We present a study on the formation of planetary systems around low mass stars similar to Trappist-1, through the accretion of either planetesimals or pebbles. The aim is to determine if the currently observed systems around low mass stars favour one scenario over the other. We ran numerous N-body simulations, coupled to a thermally evolving viscous disc model, including prescriptions for planet migration and photoevaporation. We examine the differences between the pebble and planetesimal accretion scenarios, but also look at the influences of disc mass, planetesimal size, and the percentage of solids locked up within pebbles. When comparing the resulting planetary systems to Trappist-1, we find that a wide range of initial conditions for both accretion scenarios can form planetary systems similar to Trappist-1, in terms of planet mass, periods, and resonant configurations. Typically these planets formed exterior to the water iceline and migrated in resonant convoys to close to the central star. When comparing the planetary systems formed from pebbles to those formed from planetesimals, we find a large number of similarities, including average planet masses, eccentricities, inclinations and period ratios. One major difference was that of the water content of the planets. When including the effects of ablation and full recycling of the planets envelope with the disc, planets formed from pebbles were extremely dry, whilst those formed from planetesimals were extremely wet. If the water content is not fully recycled and instead falls to the planets core, or if ablation of the water is neglected, then the planets formed from pebbles are extremely wet, similar to those formed from planetesimals. Should the water content of the Trappist-1 planets be determined accurately, this could point to a preferred formation pathway for planetary systems, or to specific physics that may be at play.
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…
The first stage of planet formation is the accumulation of dust and ice grains into mm-cm-sized pebbles. These pebbles can clump together through the streaming instability and form gravitationally bound pebble 'clouds'. Pebbles inside such a cloud will undergo mutual collisions, dissipating energy into heat. As the cloud loses energy, it gradually contracts towards solid density. We model this process and investigate two important properties of the collapse: (i) the timescale of the collapse and (ii) the temporal evolution of the pebble size distribution. Our numerical model of the pebble clou…
Observational data suggest that a belt of planetesimals is expected close to the snow line in protoplanetary disks. Assuming there is such a belt in TRAPPIST-1 system, we examine possibilities of water delivery to the planets via planetesimals from the belt. The study is accomplished by numerical simulations of dynamical evolution of a hypothetical planetesimal belt. Our results show that the inner part of the belt is dynamically unstable and planetesimals located in this region are quickly scattered away, with many of them entering the region around the planets. The main dynamical mechanism r…
We propose an expression for a local planetesimal formation rate proportional to the instantaneous radial pebble flux. The result --- a radial planetesimal distribution --- can be used as initial condition to study the formation of planetary embryos. We follow the idea that one needs particle traps to locally enhance the dust-to-gas ratio sufficiently such that particle gas interactions can no longer prevent planetesimal formation on small scales. The location of these traps can emerge everywhere in the disk. Their occurrence and lifetime is subject of ongoing research, thus they are implement…
We present a model in which planetesimal disks are built from the combination of planetesimal formation and accretion of radially drifting pebbles onto existing planetesimals. In this model, the rate of accretion of pebbles onto planetesimals quickly outpaces the rate of direct planetesimal formation in the inner disk. This allows for the formation of a high mass inner disk without the need for enhanced planetesimal formation or a massive protoplanetary disk. Our proposed mechanism for planetesimal disk growth does not require any special conditions to operate. Consequently, we expect that hig…
Streaming instability is a key mechanism in planet formation, clustering pebbles into planetesimals. It is triggered at a particular disk location where the local volume density of solids exceeds that of the gas. After their formation, planetesimals can grow by feeding from other planetesimals in the birth ring as well as by accreting inwardly drifting pebbles from the outer disk. To investigate the growth of planetesimals at a single location by the streaming instability, we test the conditions under which super-Earths are able to form within the lifetime of the gaseous disk. We modify the \t…
Forming gas giant planets by the accretion of 100 km diameter planetesimals, a typical size that results from self-gravity assisted planetesimal formation, is often thought to be inefficient. Many models therefore use small km-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals distributed radially in a minimum mass solar nebula fashion. We wish to investigate the impact of various initial radial density distributions in planetesimals with a dynamical model for the formation of planetesima…
TRAPPIST-1 is a nearby 0.08 M M-star, which was recently found to harbor a planetary system of at least seven Earth-mass planets, all within 0.1 au. The configuration confounds theorists as the planets are not easily explained by either in situ or migration models. In this Paper we present a scenario for the formation and orbital architecture of the TRAPPIST-1 system. In our model, planet formation starts at the H2O iceline, where pebble-size particles -- whose origin is the outer disk -- concentrate to trigger streaming instabilities. After their formation, planetary embryos quickly mature by…
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…
The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolut…
Planet formation models begin with proto-embryos and planetesimals already fully formed, missing out a crucial step, the formation of planetesimals/proto-embryos. In this work, we include prescriptions for planetesimal and proto-embryo formation arising from pebbles becoming trapped in short-lived pressure bumps, in thermally evolving viscous discs to examine the sizes and distributions of proto-embryos and planetesimals throughout the disc. We find that planetesimal sizes increase with orbital distance, from ~10 km close to the star to hundreds of kilometres further away. Proto-embryo masses …
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…
In the core accretion scenario, a massive core forms first and then accretes an envelope. When discussing how this core forms some divergences appear. First scenarios of planet formation predict the accretion of km-sized bodies, called planetesimals, while more recent works suggest growth by accretion of pebbles, which are cm-sized objects. These two accretion models are often discussed separately and we aim here at comparing the outcomes of the two models with identical initial conditions. We use two distinct codes: one computing planetesimal accretion, the other pebble accretion. Using a pop…
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…
Planetesimals are compact astrophysical objects roughly 1-1000 km in size, massive enough to be held together by gravity. They can grow by accreting material to become full-size planets. Planetesimals themselves are thought to form by complex physical processes from small grains in protoplanetary disks. The streaming instability (SI) model states that mm/cm-size particles (pebbles) are aerodynamically collected into self-gravitating clouds which then directly collapse into planetesimals. Here we analyze ATHENA simulations of the SI to characterize the initial properties (e.g., rotation) of peb…
Formation of Ryugu's parent planetesimal beyond the CO$_{2}$ snow line from small pebbles: insights from thermal evolution modeling
Japan Agency for Marine-Earth Science and Technology（日本海洋地球科学技术局）；Earth-Life Science Institute, Institute of Science Tokyo（东京科学研究所生命理工学研究院）；Department of Earth and Planetary Sciences, Hokkaido University（北海道大学地球行星科学系）；Faculty of Science, Ibaraki University（茨城大学理学部）；School of Science, Institute of Science Tokyo（东京科学研究所理学院）；Department of Earth, Atmospheric, and Planetary Sciences, Purdue University（普渡大学地球大气与行星科学系）
Recent work has shown that aside from the classical view of collisions by increasingly massive planetesimals, the accretion of mm- to m-sized 'pebbles' can also reproduce the mass-orbit distribution of the terrestrial planets. Here, we perform N-body simulations to study the effects of pebble accretion onto growing planetesimals of different diameters located in the inner Solar System. The simulations are run to occur during the lifetime of the gas disc while also simultaneously taking Jupiter's growth into account. We find that pebble accretion can increase the mass in the solid disc by at le…
Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of mm-cm-sized pebbles. Such clouds can form for example through the streaming instability in protoplanetary disks. We model the collapse process with a statistical model to obtain the internal structure of planetesimals with solid radii between 10 and 1,000 km. In the collapse, pebbles collide and, depending on relative speed, collisions have different outcomes. A mixture of particle sizes inside a planetesimal leads to better packing capabilities and higher densities. In this paper we app…
Mass-independent isotopic anomalies of carbonaceous and non-carbonaceous meteorites show a clear dichotomy suggesting an efficient separation of the inner and outer solar system. Observations show that ring-like structures in the distribution of mm-sized pebbles in protoplanetary disks are common. These structures are often associated with drifting pebbles being trapped by local pressure maxima in the gas disk. Similar structures may also have existed in the sun's natal disk, which could naturally explain the meteorite/planetary isotopic dichotomy. Here, we test the effects of a strong pressur…
Nearly-axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We test this hypothesis by performing global 1-D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore dif…
Wind erosion is a destructive mechanism that completely dissolves a weakly bound object like a planetesimal into its constituent particles, if the velocity relative to the ambient gas and the local gas pressure are sufficiently high. In numerical simulations we study the influence of such wind erosion on pebble and planetesimal accretion by a planetary body up to $10 R_\mathrm{Earth}$. Due to the rapid size reduction of an in-falling small body, the accretion outcome changes significantly. Erosion leads to a strong decrease in the accretion efficiency below a threshold size of the small body o…
We explore the growth of planetary embryos by planetesimal accretion up to and beyond the point where pebble accretion becomes efficient at the so-called Hill-transition mass. Both the transition mass and the characteristic mass of planetesimals formed by the streaming instability increase with increasing distance from the star. We developed a model for the growth of a large planetesimal (embryo) embedded in a population of smaller planetesimals formed in a filament by the streaming instability. The model includes in a self-consistent way the collisional mass growth of the embryo, the fragment…
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
We perform streaming instability simulations at Hill density and beyond, to demonstrate that Planetesimal formation is not completed when pebble accumulations exceed the local Hill density. We find that Hill density is not a sufficient criterion for further gravitational collapse of a pebble cloud into a planetesimal, but that additionally the accumulated mass has to be large enough to overcome turbulent diffusion. A Toomre analysis of the system indicates that linear self-gravity modes play no role on the scale of our numerical simulation. We nevertheless find that self-gravity, by vertically…
In parabolic flight experiments we studied the wind induced erosion of granular beds composed of spherical glass beads at low gravity and low ambient pressure. Varying g-levels were set by centrifugal forces. Expanding existing parameter sets to a pressure range between $p=300-1200\,$Pa and to g-levels of $g=1.1-2.2\,\rm m\,s^{-2}$ erosion thresholds are still consistent with the existing model for wind erosion on planetary surfaces by Shao & Lu (2000). These parameters were the lowest values that could technically be reached by the experiment. The experiments decrease the necessary range of e…
To avoid known difficulties in planetesimal formation such as the drift or fragmentation barriers, many scenarios have been proposed. However, in these scenarios, planetesimals form in general only at some specific locations in protoplanetary discs. On the other hand, it is generally assumed in planet formation models and population synthesis models, that planetesimals are broadly distributed in the protoplanetary disc. Here we propose a new scenario in which planetesimals can form in broad areas of the discs. Planetesimals form at the gas pressure bump formed by a first-generation planet (e.g…
Inside-Out Planet Formation (IOPF) is a theory addressing the origin of Systems of Tightly-Packed Inner Planets (STIPs) via {\it in situ} formation and growth of the planets. It predicts that a pebble ring is established at the pressure maximum associated with the dead zone inner boundary (DZIB) with an inner disk magnetorotational instability (MRI)-active region. Using direct $N$-body simulations, we study the collisional evolution of planetesimals formed from such a pebble ring, in particular examining whether a single dominant planet emerges. We consider a variety of models, including some …
I examine the standard model of planet formation, including pebble accretion, using numerical simulations. Planetary embryos large enough to become giant planets do not form beyond the ice line within a typical disk lifetime unless icy pebbles stick at higher speeds than in experiments using rocky pebbles. Systems like the Solar System (small inner planets, giant outer planets) can form if (i) icy pebbles are stickier than rocky pebbles, and (ii) the planetesimal formation efficiency increases with pebble size, which prevents the formation of massive terrestrial planets. Growth beyond the ice …
We study the collapse of pebble clouds with a statistical model to find the internal structure of comet-sized planetesimals. Pebble-pebble collisions occur during the collapse and the outcome of these collisions affect the resulting structure of the planetesimal. We expand our previous models by allowing the individual pebble sub-clouds to contract at different rates and by including the effect of gas drag on the contraction speed and in energy dissipation. Our results yield comets that are porous pebble-piles with particle sizes varying with depth. In the surface layers there is a mixture of …
We model the early stages of planet formation in the Solar System, including continual planetesimal formation, and planetesimal and pebble accretion onto planetary embryos in an evolving disk driven by a disk wind. The aim is to constrain aspects of planet formation that have large uncertainties by matching key characteristics of the Solar System. The model produces a good fit to these characteristics for a narrow range of parameter space. Planetary growth beyond the ice line is dominated by pebble accretion. Planetesimal accretion is more important inside the ice line. Pebble accretion inside…
Around the snow line, icy pebbles and silicate dust may locally pile-up and form icy and rocky planetesimals via streaming instability and/or gravitational instability. We perform 1D diffusion-advection simulations that include the back-reaction to radial drift and diffusion of icy pebbles and silicate dust, ice sublimation, release of silicate dust, and their recycling through recondensation and sticking onto pebbles outside the snow line. We use a realistic description of the scale height of silicate dust obtained from Ida et al. and that of pebbles including the effects of a Kelvin-Helmholt…
The formation of the first planetesimals and the final growth of planetary cores relies on the abundance of small pebbles. The efficiencies of both the streaming instability (SI) process, suggested to catalyze the early growth of planetesimals, and the pebble-accretion process, suggested to accelerate the growth of planetary cores, depend on the sizes of solids residing in the disk. In particular, these processes were found to be sensitive to size distribution of solids, and efficient planetesimal formation and growth through these channels require a limited pebble size distribution. Here we s…
The consistency of planet formation models suffers from the disconnection between the regime of small and large bodies. This is primarily caused by so-called growth barriers: the direct growth of larger bodies is halted at centimetre-sized objects and particular conditions are required for the formation of larger, gravitationally bound planetesimals. We aim to connect models of dust evolution and planetesimal formation to identify regions of protoplanetary discs that are favourable for the formation of kilometre-sized bodies and the first planetary embryos. We combine semi-analytical models of…
In the past decade, ALMA observations have revealed that a large fraction of protoplanetary discs contains rings in the dust continuum. These rings are the locations where pebbles accumulate, which is beneficial for planetesimal formation and subsequent planet assembly. We investigate the viability of planet formation inside ALMA rings in which pebbles are trapped by either a Gaussian-shape pressure bump or by the strong dust backreaction. Planetesimals form at the midplane of the ring via streaming instability. By conducting N-body simulations, we study the growth of these planetesimals by co…
The standard model for giant planet formation is based on the accretion of solids by a growing planetary embryo, followed by rapid gas accretion once the planet exceeds a so-called critical mass. The dominant size of the accreted solids (cm-size particles named pebbles or km to hundred km-size bodies named planetesimals) is, however, unknown. Recently, high-precision measurements of isotopes in meteorites provided evidence for the existence of two reservoirs in the early Solar System. These reservoirs remained separated from ~1 until ~ 3 Myr after the beginning of the Solar System's formation.…
Context: Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by accreting cm-to-m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This provides early enrichment to the planet's envelope, which changes the process of core growth. Aims: We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Methods: We…
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 …
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplaneta…
Previous work on protoplanetary dust growth shows halt at centimeter sizes owing to the occurrence of bouncing at velocities of $\geq$ 0.1 $ms^{-1}$ and fragmentation at velocities $\geq$ 1 $ms^{-1}$. To overcome these barriers, spatial concentration of cm-sized dust pebbles and subsequent gravitational collapse have been proposed. However, numerical investigations have shown that dust aggregates may undergo fragmentation during the gravitational collapse phase. This fragmentation in turn changes the size distribution of the solids and thus must be taken into account in order to understand the…
Exploring the conditions for forming planetesimals by the streaming instability and planetary systems by pebble accretion
Center for Star and Planet Formation, Globe Institute, University of Copenhagen（哥本哈根大学全球研究所恒星与行星形成中心）；Division of Astrophysics, Department of Physics, Lund University（隆德大学物理系天体物理学部）；New Mexico State University, Department of Astronomy（新墨西哥大学天文学系）
This chapter highlights the properties of turbulence and meso-scale flow structures in protoplanetary disks and their role in the planet formation process. Here we focus on the formation of planetesimals from a gravitational collapse of a pebble cloud. Large scale and long lived flow structures - vortices and zonal flows - are a consequence of weak magneto and hydrodynamic instabilities in the pressure and entropy stratified quasi-Keplerian shear flow interacting with the fast rotation of the disk. The vortices and zonal flows on the other hand are particle traps tapping into the radial pebble…
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 ti…
Models of planetary core growth by either planetesimal or pebble accretion are traditionally disconnected from the models of dust evolution and formation of the first gravitationally-bound planetesimals. The state-of-the-art models typically start with massive planetary cores already present. We aim to study the formation and growth of planetary cores in a pressure bump, motivated by the annular structures observed in protoplanetary disks, starting with sub-micron-sized dust grains. We connect the models of dust coagulation and drift, planetesimal formation in the streaming instability, gravit…
Context: The formation of rocky planetesimals is a long-standing problem in planet formation theory. One of the possibilities is that it results from gravitational instability as a result of pile-up of small silicate dust particles released from sublimating icy pebbles that pass the snow line. Aims: We want to understand and quantify the role of the water snow line for the formation of rock-rich and ice-rich planetesimals. In this paper, we focus on the formation of rock-rich planetesimals. A companion paper examines the combined formation of both rock-rich and ice-rich planetesimals. Methods:…
Small, pebble-sized objects and large bodies of planetesimal size both play important roles in planet formation. They form the evolutionary steps of dust growth in their own respect. However, at later times, they are also thought to provide background populations of mass that larger bodies might feed upon. What we suggest in this work is that starting at times of viscous stirring, planetesimals on eccentric orbits could simply explode as they become supersonic in comparison to small, porous planetary bodies entering Earth's atmosphere. We present a toy model of planetesimal motion and destruct…
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…
