Elena Lega

The fast Lyapunov indicator: a simple tool to detect weak chaos. Application to the structure of the main asteroidal belt

A new method is presented, based on the variaiion with time sf the length of vectors evolving in tangential space, which distinguishes very quickly between regular and chaotic motion. This method is closely related to the computation of the Lyapunov characteristic exponents, but because of the speed of computation it can be easily applied to the study of a large set of orbits. This method is tested for the 2- dimensional standard mapping, and the structure of the phase space is explored for the 4-dimensional standard map simulating the conditions of the distribution of asteroids. Then the distribution of the 716 asteroids orbiting between the 3/l and 512 Kirkwood gaps is studied. 0 1997 Elsevier Science Ltd

Fossilized condensation lines in the Solar System protoplanetary disk

The terrestrial planets and the asteroids dominant in the inner asteroid belt are water poor. However, in the protoplan-etary disk the temperature should have decreased below water-condensation level well before the disk was photo-evaporated. Thus, the global water depletion of the inner Solar System is puzzling. We show that, even if the inner disk becomes cold, there cannot be direct condensation of water. This is because the snowline moves towards the Sun more slowly than the gas itself. Thus the gas in the vicinity of the snowline always comes from farther out, where it should have already condensed, and therefore it should be dry. The appearance of ice in a range of heliocentric distances swept by the snowline can only be due to the radial drift of icy particles from the outer disk. However, if a planet with a mass larger than 20 Earth mass is present, the radial drift of particles is interrupted, because such a planet gives the disk a super-Keplerian rotation just outside of its own orbit. From this result, we propose that the precursor of Jupiter achieved this threshold mass when the snowline was still around 3 AU. This effectively fossilized the snowline at that location. In fact, even if it cooled later, the disk inside of Jupiters orbit remained ice-depleted because the flow of icy particles from the outer system was intercepted by the planet. This scenario predicts that planetary systems without giant planets should be much more rich in water in their inner regions than our system. We also show that the inner edge of the planetesimal disk at 0.7 AU, required in terrestrial planet formation models to explain the small mass of Mercury and the absence of planets inside of its orbit, could be due to the silicate condensation line, fossilized at the end of the phase of streaming instability that generated the planetesimal seeds. Thus, when the disk cooled, silicate particles started to drift inwards of 0.7 AU without being sublimated, but they could not be accreted by any pre-existing planetesimals.

Migration of Earth-sized planets in 3D radiative discs

In this paper, we address the migration of small mass planets in 3D radiative disks. Indeed, migration of small planets is known to be too fast inwards in locally isothermal conditions. However, thermal effects could reverse its direction, potentially saving planets in the inner, optically thick parts of the protoplanetary disc. This effect has been seen for masses larger than 5 Earth masses, but the minimum mass for this to happen has never been probed numerically, although it is of crucial importance for planet formation scenarios. We have extended the hydro-dynamical code FARGO to 3D, with thermal diffusion. With this code, we perform simulations of embedded planets down to 2 Earth masses. For a set of discs parameters for which outward migration has been shown in the range of

Circumplanetary disc or circumplanetary envelope

[5, 35]

Outwards migration for planets in stellar irradiated 3D discs

Earth masses, we find that the transition to inward migration occurs for masses in the range

Comparison of convergence towards invariant distributions for rotation angles, twist angles and local Lyapunov characteristic numbers

[3, 5]

First numerical investigation of a conjecture by N. N. Nekhoroshev about stability in quasi-integrable systems

Earth masses. The transition appears to be due to an unexpected phenomenon: the formation of an asymmetric cold and dense finger of gas driven by circulation and libration streamlines. We recover this phenomenon in 2D simulations where we control the cooling effects of the gas through a simple modeling of the energy equation.

Planetary Torque in 3D Isentropic Disks

We present three-dimensional simulations with nested meshes of the dynamics of the gas around a Jupiter mass planet with the JUPITER and FARGOCA codes. We implemented a radiative transfer module into the JUPITER code to account for realistic heating and cooling of the gas. We focus on the circumplanetary gas flow, determining its characteristics at very high resolution (

Reduced gas accretion on super-Earths and ice giants

80\%

On the relationship between the Bruno function and the breakdown invariant tori

of Jupiters diameter). In our nominal simulation where the temperature evolves freely by the radiative module and reaches 13000 K at the planet, a circumplanetary envelope was formed filling the entire Roche-lobe. Because of our equation of state is simplified and probably overestimates the temperature, we also performed simulations with limited maximal temperatures in the planet region (1000 K, 1500 K, and 2000 K). In these fixed temperature cases circumplanetary disks (CPDs) were formed. This suggests that the capability to form a circumplanetary disk is not simply linked to the mass of the planet and its ability to open a gap. Instead, the gas temperature at the planets location, which depends on its accretion history, plays also fundamental role. The CPDs in the simulations are hot and cooling very slowly, they have very steep temperature and density profiles, and are strongly sub-Keplerian. Moreover, the CPDs are fed by a strong vertical influx, which shocks on the CPD surfaces creating a hot and luminous shock-front. In contrast, the pressure supported circumplanetary envelope is characterized by internal convection and almost stalled rotation.