Small Planetesimals Research Articles

Post-main sequence thermal evolution of planetesimals

ABSTRACT White dwarfs that have accreted planetary materials provide a powerful tool to probe the interiors and formation of exoplanets. In particular, the high Fe/Si ratio of some white dwarf pollutants suggests that they are fragments of bodies that were heated enough to undergo large-scale melting and iron core formation. In the Solar system, this phenomenon is associated with bodies that formed early and so had short-lived radionuclides to power their melting, and/or grew large. However, if the planetary bodies accreted by white dwarfs formed during the (pre)-main sequence lifetime of the host star, they will have potentially been exposed to a second era of heating during the star’s giant branches. This work aims to quantify the effect of stellar irradiation during the giant branches on planetary bodies by coupling stellar evolution to thermal and orbital evolution of planetesimals. We find that large-scale melting, sufficient to form an iron core, can be induced by stellar irradiation, but only in close-in small bodies: planetesimals with radii ≲ 30 km originally within ∼2 au orbiting a 1–3 M⊙ host star with solar metallicity. Most of the observed white dwarf pollutants are too massive to be explained by the accretion of these small planetesimals that are melted during the giant branches. Therefore, we conclude that those white dwarfs that have accreted large masses of materials with enhanced or reduced Fe/Si remain an indicator of planetesimal’s differentiation shortly after formation, potentially linked to radiogenic heating.

Formation of Inner Planets in the Presence of a Cold Jupiter: Orbital Evolution and Relative Velocities of Planetesimals

We investigate the orbital evolution of planetesimals in the inner disk in the presence of nebula gas and a (proto-) cold Jupiter. By varying the mass, eccentricity, and semimajor axis of the planet, we study the dependence of the relative velocities of the planetesimals on these parameters. For classic small planetesimals (1016–1020 g) whose mutual gravitational interaction is negligible, gas drag introduces a size-dependent alignment of orbits and keeps the relative velocity low for similar-sized bodies, while preventing orbital alignment for different-sized planetesimals. Regardless of the location and the mass ratio of the planetesimals, increasing the mass and eccentricity or decreasing the orbital distance of the planet always lead to higher relative velocities of the planetesimals. However, for massive planetesimals, the interplay of viscous stirring, gas damping, and secular perturbation results in the lower velocity dispersion of equal-sized planetesimals when the planet is more massive or when it is located on a closer or more eccentric orbit. The random velocities of such planetesimals remain almost unperturbed when the planet is located beyond Jupiter’s current orbit or when it is less massive or less eccentric than Jupiter. Unlike small planetesimals, such large planetesimals can grow in a runaway fashion, as in the unperturbed case. Our results imply that the presence of a cold Jupiter does not impede the formation of inner rocky planets through planetesimal accretion, provided that the planetesimals are initially large.

Binary formation through gas-assisted capture and the implications for stellar, planetary, and compact object evolution

ABSTRACTBinary systems are ubiquitous and their formation requires two-body interaction and dissipation. In gaseous media, interactions between two initially unbound objects could result in gas-assisted binary formation, induced by a loss of kinetic energy to the ambient gas medium. Here, we derive analytically the criteria for gas-assisted binary capture through gas dynamical friction dissipation. We validate them with few-body simulations and explore this process in different gas-rich environments: gas-embedded star-forming regions (SFR), gas-enriched globular clusters, active galactic nucleus (AGN) discs, and protoplanetary discs. We find that gas-assisted binary capture is highly efficient in SFRs, potentially providing a main channel for the formation of binaries. It could also operate under certain conditions in gas-enriched globular clusters. Thin AGN discs could also provide a fertile ground for gas-assisted binary capture and in particular the formation of black hole/other compact object binaries, the production of gravitational-wave (GW) and other high-energy transients. Large-scale gaseous discs might be too thick to enable gas-assisted binary capture and previous estimates of the production of GW sources could be overestimated, and sensitive to specific conditions and the structure of the discs. In protoplanetary discs, while gas-assisted binary capture can produce binary Kuiper-belt objects, dynamical friction by small planetesimals is likely to be more efficient. Overall, we show that gas-assisted binary formation is robust and can contribute significantly to the binary formation rate in many environments. In fact, the gas-assisted binary capture rates are sufficiently high such that they will lead to multicaptures, and the formation of higher multiplicity systems.

Are there any pristine comets? Constraints from pebble structure

ABSTRACT We show that if comets (or any small icy planetesimals such as Kuiper belt objects) are composed of pebble piles, their internal radiogenic as well as geochemical heating results in considerably different evolutionary outcomes compared to similar past studies. We utilize a 1D thermophysical evolution code, modified to include state-of-the-art empirical measurements of pebble thermal conductivity and compression, the latter obtained through a new laboratory experiment presented here for the first time. Results indicate that due to the low pebble thermal conductivity, the peak temperatures attained during evolution are much higher than in any previous study given the same formation time. Assuming meteoritic radiogenic abundances, we find that only extremely small, sub-kilometre comets have the potential to retain the primordial, uniform, and thermally unprocessed composition from which they formed. Comets with radii in excess of about 20 km are typically swept by rapid and energetically powerful aqueous hydration reactions. Across the full range of comet sizes and formation times, evolutions result in the processing and differentiation of various volatile species, and a radially heterogeneous nucleus structure. Our computations however also indicate that the assumed fraction of radionuclides is a pivotal free parameter, because isotopic analyses of the only available cometary samples suggest that no 26Al was ever present in comet 81P/Wild 2. We show that if comets formed early in the protoplanetary disc (within 1–3 Myr), the radionuclide abundances indeed must be much smaller than those typically assumed based on meteoritic samples. We discuss the importance of our findings for the formation, present-day attributes and future research of comets.

The SKA as a Prebiotic Molecule Detector

One of the theories for the origin of life proposes that a significant fraction of prebiotic material could have arrived to Earth from outer space between 4.1 and 3.8 billion years ago. This suggests that those prebiotic compounds could have originated in interstellar space, to be later on incorporated to small Solar-system bodies and planetesimals. The recent discovery of prebiotic molecules such as hydroxylamine and ethanolamine in the interstellar medium, strongly supports this hypothesis. However, some species such as sugars, key for the synthesis of ribonucleotides and for metabolic processes, remain to be discovered in space. The unmatched sensitivity of the Square Kilometre Array (SKA) at centimeter wavelengths will be able to detect even more complex and heavier prebiotic molecules than existing instrumentation. In this contribution, we illustrate the potential of the SKA to detect simple sugars with three and four carbon atoms, using a moderate investment of observing time.

Possible thermal evolutionary pathways of irregular shaped small asteroids and planetesimals

Two distinct thermal evolutionary pathways of irregular shaped small planetesimals in the early solar system have been studied. We have taken a case study of two S-type asteroids; (243) Ida and (951) Gaspra, on the basis of their precise physical dimensions accessed by the Philip Stooke small body 3-D shape models of the NASA Planetary Data System. The 3- D shape models for the two asteroids are based on the Galileo spacecraft fly-by mission. Based on our novel thermal evolutionary code for the precise shape of the asteroids we found that the small planetary bodies that accreted within the initial 2-3 million years (Myr) experienced sintering, whereas, the bodies formed afterwards were left unconsolidated, e.g., as a rubble pile. The former set of bodies could have formed by direct aggregation of nebula dust. Whereas, the majority of the rubble pile type small planetary bodies accreted latter by the assemblage of the fragmented debris of the initially existing planetesimals. These bodies cooled over tens of million years. Generations of small planetesimals formed over time in the early solar system evolved from an ensemble of compact consolidated bodies to rubble pile bodies due to collision induced fragmentation and re-accretion.

Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores

Abstract Gas-giant planets, such as Jupiter, Saturn, and massive exoplanets, were formed via the gas accretion onto the solid cores, each with a mass of roughly 10 Earth masses. However, rapid radial migration due to disk–planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with a lot of effort, the full evolution path from dust to planets is still uncertain. Here we report the result of full simulations for collisional evolution from dust to planets in a whole disk. Dust growth with realistic porosity allows the formation of icy planetesimals in the inner disk (≲10 au), while pebbles formed in the outer disk drift to the inner disk and there grow to planetesimals. The growth of those pebbles to planetesimals suppresses their radial drift and supplies small planetesimals sustainably in the vicinity of cores. This enables rapid formation of sufficiently massive planetary cores within 0.2–0.4 million years, prior to the planetary migration. Our models shows the first gas giants form at 2–7 au in rather common protoplanetary disks, in agreement with the exoplanet and solar systems.

From dust to planets – I. Planetesimal and embryo formation

ABSTRACT 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 are also found to increase with orbital radius, ranging from $10^{-6}{\, {\rm M}_{\oplus }}$ around the iceline, to $10^{-3}{\, {\rm M}_{\oplus }}$ near the orbit of Pluto. We include prescriptions for pebble and planetesimal accretion to examine the masses that proto-embryos can attain. Close to the star, planetesimal accretion is efficient due to small planetesimals, whilst pebble accretion is efficient where pebble sizes are fragmentation limited, but inefficient when drift dominated due to low accretion rates before the pebble supply diminishes. Exterior to the iceline, planetesimal accretion becomes inefficient due to increasing planetesimal eccentricities, whilst pebble accretion becomes more efficient as the initial proto-embryo masses increase, allowing them to significantly grow before the pebble supply is depleted. Combining both scenarios allows for more massive proto-embryos at larger distances, since the accretion of planetesimals allows pebble accretion to become more efficient, allowing giant planet cores to form at distances upto $10{\, {\rm au}}$. By including more realistic initial proto-embryo and planetesimal sizes, as well as combined accretion scenarios, should allow for a more complete understanding in the beginning to end process of how planets and planetary systems form.

Thermophysical evolution of planetesimals in the primordial disc

ABSTRACT The primordial disc of small icy planetesimals, once located at 15–$30\, \mathrm{au}$ from the Sun, was disrupted by giant planet migration in the early Solar system. The primordial disc thereby became the source region of objects in the present-day Kuiper belt, scattered disc, and Oort Cloud. I present the thermophysical code ‘Numerical Icy Minor Body evolUtion Simulator’, or nimbus, and use it to study the thermophysical evolution of planetesimals in the primordial disc prior to its disruption. Such modelling is mandatory in order to understand the behaviour of dynamically new comets from the Oort Cloud, as well as the activity of Centaurs and short-period comets from the scattered disc, that return pre-processed to the vicinity of the Sun. I find that bodies in the midst of the primordial disc with diameters ranging 4–$200\, \mathrm{km}$ lost all their CO ice on time-scales of order 0.1–$10\, \mathrm{Myr}$ depending on size, through a combination of protosolar and long-lived radionuclide heating. CO and other hypervolatiles therefore require a less volatile host for their storage. I consider two possible hosts: amorphous water ice and CO2 ice. Because of the high luminosity of the protosun, some primordial disc bodies may have sustained significant crystallization, CO:CO2 segregation, and CO2 sublimation in the uppermost few tens of metres. I discuss how this may affect coma abundance ratios and distant activity in dynamically new comets.

Dynamical Avenues for Mercury’s Origin. II. In Situ Formation in the Inner Terrestrial Disk

Abstract Modern terrestrial-planet formation models are highly successful at consistently generating planets with masses and orbits analogous to those of Earth and Venus. In stark contrast to classic theoretical predictions and inferred demographics of multiplanet systems of rocky exoplanets, the mass (≳10) and orbital period (≳2) ratios between Venus and Earth and the neighboring Mercury and Mars are not common outcomes in numerically generated systems. While viable solutions to the small-Mars problem are abundant in the literature, Mercury’s peculiar origin remains rather mysterious. In this paper, we investigate the possibility that Mercury formed in a mass-depleted, inner region of the terrestrial disk (a < 0.5 au). This regime is often ignored in terrestrial-planet formation models because of the high computational cost of resolving hundreds of short-period objects over ∼100 Myr timescales. By testing multiple disk profiles and mass distributions, we identify several promising sets of initial conditions that lead to remarkably successful analog systems. In particular, our most successful simulations consider moderate total masses of Mercury-forming material (0.1–0.25 Earth masses). While larger initial masses tend to yield disproportionate Mercury analogs, smaller values often inhibit the planets’ formation as the entire region of material is easily accreted by Venus. Additionally, we find that shallow surface density profiles and larger inventories of small planetesimals moderately improve the likelihood of adequately reproducing Mercury.

Thermal expansion of liquid Fe-S alloy at high pressure

Local structure and density of liquid Fe-S alloys at high pressure have been determined in situ by combined angle and energy dispersive X-ray diffraction experiments in a multi-anvil apparatus, covering a large temperature and compositional range. Precise density measurements collected for increasing temperature allowed us to directly derive the thermal expansion coefficients for liquid Fe-S alloys as a function of composition. In turn, thermal expansion has been used to refine thermodynamic models and to address the crystallization regime of telluric planetary cores by comparing the adiabatic temperature gradient and the slope of the liquidus in the Fe-FeS system.For Fe-S cores of asteroids and small planetesimals, top-down solidification is the dominant scenario as the compositional domain for which the slope of the liquidus is greater than the adiabatic gradient is limited to a narrow portion on the Fe-rich side. However, bottom-up growth of the inner core is expected for S-poor cases, with this compositional domain expanding to more S-rich compositions with increasing pressure (size of the planetary body). In particular, bottom-up crystallization cannot be excluded for the Moon and Ganymede.

The radial structure of planetary bodies formed by the streaming instability

Comets and small planetesimals are believed to contain primordial building blocks in the form of millimeter to centimeter sized pebbles. One of the viable growing mechanisms to form these small bodies is through the streaming instability (SI) in which pebbles cluster and gravitationally collapse toward a planetesimal or comet in the presence of gas drag. However, most SI simulations are global and lack the resolution to follow the final collapse stage of a pebble cloud within its Hill radius. We aim to track the collapse of a gravitationally bound pebble cloud subject to mutual collisions and gas drag with the representative particle approach. We determine the radial pebble size distribution of the collapsed core and the impact of mutual pebble collisions on the pebble size distribution. We find that virial equilibrium is never reached during the cloud evolution and that, in general, pebbles with a given Stokes number (St) collapse toward an optically thick core in a sequence from aerodynamically largest (St ~ 0.1) to aerodynamically smallest (St ~ 2 × 10−3). We show that at the location where the core becomes optically thick, the terminal velocity vt,* ~ 60 m s−1St2 is well below the fragmentation threshold velocity. While collisional processing is negligible during cloud evolution, the collisions that do occur are sticking. These results support the observations that comets and small planetary bodies are composed of primordial pebbles in the millimeter to centimeter size range.

Spitzer’s Solar System studies of comets, centaurs and Kuiper belt objects

In its 16 years of scientific measurements, the Spitzer Space Telescope performed ground-breaking and key infrared measurements of Solar System objects near and far. Targets ranged from the smallest planetesimals to the giant planets; Spitzer helped us to reshape our understanding of these objects while also laying the groundwork for future infrared space-based observations like those to be undertaken by the James Webb Space Telescope in the 2020s. In this Review Article, we describe how Spitzer advanced our knowledge of Solar System formation and evolution through observations of small outer Solar System planetesimals—that is, comets, centaurs and Kuiper belt objects (KBOs). Relics from the early formation era of our Solar System, these objects hold important information about the processes that created them.We group Spitzer’s key contributions into three broad classes: characterization of new Solar System objects (comets D/ISON 2012 S1, C/2016 R2 and 1I/‘Oumuamua); large population surveys of known objects (comets, centaurs and KBOs); and compositional studies through spectral measurements of body surfaces and emitted materials. In the Spitzer Space Telescope’s 16 years of operation, it observed many Solar System objects and environments. In this first Review Article of a pair, Spitzer’s insights into comets, centaurs and Kuiper belt objects—all remnants of the Solar System’s formation—are summarized.

Effect of pebble flux-regulated planetesimal formation on giant planet formation

Context. The formation of gas giant planets by the accretion of 100 km diameter planetesimals is often thought to be inefficient. A diameter of this size is typical for planetesimals and results from self-gravity. Many models therefore use small kilometer-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals that are distributed radially in a minimum-mass solar-nebula way. Aims. We use a dynamical model for planetesimal formation to investigate the effect of various initial radial density distributions on the resulting planet population. In doing so, we highlight the directive role of the early stages of dust evolution into pebbles and planetesimals in the circumstellar disk on the subsequent planet formation. Methods. We implemented a two-population model for solid evolution and a pebble flux-regulated model for planetesimal formation in our global model for planet population synthesis. This framework was used to study the global effect of planetesimal formation on planet formation. As reference, we compared our dynamically formed planetesimal surface densities with ad hoc set distributions of different radial density slopes of planetesimals. Results. Even though required, it is not the total planetesimal disk mass alone, but the planetesimal surface density slope and subsequently the formation mechanism of planetesimals that enables planetary growth through planetesimal accretion. Highly condensed regions of only 100 km sized planetesimals in the inner regions of circumstellar disks can lead to gas giant growth. Conclusions. Pebble flux-regulated planetesimal formation strongly boosts planet formation even when the planetesimals to be accreted are 100 km in size because it is a highly effective mechanism for creating a steep planetesimal density profile. We find that this leads to the formation of giant planets inside 1 au already by pure 100 km planetesimal accretion. Eventually, adding pebble accretion regulated by pebble flux and planetesimal-based embryo formation as well will further complement this picture.

The aeolian-erosion barrier for the growth of metre-size objects in protoplanetary discs

ABSTRACT Aeolian erosion is a destructive process that can erode small-size planetary objects through their interaction with a gaseous environment. Aeolian erosion operates in a wide range of environments and under various conditions. Aeolian erosion has been extensively explored in the context of geophysics in terrestrial planets. Here we show that aeolian erosion of cobbles, boulders, and small planetesimals in protoplanetary discs can constitute a significant barrier for the early stages of planet formation. We use analytic calculations to show that under the conditions prevailing in protoplanetary discs small bodies ($10\!-\!10^4 \, \rm {m}$) are highly susceptible to gas-drag aeolian erosion. At this size-range aeolian erosion can efficiently erode the planetesimals down to tens-cm size and quench any further growth of such small bodies. It thereby raises potential difficulties for channels suggested to alleviate the metre-size barrier. Nevertheless, the population of ∼decimetre-size cobbles resulting from aeolian erosion might boost the growth of larger (>km size) planetesimals and planetary embryos through increasing the efficiency of pebble-accretion, once/if such large planetesimals and planetary embryos exist in the disc.

Origins of pits and troughs and degradation on a small primitive planetesimal in the Kuiper Belt: high-resolution topography of (486958) Arrokoth (aka 2014 MU69) from New Horizons

The dominant topographic features on two-lobed Kuiper Belt object (486958) Arrokoth (provisionally designated 2014 MU69) are scattered, small, circular depressions or pits up to ~1.0 km across and curvilinear troughs observed near the terminator during the New Horizons encounter of 01 January 2019. With important exceptions, evidence for an endogenic origin for pits is lacking and impact remains the most likely origin. Pit depths relative to the local surface are shallower than hypervelocity simple craters on icy moons and consistent with low velocity (~300 m/s) impacts in an icy target (the role of porosity and cohesion in cratering on Arrokoth being uncertain). There is, however, a large scatter in observed d/D, with some pits too shallow to measure reliably. The range of preservation states observed for both pits and troughs is consistent with slow but persistent degradation on the surface of this (and perhaps other) small primitive planetesimal(s) in the Kuiper Belt by agents such as micrometeorite bombardment or volatile loss, indicating that degradation does indeed occur on such bodies. Arrokoth pits could also be related to circular depressions on comet 9P/Tempel (though comparisons of surface features on Arrokoth and comets are intriguing they are limited by resolution differences and the evolved state of cometary surfaces). Two of the curvilinear troughs occur along the terminator of the Large Lobe. One trough is a shallow depression devoid of resolvable structures, the other features several linear scarps a few 10s of meters high, suggesting that coherent failure can occur on the surfaces of small Kuiper Belt objects such as Arrokoth. Several of the deepest small pits are also clustered within this walled trough, similar to tectonically associated pit chains on other planets. These pits and an obliquely viewed linear chain of elongate depressions remain the best candidates for endogenic features on Arrokoth. Subtle undulations and linear features no more than a few 10's of meters in amplitude (and even a few candidate positive relief features) are also evident in the terminator regions, indicating that the long-term evolution of this body may have been complex.

Evolution of porous dust grains in protoplanetary discs – I. Growing grains

ABSTRACT One of the main problems in planet formation, hampering the growth of small dust to planetesimals, is the so-called radial-drift barrier. Pebbles of cm to dm sizes are thought to drift radially across protoplanetary discs faster than they can grow to larger sizes, and thus to be lost to the star. To overcome this barrier, drift has to be slowed down or stopped, or growth needs to be sped up. In this paper, we investigate the role of porosity on both drift and growth. We have developed a model for porosity evolution during grain growth and applied it to numerical simulations of protoplanetary discs. We find that growth is faster for porous grains, enabling them to transition to the Stokes drag regime, decouple from the gas, and survive the radial-drift barrier. Direct formation of small planetesimals from porous dust is possible over large areas of the disc.

How planets grow by pebble accretion

Context. Proto-planets embedded in their natal disks acquire hot envelopes as they grow and accrete solids. This ensures that the material they accrete – pebbles, as well as (small) planetesimals – will vaporize to enrich their atmospheres. Enrichment modifies an envelope’s structure and significantly alters its further evolution. Aims. Our aim is to describe the formation of planets with polluted envelopes from the moment that impactors begin to sublimate to beyond the disk’s eventual dissipation. Methods. We constructed an analytical interior structure model, characterized by a hot and uniformly mixed high-Z vapor layer surrounding the core, located below the usual unpolluted radiative-convective regions. Our model assumes an ideal equation of state and focuses on identifying trends rather than precise calculations. The expressions we derived are applicable to all single-species pollutants, but we used SiO2 to visualize our results. Results. The evolution of planets with uniformly mixed polluted envelopes follows four potential phases. Initially, the central core grows directly through impacts and rainout until the envelope becomes hot enough to vaporize and absorb all incoming solids. We find that a planet reaches runaway accretion when the sum of its core and vapor mass exceeds a value that we refer to as the critical metal mass – a criterion that supersedes the traditional critical core mass. The critical metal mass scales positively with both the pollutant’s evaporation temperature and with the planet’s core mass. Hence, planets at shorter orbital separations require the accretion of more solids to reach runaway as they accrete less volatile materials. If the solids accretion rate dries up, we identify the decline of the mean molecular weight – dilution – as a mechanism to limit gas accretion during a polluted planet’s embedded cooling phase. When the disk ultimately dissipates, the envelope’s inner temperature declines and its vapor eventually rains out, augmenting the mass of the core. The energy release that accompanies this does not result in significant mass-loss, as it only occurs after the planet has substantially contracted.

Effects of protoplanetary nebula on orbital dynamics of planetesimals in the outer Solar system

Massive gaseous nebula has been a key element to formation of large solid objects (planetesimals, giant planet cores) in the early phase of the Solar system evolution. Here, we focus on its effects during the stage when giant planets have already fully formed. Dynamical effects of the nebula on motion of planetesimals stirred by planets were twofold: (i) global gravitational acceleration, and (ii) local aerodynamic drag. Thanks to decreasing gas density with radial distance, in the outer Solar system the effect of the drag was deemed to be important only for small planetesimals (sizes $$\lesssim 10$$ km). However, we find that it was possibly important up to the sizes of $$\simeq 100$$ km as well. The gravitational field of the nebula produces secular oscillations of the orbital eccentricity and inclination of planetesimals. Eventually, their pericenter may be lifted away from strong planetary influence, exhibited during close encounters, even for small bodies born in the planetary heliocentric zone. It has been previously suggested that such pathway may, in some nebula models, launch planetesimals onto large-inclination and small-eccentricity orbits in the trans-Neptunian region. These orbits would be dynamically stable to present epoch. Our simulations generally do not support such extreme cases, but we find that, after the nebula disperses, some planetesimals may indeed reach low-inclination and low-eccentricity orbits exterior to Neptune. These bodies may have been implanted into the Kuiper belt during subsequent planetesimal-driven migration of planets. This raises a possibility that some present-day KBOs may have formed in the giant-planet zone (5–20 au).

Importance of Giant Impact Ejecta for Orbits of Planets Formed during the Giant Impact Era

Abstract Terrestrial planets are believed to be formed via giant impacts of Mars-sized protoplanets. Planets formed via giant impacts have highly eccentric orbits. A swarm of planetesimals around the planets may lead to eccentricity damping for the planets via the equipartition of random energies (dynamical friction). However, dynamical friction increases eccentricities of planetesimals, resulting in high velocity collisions between planetesimals. The collisional cascade grinds planetesimals to dust until dust grains are blown out due to radiation pressure. Therefore, the total mass of planetesimals decreases due to collisional fragmentation, which weakens dynamical friction. We investigate the orbital evolution of protoplanets in a planetesimal disk, taking into account collisional fragmentation of planetesimals. For 100 km sized or smaller planetesimals, dynamical friction is insignificant for eccentricity damping of planets because of collisional fragmentation. On the other hand, giant impacts eject collisional fragments. Although the total mass of giant impact ejecta is 0.1–0.3 Earth masses, the largest impact ejecta are ∼1000 km in size. We also investigate the orbital evolution of single planets with initial eccentricities of 0.1 in a swarm of such giant impact ejecta. Although the total mass of giant impact ejecta decreases by a factor of 3 in 30 Myr, eccentricities of planets are damped down to the Earth level (∼0.01) due to interaction with giant impact ejecta. Therefore, giant impact ejecta play an important role for determination of terrestrial planet orbits.