arXiv subjects

Alessandro Morbidelli

Publications and source records attributed to Alessandro Morbidelli.

At least 163 records · Page 9Linked to original sources

arXiv2012

A Sawtooth-like Timeline for the First Billion Year of Lunar Bombardment

We revisit the early evolution of the Moon's bombardment. Our work combines modeling (based on plausible projectile sources and their dynamical decay rates) with constraints from the lunar crater record, radiometric ages of the youngest lunar basins, and the abundance of highly siderophile elements in the lunar crust and mantle. We deduce that the evolution of the impact flux did not decline exponentially over the first billion years of lunar history, but also there was no prominent and "narrow" impact spike some 3.9 Gy ago, unlike that typically envisioned in the lunar cataclysm scenario. Instead, we show the timeline of the lunar bombardment has a sawtooth-like profile, with an uptick in the impact flux near 4.1 Gy ago. The impact flux at the beginning of this weaker cataclysm was 5-10 times higher than the immediately preceding period. The Nectaris basin should have been one of the first basins formed at the sawtooth. We predict the bombardment rate since about 4.1Gy ago declined slowly and adhered relatively close to classic crater chronology models (Neukum and Ivanov (1994)). Overall we expect that the sawtooth event accounted for about 1/4 of the total bombardment suffered by the Moon since its formation. Consequently, considering that about 12-14 basins formed during the sawtooth event, we expect that the net number of basins formed on the Moon was about 45-50. From our expected bombardment timeline, we derived a new and improved lunar chronology suitable for use on Pre-Nectarian surface units. According to this chronology, a significant portion of the oldest lunar cratered terrains has an age of 4.38-4.42 Gyr. Moreover, the largest lunar basin, South Pole Aitken, is older than 4.3Gy, and therefore was not produced during the lunar cataclysm.

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arXiv2012

Dissipative Divergence of Resonant Orbits

A considerable fraction of multi-planet systems discovered by the observational surveys of extrasolar planets reside in mild proximity to first-order mean motion resonances. However, the relative remoteness of such systems from nominal resonant period ratios (e.g. 2:1, 3:2, 4:3) has been interpreted as evidence for lack of resonant interactions. Here we show that a slow divergence away from exact commensurability is a natural outcome of dissipative evolution and demonstrate that libration of critical angles can be maintained tens of percent away from nominal resonance. We construct an analytical theory for the long-term dynamical evolution of dissipated resonant planetary pairs and confirm our calculations numerically. Collectively, our results suggest that a significant fraction of the near-commensurate extrasolar planets are in fact resonant and have undergone significant dissipative evolution.

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arXiv2012

Statistical Study of the Early Solar System's Instability with 4, 5 and 6 Giant Planets

Several properties of the Solar System, including the wide radial spacing and orbital eccentricities of giant planets, can be explained if the early Solar System evolved through a dynamical instability followed by migration of planets in the planetesimal disk. Here we report the results of a statistical study, in which we performed nearly 10^4 numerical simulations of planetary instability starting from hundreds of different initial conditions. We found that the dynamical evolution is typically too violent, if Jupiter and Saturn start in the 3:2 resonance, leading to ejection of at least one ice giant from the Solar System. Planet ejection can be avoided if the mass of the transplanetary disk of planetesimals was large (M_disk>50 M_Earth), but we found that a massive disk would lead to excessive dynamical damping (e.g., final e_55 < 0.01 compared to present e_55=0.044, where e_55 is the amplitude of the fifth eccentric mode in the Jupiter's orbit), and to smooth migration that violates constraints from the survival of the terrestrial planets. Better results were obtained when the Solar System was assumed to have five giant planets initially and one ice giant, with the mass comparable to that of Uranus and Neptune, was ejected into interstellar space by Jupiter. The best results were obtained when the ejected planet was placed into the external 3:2 or 4:3 resonance with Saturn and M_disk ~ 20 M_Earth. The range of possible outcomes is rather broad in this case, indicating that the present Solar System is neither a typical nor expected result for a given initial state, and occurs, in best cases, with only a ~5% probability (as defined by the success criteria described in the main text). The case with six giant planets shows interesting dynamics but does offer significant advantages relative to the five planet case.

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arXiv2012

On the origin of the Almahata-Sitta meteorite and 2008TC3 asteroid

Asteroid 2008TC3 was a Near Earth Asteroid that impacted the Earth on 2008 October 7. Meteorites were produced by the break-up of 2008TC3 in the high atmosphere and at present, about 600 meteorites - called Almahata Sitta - coming from 2008TC3 have been recovered. A mineralogical study of Almahata Sitta fragments shows that the asteroid 2008TC3 was made of meteorites of different types (ureilites, H, L, and E chondrites). Understanding the origin of this body and how it was put together remain a challenge. Here we perform a detailed spectroscopical and dynamical investigation to show that the most likely source region of 2008TC3 is in the inner Main Belt at low inclination (i<8 degrees). We show that asteroids with spectroscopic classes that can be associated with the different meteorite types of Almahata Sitta are present in the region of the Main Belt that includes the Nysa-Polana family and objects of the Background at low inclination. Searching for a possible scenario of formation for 2008TC3, we show that there is little chance that 2008TC3 was formed by low velocity collisions between asteroids of different mineralogies, in the current asteroid belt. It seems more likely that the heterogeneous composition of 2008TC3 was a inherited from a time when the asteroid belt was in a different dynamical state, most likely in the very early Solar System. Because ureilites are fragments of a large, thermally metamorphosed asteroid, this suggests that the phases of collisional erosion (the break-up of the ureilite parent-body) and collisional accretion (the formation of the parent body of 2008TC3) overlapped for some time in the primordial asteroid belt.

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arXiv2011

Dynamical evolution of planetary systems

The apparent regularity of the motion of the giant planets of our solar system suggested for decades that said planets formed onto orbits similar to the current ones and that nothing dramatic ever happened during their lifetime. The discovery of extra-solar planets showed astonishingly that the orbital structure of our planetary system is not typical. Many giant extra-solar planets have orbits with semi major axes of $\sim 1$ AU, and some have even smaller orbital radii, sometimes with orbital periods of just a few days. Moreover, most extra-solar planets have large eccentricities, up to values that only comets have in our solar system. Why such a big diversity between our solar system and the extra-solar systems, as well as among the extra-solar systems themselves? This chapter aims to give a partial answer to this fundamental question....

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arXiv2011

Formation and Evolution of Planetary Systems in Presence of Highly Inclined Stellar Perturbers

The presence of highly eccentric extrasolar planets in binary stellar systems suggests that the Kozai effect has played an important role in shaping their dynamical architectures. However, the formation of planets in inclined binary systems poses a considerable theoretical challenge, as orbital excitation due to the Kozai resonance implies destructive, high-velocity collisions among planetesimals. To resolve the apparent difficulties posed by Kozai resonance, we seek to identify the primary physical processes responsible for inhibiting the action of Kozai cycles in protoplanetary disks. Subsequently, we seek to understand how newly-formed planetary systems transition to their observed, Kozai-dominated dynamical states. We find that theoretical difficulties in planet formation arising from the presence of a distant companion star, posed by the Kozai effect and other secular perturbations, can be overcome by a proper account of gravitational interactions within the protoplanetary disk. In particular, fast apsidal recession induced by disk self-gravity tends to erase the Kozai effect, and ensure that the disk's unwarped, rigid structure is maintained. Subsequently, once a planetary system has formed, the Kozai effect can continue to be wiped out as a result of apsidal precession, arising from planet-planet interactions. However, if such a system undergoes a dynamical instability, its architecture may change in such a way that the Kozai effect becomes operative. The results presented here suggest that planetary formation in highly inclined binary systems is not stalled by perturbations, arising from the stellar companion. Consequently, planet formation in binary stars is probably no different from that around single stars on a qualitative level. Furthermore, it is likely that systems where the Kozai effect operates, underwent a transient phase of dynamical instability in the past.

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arXiv2011

Onset of Secular Chaos in Planetary Systems: Period Doubling & Strange Attractors

As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are important, has not been thoroughly investigated. Here, we study the onset of stochastic motion in presence of dissipation, in the context of classical perturbation theory, and show that planetary systems approach chaos via a period-doubling route as dissipation is gradually reduced. Furthermore, we demonstrate that chaotic strange attractors can exist in mildly damped systems. The results presented here are of interest for understanding the early dynamical evolution of chaotic planetary systems, as they may have transitioned to chaos from a quasi-periodic state, dominated by dissipative interactions with the birth nebula.

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arXiv2011

The Effect of an Early Planetesimal-Driven Migration of the Giant Planets on Terrestrial Planet Formation

The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early migration of the giant planets is angular mometum transfer between the planets and scattered planetesimals.

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arXiv2010

Calculation of the enrichment of the giant planet envelopes during the "late heavy bombardment"

The giant planets of our solar system possess envelopes consisting mainly of hydrogen and helium but are also significantly enriched in heavier elements relatively to our Sun. In order to better constrain how these heavy elements have been delivered, we quantify the amount accreted during the so-called "late heavy bombardment", at a time when planets were fully formed and planetesimals could not sink deep into the planets. On the basis of the "Nice model", we obtain accreted masses (in terrestrial units) equal to $0.15\pm0.04 \rm\,M_\oplus$ for Jupiter, and $0.08 \pm 0.01 \rm\,M_\oplus$ for Saturn. For the two other giant planets, the results are found to depend mostly on whether they switched position during the instability phase. For Uranus, the accreted mass is $0.051 \pm 0.003 \rm\,M_\oplus$ with an inversion and $0.030 \pm 0.001 \rm\,M_\oplus$ without an inversion. Neptune accretes $0.048 \pm 0.015 \rm\,M_\oplus$ in models in which it is initially closer to the Sun than Uranus, and $0.066 \pm 0.006 \rm\,M_\oplus$ otherwise. With well-mixed envelopes, this corresponds to an increase in the enrichment over the solar value of $0.033 \pm 0.001$ and $0.074 \pm 0.007$ for Jupiter and Saturn, respectively. For the two other planets, we find the enrichments to be $2.1 \pm 1.4$ (w/ inversion) or $1.2 \pm 0.7$ (w/o inversion) for Uranus, and $2.0 \pm 1.2$ (w/ inversion) or $2.7 \pm 1.6$ (w/o inversion) for Neptune. This is clearly insufficient to explain the inferred enrichments of $\sim 4$ for Jupiter, $\sim 7$ for Saturn and $\sim 45$ for Uranus and Neptune.

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arXiv2010

Review: A Coherent and Comprehensive Model of the Evolution of the Outer Solar System

Since the discovery of the first extra-solar planets, we are confronted with the puzzling diversity of planetary systems. Processes like planet radial migration in gas-disks and planetary orbital instabilities, often invoked to explain the exotic orbits of the extra-solar planets, at first sight do not seem to have played a role in our system. In reality, though, there are several aspects in the structure of our Solar System that cannot be explained in the classic scenario of in-situ formation and smooth evolution of the giant planets. This paper describes a new view of the evolution of the outer Solar System that emerges from the so-called 'Nice model' and its recent extensions. The story provided by this model describes a very "dynamical" Solar System, with giant planets affected by both radial migrations and a temporary orbital instability. Thus, the diversity between our system and those found so far around other stars does not seem to be due to different processes that operated here and elsewhere, but rather stems from the strong sensitivity of chaotic evolutions to small differences in the initial and environmental conditions.

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arXiv2010

Evidence from the asteroid belt for a violent past evolution of Jupiter's orbit

We use the current orbital structure of large (>50km) asteroids in the main asteroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones. Minton & Malhotra (2009) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of tau ~ 0.5My. However, self-consistent numerical simulations show that the planetesimal-driven migration of the giant planets is inconsistent with an exponential change in their semi major axes on such a short time scale (Hahn & Malhotra, 1999). In fact, the typical time scale is tau > 5My. When giant planet migration on this time scale is applied to the asteroid belt, the resulting orbital distribution is incompatible with the observed one. However, the planet migration can be significantly sped up by planet-planet encounters. Consider an evolution where both Jupiter and Saturn have close encounters with a Neptune-mass planet (presumably Uranus or Neptune themselves) and where this third planet, after being scattered inwards by Saturn, is scattered outwards by Jupiter. This scenario leads to a very rapid increase in the orbital separation between Jupiter and Saturn that we show here to have only mild effects on the structure of asteroid belt. This type of evolution is called a jumping-Jupiter case. Our results suggest that the total mass and dynamical excitation of the asteroid belt before migration were comparable to those currently observed. Moreover, they imply that, before migration, the orbits of Jupiter and Saturn were much less eccentric than the current ones.

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arXiv2009

How Common are Extrasolar, Late Heavy Bombardments?

The habitability of planets is strongly affected by impacts from comets and asteroids. Indications from the ages of Moon rocks suggest that the inner Solar System experienced an increased rate of impacts roughly 3.8 Gya known as the Late Heavy Bombardment (LHB). Here we develop a model of how the Solar System would have appeared to a distant observer during its history based on the Nice model of Gomes et al. (2005). We compare our results with observed debris discs. We show that the Solar System would have been amongst the brightest of these systems before the LHB. Comparison with the statistics of debris disc evolution shows that such heavy bombardment events must be rare occurring around less than 12% of Sun-like stars.

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arXiv2009

Constructing the secular architecture of the solar system II: The terrestrial planets

We investigate the dynamical evolution of the terrestrial planets during the planetesimal-driven migration of the giant planets. A basic assumption of this work is that giant planet migration occurred after the completion of terrestrial planet formation, such as in the models that link the former to the origin of the Late Heavy Bombardment. The divergent migration of Jupiter and Saturn causes the g5 eigenfrequency to cross resonances of the form g5=gk with k ranging from 1 to 4. Consequently these secular resonances cause large-amplitude responses in the eccentricities of the terrestrial planets. We show that the resonances g5=g_4 and g5=g3 do not pose a problem if Jupiter and Saturn have a fast approach and departure from their mutual 2:1 mean motion resonance. On the other hand, the resonance crossings g5=g2 and g5=g1 are more of a concern as they tend to yield a terrestrial system incompatible with the current one. We offer two solutions to this problem. The first uses the fact that a secular resonance crossing can also damp the amplitude of a Fourier mode if the latter is large originally. A second scenario involves a 'jumping Jupiter' in which encounters between an ice giant and Jupiter, without ejection of the former, cause the latter to migrate away from Saturn much faster than if migration is driven solely by encounters with planetesimals. In this case, the g5=g2 and g5=g1 resonances can be jumped over, or occur very briefly.

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arXiv2009

Asteroids Were Born Big

How big were the first planetesimals? We attempt to answer this question by conducting coagulation simulations in which the planetesimals grow by mutual collisions and form larger bodies and planetary embryos. The size frequency distribution (SFD) of the initial planetesimals is considered a free parameter in these simulations, and we search for the one that produces at the end objects with a SFD that is consistent with asteroid belt constraints. We find that, if the initial planetesimals were small (e.g. km-sized), the final SFD fails to fulfill these constraints. In particular, reproducing the bump observed at diameter D~100km in the current SFD of the asteroids requires that the minimal size of the initial planetesimals was also ~100km. This supports the idea that planetesimals formed big, namely that the size of solids in the proto-planetary disk ``jumped'' from sub-meter scale to multi-kilometer scale, without passing through intermediate values. Moreover, we find evidence that the initial planetesimals had to have sizes ranging from 100 to several 100km, probably even 1,000km, and that their SFD had to have a slope over this interval that was similar to the one characterizing the current asteroids in the same size-range. This result sets a new constraint on planetesimal formation models and opens new perspectives for the investigation of the collisional evolution in the asteroid and Kuiper belts as well as of the accretion of the cores of the giant planets.

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arXiv2009

Dynamical Models of Terrestrial Planet Formation

We review the problem of the formation of terrestrial planets, with particular emphasis on the interaction of dynamical and geochemical models. The lifetime of gas around stars in the process of formation is limited to a few million years based on astronomical observations, while isotopic dating of meteorites and the Earth-Moon system suggest that perhaps 50-100 million years were required for the assembly of the Earth. Therefore, much of the growth of the terrestrial planets in our own system is presumed to have taken place under largely gas-free conditions, and the physics of terrestrial planet formation is dominated by gravitational interactions and collisions. The earliest phase of terrestrial-planet formation involve the growth of km-sized or larger planetesimals from dust grains, followed by the accumulations of these planetesimals into ~100 lunar- to Mars-mass bodies that are initially gravitationally isolated from one-another in a swarm of smaller planetesimals, but eventually grow to the point of significantly perturbing one-another. The mutual perturbations between the embryos, combined with gravitational stirring by Jupiter, lead to orbital crossings and collisions that drive the growth to Earth-sized planets on a timescale of 10-100 million years. Numerical treatment of this process has focussed on the use of symplectic integrators which can rapidly integrate the thousands of gravitationally-interacting bodies necessary to accurately model planetary growth. While the general nature of the terrestrial planets--their sizes and orbital parameters--seem to be broadly reproduced by the models, there are still some outstanding dynamical issues. One of these is the presence of an embryo-sized body, Mars, in our system in place of the more massive objects that simulations tend to yield. [Abridged]

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arXiv2009

The History of the Solar System's Debris Disc: Observable Properties of the Kuiper Belt

The Nice model of Gomes et al. (2005) suggests that the migration of the giant planets caused a planetesimal clearing event which led to the Late Heavy Bombardment (LHB) at 880 Myr. Here we investigate the IR emission from the Kuiper belt during the history of the Solar System as described by the Nice model. We describe a method for easily converting the results of n-body planetesimal simulations into observational properties (assuming black-body grains and a single size distribution) and further modify this method to improve its realism (using realistic grain properties and a three-phase size distribution). We compare our results with observed debris discs and evaluate the plausibility of detecting an LHB-like process in extrasolar systems. Recent surveys have shown that 4% of stars exhibit 24 um excess and 16% exhibit 70 um excess. We show that the Solar System would have been amongst the brightest of these systems before the LHB at both 24 and 70 um. We find a significant increase in 24 um emission during the LHB, which rapidly drops off and becomes undetectable within 30 Myr, whereas the 70 um emission remains detectable until 360 Myr after the LHB. Comparison with the statistics of debris disc evolution shows that such depletion events must be rare occurring around less than 12% of Sun-like stars and with this level of incidence we would expect approximately 1 of the 413 Sun-like, field stars so far detected to have a 24 um excess to be currently going through an LHB. We also find that collisional processes are important in the Solar System before the LHB and that parameters for weak Kuiper belt objects are inconsistent with the Nice model interpretation of the LHB.

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arXiv2009

Building the Terrestrial Planets: Constrained Accretion in the Inner Solar System

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include 1) the orbits, in particular the small eccentricities, and 2) the masses of the terrestrial planets -- Mars' relatively small mass in particular has not been adequately reproduced in previous simulations; 3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; 4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and 5) Earth's relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N=1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the "Nice model." We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars' mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. (abridged)

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arXiv2008

Did Saturn's rings form during the Late Heavy Bombardment ?

The origin of Saturn\' s massive ring system is still unknown. Two popular scenarios - the tidal splitting of passing comets and the collisional destruction of a satellite - rely on a high cometary flux in the past. In the present paper we attempt to quantify the cometary flux during the Late Heavy Bombardment (LHB) to assess the likelihood of both scenarios. Our analysis relies on the so-called Nice model of the origin of the LHB (Tsiganis et al., 2005; Morbidelli et al., 2005; Gomes et al., 2005) and on the size distribution of the primordial trans-Neptunian planetesimals constrained in Charnoz & Morbidelli (2007). We find that the cometary flux on Saturn during the LHB was so high that both scenarios for the formation of Saturn rings are viable in principle. However, a more detailed study shows that the comet tidal disruption scenario implies that all four giant planets should have comparable ring systems whereas the destroyed satellite scenario would work only for Saturn, and perhaps Jupiter. This is because in Saturnś system, the synchronous orbit is interior to the Roche Limit, which is a necessary condition for maintaining a satellite in the Roche zone up to the time of the LHB. We also discuss the apparent elimination of silicates from the ring parent body implied by the purity of the ice in Saturn \' s rings. The LHB has also strong implications for the survival of the Saturnian satellites: all satellites smaller than Mimas would have been destroyed during the LHB, whereas Enceladus would have had from 40% to 70% chance of survival depending on the disruption model. In conclusion, these results suggest that the LHB is the sweet moment for the formation of a massive ring system around Saturn.

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