the cores of the giant planets had to grow to tens of Earth masses in order to …
The currently available, detailed properties (e.g., isotopic ratios) of solar system planets may provide guides for constructing better approaches of 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 con…
The streaming instability is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio $ε$. Using numerical simulations of an unstratified disc, we bring three cases in different regimes into nonlinear saturation. We find that the saturation states of the two fast-growth cases are similar to its si…
Rings Around Non-Spherical Worlds: Sub-mm Dust Retention Around Triaxial Small Bodies in the Solar System
HUN-REN CSFK Konkoly Observatory, MTA Centre of Excellence（匈牙利科学院研究网络天体物理学研究中心孔科利天文台，匈牙利科学院卓越中心）；ELTE Eötvös Loránd University, Institute of Physics and Astronomy（厄特沃什·罗兰大学物理与天文学研究所）
