Final Planets Research Articles

Accretion of ice giant planets from massive protoplanets whose migration is blocked by Jupiter and Saturn

ABSTRACT The growth and dynamical evolution of protoplanets beyond Saturn through collisions and type I migration typically result in a highly chaotic dynamics, producing a diversity of outcomes depending on the initial conditions. Here we present the results of N-bodies numerical simulations aiming to make a detailed exploration of different initial conditions and potential outcomes for this dynamics. We consider Jupiter and Saturn at the imminence of crossing the 3:2 mean motion resonance in two possible positions based on the final and initial conditions of the Grand Tack and the Nice models, respectively; four different gas disc lifetimes, and a range of population sizes of planetary embryos beyond Saturn with different masses and orbital configurations in a total of 72 different setups. We present statistical analyses of our outcomes including planets that ‘jump’ to interior orbits of Jupiter, the frequency of close encounters between the planetary embryos and Jupiter, the number of ejections and collisions, and the dynamical effects for stabilizing the final planetary system in chains of mean motion resonances. Results show that independently of the initial configuration of Jupiter and Saturn and the gas lifetime, the dynamical evolution goes through three main phases. A few per cent of the simulations successfully produce Uranus and Neptune analogues, which may have implications on the ice giants’ composition and obliquities, the material ejected from the Solar System, and the conditions for the giant planet instability.

Composition constraints of the TRAPPIST-1 planets from their formation

ABSTRACT We study the formation of the TRAPPIST-1 (T1) planets starting shortly after Moon-sized bodies form just exterior to the ice line. Our model includes mass growth from pebble accretion and mergers, fragmentation, type-I migration, and eccentricity and inclination dampening from gas drag. We follow the composition evolution of the planets fed by a dust condensation code that tracks how various dust species condense out of the disc as it cools. We use the final planet compositions to calculate the resulting radii of the planets using a new planet interior structure code and explore various interior structure models. Our model reproduces the broader architecture of the T1 system and constrains the initial water mass fraction of the early embryos and the final relative abundances of the major refractory elements. We find that the inner two planets likely experienced giant impacts and fragments from collisions between planetary embryos often seed the small planets that subsequently grow through pebble accretion. Using our composition constraints, we find solutions for a two-layer model, a planet comprised of only a core and mantle, that match observed bulk densities for the two inner planets b and c. This, along with the high number of giant impacts the inner planets experienced, is consistent with recent observations that these planets are likely desiccated. However, two-layer models seem unlikely for most of the remaining outer planets, which suggests that these planets have a primordial hydrosphere. Our composition constraints also indicate that no planets are consistent with a core-free interior structure.

Refined parameters of the HD 22946 planetary system and the true orbital period of planet d

Context. Multi-planet systems are important sources of information regarding the evolution of planets. However, the long-period planets in these systems often escape detection. These objects in particular may retain more of their primordial characteristics compared to close-in counterparts because of their increased distance from the host star. HD 22946 is a bright (G = 8.13 mag) late F-type star around which three transiting planets were identified via Transiting Exoplanet Survey Satellite (TESS) photometry, but the true orbital period of the outermost planet d was unknown until now. Aims. We aim to use the Characterising Exoplanet Satellite (CHEOPS) space telescope to uncover the true orbital period of HD 22946d and to refine the orbital and planetary properties of the system, especially the radii of the planets. Methods. We used the available TESS photometry of HD 22946 and observed several transits of the planets b, c, and d using CHEOPS. We identified two transits of planet d in the TESS photometry, calculated the most probable period aliases based on these data, and then scheduled CHEOPS observations. The photometric data were supplemented with ESPRESSO (Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations) radial velocity data. Finally, a combined model was fitted to the entire dataset in order to obtain final planetary and system parameters. Results. Based on the combined TESS and CHEOPS observations, we successfully determined the true orbital period of the planet d to be 47.42489 ± 0.00011 days, and derived precise radii of the planets in the system, namely 1.362 ± 0.040 R⊕, 2.328 ± 0.039 R⊕, and 2.607 ± 0.060 R⊕ for planets b, c, and d, respectively. Due to the low number of radial velocities, we were only able to determine 3σ upper limits for these respective planet masses, which are 13.71 M⊕, 9.72 M⊕, and 26.57 M⊕. We estimated that another 48 ESPRESSO radial velocities are needed to measure the predicted masses of all planets in HD 22946. We also derived stellar parameters for the host star. Conclusions. Planet c around HD 22946 appears to be a promising target for future atmospheric characterisation via transmission spectroscopy. We can also conclude that planet d, as a warm sub-Neptune, is very interesting because there are only a few similar confirmed exoplanets to date. Such objects are worth investigating in the near future, for example in terms of their composition and internal structure.

Planetary population synthesis and the emergence of four classes of planetary system architectures

Planetary population synthesis is a helpful tool to understand the physics of planetary system formation. It builds on a global model, meaning that the model has to include a multitude of physical processes. The outcome can be statistically compared with exoplanet observations. Here, we review the population synthesis method and then use one population computed using the Generation III Bern model to explore how different planetary system architectures emerge and which conditions lead to their formation. The emerging systems can be classified into four main architectures: Class I of near in situ compositionally ordered terrestrial and ice planets, Class II of migrated sub-Neptunes, Class III of mixed low-mass and giant planets, broadly similar to the Solar System, and Class IV of dynamically active giants without inner low-mass planets. These four classes exhibit distinct typical formation pathways and are characterised by certain mass scales. We find that Class I forms from the local accretion of planetesimals followed by a giant impact phase, and the final planet masses correspond to what is expected from such a scenario, the ‘Goldreich mass’. Class II, the migrated sub-Neptune systems form when planets reach the ‘equality mass’ where accretion and migration timescales are comparable before the dispersal of the gas disc, but not large enough to allow for rapid gas accretion. Giant planets form when the ‘equality mass’ allows for gas accretion to proceed while the planet is migrating, i.e. when the critical core mass is reached. The main discriminant of the four classes is the initial mass of solids in the disc, with contributions from the lifetime and mass of the gas disc. The distinction between mixed Class III systems and Class IV dynamically active giants is in part due to the stochastic nature of dynamical interactions, such as scatterings between giant planets, rather than the initial conditions only. The breakdown of system into classes allows to better interpret the outcome of a complex model and understand which physical processes are dominant. Comparison with observations reveals differences to the actual population, pointing at limitation of theoretical understanding. For example, the overrepresentation of synthetic super-Earths and sub-Neptunes in Class I systems causes these planets to be found at lower metallicities than in observations.

Compositional turbulence and layering in the gaseous envelopes of forming planets

ABSTRACT Differential settling and growth of dust grains impact the structure of the radiative envelopes of gaseous planets during formation. Sufficiently rapid dust growth can result in envelopes with substantially reduced opacities for radiation transport, thereby facilitating planet formation. We revisit the problem and establish that dust settling and grain growth also lead to outer planetary envelopes that are prone to compositional instabilities, by virtue of their inverted mean-molecular weight gradients. Under a variety of conditions, we find that the radiative envelopes of forming planets experience compositional turbulence driven by a semi-transparent version of the thermohaline instability (’fingering convection’). The standard double-diffusive thermohaline theory does not apply here and is replaced by a simplified first-principle treatment for the semitransparent regime of interest. The compositional turbulence seems efficient at mixing dust in the radiative envelopes of planets forming at super-au distances (say 5 au) from a Sun-like star, but not so at sub-au distances (say 0.2 au). We also address the possibility of compositional layering in this context. Distinct turbulent regimes for planetary envelopes growing at sub-au versus super-au distances could leave an imprint on the final planets formed.

Rocky Histories: The Effect of High Excitations on the Formation of Rocky Planets

Rocky planets both in and outside of our solar system are observed to have a range of core-mass fractions (CMFs). Imperfect collisions can preferentially strip mantle material from a planet, changing its CMF, and are therefore thought to be the most likely cause of this observed CMF variation. However, previous work that implements these collisions into N-body simulations of planet formation has struggled to reliably form high CMF super-Earths. In this work, we specify our initial conditions and simulation parameters to maximize the prevalence of high-energy, CMF-changing collisions in order to form planets with highly diverse CMFs. High-energy collisions have a large v imp/v esc ratio, so we maximize this ratio by starting simulations with high eccentricity and inclination disks to increase the difference in their orbital velocities, maximizing v imp. Additionally, we minimize v esc by starting with small embryos. The final planets undergo more high-energy, debris-producing collisions, and experience significant CMF change over their formation. However, we find that a number of processes work together to average out the CMF of a planet over time; therefore, we do not consistently form high CMF, high-mass planets. We do form high CMF planets below 0.5 M ⊕. Additionally, we find, in these highly eccentric environments, loss of debris mass due to collisional grinding has a significant effect on final planet masses and CMFs, resulting in smaller planets and a higher average planet CMF. This work highlights the importance of improving measurements of high-density planets to better constrain their CMFs.

Constraining the origin of giant exoplanets via elemental abundance measurements

The origin of close-in giant planets is a key open question in planet formation theory. The two leading models are (i) formation at the outer disk followed by migration and (ii) in situ formation. In this work we determine the atmospheric composition of warm Jupiters for both formation scenarios. We perform N-body simulations of planetesimal accretion interior and exterior to the water ice-line for various planetary formation locations, planetary masses, and planetesimal sizes to estimate the accreted heavy-element mass and final planetary composition. We find that the two models differ significantly: migrating giant planets have 2–14 times higher metallicities than planets that form in situ. The ratio between refractories and volatiles is found to be above one for migrating planets but below 0.4 for planets that form in situ. We also identify very different trends between heavy-element enrichment and planetary mass for these two formation mechanisms. While the metallicity of migrating planets is found to increase with decreasing planetary mass, it is about constant for in situ formation. Our study highlights the importance of measuring the atmospheric composition of warm Jupiters and its connection to their formation and evolutionary paths.

Calibrated gas accretion and orbital migration of protoplanets in 1D disc models

Context. Orbital migration and gas accretion are two interdependent key processes that govern the evolution of planets in protoplanetary discs. The final planetary properties such as masses and orbital periods strongly depend on the treatment of those two processes. Aims. Our aim is to develop a simple prescription for migration and accretion in 1D disc models, calibrated with results of 3D hydro-dynamic simulations. Our focus lies on non-self-gravitating discs, but we also discuss to what degree our prescription could be applied when the discs are self-gravitating. Methods. We studied migration using torque densities. Our model for the torque density is based on existing fitting formulas, which we subsequently modify to prevent premature gap-opening. At higher planetary masses, we also apply torque densities from hydrody-namic simulations directly to our 1D model. These torque densities allow us to model the orbital evolution of an initially low-mass planet that undergoes runaway-accretion to become a massive planet. The two-way exchange of angular momentum between disc and planet is included. This leads to a self-consistent treatment of gap formation that only relies on directly accessible disc parameters. We present a formula for Bondi and Hill gas accretion in the disc-limited regime. This formula is self-consistent in the sense that mass is removed from the disc in the location from where it is accreted. The prescription is appropriate when the planet is smaller than, comparable to, or larger than the disc scale height. Results. We find that the resulting evolution in mass and semi-major axis in the 1D framework is in good agreement with those from 3D hydrodynamical simulations for a range of parameters. Conclusions. Our prescription is valuable for simultaneously modelling migration and accretion in 1D models, which allows a planet’s evolution to be followed over the entire lifetime of a disc. It is applicable also in situations where the surface density is significantly disturbed by multiple gap-opening planets or processes like infall. We conclude that it is appropriate and beneficial to apply torque densities from hydrodynamic simulations in 1D models, at least in the parameter space we study here. More work is needed in order to determine whether our approach is also applicable in an even wider parameter space and in situations with more complex disc thermodynamics, or when the disc is self-gravitating.

Emerging population of gap-opening planets around type-A stars

Context. The presence of forming planets embedded in their protoplanetary disks has been inferred from the detection of multiring structures in such disks. Most of these suspected planets are undetectable by direct imaging observations at current measurement sensitivities. Inward migration and accretion might make these putative planets accessible to the Doppler method, but the actual extent of growth and orbital evolution remains unconstrained. Aims. Under the premise that the gaps in the disk around HD 163296 originate from new-born planets, we investigate if and under which circumstances the gap-opening planets could represent progenitors of the exoplanet population detected around A-type stars. In particular, we study the dependence of final planetary masses and orbital parameters on the viscosity of the disk. Methods. The evolution of the embedded planets was simulated throughout the disk lifetime and up to 100 Myr after the dispersal of the disk, taking the evolving disk structure and a likely range of disk lifetimes into account. We modeled the temperature and density structure of the disk based on observational results following the widely used α disk prescription and we varied planetary and disk parameters within the available observational constraints. Results. We find that the final configuration of the planets is largely determined by the α viscosity parameter of the disk and less dependent on the choice for the disk lifetime and the initial planetary parameters. If we assume that planets such as those in HD 163296 evolve to form the observed exoplanet population of A-type stars, a α parameter on the order of 3.16 × 10−4 ≲ α ≲ 10−3 is required for the disks to induce sufficiently high migration rates. Depending on whether or not future direct imaging surveys will uncover a larger number of planets with mpl ≲ 3 MJup and apl ≳ 10 AU, we expect the α parameter to be at the lower or upper end of this range, always under the assumption that such disks indeed harbor wide orbit planets.

Building Terrestrial Planets: Why Results of Perfect-merging Simulations Are Not Quantitatively Reliable Approximations to Accurate Modeling of Terrestrial Planet Formation

Abstract Although it is accepted that perfect-merging is not a realistic outcome of collisions, some researchers state that perfect-merging simulations can still be considered as quantitatively reliable representations of the final stage of terrestrial planet formation. Citing the work of Kokubo & Genda, they argue that the differences between the final planets in simulations with perfect-merging and those where collisions are resolved accurately are small, and it is justified to use perfect-merging results as an acceptable approximation to realistic simulations. In this paper, we show that this argument does not stand. We demonstrate that when the mass lost during collisions is taken into account, the final masses of the planets will be so different from those obtained from perfect-merging that the latter cannot be used as an approximation. We carried out a large number of smooth particle hydrodynamics simulations of embryo–embryo collisions and determined the amount of the mass and water lost in each impact. We applied the results to collisions in a typical perfect-merging simulation and showed that even when the mass loss in each collision is as small as 10%, perfect-merging can, on average, overestimate the masses of the final planets by ∼35% and their water content by more than 18%. Our analysis demonstrates that, while perfect-merging simulations are still a powerful tool in proving concepts, they cannot be used to make predictions, draw quantitative conclusions (especially about the past history of a planetary system), or serve as a valid approximation to the simulations in which collisions are resolved accurately.

Collisional fragmentation and bulk composition tracking in rebound

ABSTRACT We present a fragmentation module and a composition tracking code for the N-body code rebound. Our fragmentation code utilizes previous semi-analytical models and follows an implementation method similar to fragmentation for the N-body code mercury. In our N-body simulations with fragmentation, we decrease the collision and planet formation time-scales by inflating the particle radii by an expansion factor f and experiment with various values of f to understand how expansion factors affect the collision history and final planetary system. As the expansion factor increases, so do the rate of mergers which produces planetary systems with more planets and planets at larger orbits. Additionally, we present a composition tracking code which follows the compositional change of homogeneous bodies as a function of mass exchange and use it to study how fragmentation and the use of an expansion factor affects volatile delivery to the inner terrestrial disc. We find that fragmentation enhances radial mixing relative to perfect merging and that on average, as f increases so does the average water mass fraction of the planets. Radial mixing decreases with increasing f as collisions happen early on, before the bodies have time to grow to excited orbits and move away from their original location.

Planet–planet scattering in presence of a companion star

ABSTRACT Planet–planet (P–P) scattering is a leading dynamical mechanism invoked to explain the present orbital distribution of exoplanets. Many stars belong to binary systems; therefore, it is important to understand how this mechanism works in the presence of a companion star. We focus on systems of three planets orbiting the primary star and estimate the time-scale for instability, finding that it scales with the Keplerian period for systems that have the same ratio between inner planet and binary semimajor axes. An empirical formula is also derived from simulations to estimate how the binary eccentricity affects the extent of the stability region. The presence of the secondary star affects the P–P scattering outcomes, causing a broadening of the final distribution in semimajor axis of the inner planet as some of the orbital energy of the planets is absorbed by the companion star. Repeated approaches to the secondary star also cause a significant reduction in the frequency of surviving two-planet systems in particular for larger values of the inner planet semimajor axis. The formation of Kozai states with the companion star increases the number of planets that may be tidally circularized. To predict the possible final distribution of planets in binaries, we have performed a large number of simulations where the initial semimajor axis of the inner planets is chosen randomly. For small values of the binary semimajor axis, the higher frequency of collision alters the final planet orbital distributions that, however, beyond 50 au appear to be scalable to wider binary separations.

The imprint of X-ray photoevaporation of planet-forming discs on the orbital distribution of giant planets

Context. Numerical models have shown that disc dispersal via internal photoevaporation driven by the host star can successfully reproduce the observed pile-up of warm Jupiters near 1–2 au. However, since a range of different mechanisms have been proposed to cause the same feature, clear observational diagnostics of disc dispersal leaving an imprint in the observed distribution of giant planets could help in constraining the dominant mechanisms. Aims. We aim to assess the impact of disc dispersal via X-ray-driven photoevaporation (XPE) on giant planet separations in order to provide theoretical constraints on the location and size of any possible features related to this process within the observed semi-major axis distribution of giant planets. Methods. For this purpose, we perform a set of 1D planet population syntheses with varying initial conditions and correlate the gas giants’ final parking locations with the X-ray luminosities of their host stars in order to quantify observables of this process within the semi-major axis versus host star X-ray luminosity plane of these systems. Results. We find that XPE does create an under-density of gas giants near the gravitational radius, with corresponding pile-ups inside and/or outside this location. However, the size and location of these features are strongly dependent on the choice of initial conditions in our model, such as the assumed formation location of the planets. Conclusions. XPE can strongly affect the migration process of giant planets and leave potentially observable signatures within the observed orbital separations of giant planets. However, due to the simplistic approach employed in our model, which lacks a self-consistent treatment of planet formation within an evolving disc, a quantitative analysis of the final planet population orbits is not possible. Our results, however, should strongly motivate future studies to include realistic disc dispersal mechanisms in global planet population synthesis models with self-consistent planet formation modules.

The post-main-sequence fate of the HR 8799 planetary system

ABSTRACT The noteworthy four-planet HR 8799 system teeters on the brink of gravitational instability and contains an A-type host star that is characteristic of the progenitors of the majority of known white dwarf planetary system hosts. Goździewski & Migaszewski have demonstrated that the system can retain all four planets for at least 1 Gyr along the main sequence if the planets evolve within an externally unperturbed 8:4:2:1 mean motion resonance configuration. Here, we propagate forward their most stable fit beyond the main sequence, and incorporate external effects from Galactic tides and stellar fly-bys. We find that (i) giant branch mass-loss always breaks the resonance, and usually triggers the ejection of two of the planets, (ii) stellar fly-bys and Galactic tides rarely break the resonance during the main-sequence and giant branch phases, but play a crucial role in determining the final planetary configurations around the eventual white dwarf host star, and (iii) the meanderings of the surviving planets vary significantly, occupying regions from under 1 au to thousands of au. The ubiquitous survival of at least one planet and the presence of the debris discs in the system should allow for dynamical pathways for the white dwarf to be metal-polluted.

Parking planets in circumbinary discs

The Kepler space mission has discovered about a dozen planets orbiting around binary stars systems. Most of these circumbinary planets lie near their instability boundaries, at about three to five binary separations. Past attempts to match these final locations through an inward migration process were only shown to be successful for the Kepler-16 system. Here, we study ten circumbinary systems and attempt to match the final parking locations and orbital parameters of the planets with a disc-driven migration scenario. We performed 2D locally isothermal hydrodynamical simulations of circumbinary discs with embedded planets and followed their migration evolution using different values for the disc viscosity and aspect ratio. We found that for the six systems with intermediate binary eccentricities (0.1 ≤ ebin ≤ 0.21), the final planetary orbits matched the observations closely for a single set of disc parameters, specifically, a disc viscosity of α = 10−4 and an aspect ratio of H∕r ~ 0.04. For these systems the planet masses are large enough to open at least a partial gap in their discs as they approach the binary, forcing the discs to become circularised and allowing for further migration towards the binary – ultimately leading to a good agreement with the observed planetary orbital parameters. For systems with very small or large binary eccentricities, the match was not as good as the very eccentric discs and the large inner cavities in these cases prevented close-in planet migration. In test simulations with higher than observed planet masses, a better agreement was found for those systems. The good agreement for six out of the ten modelled systems, where the relative difference between observed and simulated final planet orbit is ≤10% strongly supports the idea that planet migration in the disc brought the planets to their present locations.

The Great Inequality and the Dynamical Disintegration of the Outer Solar System

Abstract Using an ensemble of N-body simulations, this paper considers the fate of the outer gas giants (Jupiter, Saturn, Uranus, and Neptune) after the Sun leaves the main sequence and completes its stellar evolution. Due to solar mass loss—which is expected to remove roughly half of the star’s mass—the orbits of the giant planets expand. This adiabatic process maintains the orbital period ratios, but the mutual interactions between planets and the width of mean-motion resonances (MMR) increase, leading to the capture of Jupiter and Saturn into a stable 5:2 resonant configuration. The expanded orbits, coupled with the large-amplitude librations of the critical MMR angle, make the system more susceptible to perturbations from stellar flyby interactions. Accordingly, within about 30 Gyr, stellar encounters perturb the planets onto the chaotic subdomain of the 5:2 resonance, triggering a large-scale instability, which culminates in the ejections of all but one planet over the subsequent ∼10 Gyr. After an additional ∼50 Gyr, a close stellar encounter (with a perihelion distance less than ∼200 au) liberates the final planet. Through this sequence of events, the characteristic timescale over which the solar system will be completely dissolved is roughly 100 Gyr. Our analysis thus indicates that the expected dynamical lifetime of the solar system is much longer than the current age of the universe, but is significantly shorter than previous estimates.

Dynamics of Colombo’s Top: Generating Exoplanet Obliquities from Planet–Disk Interactions

Abstract Large planetary spin–orbit misalignments (obliquities) may strongly influence atmospheric circulation and tidal heating in a planet. A promising avenue to generate obliquities is via spin–orbit resonances, where the spin and orbital precession frequencies of a planet cross each other as the system evolves in time. One such mechanism involves a dissipating (mass-losing) protoplanetary disk that drives orbital precession of an interior planet. We study this scenario analytically in this paper, and obtain the mapping between the general initial spin orientation and the final obliquity. We show that (i) under adiabatic evolution (i.e., the disk dissipates at a sufficiently slow rate), the final planetary obliquity as a function of the initial spin orientation bifurcates into distinct tracks governed by interactions with the resonance; and (ii) under nonadiabatic evolution, a broad range of obliquities can be excited. We obtain analytical expressions for the final obliquities for various regimes of parameter space. The dynamical system studied in this paper is an example of “Colombo’s top,” and our analysis and results can be adapted to other applications.

Occurrence rates of planets orbiting M Stars: applying ABC to Kepler DR25, Gaia DR2, and 2MASS data

ABSTRACT We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii Rp = 0.5–4 R⊕ and orbital periods P = 0.5–256 d using the approximate Bayesian computation technique. This work incorporates the final Kepler DR25 planet candidate catalogue and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS point source catalogue. We apply a set of selection criteria to select a sample of 1746 Kepler M dwarf targets that host 89 associated planet candidates. These early-type M dwarfs and late K dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and colour–magnitude cuts using 2MASS magnitudes. We estimate a habitable zone occurrence rate of $f_{\textrm {M,HZ}} = 0.33^{+0.10}_{-0.12}$ for planets with 0.75–1.5 R⊕ size. We caution that occurrence rate estimates for Kepler M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of $4.2^{+0.6}_{-0.6}$ or $8.4^{+1.2}_{-1.1}$ planets per M dwarf (integrating over Rp = 0.5–4 R⊕ and P = 0.5–256 d) for our two choices of prior. These occurrence rates are greater than those for FGK dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-type M dwarfs harbour planetary systems.

Pebble-driven planet formation around very low-mass stars and brown dwarfs

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⊙ and 0.1 M⊙. 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 mass of the protoplanet (largest body from the planetesimal populations), 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 and orbital distance, and decrease with age. Around late M-dwarfs of 0.1 M⊙, these protoplanets can grow up to Earth-mass planets by pebble accretion. However, around brown dwarfs of 0.01 M⊙, planets do not grow to the masses that are greater than Mars 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 ≳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 ≳15%) or entirely rocky (water mass fraction ≲5%).

Planet formation by pebble accretion in ringed disks

Context.Pebble accretion is expected to be the dominant process for the formation of massive solid planets, such as the cores of giant planets and super-Earths. So far, this process has been studied under the assumption that dust coagulates and drifts throughout the full protoplanetary disk. However, observations show that many disks are structured in rings that may be due to pressure maxima, preventing the global radial drift of the dust.Aims.We aim to study how the pebble-accretion paradigm changes if the dust is confined in a ring.Methods.Our approach is mostly analytic. We derived a formula that provides an upper bound to the growth of a planet as a function of time. We also numerically implemented the analytic formulæ to compute the growth of a planet located in a typical ring observed in the DSHARP survey, as well as in a putative ring rescaled at 5 AU.Results.Planet Type I migration is stopped in a ring, but not necessarily at its center. If the entropy-driven corotation torque is desaturated, the planet is located in a region with low dust density, which severely limits its accretion rate. If the planet is instead near the ring’s center, its accretion rate can be similar to the one it would have in a classic (ringless) disk of equivalent dust density. However, the growth rate of the planet is limited by the diffusion of dust in the ring, and the final planet mass is bounded by the total ring mass. The DSHARP rings are too far from the star to allow the formation of massive planets within the disk’s lifetime. However, a similar ring rescaled to 5 AU could lead to the formation of a planet incorporating the full ring mass in less than 1/2 My.Conclusions.The existence of rings may not be an obstacle to planet formation by pebble-accretion. However, for accretion to be effective, the resting position of the planet has to be relatively near the ring’s center, and the ring needs to be not too far from the central star. The formation of planets in rings can explain the existence of giant planets with core masses smaller than the so-called pebble isolation mass.