arXiv subjects

Alessandro Morbidelli

Publications and source records attributed to Alessandro Morbidelli.

At least 109 records · Page 6Linked to original sources

arXiv2017

Breaking the Chains: Hot Super-Earth systems from migration and disruption of compact resonant chains

"Hot super-Earths" (or "Mini-Neptunes") between 1 and 4 times Earth's size with period shorter than 100 days orbit 30-50\% of Sun-like type stars. Their orbital configuration -- measured as the period ratio distribution of adjacent planets in multi-planet systems -- is a strong constraint for formation models. Here we use N-body simulations with synthetic forces from an underlying evolving gaseous disk to model the formation and long-term dynamical evolution of super-Earth systems. While the gas disk is present, planetary embryos grow and migrate inward to form a resonant chain anchored at the inner edge of the disk. These resonant chains are far more compact than the observed super-Earth systems. Once the gas dissipates resonant chains may become dynamically unstable. They undergo a phase of giant impacts that spreads the systems out. Disk turbulence has no measurable effect on the outcome. Our simulations match observations if a small fraction of resonant chains remain stable, while most super-Earths undergo a late dynamical instability. Our statistical analysis restricts the contribution of stable systems to less than $25\%$. Our results also suggest that the large fraction of observed single planet systems does not necessarily imply any dichotomy in the architecture of planetary systems. Finally, we use the low abundance of resonances in Kepler data to argue that, in reality, the survival of resonant chains happens likely only in $\sim 5\%$ of the cases. This leads to a mystery: in our simulations only 50-60\% of resonant chains became unstable whereas at least 75\% (and probably 90-95\%) must be unstable to match observations.

astro-ph.EP↗

arXiv2017

Extreme Secular Excitation of Eccentricity Inside Mean Motion Resonance: Driving Small Bodies into Star-Grazing Orbits by Planetary Perturbations

It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like $β$-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Our semi-analytic model for the restricted planar three-body problem does not make use of any series expansion and therefore is valid for any values of eccentricities and semi-major axes ratios. The model is based on the application of the adiabatic principle, which is valid when the precession period of the longitude of pericenter of the planetesimal is much longer than the libration period in the mean motion resonance. This holds down to vanishingly small eccentricities in resonances of order larger than 1. We provide a Mathematica notebook with the implementation of the model allowing direct use to the interested reader. We confirm that the 4:1 mean motion resonance with a moderately eccentric planet is the most powerful one to lift the eccentricity of planetesimals from nearly circular orbits to star-grazing ones. However, if the planet is too eccentric, we find that this resonances becomes unable to pump the planetesimal's eccentricity to very high value. The inclusion of the General Relativity effect imposes a condition on the mass of the planet to drive the planetsimals into star-grazing orbits. For a planetesimal at $\sim$1 AU around a solar-mass star (or white dwarf), we find a threshold planetary mass of about 17 Earth masses. We finally derive an analytical formula for this critical mass.

astro-ph.EP↗

arXiv2017

Constraining the giant planets' initial configuration from their evolution: implications for the timing of the planetary instability

Recent works on planetary migration show that the orbital structure of the Kuiper belt can be very well reproduced if before the onset of the planetary instability Neptune underwent a long-range planetesimal-driven migration up to $\sim$28 au. However, considering that all giant planets should have been captured in mean motion resonances among themselves during the gas-disk phase, it is not clear whether such a very specific evolution for Neptune is possible, nor whether the instability could have happened at late times. Here, we first investigate which initial resonant configuration of the giant planets can be compatible with Neptune being extracted from the resonant chain and migrating to $\sim$28 au before that the planetary instability happened. We address the late instability issue by investigating the conditions where the planets can stay in resonance for about 400 My. Our results indicate that this can happen only in the case where the planetesimal disk is beyond a specific minimum distance $δ_{stab}$ from Neptune. Then, if there is a sufficient amount of dust produced in the planetesimal disk, that drifts inwards, Neptune can enter in a slow dust-driven migration phase for hundreds of Mys until it reaches a critical distance $δ_{mig}$ from the disk. From that point, faster planetesimal-driven migration takes over and Neptune continues migrating outward until the instability happens. We conclude that, although an early instability reproduces more easily the evolution of Neptune required to explain the structure of the Kuiper belt, such evolution is also compatible with a late instability.

astro-ph.EP↗

arXiv2017

Is the Grand Tack model compatible with the orbital distribution of main belt asteroids?

The Asteroid Belt is characterized by the radial mixing of bodies with different physical properties, a very low mass compared to Minimum Mass Solar Nebula expectations and has an excited orbital distribution. Models of the evolution of the Asteroid Belt show that the origin of its structure is strongly linked to the process of terrestrial planet formation. The Grand Tack model presents a possible solution to the conundrum of reconciling the small mass of Mars with the properties of the Asteroid Belt, including the mass depletion, radial mixing and orbital excitation. However, while the inclination distribution produced in the Grand Tack model is in good agreement with the one observed, the eccentricity distribution is skewed towards values larger than those found today. Here, we evaluate the evolution of the orbital properties of the Asteroid Belt from the end of the Grand Tack model (at the end of the gas nebula phase when planets emerge from the dispersing gas disk), throughout the subsequent evolution of the Solar System including an instability of the Giant Planets approximately 400 My later. Before the instability, the terrestrial planets were modeled on dynamically cold orbits with Jupiter and Saturn locked in a 3:2 mean motion resonance. The model continues for an additional 4.1 Gy after the giant planet instability. Our results show that the eccentricity distribution obtained in the Grand Tack model evolves towards one very similar to that currently observed, and the semimajor axis distribution does the same. The inclination distribution remains nearly unchanged with a slight preference for depletion at low inclination; this leads to the conclusion that the inclination distribution at the end of the Grand Tack is a bit over-excited.

astro-ph.EP↗

arXiv2016

Challenges in Planet Formation

Over the past two decades, large strides have been made in the field of planet formation. Yet fundamental questions remain. Here we review our state of understanding of five fundamental bottlenecks in planet formation. These are: 1) the structure and evolution of protoplanetary disks; 2) the growth of the first planetesimals; 3) orbital migration driven by interactions between proto-planets and gaseous disk; 4) the origin of the Solar System's orbital architecture; and 5) the relationship between observed super-Earths and our own terrestrial planets. Given our lack of understanding of these issues, even the most successful formation models remain on shaky ground.

astro-ph.EP↗

arXiv2016

Evolution of Protoplanetary Discs with Magnetically Driven Disc Winds

Aims: We investigate the evolution of protoplanetary discs (PPDs hereafter) with magnetically driven disc winds and viscous heating. Methods: We consider an initially massive disc with ~0.1 Msun to track the evolution from the early stage of PPDs. We solve the time evolution of surface density and temperature by taking into account viscous heating and the loss of the mass and the angular momentum by the disc winds within the framework of a standard alpha model for accretion discs. Our model parameters, turbulent viscosity, disc wind mass loss, and disc wind torque, which are adopted from local magnetohydrodynamical simulations and constrained by the global energetics of the gravitational accretion, largely depends on the physical condition of PPDs, particularly on the evolution of the vertical magnetic flux in weakly ionized PPDs. Results: Although there are still uncertainties concerning the evolution of the vertical magnetic flux remaining, surface densities show a large variety, depending on the combination of these three parameters, some of which are very different from the surface density expected from the standard accretion. When a PPD is in a "wind-driven accretion" state with the preserved vertical magnetic field, the radial dependence of the surface density can be positive in the inner region <1-10 au. The mass accretion rates are consistent with observations, even in the very low level of magnetohydrodynamical turbulence. Such a positive radial slope of the surface density gives a great impact on planet formation because (i)it inhibits the inward drift or even results in the outward drift of pebble/boulder-sized solid bodies, and (ii) it also makes the inward type-I migration of proto-planets slower or even reversed. Conclusions: The variety of our calculated PPDs should yield a wide variety of exoplanet systems.

astro-ph.EP↗

arXiv2016

Yarkovsky V-shape identification of asteroid families

There are only a few known main belt (MB) asteroid families with ages greater than 2 Gyr (Brož et al. 2013, Spoto et al. 2015). Estimates based on the family producing collision rate suggest that the lack of >2 Gyr-old families may be due to a selection bias in current techniques used to identify families. Family fragments disperse in their orbital elements, semi-major axis, $a$, eccentricity, $e$, and inclination, $i$, due to secular resonances, close encounters with massive asteroids and the non-gravitational Yarkovsky force. This causes the family fragments to be indistinguishable from the background of the main belt making them more difficult to identify with the hierarchical clustering method (HCM) with increasing family age. The discovery of the Eulalia and new Polana families in the inner belt relied on new techniques because Yarkovsky spreading made them too disperse to be identified using the classical HCM. The technique used to discover the new Polana and Eulalia families is modified to identify asteroid families by searching for correlations between $a$ and asteroid diameter, $D$, or absolute magnitude, $H$. A group of asteroids is identified as a collisional family if its boundary in the $a$ vs. 1/$D$ or $a$ vs. $H$ planes has a characteristic V-shape which is due to the size dependent Yarkovsky spreading. The V-shape boundary is identified with two separate techniques. The first identifies a border by measuring the drop between the number of objects inside and outside of the border. The second identifies the V-shape border by measuring the number density of objects in $a$ vs. 1/$D$,$H$ space. The V-shape techniques are demonstrated on known families Erigone, Vesta, Koronis, and families difficult to identify by HCM such as Flora, Baptistina, new Polana, Eulalia and Karin. Application of the technique in a search for >2 Gyr-old families throughout the MB is discussed.

astro-ph.EP↗

arXiv2016

The Asteroid Belt as a Relic From a Chaotic Early Solar System

The orbital structure of the asteroid belt holds a record of the Solar System's dynamical history. The current belt only contains ${\rm \sim 10^{-3}}$ Earth masses yet the asteroids' orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter's orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth's orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter and Saturn's early orbits were chaotic. Stochastic variations in the gas giants' orbits cause resonances to continually jump across the main belt and excite the asteroids' orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants' current orbits were achieved later, during an instability in the outer Solar System. Although it is well known that the present-day Solar System exhibits chaotic behavior, our results suggest that the early Solar System may also have been chaotic.

astro-ph.EP↗

arXiv2016

Highly siderophile elements were stripped from Earth's mantle by iron sulfide segregation

Highly siderophile elements (HSEs) are strongly depleted in the bulk silicate Earth (BSE) but are present in near-chondritic relative abundances. The conventional explanation is that the HSEs were stripped from the mantle by the segregation of metal during core formation but were added back in near-chondritic proportions by late accretion, after core formation had ceased. Here we show that metal-silicate equilibration and segregation during Earth's core formation actually increased HSE mantle concentrations because HSE partition coefficients are relatively low at the high pressures of core formation within Earth. The pervasive exsolution and segregation of iron sulfide liquid from silicate liquid (the "Hadean matte") stripped magma oceans of HSEs during cooling and crystallization, before late accretion, and resulted in slightly suprachondritic palladium/iridium and ruthenium/iridium ratios.

astro-ph.EP↗

arXiv2016

Planet Formation Imager (PFI): science vision and key requirements

The Planet Formation Imager (PFI) project aims to provide a strong scientific vision for ground-based optical astronomy beyond the upcoming generation of Extremely Large Telescopes. We make the case that a breakthrough in angular resolution imaging capabilities is required in order to unravel the processes involved in planet formation. PFI will be optimised to provide a complete census of the protoplanet population at all stellocentric radii and over the age range from 0.1 to about 100 Myr. Within this age period, planetary systems undergo dramatic changes and the final architecture of planetary systems is determined. Our goal is to study the planetary birth on the natural spatial scale where the material is assembled, which is the "Hill Sphere" of the forming planet, and to characterise the protoplanetary cores by measuring their masses and physical properties. Our science working group has investigated the observational characteristics of these young protoplanets as well as the migration mechanisms that might alter the system architecture. We simulated the imprints that the planets leave in the disk and study how PFI could revolutionise areas ranging from exoplanet to extragalactic science. In this contribution we outline the key science drivers of PFI and discuss the requirements that will guide the technology choices, the site selection, and potential science/technology tradeoffs.

astro-ph.IM↗

arXiv2016

The inclination of the planetary system relative to the solar equator may be explained by the presence of Planet 9

We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the Solar System. We find that, given the large distance of planet 9, the dynamics of the inner giant planets can be decomposed into a classic Lagrange-Laplace dynamics relative to their own invariant plane (the plane orthogonal to their total angular momentum vector) and a slow precession of said plane relative to the total angular momentum vector of the Solar System, including planet 9. Under some specific configurations for planet 9, this precession can explain the current tilt of approximately 6 degrees between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets' invariant plane as a function of the planet 9's mass, inclination, eccentricity and semimajor axis, and some numerical simulations of the equations of motion of the giant planets and planet 9 are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets' invariant plane, which also constrain the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow explaining the current solar tilt are compatible with those proposed to explain the orbital confinement of the most distant Kuiper belt objects. Thus, this work on the one hand gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and, on the other hand, adds new constraints to the orbital elements of planet 9.

astro-ph.EP↗

arXiv2016

Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt

It is generally accepted today that our solar system has undergone a phase during which the orbits of the giant planets became very unstable. In recent years, many studies have identified traces of this event and have provided reasonable justification for this occurrence. The magnitude (in terms of orbital variation) and the timing of the instability though (early or late with respect to the dispersal of the gas disk) still remains an open debate. The terrestrial planets seem to set a strict constraint: either the giant planet instability happened early, while the terrestrial planets were still forming, or the orbits of Jupiter and Saturn had to separate from each other impulsively, with a large enough `jump' in semimajor axis (Brasser et al. 2009; Kaib and Chambers 2016) for the terrestrial planets to remain stable. Because a large orbital jump is a low probability event, the early instability hypothesis seems to be favored. However, the asteroid belt would also evolve in a different way, assuming different instability amplitudes. These two constraints need to match each other in order to favor one scenario over the other. Considering an initially dynamically cold disk of asteroids, Morbidelli et al. (2010) concluded that a comparably large jump is needed to reconstruct the current asteroid belt. Here we confirm the same conclusion, but considering an asteroid population already strongly excited in eccentricity, such as that produced in the Grand Tack scenario (Walsh et al. 2011). Because the asteroids existed since the time of removal of the gas disk, unlike the terrestrial planets, this constraint on the width of the giant planet jump is valid regardless of whether the instability happened early or late. Hence, at this stage, assuming an early instability does not appear to provide any advantage in terms of the probabilistic reconstruction of the solar system structure.

astro-ph.EP↗

arXiv2016

Collisionless Encounters and the Origin of the Lunar Inclination

The Moon is generally thought to have formed from the debris ejected by the impact of a planet-sized object with the proto-Earth towards the end of planetary accretion. Modeling of the impact process predicts that the lunar material was disaggregated into a circumplanetary disk and that lunar accretion subsequently placed the Moon in a near equatorial orbit. Forward integration of the lunar orbit from this initial state predicts a modern inclination at least an order of magnitude smaller than the lunar value, a long-standing discrepancy known as the lunar inclination problem. Here we show that the modern lunar orbit provides a sensitive record of gravitational interactions with Earth-crossing planetesimals not yet accreted at the time of the Moon-forming event. The excited lunar orbit can naturally be reproduced via interaction with a small quantity of mass (corresponding to 0.0075-0.015 ME eventually accreted to the Earth) carried by a few bodies, consistent with constraints and models of late accretion. While the process has a stochastic element, the observed value of the lunar inclination is among the most likely outcomes for a wide range of parameters. The excitation of the lunar orbit is most readily reproduced via collisionless encounters with strong tidal dissipation on the early Earth. This mechanism obviates the necessity of previously proposed (but idealized) excitation mechanisms and can constrain the planet formation context of the Moon-forming event and the pristineness of the dynamical state of the Earth-Moon system.

astro-ph.EP↗

arXiv2016

The radial dependence of pebble accretion rates: A source of diversity in planetary systems I. Analytical formulation

Context. The classical "planetesimal" accretion scenario for the formation of planets has recently evolved with the idea that "pebbles", centimeter- to meter-sized icy grains migrating in protoplanetary disks, can control planetesimal and/or planetary growth. Aims. We investigate how pebble accretion depends on disk properties and affects the formation of planetary systems Methods. We construct analytical models of pebble accretion onto planetary embryos that consistently account for the mass and orbital evolution of the pebble flow and reflect disk structure. Results. We derive simple formulas for pebble accretion rates in the so-called "settling" regime for planetary embryos with more than 100 km in size. For relatively smaller embryos or in outer disk regions, the accretion mode is 3D, meaning that the thickness of the pebble flow must be taken into account, and resulting in an accretion rate that is independent of the embryo mass. For larger embryos or in inner regions, the accretion is in a 2D mode, i.e., the pebble disk may be considered to be infinitely thin. We show that the radial dependence of the pebble accretion rata is different (even the sign of the power-law exponent changes) for different disk conditions such as the disk heating source (viscous heating or stellar irradiation), the drag law (Stokes or Epstein, and weak or strong coupling), and in the 2D or 3D accretion modes. We also discuss the effect of the sublimation/destruction of icy pebbles inside the snow line. Conclusions. Pebble accretion easily produces a large diversity of planetary systems. In other words, to correctly infer the results of planet formation through pebble accretion, detailed prescriptions of disk evolution and pebble growth, sublimation/destruction and migration are required.

astro-ph.EP↗

arXiv2016

Impact-induced melting during accretion of the Earth

Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate equilibration and thus geochemical fractionation that results from core-mantle differentiation. The accretional collisions involved in forming the terrestrial planets of the inner Solar System have been calculated by previous studies using N-body accretion simulations. Here we use the output from such simulations to determine the volumes of melt produced and thus the pressure and temperature conditions of metal-silicate equilibration, after each impact, as Earth-like planets accrete. For these calculations a parametrised melting model is used that takes impact velocity, impact angle and the respective masses of the impacting bodies into account. The evolution of metal-silicate equilibration pressures (as defined by evolving magma ocean depths) during Earth's accretion depends strongly on the lifetime of impact-generated magma oceans compared to the time interval between large impacts. In addition, such results depend on starting parameters in the N-body simulations, such as the number and initial mass of embryos. Thus, there is the potential for combining the results, such as those presented here, with multistage core formation models to better constrain the accretional history of the Earth.

astro-ph.EP↗

arXiv2016

Oxygen isotopic evidence for vigorous mixing during the Moon-forming Giant Impact

Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in Δ"17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average Δ"17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.

astro-ph.EP↗

arXiv2015

Suppression of type I migration by disk winds

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.

astro-ph.EP↗

arXiv2015

Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

astro-ph.EP↗