We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs, in the (sub)stellar mass range between $0.01 \ M_{\odot}$ and $0.1 \ M_{\odot}$. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial masses of the protoplanets (largest bodies from the planetesimal size distributions), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary disk evolution. We find that the initial protoplanets form with masses that increase with host mass, orbital distance and decrease with disk age. Around late M-dwarfs of $0.1 \ M_{\odot}$, these protoplanets can grow up to Earth-mass planets by pebble accretion. However, around brown dwarfs of $0.01 \ M_{\odot}$, planets do not grow larger than Mars mass when the initial protoplanets are born early in self-gravitating disks, and their growth stalls at around $0.01$ Earth-mass when they are born late in non-self-gravitating disks. Around these low mass stars and brown dwarfs, we find no channel for gas giant planet formation because the solid cores remain too small. When the initial protoplanets form only at the water-ice line, the final planets typically have ${\gtrsim} 15\%$ water mass fraction. Alternatively, when the initial protoplanets form log-uniformly distributed over the entire protoplanetary disk, the final planets are either very water-rich (water mass fraction ${\gtrsim}15\%$) or entirely rocky (water mass fraction ${\lesssim}5\%$).
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 …
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…
We investigate the formation of icy super-Earth mass planets within a gravitationally unstable ring of solids orbiting at 250-750 AU around a 1 solar mass star. Coagulation calculations demonstrate that a system of a few large oligarchs and a swarm of pebbles generates a super-Earth within 100-200 Myr at 250 AU and within 1-2 Gyr at 750 AU. Systems with more than ten oligarchs fail to yield super-Earths over the age of the solar system. As these systems evolve, destructive collisions produce detectable debris disks with luminosities of $10^{-5}$ to $10^{-3}$ relative to the central star.
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…
In the pebble accretion scenario, the pebbles that form planets drift inward from the outer disk regions, carrying water ice with them. At the water ice line, the water ice on the inward drifting pebbles evaporates and is released into the gas phase, resulting in water-rich gas and dry pebbles that move into the inner disk regions. Large planetary cores can block the inward drifting pebbles by forming a pressure bump outside their orbit in the protoplanetary disk. Depending on the relative position of a growing planetary core relative to the water ice line, water-rich pebbles might be blocked …
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…
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…
In the general classical picture of pebble-based core growth, planetary cores grow by accretion of single pebble species. The growing planet may reach the so-called pebble isolation mass, at which it induces a pressure bump that blocks inward drifting pebbles exterior to its orbit, thereby stalling core growth by pebble accretion. In recent hydrodynamic simulations, pebble filtration by the pressure bump depends on several parameters including core mass, disc structure, turbulent viscosity and pebble size. We investigated how accretion of multiple, instead of single, pebble species affects cor…
Inside-Out Planet Formation (IOPF; Chatterjee & Tan 2014, hereafter CT14) is a scenario for sequential in situ planet formation at the pressure traps of retreating dead zone inner boundaries (DZIBs) motivated to explain the many systems with tightly packed inner planets (STIPs) discovered by Kepler. The scenario involves build-up of a pebble-dominated protoplanetary ring, supplied by radial drift of pebbles from the outer disk. It may also involve further build-up of planetary masses to gap-opening scales via continued pebble accretion. Here we study radial drift & growth of pebbles delivered …
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. 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. 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. We f…
Measured disk masses seem to be too low to form the observed population of planetary systems. In this context, we develop a population synthesis code in the pebble accretion scenario, to analyse the disk mass dependence on planet formation around low mass stars. We base our model on the analytical sequential model presented in Ormel et al. 2017 and analyse the populations resulting from varying initial disk mass distributions. Starting out with seeds the mass of Ceres near the ice-line formed by streaming instability, we grow the planets using the Pebble Accretion process and migrate them inwa…
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…
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 mo…
A substantial number of super-Earths have been discovered, and atmospheres of transiting super-Earths have also been observed by transmission spectroscopy. Several lines of observational evidence indicate that most super-Earths do not possess massive H$_2$/He atmospheres. However, accretion and retention of less massive atmospheres on super-Earths challenge planet formation theory. We consider the following three mechanisms: (i) envelope heating by pebble accretion, (ii) mass loss during giant impacts, and (iii) atmospheric loss by stellar X-ray and EUV photoevaporation. We investigate whether…
Pebbles of millimeter sizes are abundant in protoplanetary discs around young stars. Chondrules inside primitive meteorites - formed by melting of dust aggregate pebbles or in impacts between planetesimals - have similar sizes. The role of pebble accretion for terrestrial planet formation is nevertheless unclear. Here we present a model where inwards-drifting pebbles feed the growth of terrestrial planets. The masses and orbits of Venus, Earth, Theia (which later collided with the Earth to form the Moon) and Mars are all consistent with pebble accretion onto protoplanets that formed around Mar…
Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores. II. Dependence on Pebble Bulk Density and Disk Temperature
Chemical compositions of giant planets provide a means to constrain how and where they form. Traditionally, super-stellar elemental abundances in giant planets were thought to be possible due to accretion of metal-rich solids. Such enrichments are accompanied by oxygen-rich compositions (i.e. C/O below the disc's value, assumed to be solar, C/O=0.54). Without solid accretion the planets are expected to have sub-solar metallicity, but high C/O ratios. This arises because the solids are dominated by oxygen-rich species, e.g. H$_2$O and CO$_2$, which freeze out in the disk earlier than CO, leavin…
Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of …
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…
We investigate the pebble isolation mass for a planet on a fixed eccentric orbit in its protoplanetary disc by conducting a set of 2D hydrodynamical simulations including dust turbulent diffusion. A range of planet eccentricities up to $e=0.2$ is adopted. Our simulations also cover a range of $α-$turbulent viscosities, and for each pair $\{α,e\}$ the pebble isolation mass is estimated as the minimum planet mass in our simulations such that solids with a Stokes number $\gtrsim 0.05$ do not flow across the planet orbit and remain trapped around a pressure bump outside the planet gap. For $α<10^{…
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…
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…
The similar orbital distances and detection rates of debris disks and the prominent rings observed in protoplanetary disks suggest a potential connection between these structures. We explore this connection with new calculations that follow the evolution of rings of pebbles and planetesimals as they grow into planets and generate dusty debris. Depending on the initial solid mass and planetesimal formation efficiency, the calculations predict diverse outcomes for the resulting planet masses and accompanying debris signature. When compared with debris disk incidence rates as a function of lumino…
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…
Recent observations of extrasolar gas giants suggest super-stellar C/O ratios in planetary atmospheres, while interior models of observed extrasolar giant planets additionally suggest high heavy element contents. Furthermore, recent observations of protoplanetary disks revealed super-solar C/H ratios, which are explained by inward drifting and evaporating pebbles, enhancing the volatile content of the disk. We investigate how the inward drift and evaporation of volatile rich pebbles influences the atmospheric C/O ratio and heavy element content of giant planets growing by pebble and gas accret…
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…
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…
We present a simple model for low-mass planet formation and subsequent evolution within "transition" discs. We demonstrate quantitatively that the predicted and observed structure of such discs are prime birthsites of planets. Planet formation is likely to proceed through pebble accretion, should a planetary embryo ($M\gtrsim 10^{-4}\,$M$_\oplus$) form. Efficient pebble accretion is likely to be unavoidable in transition disc dust traps, as the size of the dust particles required for pebble accretion are those which are most efficiently trapped in the transition disc dust trap. Rapid pebble ac…
The growth of a pebble accreting planetary core is stopped when reaching its \textit{isolation mass} that is due to a pressure maximum emerging at the outer edge of the gap opened in gas. This pressure maximum traps the inward drifting pebbles stopping the accretion of solids onto the core. On the other hand, a large amount of pebbles ($\sim 100M_\oplus$) should flow through the orbit of the core until reaching its isolation mass. The efficiency of pebble accretion increases if the core grows in a dust trap of the protoplanetary disc. Dust traps are observed as ring-like structures by ALMA sug…
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…
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…
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…
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…
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…
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…
Pebble accretion is one of the major theories in planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous study, Paper I, we focused on the shear regime of pebble accretion, and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that in the unperturbed flow, in particular when ${\rm St}\lesssim10^{-3}$, where St is the…
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 …
We run numerical simulations to study the accretion of gas and dust grains onto gas giant planets embedded into massive protoplanetary discs. The outcome is found to depend on the disc cooling rate, planet mass, grain size and irradiative feedback from the planet. If radiative cooling is efficient, planets accrete both gas and pebbles rapidly, open a gap and usually become massive brown dwarfs. In the inefficient cooling case, gas is too hot to accrete onto the planet but pebble accretion continues and the planets migrate inward rapidly. Radiative feedback from the planet tends to suppress gas…
Systems with tightly-packed inner planets (STIPs) are very common. Chatterjee & Tan proposed Inside-Out Planet Formation (IOPF), an in situ formation theory, to explain these planets. IOPF involves sequential planet formation from pebble-rich rings that are fed from the outer disk and trapped at the pressure maximum associated with the dead zone inner boundary (DZIB). Planet masses are set by their ability to open a gap and cause the DZIB to retreat outwards. We present models for the disk density and temperature structures that are relevant to the conditions of IOPF. For a wide range of DZIB …
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…
One of the main scenarios of planet formation is the core accretion model where a massive core forms first and then accretes a gaseous envelope. This core forms by accreting solids, either planetesimals, or pebbles. A key constraint in this model is that the accretion of gas must proceed before the dissipation of the gas disc. Classical planetesimal accretion scenario predicts that the time needed to form a giant planets core is much longer than the time needed to dissipate the disc. This difficulty led to the development of another accretion scenario, in which cores grow by accretion of pebbl…
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…
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…
We present a synergic study of protoplanetary disks to investigate links between inner disk gas molecules and the large-scale migration of solid pebbles. The sample includes 63 disks where two types of measurements are available: i) spatially-resolved disk images revealing the radial distribution of disk pebbles (mm-cm dust grains), from millimeter observations with ALMA or the SMA, and ii) infrared molecular emission spectra as observed with Spitzer. The line flux ratios of H2O with HCN, C2H2, and CO2 all anti-correlate with the dust disk radius R$_{dust}$, expanding previous results found by…
Though ~10 Earth mass rocky/icy cores are commonly held as a prerequisite for the formation of gas giants, theoretical models still struggle to explain how these embryos can form within the lifetimes of gaseous circumstellar disks. In recent years, aerodynamic-aided accretion of "pebbles," objects ranging from centimeters to meters in size, has been suggested as a potential solution to this long-standing problem. While pebble accretion has been demonstrated to be extremely effective in local simulations that look at the detailed behavior of these pebbles in the vicinity of a single planetary e…
Giant planets migrate though the protoplanetary disc as they grow. We investigate how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 3…
Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there has not been any global N-body simulations that compare the outcomes of planet formation via pebble accretion with observed extrasolar planetary systems. Aims. In this paper, we study the effects of a range of initial parameters of planet formation via pebble accretion, and present the first results of our simulations. Methods. We incorporate the pebble acc…
Observations of the population of cold Jupiter planets ($r>$1 AU) show that nearly all of these planets orbit their host star on eccentric orbits. For planets up to a few Jupiter masses, eccentric orbits are thought to be the outcome of planet-planet scattering events taking place after gas dispersal. We simulate the growth of planets via pebble and gas accretion as well as the migration of multiple planetary embryos in their gas disc. We then follow the long-term dynamical evolution of our formed planetary system up to 100 Myr after gas disc dispersal. We investigate the importance of the ini…
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 …
