arXiv subjects

A. Morbidelli

Publications and source records attributed to A. Morbidelli.

At least 19 recordsLinked to original sources

arXiv2025

On the formation of multiple dust-trapping rings in the inner Solar system

Isotopic properties of meteorites provide evidence that multiple dust trap or pressure bumps had to form and persist in the inner Solar System on a timescale of millions of years. The formation of a pressure bump at the outer edge of the gap opened by Jupiter blocks particles drifting from the outer to the inner disk. This is not enough to preserve dust in the inner disk. However, in low viscosity disks, under specific condition on the gas cooling time, massive planets can also open secondary gaps, separated by density bumps, inward of the main gap. The majority of studies have been done in two dimensional equatorial simulations with prescribed disk cooling. Recent results have shown that including the treatment of radiation transport is key to determine the formation of secondary gaps. We extend previous studies to three dimensional disks including radiative effects and we also consider non ideal MHD effects, in disks with prescribed cooling time. We perform three dimensional hydrodynamical numerical simulations with self consistent treatment of radiative effects and including the magnetic field with non ideal Ohmic and Ambipolar effects. We show that in a disk with low bulk viscosity and consistent treatment of radiative effects, planetary masses close to the pebble isolation mass as well as a Jupiter massive planet open multiple gaps. In the presence of non ideal MHD effects multiple gaps and rings are also formed by a Jupiter massive planet.In conclusion the formation of multiple gaps and rings inside the planetary orbit is crucial to preserve dust reservoirs. Such reservoirs are pushed towards the inner part of the disk during Jupiter runaway growth and are persistent after Jupiter's growth. Multiple dust reservoirs could therefore be present in the inner Solar System since the formation of Jupiter's solid core if the disk had low-viscosity.

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arXiv2024

Tungsten isotope evolution during Earth's formation and new constraints on the viability of accretion simulations

The Hf-W isotopic system is the reference chronometer for determining the chronology of Earth's accretion and differentiation. However, its results depend strongly on uncertain parameters, including the extent of metal-silicate equilibration and the siderophility of tungsten. Here we show that a multistage core-formation model based on N-body accretion simulations, element mass balance and metal-silicate partitioning, largely eliminates these uncertainties. We modified the original model of Rubie et al. (2015) by including (1) smoothed particle hydrodynamics estimates of the depth of melting caused by giant impacts and (2) the isotopic evolution of 182W. We applied two metal-silicate fractionation mechanisms: one when the metal delivered by the cores of large impactors equilibrates with only a small fraction of the impact-induced magma pond and the other when metal delivered by small impactors emulsifies in global magma oceans before undergoing progressive segregation. The latter is crucial for fitting the W abundance and 182W anomaly of Earth's mantle. In addition, we show, for the first time, that the duration of magma ocean solidification has a major effect on Earth's tungsten isotope anomaly. We re-evaluate the six Grand Tack N-body simulations of Rubie et al. (2015). Only one reproduces epsilon182W=1.9+/-0.1 of Earth's mantle, otherwise accretion is either too fast or too slow. Depending on the characteristics of the giant impacts, results predict that the Moon formed either 143-183 Myr or 53-62 Myr after the start of the solar system. Thus, independent evaluations of the Moon's age provide an additional constraint on the validity of accretion simulations.

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arXiv2024

Gas dynamics around a Jupiter-mass planet I. Influence of protoplanetary disk properties

Giant planets grow and acquire their gas envelope during the disk phase. At the time of the discovery of giant planets in their host disk, it is important to understand the interplay between the host disk and the envelope and circum-planetary disk properties of the planet. Our aim is to investigate the dynamical and physical structure of the gas in the vicinity of a Jupiter-mass planet and study how protoplanetary disk propertiesy, determine the planetary system as well as the accretion rate inside the planet's Hill sphere.We ran global 3D simulations with the grid-based code fargOCA, using a fully radiative equation of state and a dust-to-gas ratio of 0.01. We explored three models. The nominal one features a disk with surface density, Sigma, corresponding to the MMSN at the planet's location, characterised by an alpha viscosity value of 0.004. The second model has a surface density ten times smaller than the nominal one and the same viscosity. In the third model, we also reduced the viscosity value by a factor of 10. During gap formation gas is heated by compression and cools according to opacity, density, and temperature values. In the analysis of our disks, we find that the gas flowing into the Hill sphere is approximately scaled as the product Sigma nu , as expected from viscous transport while The accretion rate is scaled as sqrt(Sigma nu ).Previous studies have shown that pressure or rotationally supported structures are formed around giant planets, depending on the equation of state (EoS) or on the opacity. In the case of a fully radiative EoS and a constant dust to gas ratio of 0.01, we find that low-mass and low-viscosity circum-stellar disks favour the formation of a rotationally supported circum-planetary disk. Gas accretion leading to the doubling time of the planetary system >10^5 years has only been found in the case of a low-viscosity disk.

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arXiv2024

Terrestrial planet formation from a ring: long-term simulations accounting for the giant planet instability

The process leading to the formation of the terrestrial planet remains elusive. In a previous publication, we have shown that, if the first generation of planetesimals forms in a ring at about 1 AU and the gas disk's density peaks at the ring location, planetary embryos of a few martian masses can grow and remain in the ring. In this work, we extend our simulations beyond the gas-disk stage, covering 200 Myr and accounting for the phase of giant planet instability, assumed to happen at different times. About half of the simulations form a pair of Venus and Earth analogues and, independently, about 10% form a Mars analogue. We find that the timing of the giant planet instability affects statistically the terrestrial system's excitation state and the timing of the last giant impacts. Hence a late instability (about 60 to 100 Myr after the Solar system's birth) is more consistent with a late Moon-formation time, as suggested by radioactive chronometers. However, the late veneer mass (LVM: mass accreted after the last giant impact) of Earth-sized planets suffering a giant impact after 80 My is usually an order of magnitude lower than the value inferred from geochemistry. In addition, the final angular momentum deficit (AMD) of the terrestrial planets tends to be too high. We tested the effect on the final AMD of the generation of debris during collisions and found that it is too small to change these conclusions. We argue that the best-case scenario is that the Moon-forming event occurred between 50 and 80 My, possibly just following the giant planet instability.

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arXiv2024

Dynamics of the Beta Pictoris planetary system and its falling evaporating bodies

For decades, the spectral variations of Beta Pictoris have been modelled as the result of the evaporation of exocomets close to the star, termed falling evaporating bodies (FEBs). Resonant perturbations by a giant planet have been proposed to explain the dynamical origin of these stargrazers. The disk is now known to harbour two giant planets, Beta Pic b and c, orbiting the star at 9.9 au and 2.7 au. While the former almost matches the planet formerly suspected, the discovery of the latter complicates the picture. We first question the stability of the two-planet system. Then we investigate the dynamics of a disk of planetesimals orbiting the star with both planets to check the validity of the FEB generation mechanism. Symplectic N-body simulations are used to determine which regions of the planetesimal disk are dynamically stable. Then we focus on regions where disk particles are able to reach high eccentricities thanks to resonant mechanisms. The first result is that the system is dynamically stable. Both planets may temporarily fall in 7:1 mean motion resonance (MMR). Then, simulations reveal that the whole region extending between ~1.5 au and ~25 au is unstable to planetary perturbations. However, a disk below 1.5 au survives, which appears to constitute an active source of FEBs via high-order MMRs with Beta Pic c. Beta Pic b acts as a distant perturber that helps sustain the whole process. These simulations rule out the preceding FEB generation mechanism model, which placed their origin at around 4-5 au. Conversely, FEBs are likely to originate from a region much further in and related to MMRs with Beta Pic c. That mechanism also appears to last longer, as new planetesimals are able to continuously enter the MMRs and evolve towards the FEB state. Subsequently, the physical nature of the FEBs may differ from that previously thought, and presumably may not be icy.

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arXiv2023

A super-massive Neptune-sized planet

Neptune-sized planets exhibit a wide range of compositions and densities, depending onf cators related to their formation and evolution history, such as the distance from their host stars and atmospheric escape processes. They can vary from relatively low-density planets with thick hydrogen-helium atmospheres to higher-density planets with a substantial amount of water or a rocky interior with a thinner atmosphere, such as HD 95338 b, TOI-849 b and TOI-2196 b. The discovery of exoplanets in the hot-Neptune desert, a region close to the host stars with a deficit of Neptune-sized planets, provides insights into the formation and evolution of planetary systems, including the existence of this region itself. Here we show observations of the transiting planet TOI-1853 b, which has a radius of 3.46 +- 0.08 Earth radii and orbits a dwarf star every 1.24 days. This planet has a mass of 73.2 +- 2.7 Earth masses, almost twice that of any other Neptune-sized planet known so far, and a density of 9.7 +- 0.8 grams per cubic centimetre. These values place TOI-1853 b in the middle of the Neptunian desert and imply that heavy elements dominate its mass. The properties of TOI-1853 b present a puzzle for conventional theories of planetary formation and evolution, and could be the result of several proto-planet collisions or the final state of an initially high-eccentricity planet that migrated closer to its parent star.

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arXiv2023

An improved model of metal/silicate differentiation during Earth's accretion

We improved the algorithm presented in Rubie et al. (2015) to model the chemical evolution of Earth driven by iron/silicate differentiation during the planet's accretion. The pressure at which the equilibration occurs during a giant impact is no longer a free parameter but is determined by the smooth particle hydrodynamic (SPH) simulations of Nakajima et al. (2021). Moreover, impacting planetesimals are now assumed to be too small to cause melting and differentiation and thus their materials are stored in the crystalline upper mantle of the growing planet until a hydrostatically relaxed global magma ocean forms in the aftermath of a giant impact, whose depth is also estimated from Nakajima et al. (2021). With these changes, not all dynamical simulations lead to a satisfactory reproduction of the chemical composition of the bulk silicate Earth (BSE). Thus, the latter becomes diagnostic of the success of dynamical models. In the successful cases also the BSE abundances of W and Mo can be reproduced, that were previously hard to fit (Jennings et al., 2021).

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arXiv2023

In-situ enrichment in heavy elements of hot Jupiters

Context: Radius and mass measurements of short-period giant planets reveal that many of these planets contain a large amount of heavy elements, in sharp contrast with the expectations of the conventional core-accretion model for the origin of giant planets. Aims: The proposed explanations for the heavy-element enrichment of giant planets fall short of explaining the most enriched planets. We look for additional processes that can explain the full envelope of inferred enrichments. Methods: We revisit the dynamics of pebbles and dust in the vicinity of giant planets using analytic estimates. Although our results are derived in the framework of a viscous alpha-disk we also discuss the case of disks driven by angular momentum removal in magnetized winds. Results: When giant planets are far from the star, dust and pebbles are confined in a pressure bump at the outer edge of the planet-induced gap. Instead, when the planets reach the inner part of the disk (r << 2 au), dust penetrates the gap together with the gas. The dust/gas ratio can be enhanced by more than an order of magnitude if radial drift of dust is not impeded farther out by other barriers. Thus, hot planets undergoing runaway gas accretion can swallow a large amount of dust. Conclusions: Whereas the gas accreted by giant planets in the outer disk is very dust-poor, that accreted by hot planets can be extremely dust-rich. Thus, provided that a large fraction of the atmosphere of hot-Jupiters is accreted in situ, a large amount of dust can be accreted as well. We draw a distinction between this process and pebble accretion, which is ineffective at small stellocentric radii, even for super-Earths. Giant planets farther out in the disk are extremely effective barriers against the flow of pebbles and dust across their gap.

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arXiv2023

Cold Jupiters and improved masses in 38 Kepler and K2 small planet systems from 3661 HARPS-N radial velocities. No excess of cold Jupiters in small planet systems

The exoplanet population characterized by relatively short orbital periods ($P<100$ d) around solar-type stars is dominated by super-Earths and sub-Neptunes. However, these planets are missing in our Solar System and the reason behind this absence is still unknown. Two theoretical scenarios invoke the role of Jupiter as the possible culprit: Jupiter may have acted as a dynamical barrier to the inward migration of sub-Neptunes from beyond the water iceline; alternatively, Jupiter may have reduced considerably the inward flux of material (pebbles) required to form super-Earths inside that iceline. Both scenarios predict an anti-correlation between the presence of small planets (SPs) and that of cold Jupiters (CJs) in exoplanetary systems. To test that prediction, we homogeneously analyzed the radial-velocity (RV) measurements of 38 Kepler and K2 transiting SP systems gathered over almost 10 years with the HARPS-N spectrograph, as well as publicly available RVs collected with other facilities. We detected five CJs in three systems, two in Kepler-68, two in Kepler-454, and a very eccentric one in K2-312. We derived an occurrence rate of $9.3^{+7.7}_{-2.9}\%$ for CJs with $0.3-13~M_{Jup}$ and 1-10 AU, which is lower but still compatible at $1.3\sigma$ with that measured from RV surveys for solar-type stars, regardless of the presence or absence of SPs. The sample is not large enough to draw a firm conclusion about the predicted anti-correlation between SPs and CJs; nevertheless, we found no evidence of previous claims of an excess of CJs in SP systems. As an important by-product of our analyses, we homogeneously determined the masses of 64 Kepler and K2 small planets, reaching a precision better than 5, 7.5 and 10$\sigma$ for 25, 13 and 8 planets, respectively. Finally, we release the 3661 HARPS-N radial velocities used in this work to the scientific community. [Abridged]

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arXiv2023

Terrestrial planet formation from a ring

It has been long proposed that, if all the terrestrial planets form within a tiny ring of solid material at around 1 AU, the concentrated mass-distance distribution of the current system can be reproduced. Recent planetesimal formation models also support this idea. In this study, we revisit the ring model by performing a number of high-resolution N-body simulations for 10 Myr of a ring of self-interacting planetesimals, with various radial distributions of the gas disc. We found that even if all the planetesimals form at ~1 AU in a minimum mass solar nebula-like disc, the system tends to spread radially as accretion proceeds, resulting in a system of planetary embryos lacking mass-concentration at ~1 AU. Modifying the surface density of the gas disc into a concave shape with a peak at ~1 AU helps to maintain mass concentrated at ~1 AU and solve the radial dispersion problem. We further propose that such a disc should be short lived (<= 1 Myr) and with a shallower radial gradient in the innermost region (< 1 AU) than previously proposed to prevent a too-rapid growth of Earth. Future studies should extend to ~100 Myr the most promising simulations and address in a self-consistent manner the evolution of the asteroid belt and its role in the formation of the terrestrial planets.

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arXiv2023

Keck, Gemini, and Palomar 200-inch visible photometry of red and very-red Neptunian Trojans

Neptunian Trojans (NTs), trans-Neptunian objects in 1:1 mean-motion resonance with Neptune, are generally thought to have been captured from the original trans-Neptunian protoplanetary disk into co-orbital resonance with the ice giant during its outward migration. It is possible, therefore, that the colour distribution of NTs is a constraint on the location of any colour transition zones that may have been present in the disk. In support of this possible test, we obtained $g$, $r$, and $i$-band observations of 18 NTs, more than doubling the sample of NTs with known visible colours to 31 objects. Out of the combined sample, we found $\approx$4 objects with $g$-$i$ colours of $>$1.2 mags placing them in the very red (VR) category as typically defined. We find, without taking observational selection effects into account, that the NT $g$-$i$ colour distribution is statistically distinct from other trans-Neptunian dynamical classes. The optical colours of Jovian Trojans and NTs are shown to be less similar than previously claimed with additional VR NTs. The presence of VR objects among the NTs may suggest that the location of the red to VR colour transition zone in the protoplanetary disk was interior to 30-35 au.

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arXiv2022

Gas accretion onto Jupiter mass planets in discs with laminar accretion flows

(Abridged) Studies have shown that a Jovian mass planet embedded in a viscous protoplanetary disc (PPD) can accrete gas efficiently through the gap and doubles its mass in $\sim 0.1$ Myr. The planet also migrates inwards on a timescale of $\sim 0.1$ Myr. These timescales are short compared to PPD lifetimes, and raise questions about the origins of cold giant exoplanets. However, PPDs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered PPDs. We use 3D hydrodynamical simulations of planets embedded in PPDs, in which a constant radial mass flux towards the star of ${\dot m} = 10^{-8}$ M$_{\odot}$ yr$^{-1}$ is sustained. We consider a classical viscous alpha model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers are parameterised by their column densities $\Sigma_{\rm A}$, and we consider values in the range 0.1 to 10 g cm$^{-2}$. The viscous model gives results in agreement with previous studies. We find the accretion rate onto the planet in the layered models crucially depends on the planet's ability to block the wind-induced mass flow. For $\Sigma_{\rm A}=10$ g cm$^{-2}$, the planet torque can block the mass flow through the disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For $\Sigma_{\rm A}=0.1$ g cm$^{-2}$, accretion is fast and the mass doubling time is 0.2 Myr. Although the radial mass flow through the layered disc models is always $10^{-8}$ M$_{\odot}$ yr$^{-1}$, adopting different values of $\Sigma_{\rm A}$ leads to very different gas accretion rates onto gas giant planets.

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arXiv2022

The Metal-Silicate Partitioning of Carbon During Earth's Accretion and its Distribution in the Early Solar System

Carbon is an essential element for the existence and evolution of life on Earth. Its abundance in Earth's crust and mantle (the Bulk Silicate Earth, BSE) is surprisingly high given that carbon is strongly siderophile (metal-loving) at low pressures and temperatures, and hence should have segregated almost completely into Earth's core during accretion. Estimates of the concentration of carbon in the BSE lie in the range 100-260 ppm and are much higher than expected based on simple models of core-mantle differentiation. Here we show through experiments at the putative conditions of Earth's core formation (49-71 GPa and 3600-4000 K) that carbon is significantly less siderophile at these conditions than at the low pressures ($\leq$13 GPa) and temperatures ($\leq$2500 K) of previous large volume press studies, but at least an order of magnitude more siderophile than proposed recently based on an experimental approach that is similar to ours. Using our new data along with previously published results, we derive a new parameterization of the pressure-temperature dependence of the metal-silicate partitioning of carbon. We apply this parameterization in a model that combines planet formation and core-mantle differentiation that is based on astrophysical N-body accretion simulations. Because differentiated planetesimals were almost completely depleted in carbon due to sublimation at high temperatures, almost all carbon in the BSE was added by the accretion of fully-oxidized carbonaceous chondrite material from the outer solar system. Carbon is added to the mantle continuously throughout accretion and its concentration reaches values within the BSE range (e.g. 140$\pm$40 ppm) at the end of accretion. The corresponding final core and bulk Earth carbon concentrations are 1270$\pm$300 ppm and 495$\pm$125 ppm respectively.

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arXiv2021

Migration of Jupiter mass planets in discs with laminar accretion flows

Migration of giant planets in discs with low viscosity has been studied recently. The proportionality between migration speed and the disc's viscosity is broken by the presence of vortices that appear at the edges of the planet-induced gap. Our goal is to investigate vortex-driven migration in low-viscosity discs in the presence of radial advection of gas, as expected from angular momentum removal by magnetised disc winds. We performed three dimensional simulations using the grid-based code FARGOCA. We mimicked the effects of a disc wind by applying a synthetic torque on a surface layer of the disc characterised by a prescribed column density Sigma_A so that it results in a disc accretion rate of 10^-8 Solar masses per year. Discs with this structure are called 'layered' and the layer where the torque is applied is denoted as 'active'. We also consider the case of accretion focussed near the disc midplane to mimic transport properties induced by a large Hall effect or by weak Ohmic diffusion. We observe two migration phases: in the first phase, the migration of the planet is driven by the vortex and is directed inwards. This phase ends when the vortex disappear. Migration depends on the ability of the torque from the planet to block the accretion flow. When the flow is fast and unimpeded (small Sigma_A) migration is very slow. When the accretion flow is completely blocked, migration is faster and the speed is controlled by the rate at which the accretion flow refills the gap behind the migrating planet. The migration speed of a giant planet in a layered protoplanetary disc depends on the thickness of the accreting layer. The lack of large-scale migration apparently experienced by the majority of giant exoplanets can be explained if the accreting layer is sufficiently thin to allow unimpeded accretion through the disc.

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arXiv2020

Migration of Jupiter mass planets in low viscosity discs

Type-II migration of giant planets has a speed proportional to the disc's viscosity for values of the alpha viscosity parameter larger than 1.e-4 . At lower viscosities previous studies, based on 2D simulations have shown that migration can be very chaotic and often characterized by phases of fast migration. The reason is that in low-viscosity discs vortices appear due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Our aim is to study migration in low viscosity 3D discs. We performed numerical simulations using 2D (including self-gravity) and 3D codes. After selecting disc masses for which self-gravity is not important, 3D simulations without self-gravity can be safely used. In our nominal simulation only numerical viscosity is present. We then performed simulations with prescribed viscosity to assess the threshold below which the new migration processes appear. We show that for alpha viscosity <= 1.e-5 two migration modes are possible which differ from classical Type-II migration, in the sense that they are not proportional to the disc's viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. We call this type of migration "vortex-driven migration". This migration is very slow and cannot continue indefinitely, because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planet's eccentricity grows to a value ~0.2 due to inefficient eccentricity damping by corotation resonances. This second, faster migration mode appears to be typical of 2D models in discs with slower damping of temperature's perturbations.

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arXiv2020

A re-assessment of the Kuiper belt size distribution for sub-kilometer objects, revealing collisional equilibrium at small sizes

We combine several constraints provided by the crater records on Arrokoth and the worlds of the Pluto system to compute the size-frequency distribution (SFD) of the crater production function for craters with diameter D<10km. For this purpose, we use a Kuiper belt objects (KBO) population model calibrated on telescopic surveys, that describes also the evolution of the KBO population during the early Solar System. We further calibrate this model using the crater record on Pluto, Charon and Nix. Using this model, we compute the impact probability on Arrokoth, integrated over the age of the Solar System. This probability is then used together with other observational constraints to determine the slope of the crater-production function on Arrokoth. In addition, we use our Kuiper belt model also to compare the impact rates and velocities of KBOs on Arrokoth with those on Charon, integrated over the crater retention ages of their respective surfaces. This allows us to establish a relationship between the spatial density of sub-km craters on Arrokoth and of D~20km craters on Charon. Together, all these considerations suggest the crater production function on these worlds has a cumulative power law slope of -1.5<q<-1.2. Converted into a projectile SFD slope, we find -1.2<q_KBO<-1.0. These values are close to the cumulative slope of main belt asteroids in the 0.2--2~km range, a population in collisional equilibrium. For KBOs, however, this slope appears to extend from ~2km down to objects a few tens of meters in diameter, as inferred from sub-km craters on Arrokoth. From the measurement of the dust density in the Kuiper belt made by the New Horizons mission, we predict that the SFD of the KBOs becomes steep again below ~10-30m. All these considerations strongly indicate that the size distribution of the KBO population is in collisional equilibrium.

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arXiv2020

No evidence for interstellar planetesimals trapped in the Solar System

In two recent papers published in MNRAS, Namouni and Morais (2018, 2020) claimed evidence for the interstellar origin of some small Solar System bodies, including i) objects in retrograde co-orbital motion with the giant planets, and ii) the highly-inclined Centaurs. Here, we discuss the flaws of those papers that invalidate the authors' conclusions. Numerical simulations backwards in time are not representative of the past evolution of real bodies. Instead, these simulations are only useful as a means to quantify the short dynamical lifetime of the considered bodies and the fast decay of their population. In light of this fast decay, if the observed bodies were the survivors of populations of objects captured from interstellar space in the early Solar System, these populations should have been implausibly large (e.g. about 10 times the current main asteroid belt population for the retrograde coorbital of Jupiter). More likely, the observed objects are just transient members of a population that is maintained in quasi-steady state by a continuous flux of objects from some parent reservoir in the distant Solar System. We identify in the Halley type comets and the Oort cloud the most likely sources of retrograde coorbitals and highly-inclined Centaurs.

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arXiv2020

Subsolar Al/Si and Mg/Si ratios of non-carbonaceous chondrites reveal planetesimal formation during early condensation in the protoplanetary disk

The Al/Si and Mg/Si ratios in non-carbonaceous chondrites are lower than the solar (i.e., CI-chondritic) values, in sharp contrast to the non-CI carbonaceous meteorites and the Earth, which are enriched in refractory elements and have Mg/Si ratios that are solar or larger. We show that the formation of a first generation of planetesimals during the condensation of refractory elements implies the subsequent formation of residual condensates with strongly sub-solar Al/Si and Mg/Si ratios. The mixing of residual condensates with different amounts of material with solar refractory/Si element ratios explains the Al/Si and Mg/Si values of non-carbonaceous chondrites. To match quantitatively the observed ratios, we find that the first-planetesimals should have accreted when the disk temperature was ~1,330-1,400 K depending on pressure and assuming a solar C/O ratio of the disk. We discuss how this model relates to our current understanding of disk evolution, grain dynamics, and planetesimal formation. We also extend the discussion to moderately volatile elements (e.g., Na), explaining how it may be possible that the depletion of these elements in non-carbonaceous chondrites is correlated with the depletion of refractory elements (e.g., Al). Extending the analysis to Cr, we find evidence for a higher than solar C/O ratio in the protosolar disk's gas when/where condensation from a fractionated gas occurred. Finally, we discuss the possibility that the supra-solar Al/Si and Mg/Si ratios of the Earth are due to the accretion of ~40% of the mass of our planet from the first-generation of refractory-rich planetesimals.

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