The presence of rings and gaps in protoplanetary discs are often ascribed to planet-disc interactions, where dust and pebbles are trapped at the edges of planetary induced gas gaps. Recent work has shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and ability to radially transport solids in protoplanetary discs. We perform a series of N-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We consider two planetary systems: one akin to the young Solar System, and another one inspired by HL Tau. In both systems, the close proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disc soon after formation. Planetesimals that end up on eccentric orbits interior of 10au experience efficient ablation, and lose all mass before they reach the innermost disc region. In our nominal Solar System simulation with $\dot{M}_0=10^{-7}\, M_{\odot}\, \textrm{yr}^{-1}$ and $α=10^{-2}$, we find that 70% of the initial planetesimal mass has been ablated after 500kyr. The ablation rate in HL Tau is lower, and only 11% of the initial planetesimal mass has been ablated after 1Myr. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solids grow to pebbles in the disc midplane, this results in a pebble flux of $\sim 10-100\,M_{\oplus}\textrm{Myr}^{-1}$ through the inner disc. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary discs.
Hydrous minerals are found on the surfaces of asteroids, but their origin is not clear. If their origin is endogenic, the hydrous minerals that were formed in the inner part of a planetesimal (or parent body) should come out on to the surface without dehydration. If their origin is exogenic, the source of hydrous minerals accreting onto asteroids is needed. Collisions in the asteroid belt would be related to both origins because collisions excavate the surface and eject the materials. However, the fate of hydrous minerals in large planetesimals during the collisional process has not been well …
We perform $N$-body simulations of the early phases of open cluster evolution including a large population of planetesimals, initially arranged in Kuiper-belt like discs around each star. Using a new, 4th-order and time-reversible $N$-body code on Graphics Processing Units (GPUs), we evolve the whole system under the stellar gravity, i.e. treating planetesimals as test particles, and consider two types of initial cluster models, similar to IC348 and the Hyades, respectively. In both cases, planetesimals can be dynamically excited, transferred between stars or liberated to become free-floating …
The growth time scales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. We quantify the timescales and spatial distribution of planetary embryos via collisional growth and fragmentation of dynamically forming 100km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. We connect a on…
A critical phase in the standard model for planet formation is the runaway growth phase. During runaway growth bodies in the 0.1--100 km size range (planetesimals) quickly produce a number of much larger seeds. The runaway growth phase is essential for planet formation as the emergent planetary embryos can accrete the leftover planetesimals at large gravitational focusing factors. However, torques resulting from turbulence-induced density fluctuations may violate the criterion for the onset of runaway growth, which is that the magnitude of the planetesimals' random (eccentric) motions are less…
By logging encounters between planetesimals and planets we compute the distribution of encounters in a numerically integrated two planet system that is migrating due to interactions with an exterior planetesimal belt. Capture of an irregular satellite in orbit about a planet through an exchange reaction with a binary planetesimal is only likely when the binary planetesimal undergoes a slow and close encounter with the planet. In our simulations we find that close and slow encounters between planetesimals and a planet primarily occur with the outermost and not innermost planet. Taking care to c…
Massive planetary cores ($\sim 10$ Earth masses) trigger rapid gas accretion to form gas giant planets \rev{such as} Jupiter and Saturn. We investigate the core growth and the possibilities for cores to reach such a critical core mass. At the late stage, planetary cores grow through collisions with small planetesimals. Collisional fragmentation of planetesimals, which is induced by gravitational interaction with planetary cores, reduces the amount of planetesimals surrounding them, and thus the final core masses. Starting from small planetesimals that the fragmentation rapidly removes, less ma…
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…
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…
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…
HR 8799 is a four planet system that also hosts a debris disk. By numerically integrating both planets and a planetesimal disk, we find interactions between an exterior planetesimal disk and the planets can influence the lifetime of the system. We first consider resonant planetary configurations that remained stable for at least 7 Myrs sans debris disk. An exterior debris disk with only 1 per cent the mass of the outermost planet (approximately a Neptune mass) was sufficiently large enough to pull the system out of resonance after 2 to 6 Myrs. Secondly, we consider configurations which are uns…
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…
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…
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust t…
Turbulence in protoplanetary disks affects planet formation in many ways. While small dust particles are mainly affected by the aerodynamical coupling with turbulent gas velocity fields, planetesimals and larger bodies are more affected by gravitational interaction with gas density fluctuations. For the latter process, a number of numerical simulations have been performed in recent years, but a fully parameter-independent understanding has not been yet established. In this study, we present simple scaling relations for the planetesimal stirring rate in turbulence driven by magnetorotational in…
Roughly 1000 white dwarfs are known to be polluted with planetary material, and the progenitors of this material are typically assumed to be asteroids. The dynamical architectures which perturb asteroids into white dwarfs are still unknown, but may be crucially dependent on moons liberated from parent planets during post-main-sequence gravitational scattering. Here, we trace the fate of these exomoons, and show that they more easily achieve deep radial incursions towards the white dwarf than do scattered planets. Consequently, moons are likely to play a significant role in white dwarf pollutio…
The orbital architecture of the Solar System is thought to have been sculpted by a dynamical instability among the giant planets. During the instability a primordial outer disk of planetesimals was destabilized and ended up on planet-crossing orbits. Most planetesimals were ejected into interstellar space but a fraction were trapped on stable orbits in the Kuiper belt and Oort cloud. We use a suite of N-body simulations to map out the diversity of planetesimals' dynamical pathways. We focus on two processes: tidal disruption from very close encounters with a giant planet, and loss of surface v…
The growth of small planetesimals into large planetary embryos occurs much before the dispersal of the gas from the protoplanetary disk. The planetesimal - gaseous-disk interactions give rise to migration and orbital evolution of the planetesimals/planets. Small planetesimals are dominated by aerodynamic gas drag. Large protoplanets, $m\sim0.1M_{\oplus}$, are dominated by type I migration \emph{differential} torque. There is an additional mass range, $m\sim10^{21}-10^{25}g$ of \emph{intermediate mass} planetesimals (IMPs), where gravitational interactions with the disk dominate over aerodynami…
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 o…
'Oumuamua, the first bona-fide interstellar planetesimal, was discovered passing through our Solar System on a hyperbolic orbit. This object was likely dynamically ejected from an extrasolar planetary system after a series of close encounters with gas giant planets. To account for 'Oumuamua's detection, simple arguments suggest that ~1 Earth mass of planetesimals are ejected per Solar mass of Galactic stars. However, that value assumes mono-sized planetesimals. If the planetesimal mass distribution is instead top-heavy the inferred mass in interstellar planetesimals increases to an implausibly…
This paper considers how planetesimal impacts affect planetary atmospheres. Atmosphere evolution depends on the ratio of gain from volatiles to loss from atmosphere stripping f_v; for constant bombardment, atmospheres with f_v<1 are destroyed in finite time, but grow linearly with time for f_v>1. An impact outcome prescription is used to characterise how f_v depends on planetesimal impact velocities, size distribution and composition. Planets that are low mass and/or close to the star have atmospheres that deplete in impacts, while high mass and/or distant planets grow secondary atmospheres. D…
Observations of exoplanetary spectra are leading to unprecedented constraints on their atmospheric elemental abundances, particularly O/H, C/H, and C/O ratios. Recent studies suggest that elemental ratios could provide important constraints on formation and migration mechanisms of giant exoplanets. A fundamental assumption in such studies is that the chemical composition of the planetary envelope represents the sum-total of compositions of the accreted gas and solids during the formation history of the planet. We investigate the efficiency with which accreted planetesimals ablate in a giant pl…
The composition of giant planets reflects their formation history. Planetesimal accretion during the phase of planetary migration could lead to the delivery of heavy elements into giant planets. In our previous paper (Shibata et al. 2020) we showed that planetesimal accretion during planetary migration occurs in a rather narrow region of the protoplanetary disk, which we refer as "the sweet spot for accretion". The goal of this paper is to reveal the nature of the sweet spot and investigate the role of the sweet spot in determining the composition of gas giant planets. We analytically derive t…
Core Accretion, the most widely accepted scenario for planet formation, postulates existence of km-sized solid bodies, called planetesimals, arranged in a razor-thin disc in the earliest phases of planet formation. In the Tidal Downsizing hypothesis, an alternative scenario for formation of planets, grain growth, sedimentation and formation of planetary cores occur inside dense and massive gas clumps formed in the outer cold disc by gravitational instability. As a clump migrates inward, tidal forces of the star remove all or most of the gas from the clump, downsizing it to a planetary mass bod…
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…
Astronomical observations reveal that protoplanetary disks around young stars commonly have ring- and gap-like structures in their dust distributions. These features are associated with pressure bumps trapping dust particles at specific locations, which simulations show are ideal sites for planetesimal formation. Here we show that our Solar System may have formed from rings of planetesimals -- created by pressure bumps -- rather than a continuous disk. We model the gaseous disk phase assuming the existence of pressure bumps near the silicate sublimation line (at $T \sim$1400~K), water snowline…
Current protoplanetary dust coagulation theory does not predict dry silicate planetesimals, in tension with the Earth. While remedies to this predicament have been proposed, they have generally failed numerical studies, or are in tension with the Earth's (low, volatility dependent) volatile and moderately volatile elemental abundances. Expanding on the work of Boley et al. (2014), we examine the implications of molten grain collisions and find that they may provide a solution to the dry silicate planetesimal problem. Further, the source of the heating, be it the hot inner disk or an FU Orionis…
Several hundred stars older than 10 million years have been observed to have infrared excesses. These observations are explained by dust grains formed by the collisional fragmentation of hidden planetesimals. Such dusty planetesimal discs are known as debris discs. In a dynamically cold planetesimal disc, collisional coagulation of planetesimals produces planetary embryos which then stir the surrounding leftover planetesimals. Thus, the collisional fragmentation of planetesimals that results from planet formation forms a debris disc. We aim to determine the properties of the underlying planete…
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）
Observations of small extrasolar planets with a wide range of densities imply a variety of planetary compositions and structures. Currently, the only technique to measure the bulk composition of extrasolar planetary systems is the analysis of planetary debris accreting onto white dwarfs, analogous to abundance studies of meteorites. We present measurements of the carbon and oxygen abundances in the debris of planetesimals at ten white dwarfs observed with the Hubble Space Telescope, along with C/O ratios of debris in six systems with previously reported abundances. We find no evidence for carb…
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 …
Two distinct thermal evolutionary pathways of irregular shaped small planetesimals in the early solar system have been studied. We have taken a case study of two S-type asteroids; (243) Ida and (951) Gaspra, on the basis of their precise physical dimensions accessed by the Philip Stooke small body 3-D shape models of the NASA Planetary Data System. The 3- D shape models for the two asteroids are based on the Galileo spacecraft fly-by mission. Based on our novel thermal evolutionary code for the precise shape of the asteroids we found that the small planetary bodies that accreted within the ini…
Population synthesis models of planetary systems developed during the last $\sim$15 years could reproduce several of the observables of the exoplanet population, and also allowed to constrain planetary formation models. We present our planet formation model, which calculates the evolution of a planetary system during the gaseous phase. The code incorporates relevant physical phenomena for the formation of a planetary system, like photoevaporation, planet migration, gas accretion, water delivery in embryos and planetesimals, a detailed study of the orbital evolution of the planetesimal populati…
We present a model in which planetesimal disks are built from the combination of planetesimal formation and accretion of radially drifting pebbles onto existing planetesimals. In this model, the rate of accretion of pebbles onto planetesimals quickly outpaces the rate of direct planetesimal formation in the inner disk. This allows for the formation of a high mass inner disk without the need for enhanced planetesimal formation or a massive protoplanetary disk. Our proposed mechanism for planetesimal disk growth does not require any special conditions to operate. Consequently, we expect that hig…
Chondrules are one of the most primitive elements that can serve as a fundamental clue as to the origin of our Solar system. We investigate a formation scenario of chondrules that involves planetesimal collisions and the resultant impact jetting. Planetesimal collisions are the main agent to regulate planetary accretion that corresponds to the formation of terrestrial planets and cores of gas giants. The key component of this scenario is that ejected materials can melt when the impact velocity between colliding planetesimals exceeds about 2.5 km s$^{-1}$. The previous simulations show that the…
Chondrules are millimeter-sized spherules that dominate primitive meteorites (chondrites) originating from the asteroid belt. The incorporation of chondrules into asteroidal bodies must be an important step in planet formation, but the mechanism is not understood. We show that the main growth of asteroids can result from gas-drag-assisted accretion of chondrules. The largest planetesimals of a population with a characteristic radius of 100 km undergo run-away accretion of chondrules within ~3 Myr, forming planetary embryos up to Mars sizes along with smaller asteroids whose size distribution m…
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…
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…
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…
This review chapter for young researchers presents our current understanding of debris discs. It introduces some of their basic properties and observables, and describes how we think they form and collisionally evolve. Special emphasis is dedicated to ALMA observations of the dust and gas, which constrains the distribution of planetesimals, their volatile composition, and potential volatile delivery to planetary atmospheres.
Planetary systems have their origin in the gravitational collapse of a cloud of gas and dust. Through a process of accretion, is formed a massive star and a disk of planetesimals orbiting the star. Using a formalism analogous to quantum mechanics (quantum-like model), the star-planetesimal system is described and the flow quantizing the gravitational field theoretical model parameters are obtained. Goodness of fit (chi-square) of the observed data with model quantum-like, to the solar system, satellites, exoplanets and protoplanetary disk around HL Tauri is determined. Shows that the radius, e…
Most models of volatile delivery to accreting terrestrial planets assume that the carriers for water are similar in water content to the carbonaceous chondrites in our Solar System. Here we suggest that the water content of primitive bodies in many planetary systems may actually be much higher, as carbonaceous chondrites have lost some of their original water due to heating from short-lived radioisotopes that drove parent body alteration. Using N-body simulations, we explore how planetary accretion would be different if bodies beyond the water line contained a water mass fraction consistent wi…
Planet formation scenarios and the observed planetary dynamics in binaries pose a number of theoretical challenges, especially in what concerns circumbinary planetary systems. We explore the dynamical stirring of a planetesimal circumbinary disk in the epoch when the gas component disappears. For this purpose, following theoretical approaches by Heppenheimer (1978) and Moriwaki and Nakagawa (2004), we develop a secular theory for the dynamics of planetesimals in circumbinary disks. If the binary is eccentric and its components have unequal masses, a spiral density wave is generated, engulfing …
We investigate the outcome of collisions of Ceres-sized planetesimals composed of a rocky core and a shell of water ice. These collisions are not only relevant for explaining the formation of planetary embryos in early planetary systems, but also provide insight into the formation of asteroid families and possible water transport via colliding small bodies. Earlier studies show characteristic collision velocities exceeding the bodies' mutual escape velocity which - along with the distribution of the impact angles - cover the collision outcome regimes 'partial accretion', 'erosion', and 'hit-an…
Planet formation begins with collisional growth of small planetesimals accumulating into larger ones. Such growth occurs while planetesimals are embedded in a gaseous protoplanetary disc. However, small-planetesimals experience collisions and gas-drag that lead to their destruction on short timescales, not allowing, or requiring fine tuned conditions for the efficient growth of $\sim$ metre-size objects. Here we show that $\sim10^{4}$ interstellar objects such as the recently detected 1I/2017-U1 ('Oumuamua) could have been captured, and become part of the young Solar System, together with up t…
We compute the maximum mass a growing planetary embryo can reach depending on the size of accreted planetesimals or pebbles, to infer the possibility of growing the cores of giant planets, and giant planets themselves. We compute the internal structure of the gas envelope of planetary embryos, to determine the core mass that is necessary to bind an envelope large enough to destroy planetesimals or pebbles while they are gravitationally captured. We also consider the effect of the advection wind originating from the protoplanetary disk, following the results of Ormel et al. (2015). We show that…
Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar clus…
Recent works on planetary migration show that the orbital structure of the Kuiper belt can be very well reproduced if before the onset of the planetary instability Neptune underwent a long-range planetesimal-driven migration up to $\sim$28 au. However, considering that all giant planets should have been captured in mean motion resonances among themselves during the gas-disk phase, it is not clear whether such a very specific evolution for Neptune is possible, nor whether the instability could have happened at late times. Here, we first investigate which initial resonant configuration of the gi…
Vega has been shown to host multiple dust populations, including both hot exo-zodiacal dust at sub-AU radii and a cold debris disk extending beyond 100 AU. We use dynamical simulations to show how Vega's hot dust can be created by long-range gravitational scattering of planetesimals from its cold outer regions. Planetesimals are scattered progressively inward by a system of 5-7 planets from 30-60 AU to very close-in. In successful simulations the outermost planets are typically Neptune-mass. The back-reaction of planetesimal scattering causes these planets to migrate outward and continually in…
Global models of planet formation tend to begin with an initial set of planetary embryos for the sake simplicity. While this approach gives valuable insights on the evolution of the initial embryos, the initial distribution itself is a bold assumption. Limiting oneself to an initial distribution may neglect essential physics that precedes, or follows said initial distribution. We wish to investigate the effect of dynamic planetary embryo formation on the formation of planetary systems. The presented framework begins with an initial disk of gas, dust and pebbles. The disk evolution, the formati…
