Alessandro Morbidelli

Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets

The petrology record on the Moon suggests that a cataclysmic spike in the cratering rate occurred ∼700 million years after the planets formed; this event is known as the Late Heavy Bombardment (LHB). Planetary formation theories cannot naturally account for an intense period of planetesimal bombardment so late in Solar System history. Several models have been proposed to explain a late impact spike, but none of them has been set within a self-consistent framework of Solar System evolution. Here we propose that the LHB was triggered by the rapid migration of the giant planets, which occurred after a long quiescent period. During this burst of migration, the planetesimal disk outside the orbits of the planets was destabilized, causing a sudden massive delivery of planetesimals to the inner Solar System. The asteroid belt was also strongly perturbed, with these objects supplying a significant fraction of the LHB impactors in accordance with recent geochemical evidence. Our model not only naturally explains the LHB, but also reproduces the observational constraints of the outer Solar System.

Chaotic capture of Jupiter's Trojan asteroids in the early Solar System

Jupiters Trojans are asteroids that follow essentially the same orbit as Jupiter, but lead or trail the planet by an angular distance of ∼60 degrees (co-orbital motion). They are hypothesized to be planetesimals that formed near Jupiter and were captured onto their current orbits while Jupiter was growing, possibly with the help of gas drag and/or collisions. This idea, however, cannot explain some basic properties of the Trojan population, in particular its broad orbital inclination distribution, which ranges up to ∼40 degrees (ref. 8). Here we show that the Trojans could have formed in more distant regions and been subsequently captured into co-orbital motion with Jupiter during the time when the giant planets migrated by removing neighbouring planetesimals. The capture was possible during a short period of time, just after Jupiter and Saturn crossed their mutual 1:2 resonance, when the dynamics of the Trojan region were completely chaotic. Our simulations of this process satisfactorily reproduce the orbital distribution of the Trojans and their total mass.

DISK SURFACE DENSITY TRANSITIONS AS PROTOPLANET TRAPS

The tidal torque exerted by a protoplanetary disk with power-law surface density and temperature profiles onto anembedded protoplanetary embryois generally anegative quantity that leads to the embryoinward migration. Here we investigate how the tidal torque balance is affected at a disk surface density radial jump. The jump has two consequences:(1)Itaffects thedifferential Lindbladtorque.Inparticular,ifthediskismerelyemptyontheinnerside,the differential Lindblad torque almost amounts to the large negative outer Lindblad torque. (2) It affects the corotation torque, which is a quantity very sensitive to the local gradient of the disk surface density. In particular, if the disk is depleted on the inside and the jump occurs radially over a few pressure scale heights, the corotation torque is a positive quantity that ismuchlargerthan inapower-lawdisk.Weshow bymeans ofcustomized numerical simulations of low-massplanetsembedded inprotoplanetarynebulaewithasurfacedensity jump that thesecond effect isdominant; that is, that the corotation torque largely dominates the differential Lindblad torque on the edge of a central depletion, even a shallow one. Namely, a disk surface density jump of about 50% over 3–5 disk thicknesses suffices to cancel out the total torque. As a consequence, the type I migration of low-mass objects reaching the jump should be halted, and all these objects should be trapped there provided some amount of dissipation is present in the disk to prevent the corotation torque saturation. As dissipation is provided by turbulence, which induces a jitter of the planet semimajor axis, we investigate under which conditions the trapping process overcomes the trend of turbulence to induce stochastic migration across the disk. We show that a cavity with a large outer to inner surface density ratio efficiently traps embryos from 1 to 15 M� , at any radius up to 5 AU from the central object, in a disk that has same surface density profile as the minimum mass solar nebula (MMSN). Shallow surface density transitions require light disks to efficiently trap embryos. In the case of the MMSN, this could happen in the very central parts (r < 0:03 AU). We discusswhereinaprotoplanetarydiskonecanexpectasurfacedensityjump.Thiseffectcouldconstituteasolutionto the well-known problem that the buildup of the first protogiant solid core in a disk takes much longer than its type I migration toward the central object. Subject headings: accretion, accretion disks — hydrodynamics — methods: numerical — planetary systems: formation — planetary systems: protoplanetary disks

Contamination of the asteroid belt by primordial trans-Neptunian objects

The main asteroid belt, which inhabits a relatively narrow annulus ∼2.1–3.3 au from the Sun, contains a surprising diversity of objects ranging from primitive ice–rock mixtures to igneous rocks. The standard model used to explain this assumes that most asteroids formed in situ from a primordial disk that experienced radical chemical changes within this zone. Here we show that the violent dynamical evolution of the giant-planet orbits required by the so-called Nice model leads to the insertion of primitive trans-Neptunian objects into the outer belt. This result implies that the observed diversity of the asteroid belt is not a direct reflection of the intrinsic compositional variation of the proto-planetary disk. The dark captured bodies, composed of organic-rich materials, would have been more susceptible to collisional evolution than typical main-belt asteroids. Their weak nature makes them a prodigious source of micrometeorites—sufficient to explain why most are primitive in composition and are isotopically different from most macroscopic meteorites.

The formation of the Kuiper belt by the outward transport of bodies during Neptune's migration

The ‘dynamically cold Kuiper belt’ consists of objects on low-inclination orbits between ∼40 and ∼50 au from the Sun. It currently contains material totalling less than a tenth the mass of the Earth, which is surprisingly low because, according to accretion models, the objects would not have grown to their present size unless the cold Kuiper belt originally contained tens of Earth masses of solids. Although several mechanisms have been proposed to produce the observed mass depletion, they all have significant limitations. Here we show that the objects currently observed in the dynamically cold Kuiper belt were most probably formed within ∼35 au and were subsequently pushed outward by Neptunes 1:2 mean motion resonance during its final phase of migration. Combining our mechanism with previous work, we conclude that the entire Kuiper belt formed closer to the Sun and was transported outward during the final stages of planet formation.

The Structure of the Kuiper Belt: Size Distribution and Radial Extent

The size distribution in the Kuiper Belt records physical processes operating during the formation and subsequent evolution of the solar system. This paper reports a study of the apparent magnitude distribution of faint objects in the Kuiper Belt, obtained via deep imaging on the Canada-France-Hawaii Telescope and the ESO Very Large Telescope UT1. We —nd that the entire range of observed objects (magnitudes is well represented by an unbroken power law, with the number of objects per m R D 20¨27) square degree brighter than magnitude R being of the form with a \ 0.69 and &(m R \ R) \ 10a(R~R0),

Superexponential stability of KAM tori

We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/σ)], σ being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.

The structure of protoplanetary discs around evolving young stars

The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time scales of several million years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height, and density. The commonly used disc structure of the minimum mass solar nebula (MMSN) is a simple power law in all these quantities. However, protoplanetary disc models with both viscous and stellar heating show several bumps and dips in temperature, scale height, and density caused by transitions in opacity, which are missing in the MMSN model. These play an important role in the formation of planets, since they can act as sweet spots for forming planetesimals via the streaming instability and affect the direction and magnitude of type-I migration. We present 2D simulations of accretion discs that feature radiative cooling and viscous and stellar heating, and they are linked to the observed evolutionary stages of protoplanetary discs and their host stars. These models allow us to identify preferred planetesimal and planet formation regions in the protoplanetary disc as a function of the discs metallicity, accretion rate, and lifetime. We derive simple fitting formulae that feature all structural characteristics of protoplanetary discs during the evolution of several Myr. These fits are straightforward for applying to modelling any growth stage of planets where detailed knowledge of the underlying disc structure is required. (Less)

Separating gas-giant and ice-giant planets by halting pebble accretion

In the solar system giant planets come in two flavours: gas giants (Jupiter and Saturn) with massive gas envelopes, and ice giants (Uranus and Neptune) with much thinner envelopes around their cores. It is poorly understood how these two classes of planets formed. High solid accretion rates, necessary to form the cores of giant planets within the life-time of protoplanetary discs, heat the envelope and prevent rapid gas contraction onto the core, unless accretion is halted. We find that, in fact, accretion of pebbles (similar to cm sized particles) is self-limiting: when a core becomes massive enough it carves a gap in the pebble disc. This halt in pebble accretion subsequently triggers the rapid collapse of the super-critical gas envelope. Unlike gas giants, ice giants do not reach this threshold mass and can only bind low-mass envelopes that are highly enriched by water vapour from sublimated icy pebbles. This offers an explanation for the compositional difference between gas giants and ice giants in the solar system. Furthermore, unlike planetesimal-driven accretion scenarios, our model allows core formation and envelope attraction within disc life-times, provided that solids in protoplanetary discs are predominantly made up of pebbles. Our results imply that the outer regions of planetary systems, where the mass required to halt pebble accretion is large, are dominated by ice giants and that gas-giant exoplanets in wide orbits are enriched by more than 50 Earth masses of solids.

MASS AND ORBIT DETERMINATION FROM TRANSIT TIMING VARIATIONS OF EXOPLANETS

The timing variations of transits of an exoplanet provide means of detecting additional planets in the system. The short-period and resonant variations of the transit signal are probably the most diagnostic of the perturbing planets mass and orbit. The method can be sensitive to small perturbing masses near the transiting planet and for orbits at mean motion resonances. It is not evident, however, how the mass and orbit of the perturbing planet can be determined from the observed variations of transit times. This is a difficult inverse problem. Direct N-body integrations are computationally too expensive to provide an adequate sampling of parameter space. Here we develop an alternative method based on analytic perturbation theory. We find that this new method is typically ~104 times faster than direct N-body integrations. The perturbation theory that we use here has an adequate precision to predict timing variations for most planetary orbits except those with very large eccentricities where the expansion of the disturbing function is divergent. By applying the perturbation method to the inverse problem we determine the number and precision of the measured transit times that are required for the unique and correct characterization of the perturbing planet. We find that the required precision is typically a small fraction (~15%-30%) of the full transit timing variation amplitude. Very high precision observations of transits will therefore be needed. We discuss the optimal observation strategy to characterize a planetary system from the transit timing variations. We find that the timing of secondary transits, if measured with adequate precision, can help to alleviate the problem with the degeneracy of solutions of the inverse problem.