arXiv subjects

Alessandro Morbidelli

Publications and source records attributed to Alessandro Morbidelli.

At least 91 records · Page 5Linked to original sources

arXiv2018

A study of 3-dimensional shapes of asteroid families with an application to Eos

In order to fully understand the shapes of asteroids families in the 3-dimensional space of the proper elements $(a_{\rm p}, e_{\rm p}, \sin I_{\rm p})$ it is necessary to compare observed asteroids with N-body simulations. To this point, we describe a rigorous yet simple method which allows for a selection of the observed asteroids, assures the same size-frequency distribution of synthetic asteroids, accounts for a background population, and computes a $χ^2$ metric. We study the Eos family as an example, and we are able to fully explain its non-isotropic features, including the distribution of pole latitudes $β$. We confirm its age $t = (1.3\pm0.3)\,{\rm Gyr}$; while this value still scales with the bulk density, it is verified by a Monte-Carlo collisional model. The method can be applied to other populous families (Flora, Eunomia, Hygiea , Koronis, Themis, Vesta, etc.).

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arXiv2018

Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Massive planets form within the lifetime of protoplanetary disks and undergo orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and the second planet is locked in resonance. We detail the resonant trapping comparing semi-analytical formulae and numerical simulations in the case of two equal-mass coplanar planets trapped in first order resonances. We describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using expanded and non-expanded Hamiltonians. We show that during convergent migration the planets evolve along these families of equilibria. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that the resonant configurations achieved by migration can become unstable after the removal of the disk. We probe the stability of the resonances as a function of planetary mass. To do this, we fictitiously increase the masses of the planets, adiabatically maintaining the low-amplitude libration regime until instability. We discuss two hypotheses for instability: low-order secondary resonance of the libration frequency with a fast synodic frequency, and minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low-amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter still play the decisive role in the destabilisation of resonant pairs. We show that, as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.

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arXiv2018

Dynamical effects on the classical Kuiper Belt during the excited-Neptune model

The link between the dynamical evolution of the giant planets and the Kuiper Belt orbital structure can provide clues and insight about the dynamical history of the Solar System. The classical region of the Kuiper Belt has two populations (the cold and hot populations) with completely different physical and dynamical properties. These properties have been explained in the framework of a subset of the simulations of the Nice Model, in which Neptune remained on a low-eccentricity orbit (Neptune's eccentricity is never larger than 0.1) throughout the giant planet instability. However, recent simulations have showed that the remaining Nice model simulations, in which Neptune temporarily acquires a large-eccentricity orbit (larger than 0.1), are also consistent with the preservation of the cold population (inclination smaller than 4 degrees), if the latter formed in situ. However, the resulting a cold population showed in many of the simulations eccentricities larger than those observed for the real population. We focus on a short period of time which is characterized by Neptune's large eccentricity and a slow precession of Neptune's perihelion. We show that if self-gravity is considered in the disk, the precession rate of the particles longitude of perihelion is slowed down. This, combined with the effect of mutual scattering among the bodies, which spreads all orbital elements, allows some objects to return to low eccentricities. However, we show that if the cold population originally had a small total mass, this effect is negligible. Thus, we conclude that the only possibilities to keep at low eccentricity some cold-population objects during a high-eccentricity phase of Neptune are that (i) either Neptune's precession was rapid, as suggested by Batygin et al. (2011) or (ii) Neptune's slow precession phase was long enough to allow some particles to experience a full secular cycle.

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arXiv2018

The excitation of a primordial cold asteroid belt as an outcome of the planetary instability

The main asteroid belt (MB) is low in mass but dynamically excited. Here we propose a new mechanism to excite the MB during the giant planet ('Nice model') instability, which is expected to have featured repeated close encounters between Jupiter and one or more ice giants ('Jumping Jupiter' -- JJ). We show that, when Jupiter temporarily reaches a high enough level of excitation, both in eccentricity and inclination it induces strong forced vectors of eccentricity and inclination across the MB region. Because during the JJ instability Jupiter's orbit `jumps' around, the forced vectors keep changing both in magnitude and phase throughout the whole MB region. The entire cold primordial MB is thus excited as a natural outcome of the JJ instability. The level of such an excitation, however, is typically larger than the current orbital excitation observed in the MB. We show that the subsequent evolution of the Solar System is capable of reshaping the resultant over-excited MB to its present day orbital state, and that a strong mass depletion ($\sim$90$\%$) is associated to the JJ instability phase and its subsequent evolution throughout the age of the Solar System.

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arXiv2018

Migration of Planets Into and Out of Mean Motion Resonances in Protoplanetary Discs: Overstability of Capture and Nonlinear Eccentricity Damping

A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture into first-order mean motion resonances (MMRs) using a parametrized planet migration model that takes into account nonlinear eccentricity damping due to planet-disk interaction. This parametrization is based on numerical hydrodynamical simulations and is more realistic than the simple linear parametrization widely used in previous analytic studies. We find that nonlinear eccentricity damping can significantly influence the stability and outcome of resonance capture. In particular, the equilibrium eccentricity of the planet captured into MMRs become larger, and the captured MMR state tends to be more stable compared to the prediction based on the simple migration model. In addition, when the migration is sufficiently fast or/and the planet mass ratio is sufficiently small, we observe a novel phenomenon of eccentricity overshoot, where the planet's eccentricity becomes very large before settling down to the lower equilibrium value. This can lead to the ejection of the smaller planet if its eccentricity approaches unity during the overshoot. This may help explain the lack of low-mass planet companion of hot Jupiters when compared to warm Jupiters.

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arXiv2018

Debiased orbit and absolute-magnitude distributions for near-Earth objects

The debiased absolute-magnitude and orbit distributions as well as source regions for near-Earth objects (NEOs) provide a fundamental frame of reference for studies of individual NEOs and more complex population-level questions. We present a new four-dimensional model of the NEO population that describes debiased steady-state distributions of semimajor axis, eccentricity, inclination, and absolute magnitude $H$ in the range $17<H<25$. The modeling approach improves upon the methodology originally developed by Bottke et al. (2000; Science 288, 2190-2194) in that it is, for example, based on more realistic orbit distributions and uses source-specific absolute-magnitude distributions that allow for a power-law slope that varies with $H$. We divide the main asteroid belt into six different entrance routes or regions (ER) to the NEO region: the $ν_6$, 3:1J, 5:2J and 2:1J resonance complexes as well as Hungarias and Phocaeas. In addition we include the Jupiter-family comets as the primary cometary source of NEOs. We calibrate the model against NEO detections by Catalina Sky Surveys' stations 703 and G96 during 2005-2012, and utilize the complementary nature of these two systems to quantify the systematic uncertainties associated to the resulting model. The most important ERs are the $ν_6$ and 3:1J resonance complexes with JFCs contributing a few percent of NEOs on average. We predict that there are $962^{+52}_{-56}$ ($802^{+48}_{-42}\times10^3$) NEOs with $H<17.75$ ($H<25$) and these numbers are in agreement with the most recent estimates found in the literature (the uncertainty estimates only account for the random component).

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arXiv2018

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

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. 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. 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. 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. 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.

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arXiv2018

Formation of close-in super-Earths in evolving protoplanetary disks due to disk winds

Planets with masses larger than about 0.1 Earth-masses undergo rapid inward migration (type I migration) in a standard protoplanetary disk. Recent magnetohydrodynamical simulations revealed the presence of magnetically driven disk winds, which would alter the disk profile and the type I migration in the close-in region. We investigate orbital evolution of planetary embryos in disks that viscously evolve under the effects of disk winds. The aim is to discuss effects of altered disk profiles on type I migration. In addition, we aim to examine whether observed distributions of close-in super-Earths can be reproduced by simulations that include effects of disk winds. We perform N-body simulations of super-Earth formation from planetary embryos, in which a recent model for disk evolution is used. We explore a wide range of parameters and draw general trends. We also carry out N-body simulations of close-in super-Earth formation from embryos in such disks under various conditions. We find that the type I migration is significantly suppressed in many cases. Even in cases in which inward migration occurs, the migration timescale is lengthened to 1 Myr, which mitigates the type I migration problem. This is because the gas surface density is decreased and has a flatter profile in the close-in region due to disk winds. We find that when the type I migration is significantly suppressed, planets undergo late orbital instability during the gas depletion, leading to a non-resonant configuration. We also find that observed distributions of close-in super-Earths (e.g., period ratio, mass ratio) can be reproduced. In addition, we show that in some results of simulations, systems with a chain of resonant planets, like the TRAPPIST-1 system, form.

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arXiv2018

Accretion Processes

In planetary science, accretion is the process in which solids agglomerate to form larger and larger objects and eventually planets are produced. The initial conditions are a disc of gas and microscopic solid particles, with a total mass of about 1% of the gas mass. Accretion has to be effective and fast. Effective, because the original total mass in solids in the solar protoplanetary disk was probably of the order of ~ 300 Earth masses, and the mass incorporated into the planets is ~100 Earth masses. Fast, because the cores of the giant planets had to grow to tens of Earth masses in order to capture massive doses of hydrogen and helium from the disc before the dispersal of the latter, i.e. in a few millions of years. There is probably not one accretion process but several, depending on the scale at which accretion operates. A first process is the sticking of microscopic dust into larger grains and pebbles. A second process is the formation of an intermediate class of objects called planetesimals. A third accretion process has to lead from planetesimals to planets. Actually, several processes can be involved in this step, from collisional coagulation among planetesimals to the accretion of small particles under the effect of gas drag, to giant impacts between protoplanets. This chapter will detail all these processes, adopting a historical perspective: i.e. from the classic processes investigated in the past decades to those unveiled in the last years.

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arXiv2018

Size-dependent modification of asteroid family Yarkovsky V-shapes

The thermal properties of the surfaces of asteroids determine the magnitude of the drift rate cause by the Yarkovsky force. In the general case of Main Belt asteroids, the Yarkovsky force is indirectly proportional to the thermal inertia, $Γ$. Following the proposed relationship between $Γ$ and asteroid diameter $D$, we find that asteroids' Yarkovsky drift rates might have a more complex size dependence than previous thought, leading to a curved family V-shape boundary in semi-major axis, a, vs. 1/$D$ space. This implies that asteroids are drifting faster at larger sizes than previously considered decreasing on average the known ages of asteroid families. The V-Shape curvature is determined for $>$25 families located throughout the Main Belt to quantify the Yarkovsky size-dependent drift rate. We find that there is no correlation between family age and V-shape curvature. In addition, the V-shape curvature decreases for asteroid families with larger heliocentric distances suggesting that the relationship between $Γ$ and $D$ is weaker in the outer MB possibly due to homogenous surface roughness among family members.

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arXiv2018

Pebble isolation mass --- scaling law and implications for the formation of super-Earths and gas giants

The growth of a planetary core by pebble accretion stops at the so called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. If the isolation mass is very small, then gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For larger values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter $α$. We find that small pebbles, coupled to the gas, with Stokes number $τ_{\rm f}<0.005$ can drift through the partial gap at pebble isolation mass. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate through the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size. We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. Compared to models neglecting the dependence of the pebble isolation mass on the $α$-viscosity, our models including this effect result in larger core masses for giant planets. These larger core masses are more akin to the core masses of the giant planets in the Solar System.

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arXiv2017

Checking the Compatibility of the Cold Kuiper Belt with a Planetary Instability Migration Model

The origin of the orbital structure of the cold component of the Kuiper belt is still a hot subject of investigation. Several features of the solar system suggest that the giant planets underwent a phase of global dynamical instability, but the actual dynamical evolution of the planets during the instability is still debated. To explain the structure of the cold Kuiper belt, Nesvorny (2015, AJ 150,68) argued for a soft instability, during which Neptune never achieved a very eccentric orbit. Here we investigate the possibility of a more violent instability, from an initially more compact fully resonant configuration of 5 giant planets. We show that the orbital structure of the cold Kuiper belt can be reproduced quite well provided that the cold population formed in situ, with an outer edge between 44 and 45 au and never had a large mass.

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arXiv2017

Formation, stratification, and mixing of the cores of Earth and Venus

Earth possesses a persistent, internally-generated magnetic field, whereas no trace of a dynamo has been detected on Venus, at present or in the past, although a high surface temperature and recent resurfacing events may have removed paleomagnetic evidence. Whether or not a terrestrial body can sustain an internally generated magnetic field by convection inside its metallic fluid core is determined in part by its initial thermodynamic state and its compositional structure, both of which are in turn set by the processes of accretion and differentiation. Here we show that the cores of Earth- and Venus-like planets should grow with stable compositional stratification unless disturbed by late energetic impacts. They do so because higher abundances of light elements are incorporated into the liquid metal that sinks to form the core as the temperatures and pressures of metal-silicate equilibration increase during accretion. We model this process and determine that this establishes a stable stratification that resists convection and inhibits the onset of a geodynamo. However, if a late energetic impact occurs, it could mechanically stir the core creating a single homogenous region within which a long-lasting geodynamo would operate. While Earth's accretion has been punctuated by a late giant impact with likely enough energy to mix the core (e.g. the impact that formed the Moon), we hypothesize that the accretion of Venus is characterized by the absence of such energetic giant impacts and the preservation of its primordial stratifications.

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arXiv2017

Dynamical Evolution Induced by Planet Nine

The observational census of trans-Neptunian objects with semi-major axes greater than ~250 AU exhibits unexpected orbital structure that is most readily attributed to gravitational perturbations induced by a yet-undetected, massive planet. Although the capacity of this planet to (i) reproduce the observed clustering of distant orbits in physical space, (ii) facilitate dynamical detachment of their perihelia from Neptune, and (iii) excite a population of long-period centaurs to extreme inclinations is well established through numerical experiments, a coherent theoretical description of the dynamical mechanisms responsible for these effects remains elusive. In this work, we characterize the dynamical processes at play, from semi-analytic grounds. We begin by considering a purely secular model of orbital evolution induced by Planet Nine, and show that it is at odds with the ensuing stability of distant objects. Instead, the long-term survival of the clustered population of long-period KBOs is enabled by a web of mean-motion resonances driven by Planet Nine. Then, by taking a compact-form approach to perturbation theory, we show that it is the secular dynamics embedded within these resonances that regulates the orbital confinement and perihelion detachment of distant Kuiper belt objects. Finally, we demonstrate that the onset of large-amplitude oscillations of orbital inclinations is accomplished through capture of low-inclination objects into a high-order secular resonance and identify the specific harmonic that drives the evolution. In light of the developed qualitative understanding of the governing dynamics, we offer an updated interpretation of the current observational dataset within the broader theoretical framework of the Planet Nine hypothesis.

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arXiv2017

Effects of global gas flows on type I migration

Magnetically-driven disk winds would alter the surface density slope of gas in the inner region of a protoplanetary disk $(r \lesssim 1 {\rm au})$. This in turn affects planet formation. Recently, the effect of disk wind torque has been considered with the suggestion that it would carve out the surface density of the disk from inside and would induce global gas flows (wind-driven accretion). We aim to investigate effects of global gas flows on type I migration and also examine planet formation. A simplified approach was taken to address this issue, and N-body simulations with isolation-mass planets were also performed. In previous studies, the effect of gas flow induced by turbulence-driven accretion has been taken into account for its desaturation effect of the corotation torque. If more rapid gas flows (e.g., wind-driven accretion) are considered, the desaturation effect can be modified. In MRI-inactive disks, in which the wind-driven accretion dominates the disk evolution, the gas flow at the midplane plays an important role. If this flow is fast, the corotation torque is efficiently desaturated. Then, the fact that the surface density slope can be positive in the inner region due to the wind torque can generate an outward migration region extended to super-Earth mass planets. In this case, we observe that no planets fall onto the central star in N-body simulations with migration forces imposed to reproduce such migration pattern. We also see that super-Earth mass planets can undergo outward migration. Relatively rapid gas flows affects type I migration and thus the formation of close-in planets.

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arXiv2017

A Martian Origin for the Mars Trojan Asteroids

Seven of the nine known Mars Trojan asteroids belong to an orbital cluster named after its largest member 5261 Eureka. Eureka is likely the progenitor of the whole cluster, which formed at least 1 Gyr ago. It was suggested that the thermal YORP effect spun-up Eureka resulting with fragments being ejected by the rotational-fission mechanism. Eureka's spectrum exhibits a broad and deep absorption band around 1 μm, indicating an olivine-rich composition. Here we show evidence that the Trojan Eureka cluster progenitor could have originated as impact debris excavated from the Martian mantle. We present new near-infrared observations of two Trojans (311999 2007 NS2 and 385250 2001 DH47) and find that both exhibit an olivine-rich reflectance spectrum similar to Eureka's. These measurements confirm that the progenitor of the cluster has an achondritic composition. Olivine-rich reflectance spectra are rare amongst asteroids but are seen around the largest basins on Mars. They are also consistent with some Martian meteorites (e.g. Chassigny), and with the material comprising much of the Martian mantle. Using numerical simulations, we show that the Mars Trojans are more likely to be impact ejecta from Mars than captured olivine-rich asteroids transported from the main belt. This result links directly specific asteroids to debris from the forming planets.

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arXiv2017

Initial velocity V-shapes of young asteroid families

Ejection velocity fields of asteroid families are largely unconstrained due to the fact that members disperse relatively quickly on Myr time-scales by secular resonances and the Yarkovsky effect. The spreading of fragments in $a$ by the Yarkovsky effect is indistinguishable from the spreading caused by the initial ejection of fragments. By examining families $<$20 Myrs-old, we can use the V-shape identification technique to separate family shapes that are due to the initial ejection velocity field and those that are due to the Yarkovsky effect. $<$20 Myr-old asteroid families provide an opportunity to study the velocity field of family fragments before they become too dispersed. Only the Karin family's initial velocity field has been determined and scales inversely with diameter, $D^{-1}$. We have applied the V-shape identification technique to constrain young families' initial ejection velocity fields by measuring the curvature of their fragments' V-shape correlation in semi-major axis, $a$, vs. $D^{-1}$ space. Curvature from a straight line implies a deviation from a scaling of $D^{-1}$. We measure the V-shape curvature of 11 young asteroid families including the \FYnospace, Aeolia, Brangane, Brasilia, Clarissa, Iannini, Karin, Konig, Koronis(2), Theobalda and Veritas asteroid families. We find that the majority of asteroid families have initial ejection velocity fields consistent with $\sim D^{-1}$ supporting laboratory impact experiments and computer simulations of disrupting asteroid parent bodies.

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arXiv2017

Reconstructing the size distribution of the primordial Main Belt

In this work we aim to constrain the slope of the size distribution of main-belt asteroids, at their primordial state. To do so we turn out attention to the part of the main asteroid belt between 2.82 and 2.96~AU, the so-called "pristine zone", which has a low number density of asteroids and few, well separated asteroid families. Exploiting these unique characteristics, and using a modified version of the hierarchical clustering method we are able to remove the majority of asteroid family members from the region. The remaining, background asteroids should be of primordial origin, as the strong 5/2 and 7/3 mean-motion resonances with Jupiter inhibit transfer of asteroids to and from the neighboring regions. The size-frequency distribution of asteroids in the size range $17<D(\rm{km})<70$ has a slope $q\simeq-1$. Using Monte-Carlo methods, we are able to simulate, and compensate for the collisional and dynamical evolution of the asteroid population, and get an upper bound for its size distribution slope $q=-1.43$. In addition, applying the same 'family extraction' method to the neighboring regions, i.e. the middle and outer belts, and comparing the size distributions of the respective background populations, we find statistical evidence that no large asteroid families of primordial origin had formed in the middle or pristine zones.

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