arXiv subjects

Alessandro Morbidelli

Publications and source records attributed to Alessandro Morbidelli.

At least 145 records · Page 8Linked to original sources

arXiv2014

Stellar irradiated discs and implications on migration of embedded planets III: viscosity transitions

The migration strength and direction of embedded low-mass planets depends on the disc structure. In discs with an efficient radiative transport, the migration can be directed outwards for planets with more than 3-5 Earth masses. This is due to the entropy driven corotation torque, a process that extends the lifetimes of growing planetary embryos. We investigate the influence on the disc structure caused by a jump in the alpha parameter of the viscosity to model a dead-zone structure in the disc. We focus on M-dot discs, which have a constant net mass flux. Using the resulting disc structure, we investigate the consequences for the formation of planetesimals and determine the regions of outward migration for proto-planets. We performed numerical hydrosimulations of M-dot discs in the r-z-plane. We used the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation as well as a two-temperature solver that includes radiation transport in the flux-limited diffusion approximation. Viscosity transitions inside the disc create transitions in density that stop inward migration for small planets through the so-called "planet trap" mechanism. This mechanism also works for planets down to M_P > 0.5M_E. Additionally, the viscosity transitions change the pressure gradient in the disc, which facilitates planetesimal formation via the streaming instability. However, a very steep transition in viscosity is needed to achieve in a pressure bump in the disc. The transition in viscosity facilitates planetesimal formation and can stop the migration of small-mass planets (M_P>0.5M_E), but still does not halt inward migration of smaller planets and planetesimals that are affected by gas drag. A very steep, probably unrealistic viscosity gradient is needed to trap planets of smaller masses and halt gas-drag-driven planetesimal migration at a pressure bump.

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arXiv2014

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation (Hansen 2009, Walsh et al. 2011) has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk--a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies--the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as `primitive' bodies). We find here that the planets will accrete on order 1-2% of their total mass from primitive planetesimals scattered onto planet-crossing orbits during the formation of the planets. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. While the radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system, we find that the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event.

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arXiv2014

Constraining the Cratering Chronology of Vesta

Vesta has a complex cratering history, with ancient terrains as well as recent large impacts that have led to regional resurfacing. Crater counts can help constrain the relative ages of different units on Vesta's surface, but converting those crater counts to absolute ages requires a chronology function. We present a cratering chronology based on the best current models for the dynamical evolution of asteroid belt, and calibrate it to Vesta using the record of large craters on its surface. While uncertainties remain, our chronology function is broadly consistent with an ancient surface of Vesta as well as other constraints such as the bombardment history of the rest of the inner Solar System and the Ar-Ar age distribution of howardite, eucrite and diogenite (HED) meteorites from Vesta.

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arXiv2014

Lunar and Terrestrial Planet Formation in the Grand Tack Scenario

We present conclusions from a large number of N-body simulations of the giant impact phase of terrestrial planet formation. We focus on new results obtained from the recently proposed Grand Tack model, which couples the gas-driven migration of giant planets to the accretion of the terrestrial planets. The giant impact phase follows the oligarchic growth phase, which builds a bi-modal mass distribution within the disc of embryos and planetesimals. By varying the ratio of the total mass in the embryo population to the total mass in the planetesimal population and the mass of the individual embryos, we explore how different disc conditions control the final planets. The total mass ratio of embryos to planetesimals controls the timing of the last giant (Moon forming) impact and its violence. The initial embryo mass sets the size of the lunar impactor and the growth rate of Mars. After comparing our simulated outcomes with the actual orbits of the terrestrial planets (angular momentum deficit, mass concentration) and taking into account independent geochemical constraints on the mass accreted by the Earth after the Moon forming event and on the timescale for the growth of Mars, we conclude that the protoplanetary disc at the beginning of the giant impact phase must have had most of its mass in Mars-sized embryos and only a small fraction of the total disc mass in the planetesimal population. From this, we infer that the Moon forming event occurred between $\sim$60 and $\sim$130 My after the formation of the first solids, and was caused most likely by an object with a mass similar to that of Mars.

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arXiv2014

Earth-like Habitats in Planetary Systems

Understanding the concept of habitability is related to an evolutionary knowledge of the particular planet-in-question. Additional indications so-called "systemic aspects" of the planetary system as a whole governs a particular planet's claim on habitability. Here we focus on such systemic aspects and discuss their relevance to the formation of an 'Earth-like' habitable planet. We summarize our results obtained by lunar sample work and numerical models within the framework of the Research Alliance "Planetary Evolution and Life". We consider various scenarios which simulate the dynamical evolution of the Solar System and discuss the likelihood of forming an Earth-like world orbiting another star. Our model approach is constrained by observations of the modern Solar System and the knowledge of its history. Results suggest that the long-term presence of terrestrial planets is jeopardized due to gravitational interactions if giant planets are present. But habitability of inner rocky planets may be supported in those planetary systems hosting giant planets. Gravitational interactions within a complex multiple-body structure including giant planets may supply terrestrial planets with materials which formed in the colder region of the proto-planetary disk. During these processes, water, the prime requisite for habitability, is delivered to the inner system. This may occur either during the main accretion phase of terrestrial planets or via impacts during a post-accretion bombardment. Results for both processes are summarized and discussed with reference to the lunar crater record. Starting from a scenario involving migration of the giant planets this contribution discusses the delivery of water to Earth, the modification of atmospheres by impacts in a planetary system context and the likelihood of the existence of extrasolar Earth-like habitable worlds.

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arXiv2014

Stellar irradiated discs and implications on migration of embedded planets II: accreting-discs

The strength and direction of migration of embedded low mass planets depends on the disc's structure. It has been shown that, in discs with viscous heating and radiative transport, the migration can be directed outwards. In this paper we investigate the influence of a constant dM/dt-flux through the disc, as well as the influence of the disc's metallicity on the disc's thermodynamics. We focus on dM/dt discs, which have a net mass flux through them. Utilizing the resulting disc structure, we determine the regions of outward migration in the disc. We perform numerical hydrosimulations of dM/dt discs with viscous heating, radiative cooling and stellar irradiation in 2D in the r-z-plane. We use the explicit/implicit hydrodynamical code FARGOCA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration of embedded planets is studied by using torque formulae. For a disc of gas surface density and viscosity, we find that the discs thermal structure depends on the product Sigma_G νand the amount of heavy elements, while the migration of planets additionally to the mentioned quantities, depends on the amount of viscosity itself. As a result of this, the disc structure can not be approximated by simple power laws. During the lifetime of the disc, the structure of the disc changes significantly in a non-linear way in the inner parts. In the late stages of the discs evolution, outward migration is only possible if the metallicity of the disc is high. For low metallicity, planets would migrate inwards and could potentially be lost. The presented disc structures and migration maps have important consequences on the formation of planets, as they can give hints on the different formation mechanisms for different types of planets as a function of metallicity.

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arXiv2014

The Absolute Magnitude Distribution of Kuiper Belt Objects

Here we measure the absolute magnitude distributions (H-distribution) of the dynamically excited and quiescent (hot and cold) Kuiper Belt objects (KBOs), and test if they share the same H-distribution as the Jupiter Trojans. From a compilation of all useable ecliptic surveys, we find that the KBO H-distributions are well described by broken power-laws. The cold population has a bright-end slope, $α_{\textrm{1}}=1.5_{-0.2}^{+0.4}$, and break magnitude, $H_{\textrm{B}}=6.9_{-0.2}^{+0.1}$ (r'-band). The hot population has a shallower bright-end slope of, $α_{\textrm{1}}=0.87_{-0.2}^{+0.07}$, and break magnitude $H_{\textrm{B}}=7.7_{-0.5}^{+1.0}$. Both populations share similar faint end slopes of $α_2\sim0.2$. We estimate the masses of the hot and cold populations are $\sim0.01$ and $\sim3\times10^{-4} \mbox{ M$_{\bigoplus}$}$. The broken power-law fit to the Trojan H-distribution has $α_\textrm{1}=1.0\pm0.2$, $α_\textrm{2}=0.36\pm0.01$, and $H_{\textrm{B}}=8.3$. The KS test reveals that the probability that the Trojans and cold KBOs share the same parent H-distribution is less than 1 in 1000. When the bimodal albedo distribution of the hot objects is accounted for, there is no evidence that the H-distributions of the Trojans and hot KBOs differ. Our findings are in agreement with the predictions of the Nice model in terms of both mass and H-distribution of the hot and Trojan populations. Wide field survey data suggest that the brightest few hot objects, with $H_{\textrm{r'}}\lesssim3$, do not fall on the steep power-law slope of fainter hot objects. Under the standard hierarchical model of planetesimal formation, it is difficult to account for the similar break diameters of the hot and cold populations given the low mass of the cold belt.

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arXiv2013

Geochemical and planetary dynamical views on the origin of Earth's atmosphere and oceans

Earth's volatile elements (H, C, and N) are essential to maintaining habitable conditions for metazoans and simpler life forms. However, identifying the sources (comets, meteorites, and trapped nebular gas) that supplied volatiles to Earth is not straightforward because secondary processes like mantle degassing, crustal recycling, and escape to space modified the composition of the atmosphere. Here, we review two complementary approaches to investigate the origin of Earth's atmosphere and oceans. The geochemical approach uses volatile element abundances and isotopic compositions to identify the possible contributors to the atmosphere and to disentangle the processes that shaped it. In that respect, noble gases (He, Ne, Ar, Kr, and Xe), elements that are chemically inert and possess several isotopes produced by radioactivity, play a critical role. The dynamical approach uses our knowledge of planetary dynamics to track volatile delivery to the Earth, starting with dust transport in the disk to planet-building processes. The main conclusion is that Earth acquired most of its major volatile elements by accretion of planetesimals or embryos akin to volatile-rich meteorites. At the same time, solar/meteoritic noble gases were captured by embryos and some gases were lost to space, by hydrodynamic escape and large impacts. Comets did not contribute much H, C, and N but may have delivered significant noble gases, which could represent the only fingerprints of the bombardment of our planet with icy bodies. The processes that governed the delivery of volatile elements to the Earth are thought to be relatively common and it is likely that Earth-like planets covered with oceans exist in extra-solar systems.

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arXiv2013

The Long-Term Dynamical Evolution of Planetary Systems

This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then describe such interactions in more tightly-packed planetary systems. As planet-planet interactions build up, some systems become dynamically unstable, leading to strong encounters and ultimately either ejections or collisions of planets. After discussing the basic physical processes involved, we consider how these interactions apply to extrasolar planetary systems and explore the constraints provided by observed systems. The presence of a residual planetesimal disc can lead to planetary migration and hence cause instabilities induced by resonance crossing; however, such discs can also stabilise planetary systems. The crowded birth environment of a planetary system can have a significant impact: close encounters and binary companions can act to destabilise systems, or sculpt their properties. In the case of binaries, the Kozai mechanism can place planets on extremely eccentric orbits which may later circularise to produce hot Jupiters.

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arXiv2013

Analytical Treatment of Planetary Resonances

An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary disk-driven migration, a qualitative description of the dynamical evolution of resonant planets remains largely elusive. Aided by the pioneering works of the last century, we formulate an approximate, integrable theory for first-order resonant motion. We utilize the developed theory to construct an intuitive, geometrical representation of resonances within the context of the unrestricted three-body problem. Moreover, we derive a simple analytical criterion for the appearance of secondary resonances between resonant and secular motion. Subsequently, we demonstrate the onset of rapid chaotic motion as a result of overlap among neighboring first-order mean-motion resonances, as well as the appearance of slow chaos as a result of secular modulation of the planetary orbits. Finally, we take advantage of the integrable theory to analytically show that, in the adiabatic regime, divergent encounters with first-order mean-motion resonances always lead to persistent apsidal anti-alignment.

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arXiv2013

Early Dynamical Instabilities in the Giant Planet Systems

The observed wide eccentricity distribution of extrasolar giant planets is thought to be the result of dynamical instabilities and gravitational scattering among planets. Previously, it has been assumed that the orbits in giant planet systems become gravitationally unstable after the gas nebula dispersal. It was not well understood, however, how these unstable conditions were established in the first place. In this work we numerically simulate the evolution of systems of three planets as the planets sequentially grow to Jupiter's mass, and dynamically interact among themselves and with the gas disk. We use the hydro-dynamical code FARGO that we modified by implementing the $N$-body integrator SyMBA. The new code can handle close encounters and collisions between planets. To test their stability, the planetary systems were followed with SyMBA for up to $10^8$ yr after the gas disk dispersal. We find that dynamics of the growing planets is complex, because migration and resonances raise their orbital eccentricities, and cause dynamical instabilities when gas is still around. If the dynamical instabilities occur early, planets can be removed by collisions and ejections, and the system rearranges into a new, more stable configuration. In this case, the planetary systems emerging from the gas disks are expected to be stable, and would need to be destabilized by other means (low-mass planets, planetesimal disks, etc.). Alternatively, for the giant planet system to be intrinsically unstable upon the gas disk dispersal, a special timing would be required with the growth of (at least some of) the giant planets having to occur near the end of the gas disk lifetime.

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arXiv2013

Capture of Trojans by Jumping Jupiter

Jupiter Trojans are thought to be survivors of a much larger population of planetesimals that existed in the planetary region when planets formed. They can provide important constraints on the mass and properties of the planetesimal disk, and its dispersal during planet migration. Here we tested a possibility that the Trojans were captured during the early dynamical instability among the outer planets (aka the Nice model), when the semimajor axis of Jupiter was changing as a result of scattering encounters with an ice giant. The capture occurs in this model when Jupiter's orbit and its Lagrange points become radially displaced in a scattering event and fall into a region populated by planetesimals (that previously evolved from their natal transplanetary disk to ~5 AU during the instability). Our numerical simulations of the new capture model, hereafter jump capture, satisfactorily reproduce the orbital distribution of the Trojans and their total mass. The jump capture is potentially capable of explaining the observed asymmetry in the number of leading and trailing Trojans. We find that the capture probability is (6-8)x10^-7 for each particle in the original transplanetary disk, implying that the disk contained (3-4)x10^7 planetesimals with absolute magnitude H<9 (corresponding to diameter D=80 km for a 7% albedo). The disk mass inferred from this work, M_disk=14-28 M_Earth, is consistent with the mass deduced from recent dynamical simulations of the planetary instability.

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arXiv2013

The Eos family halo

We study K-type asteroids in the broad surroundings of the Eos family because they seem to be intimately related, according to their colours measured by the Sloan Digital Sky Survey. Such `halos' of asteroid families have been rarely used as constraints for dynamical studies to date. We explain its origin as bodies escaping from the family `core' due to the Yarkovsky semimajor-axis drift and interactions with gravitational resonances, mostly with the 9/4 mean-motion resonance with Jupiter at 3.03 AU. Our N-body dynamical model allows us to independently estimate the age of the family 1.5 to 1.9 Gyr. This is approximately in agreement with the previous age estimate by Vokrouhlický et al. (2006) based on a simplified model (which accounts only for changes of semimajor axis). We can also constrain the geometry of the disruption event which had to occur at the true anomaly f =~ 120 to 180 deg.

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arXiv2012

Stellar irradiated discs and implications on migration of embedded planets I: equilibrium discs

The strength and direction of migration of low mass planets depends on the disc's thermodynamics. In discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. We investigate the influence of opacity and stellar irradiation on the disc thermodynamics. Utilizing the resulting disc structure, we determine the regions of outward migration. We perform two-dimensional numerical simulations of equilibrium discs with viscous heating, radiative cooling and stellar irradiation. We use the hydrodynamical code NIRVANA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration is studied by using torque formulae. In the constant opacity case, we reproduce the analytical results of a black-body disc: the stellar irradiation dominates in the outer regions -- leading to flaring -- while the viscous heating dominates close to the star. We find that the inner edge of the disc should not be significantly puffed-up by the stellar irradiation. If the opacity depends on the local density and temperature, the structure of the disc is different, and several bumps in the aspect ratio H/r appear, due to transitions between different opacity regimes. The bumps in the disc can shield the outer disc from stellar irradiation. Stellar irradiation is an important factor for determining the disc structure and has dramatic consequences for the migration of embedded planets. Compared to discs with only viscous heating, a stellar irradiated disc features a much smaller region of outward migration for a range of planetary masses. This suggests that the region where the formation of giant planet cores takes place is smaller, which in turn might lead to a shorter growth phase.

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arXiv2012

Circum-planetary discs as bottlenecks for gas accretion onto giant planets

With hundreds of exoplanets detected, it is necessary to revisit giant planets accretion models to explain their mass distribution. In particular, formation of sub-jovian planets remains unclear, given the short timescale for the runaway accretion of massive atmospheres. However, gas needs to pass through a circum-planetary disc. If the latter has a low viscosity (as expected if planets form in "dead zones"), it might act as a bottleneck for gas accretion. We investigate what the minimum accretion rate is for a planet under the limit assumption that the circum-planetary disc is totally inviscid, and the transport of angular momentum occurs solely because of the gravitational perturbations from the star. To estimate the accretion rate, we present a steady-state model of an inviscid circum-planetary disc, with vertical gas inflow and external torque from the star. Hydrodynamical simulations of a circum-planetary disc were conducted in 2D, in a planetocentric frame, with the star as an external perturber in order to measure the torque exerted by the star on the disc. The disc shows a two-armed spiral wave caused by stellar tides, propagating all the way in from the outer edge of the disc towards the planet. The stellar torque is small and corresponds to a doubling time for a Jupiter mass planet of the order of 5 Myrs. Given the limit assumptions, this is clearly a lower bound of the real accretion rate. This result shows that gas accretion onto a giant planet can be regulated by circum-planetary discs. This suggests that the diversity of masses of extra-solar planets may be the result of different viscosities in these discs.

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arXiv2012

NOTE: Explaining why the Uranian satellites have equatorial prograde orbits despite the large planetary obliquity

We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98 degrees.

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arXiv2012

Dynamics of pebbles in the vicinity of a growing planetary embryo: hydro-dynamical simulations

Understanding the growth of the cores of giant planets is a difficult problem. Recently, Lambrechts and Johansen (2012; LJ12) proposed a new model in which the cores grow by the accretion of pebble-size objects, as the latter drift towards the star due to gas drag. Here, we investigate the dynamics of pebble-size objects in the vicinity of planetary embryos of 1 and 5 Earth masses and the resulting accretion rates. We use hydrodynamical simulations, in which the embryo influences the dynamics of the gas and the pebbles suffer gas drag according to the local gas density and velocities. The pebble dynamics in the vicinity of the planetary embryo is non-trivial, and it changes significantly with the pebble size. Nevertheless, the accretion rate of the embryo that we measure is within an order of magnitude of the rate estimated in LJ12 and tends to their value with increasing pebble-size. We conclude that the model by LJ12 has the potential to explain the rapid growth of giant planet cores. The actual accretion rates however, depend on the surface density of pebble size objects in the disk, which is unknown to date.

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arXiv2012

Building Terrestrial Planets

This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical models with geochemical, cosmochemical and chronological constraints, in order to outline a comprehensive scenario of the early evolution of our Solar System. Given that the giant planets formed first in the protoplanetary disk, we stress the sensitive dependence of the terrestrial planet accretion process on the orbital architecture of the giant planets and on their evolution. This suggests a great diversity among the terrestrial planets populations in extrasolar systems. Issues such as the cause for the different masses and accretion timescales between Mars and the Earth and the origin of water (and other volatiles) on our planet are discussed at depth.

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