Planetesimal Disk Research Articles

The scattered disc of HR 8799

HR~8799 is a young F0-type star with four directly imaged giant planets and two debris belts, one located exterior and another one interior to the region occupied by the planetary orbits. Having an architecture similar to that of our Solar System, but also revealing dissimilarities such as high masses of planets, a huge radial extent and a high mass of the outer debris belt, HR~8799 is considered to be a benchmark to test formation and evolution models of planetary systems. Here we focus on the outer debris ring and its relation to the planets. We demonstrate that the models of the outer disc, proposed previously to reproduce Herschel observations, are inconsistent with the ALMA data, and vice versa. In an attempt to find a physically motivated model that would agree with both observational sets, we perform collisional simulations. We show that a narrow planetesimal belt and a radiation pressure induced dust halo cannot account for the observed radial brightness profiles. A single, wide planetesimal disc does not reproduce the data either. Instead, we propose a two-population model, comprising a Kuiper-Belt-like structure of a low-eccentricity planetesimal population ("the classical Kuiper Belt") and a high-eccentricity population of comets ("scattered disc"). We argue that such a structure of the exo-Kuiper belt of HR~8799 could be explained with planet migration scenarios analogous to those proposed for the Kuiper Belt of the Solar System.

Origin of 1I/’Oumuamua. I. An Ejected Protoplanetary Disk Object?

Abstract 1I/’Oumuamua is the first interstellar interloper to have been detected. Because planetesimal formation and ejection of predominantly icy objects are common by-products of the star and planet formation processes, in this study we address whether 1I/’Oumuamua could be representative of this background population of ejected objects. The purpose of the study of its origin is that it could provide information about the building blocks of planets in a size range that remains elusive to observations, helping to constrain planet formation models. We compare the mass density of interstellar objects inferred from its detection to that expected from planetesimal disks under two scenarios: circumstellar disks around single stars and wide binaries, and circumbinary disks around tight binaries. Our study makes use of a detailed study of the PanSTARRS survey volume; takes into account that the contribution from each star to the population of interstellar planetesimals depends on stellar mass, binarity, and planet presence; and explores a wide range of possible size distributions for the ejected planetesimals, based on solar system models and observations of its small-body population. We find that 1I/’Oumuamua is unlikely to be representative of a population of isotropically distributed objects, favoring the scenario that it originated from the planetesimal disk of a young nearby star whose remnants are highly anisotropic. Finally, we compare the fluxes of meteorites and micrometeorites observed on Earth to those inferred from this population of interstellar objects, concluding that it is unlikely that one of these objects is already part of the collected meteorite samples.

Gap formation in planetesimal discs via divergently migrating planets

While many observed debris disks are thought to have gaps suggestive of the presence of planets, direct imaging surveys do not find many high mass planets in these systems. We investigate if divergent migration is a viable mechanism for forming gaps in young debris disks with planets of low enough mass to currently elude detection. We perform numerical integrations of planet pairs embedded in planetesimal disks to assess the conditions for which divergent, planetesimal-driven migration occurs and gaps form within the disk. Gap widths and the migration rate of planets within a pair depend on both disk mass and the degree to which the planets share disk material. We find that planet pairs with planets more massive than Neptune can produce gaps with widths similar to their orbit distance within 10 Myr at orbit separations probed by direct imaging campaigns. Pairs of migrating super-Earths likely cannot form observable gaps on the same time and distance scales, however. Inferring the responsible planet masses from these gaps while neglecting migration could overestimate the mass of planets by more than an order of magnitude.

The Origin of the Heavy-element Content Trend in Giant Planets via Core Accretion

Abstract We explore the origin of the trend of heavy elements in observed massive exoplanets. Coupling of better measurements of the mass (M p ) and radius of exoplanets with planet structure models enables estimating the total heavy-element mass (M Z ) in these planets. The corresponding relation is characterized by a power-law profile, . We develop a simplified but physically motivated analysis to investigate how the power-law profile can be produced under the current picture of planet formation. Making use of the existing semi-analytical formulae of accretion rates of pebbles and planetesimals, our analysis shows that the relation can be reproduced well if it traces the final stage of planet formation. In the stage, planets accrete solids from gapped planetesimal disks, and gas accretion is limited by disk evolution. We find that dust accretion accompanying gas accretion does not contribute to M Z for planets with . Our findings are broadly consistent with those of previous studies, yet we explicitly demonstrate how planetesimal dynamics is crucial for better understanding the relation. While our approach is simple, we can reproduce the trend of a correlation between planet metallicity and M p that is obtained by detailed population synthesis calculations when the same assumption is adopted. Our analysis suggests that pebble accretion would not play a direct role at the final stage of planet formation, whereas radial drift of pebbles might be important indirectly for metal enrichment of planets. Detailed numerical simulations and more observational data are required for confirming our analysis.

Evidence for very early migration of the Solar System planets from the Patroclus–Menoetius binary Jupiter Trojan

The orbital distribution of trans-Neptunian objects provides strong evidence for the radial migration of Neptune1,2. The outer planets’ orbits are thought to have become unstable during the early stages3, with Jupiter having scattering encounters with a Neptune-class planet4. As a consequence, Jupiter jumped inwards by a fraction of an au, as required from inner Solar System constraints5,6, and obtained its current orbital eccentricity. The timing of these events is often linked to the lunar Late Heavy Bombardment that ended ~700 Myr after the dispersal of the protosolar nebula (t0)7,8. Here, we show instead that planetary migration started shortly after t0. Such early migration is inferred from the survival of the Patroclus–Menoetius binary Jupiter Trojan9. The binary formed at t ≲ t010,11 within a massive planetesimal disk once located beyond Neptune12,13. The longer the binary stayed in the disk, the greater the likelihood that collisions would strip its components from one another. The simulations of its survival indicate that the disk had to have been dispersed by migrating planets within ≲100 Myr of t0. This constraint implies that the planetary migration is unrelated to the formation of the youngest lunar basins. The Patroclus–Menoetius Jupiter Trojan binary could survive its travel from the Kuiper belt to Jupiter’s orbit only if the giant planets’ migrations happened within ~100 Myr after the birth of the Solar System and not after ~700 Myr, as suggested instead by the Late Heavy Bombardment.

Resonant multi-lane patterns in circumbinary young debris disks

AbstractFormation of resonant multi-lane patterns in circumbinary young debris disks with planets is considered in a set of representative massively simulated models. We find that the long term-stable resonant patterns are generically formed, shepherded by embedded planets. The patterns are multi-lane, i.e., they consist of several concentric rings. Statistical dependences of their parameters on the planetary parameters are recovered. Relevant additional massive simulations of planetesimal disks in systems with parameters of Kepler-16, 34, and 35 are accomplished and described. We find that co-orbital patterns generically form in systems with moderate orbital eccentricities of the binary’s and planetary orbits (like in Kepler-16 and 35 cases).

Dynamical Evolution of the Early Solar System

Several properties of the Solar System, including the wide radial spacing of the giant planets, can be explained if planets radially migrated by exchanging orbital energy and momentum with outer disk planetesimals. Neptune's planetesimal-driven migration, in particular, has a strong advocate in the dynamical structure of the Kuiper belt. A dynamical instability is thought to have occurred during the early stages with Jupiter having close encounters with a Neptune-class planet. As a result of the encounters, Jupiter acquired its current orbital eccentricity and jumped inward by a fraction of an astronomical unit, as required for the survival of the terrestrial planets and from asteroid belt constraints. Planetary encounters also contributed to capture of Jupiter Trojans and irregular satellites of the giant planets. Here we discuss the dynamical evolution of the early Solar System with an eye to determining how models of planetary migration/instability can be constrained from its present architecture. Specifically, we review arguments suggesting that the Solar System may have originally contained a third ice giant on a resonant orbit between Saturn and Uranus. This hypothesized planet was presumably ejected into interstellar space during the instability. The Kuiper belt kernel and other dynamical structures in the trans-Neptunian region may provide evidence for the ejected planet. We favor the early version of the instability where Neptune migrated into the outer planetesimal disk within a few tens of millions of years after the dispersal of the protosolar nebula. If so, the planetary migration/instability was not the cause of the Late Heavy Bombardment. Mercury's orbit may have been excited during the instability.

A gap in the planetesimal disc around HD 107146 and asymmetric warm dust emission revealed by ALMA

While detecting low mass exoplanets at tens of au is beyond current instrumentation, debris discs provide a unique opportunity to study the outer regions of planetary systems. Here we report new ALMA observations of the 80-200 Myr old Solar analogue HD 107146 that reveal the radial structure of its exo-Kuiper belt at wavelengths of 1.1 and 0.86 mm. We find that the planetesimal disc is broad, extending from 40 to 140 au, and it is characterised by a circular gap extending from 60 to 100 au in which the continuum emission drops by about 50%. We also report the non-detection of the CO J=3-2 emission line, confirming that there is not enough gas to affect the dust distribution. To date, HD 107146 is the only gas-poor system showing multiple rings in the distribution of millimeter sized particles. These rings suggest a similar distribution of the planetesimals producing small dust grains that could be explained invoking the presence of one or more perturbing planets. Because the disk appears axisymmetric, such planets should be on circular orbits. By comparing N-body simulations with the observed visibilities we find that to explain the radial extent and depth of the gap, it would be required the presence of multiple low mass planets or a single planet that migrated through the disc. Interior to HD 107146's exo-Kuiper belt we find extended emission with a peak at ~20 au and consistent with the inner warm belt that was previously predicted based on 22$\mu$m excess as in many other systems. This warm belt is the first to be imaged, although unexpectedly suggesting that it is asymmetric. This could be due to a large belt eccentricity or due to clumpy structure produced by resonant trapping with an additional inner planet.

Bi-lobed Shape of Comet 67P from a Collapsed Binary

Abstract The Rosetta spacecraft observations revealed that the nucleus of comet 67P/Churyumov–Gerasimenko consists of two similarly sized lobes connected by a narrow neck. Here, we evaluate the possibility that 67P is a collapsed binary. We assume that the progenitor of 67P was a binary and consider various physical mechanisms that could have brought the binary components together, including small-scale impacts and gravitational encounters with planets. We find that 67P could be a primordial body (i.e., not a collisional fragment) if the outer planetesimal disk lasted ≲10 Myr before it was dispersed by migrating Neptune. The probability of binary collapse by impact is ≃30% for tightly bound binaries. Most km-class binaries become collisionally dissolved. Roughly 10% of the surviving binaries later evolve to become contact binaries during the disk dispersal, when bodies suffer gravitational encounters with Neptune. Overall, the processes described in this work do not seem to be efficient enough to explain the large fraction (∼67%) of bi-lobed cometary nuclei inferred from spacecraft imaging.

The origin of interstellar asteroidal objects like 1I/2017 U1 ‘Oumuamua

ABSTRACT We study the origin of the interstellar object 1I/2017 U1 ‘Oumuamua by juxtaposing estimates based on the observations with simulations. We speculate that objects like ‘Oumuamua are formed in the debris disc as left over from the star and planet formation process, and subsequently liberated. The liberation process is mediated either by interaction with other stars in the parental star cluster, by resonant interactions within the planetesimal disc or by the relatively sudden mass loss when the host star becomes a compact object. Integrating ‘Oumuamua backward in time in the Galactic potential together with stars from the Gaia-TGAS catalogue we find that about 1.3 Myr ago ‘Oumuamua passed the nearby star HIP 17288 within a mean distance of 1.3 pc. By comparing nearby observed L-dwarfs with simulations of the Galaxy, we conclude that the kinematics of ‘Oumuamua is consistent with relatively young objects of 1.1–1.7 Gyr. We just met ‘Oumuamua by chance, and with a derived mean Galactic density of ∼3 × 105 similarly sized objects within 100 au from the Sun or ∼1014 per cubic parsec we expect about 2–12 such visitors per year within 1 au from the Sun.

Formation of terrestrial planets in eccentric and inclined giant planet systems

Aims. Evidence of mutually inclined planetary orbits has been reported for giant planets in recent years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the formation of inclined terrestrial planets. Methods. We performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under the combined action of Type II migration and planet-planet scattering. Fourteen two- and three-planet configurations were selected, with diversified masses, semi-major axes (resonant configurations or not), eccentricities, and inclinations (including coplanar systems) at the dispersal of the gas disc. We then followed the gravitational interactions of these systems with an inner disc of planetesimals and embryos (nine runs per system), studying in detail the final configurations of the formed terrestrial planets. Results. In addition to the well-known secular and resonant interactions between the giant planets and the outer part of the disc, giant planets on inclined orbits also strongly excite the planetesimals and embryos in the inner part of the disc through the combined action of nodal resonance and the Lidov–Kozai mechanism. This has deep consequences on the formation of terrestrial planets. While coplanar giant systems harbour several terrestrial planets, generally as massive as the Earth and mainly on low-eccentric and low-inclined orbits, terrestrial planets formed in systems with mutually inclined giant planets are usually fewer, less massive (<0.5 M⊕), and with higher eccentricities and inclinations. This work shows that terrestrial planets can form on stable inclined orbits through the classical accretion theory, even in coplanar giant planet systems emerging from the disc phase.

What and whence 1I/‘Oumuamua: a contact binary from the debris of a young planetary system?

The first confirmed interstellar interloper in our Solar System, 1I/`Oumuamua, is likely to be a minor body ejected from another star, but its brief flyby and faintness made it difficult to study. Two remarkable properties are its large (up to 2.5 mag) rotational variability and its motion relative to the Sun before encounter. The former suggests an extremely elongated shape (aspect ratio ~10) and the latter an origin from the protoplanetary disk of a young star in a nearby association. Against expectations, it is also not comet-like. 1I/`Oumuamua's variability can also be explained if it is a contact binary composed of near-equilibrium ellipsoidal components and heterogeneous surfaces, i.e. brighter, dust-mantled inner-facing hemispheres and darker, dust-free outer-facing poles. Such shapes are a plausible outcome of radiation, tides and collisions in systems where planets are clearing planetesimal disks. The probability that 1I/`Oumuamua has the same motion as a young (<~100 Myr) stellar association by coincidence is <1%. If it is young, its detection vs. more numerous, older counterparts could be explained as a selection effect due to darkening of surfaces by Galactic cosmic rays and loss of dust. 1I/`Oumuamua's apparent lack of ices can be explained if ejected rocky planetesimals are characteristically smaller and thus far more numerous than their icy counterparts: the Solar System may currently host several such objects captured by the combined gravity of Jupiter and the Sun.

Formation of the terrestrial planets in the solar system around 1 au via radial concentration of planetesimals

Context. No planets exist inside the orbit of Mercury and the terrestrial planets of the solar system exhibit a localized configuration. According to thermal structure calculation of protoplanetary disks, a silicate condensation line (~1300 K) is located around 0.1 au from the Sun except for the early phase of disk evolution, and planetesimals could have formed inside the orbit of Mercury. A recent study of disk evolution that includes magnetically driven disk winds showed that the gas disk obtains a positive surface density slope inside ~1 au from the central star. In a region with positive midplane pressure gradient, planetesimals undergo outward radial drift. Aims. We investigate the radial drift of planetesimals and type I migration of planetary embryos in a disk that viscously evolves with magnetically driven disk winds. We show a case in which no planets remain in the close-in region. Methods. Radial drifts of planetesimals are simulated using a recent disk evolution model that includes effects of disk winds. The late stage of planet formation is also examined by performing N-body simulations of planetary embryos. Results. We demonstrate that in the middle stage of disk evolution, planetesimals can undergo convergent radial drift in a magnetorotational instability (MRI)-inactive disk, in which the pressure maximum is created, and accumulate in a narrow ring-like region with an inner edge at ~0.7 au from the Sun. We also show that planetary embryos that may grow from the narrow planetesimal ring do not exhibit significant type I migration in the late stage of disk evolution. Conclusions. The origin of the localized configuration of the terrestrial planets of the solar system, in particular the deficit of close-in planets, can be explained by the convergent radial drift of planetesimals in disks with a positive pressure gradient in the close-in region.

“Horseshoe” Structures in the Debris Disks of Planet-Hosting Binary Stars

The formation of a planetary system from the protoplanetary disk leads to destruction of the latter; however, a debris disk can remain in the form of asteroids and cometary material. The motion of planets can cause the formation of coorbital structures from the debris disk matter. Previous calculations have shown that such a ring-like structure is more stable if there is a binary star in the center of the system, as opposed to a single star. To analyze the properties of the coorbital structure, we have calculated a grid of models of binary star systems with a circumbinary planet moving in a planetesimal disk. The calculations are performed considering circular orbits of the stars and the planet; the mass and position of the planet, as well as the mass ratio of the stars, are varied. The analysis of the models shows that the width of the coorbital ring and its stability significantly depend on the initial parameters of the problem. Additionally, the empirical dependences of the width of the coorbital structure on the parameters of the system have been obtained, and the parameters of the models with the most stable coorbital structures have been determined. The results of the present study can be used for the search of planets around binary stars with debris disks.

The Delivery of Water During Terrestrial Planet Formation

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. We review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets.

Producing Distant Planets by Mutual Scattering of Planetary Embryos

Abstract It is likely that multiple bodies with masses between those of Mars and Earth (“planetary embryos”) formed in the outer planetesimal disk of the solar system. Some of these were likely scattered by the giant planets into orbits with semimajor axes of hundreds of au. Mutual torques between these embryos may lift the perihelia of some of them beyond the orbit of Neptune, where they are no longer perturbed by the giant planets, so their semimajor axes are frozen in place. We conduct N-body simulations of this process and its effect on smaller planetesimals in the region of the giant planets and the Kuiper Belt. We find that (i) there is a significant possibility that one sub-Earth mass embryo, or possibly more, is still present in the outer solar system; (ii) the orbit of the surviving embryo(s) typically has perihelion of 40–70 au, semimajor axis less than 200 au, and inclination less than 30°; (iii) it is likely that any surviving embryos could be detected by current or planned optical surveys or have a significant effect on solar system ephemerides; (iv) whether or not an embryo has survived to the present day, its dynamical influence earlier in the history of the solar system can explain the properties of the detached disk (defined in this paper as containing objects with perihelia &gt;38 au and semimajor axes between 80 and 500 au).

Effects of Planetesimal Accretion on the Thermal and Structural Evolution of Sub-Neptunes

Abstract A remarkable discovery of NASA’s Kepler mission is the wide diversity in the average densities of planets of similar mass. After gas disk dissipation, fully formed planets could interact with nearby planetesimals from a remnant planetesimal disk. These interactions would often lead to planetesimal accretion due to the relatively high ratio between the planet size and the hill radius for typical planets. We present calculations using the open-source stellar evolution toolkit mesa (Modules for Experiments in Stellar Astrophysics) modified to include the deposition of planetesimals into the H/He envelopes of sub-Neptunes (∼1–20 M ⊕). We show that planetesimal accretion can alter the mass–radius isochrones for these planets. The same initial planet, as a result of the same total accreted planetesimal mass, can have up to ≈5% difference in mean densities approximately several gigayears after the last accretion due to the inherent stochasticity of the accretion process. During the phase of rapid accretion, these differences are more dramatic. The additional energy deposition from the accreted planetesimals increase the ratio between the planet’s radius to that of the core during rapid accretion, which in turn leads to enhanced loss of atmospheric mass. As a result, the same initial planet can end up with very different envelope mass fractions. These differences manifest as differences in mean densities long after accretion stops. These effects are particularly important for planets that are initially less massive than ∼10 M ⊕ and with envelope mass fractions less than ∼10%, thought to be the most common type of planets discovered by Kepler.

Simulations of the Solar System's Early Dynamical Evolution with a Self-gravitating Planetesimal Disk

Abstract Over the course of the last decade, the Nice model has dramatically changed our view of the solar system’s formation and early evolution. Within the context of this model, a transient period of planet–planet scattering is triggered by gravitational interactions between the giant planets and a massive primordial planetesimal disk, leading to a successful reproduction of the solar system’s present-day architecture. In typical realizations of the Nice model, self-gravity of the planetesimal disk is routinely neglected, as it poses a computational bottleneck to the calculations. Recent analyses have shown, however, that a self-gravitating disk can exhibit behavior that is dynamically distinct, and this disparity may have significant implications for the solar system’s evolutionary path. In this work, we explore this discrepancy utilizing a large suite of Nice model simulations with and without a self-gravitating planetesimal disk, taking advantage of the inherently parallel nature of graphic processing units. Our simulations demonstrate that self-consistent modeling of particle interactions does not lead to significantly different final planetary orbits from those obtained within conventional simulations. Moreover, self-gravitating calculations show similar planetesimal evolution to non-self-gravitating numerical experiments after dynamical instability is triggered, suggesting that the orbital clustering observed in the distant Kuiper Belt is unlikely to have a self-gravitational origin.

Orbital Modification of the Himalia Family during an Early Solar System Dynamical Instability

Abstract Among the irregular satellites orbiting Jupiter, the Himalia family is characterized by a high velocity dispersion of several hundred among its members, inconsistent with a collisional origin. Efforts to account for this through internecine gravitational interactions do not readily reproduce this feature. Here, we revisit the problem in the context of recent cosmogonical models, where the giant planets migrated significantly through interaction with a planetesimal disk and suffered encounters with planetesimals and planet-sized objects. Our starting assumption is that family formation either predated this phase or occurred soon after its onset. We simulate numerically the diffusive effect of three distinct populations of perturbers on a set of test particles representing the family: Moon-sized (MPT) and Pluto-sized (PPT) planetesimals, and planetary-mass objects (PMO) with masses typical of ice-giant planets. We find that PPT flybys are inefficient, but encounters with MPTs raise the of ∼60% of our test particles to with respect to Himalia, in agreement with observations. As MPTs may not have been abundant in the disk, we simulate encounters between Jupiter and PMOs. We find that too few encounters generate less dispersion than MPTs while too many essentially destroy the family. For PMO masses in the range , the family orbital distribution is reproduced by a few tens of encounters.

PENTACLE: Parallelized particle–particle particle-tree code for planet formation

Abstract We have newly developed a parallelized particle–particle particle-tree code for planet formation, PENTACLE, which is a parallelized hybrid N-body integrator executed on a CPU-based (super)computer. PENTACLE uses a fourth-order Hermite algorithm to calculate gravitational interactions between particles within a cut-off radius and a Barnes–Hut tree method for gravity from particles beyond. It also implements an open-source library designed for full automatic parallelization of particle simulations, FDPS (Framework for Developing Particle Simulator), to parallelize a Barnes–Hut tree algorithm for a memory-distributed supercomputer. These allow us to handle 1–10 million particles in a high-resolution N-body simulation on CPU clusters for collisional dynamics, including physical collisions in a planetesimal disc. In this paper, we show the performance and the accuracy of PENTACLE in terms of $\tilde{R}_{\rm cut}$ and a time-step Δt. It turns out that the accuracy of a hybrid N-body simulation is controlled through $\Delta t / \tilde{R}_{\rm cut}$ and $\Delta t / \tilde{R}_{\rm cut} \sim 0.1$ is necessary to simulate accurately the accretion process of a planet for ≥106 yr. For all those interested in large-scale particle simulations, PENTACLE, customized for planet formation, will be freely available from https://github.com/PENTACLE-Team/PENTACLE under the MIT licence.