Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Co-orbital satellites of Saturn: congenital formation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Nebular gas drag and planetary accretion with eccentric high-mass planets

Aims.We investigate the dynamics of pebbles immersed in a gas disk interacting with a planet on an eccentric orbit. The model has a prescribed gap in the disk around the location of the planetary orbit, as is expected for a giant planet with a mass in the range of 0.1-1 Jupiter masses. The pebbles with sizes in the range of 1 cm to 3 m are placed in a ring outside of the giant planet orbit at distances between 10 and 30 planetary Hill radii. The process of the accumulation of pebbles closer to the gap edge, its possible implication for the planetary accretion, and the importance of the mass and the eccentricity of the planet in this process are the motivations behind the present contribution. Methods. We used the Bulirsch-Stoer numerical algorithm, which is computationally consistent for close approaches, to integrate the Newtonian equations of the planar (2D), elliptical restricted three-body problem. The angular velocity of the gas disk was determined by the appropriate balance between the gravity, centrifugal, and pressure forces, such that it is sub-Keplerian in regions with a negative radial pressure gradient and super-Keplerian where the radial pressure gradient is positive. Results. The results show that there are no trappings in the 1:1 resonance around the L 4 and L5 Lagrangian points for very low planetary eccentricities (e2 < 0.07). The trappings in exterior resonances, in the majority of cases, are because the angular velocity of the disk is super-Keplerian in the gap disk outside of the planetary orbit and because the inward drift is stopped. Furthermore, the semi-major axis location of such trappings depends on the gas pressure profile of the gap (depth) and is a = 1.2 for a planet of 1 MJ. A planet on an eccentric orbit interacts with the pebble layer formed by these resonances. Collisions occur and become important for planetary eccentricity near the present value of Jupiter (e 2 = 0.05). The maximum rate of the collisions onto a planet of 0.1 MJ occurs when the pebble size is 37.5 cm ≤ s < 75 cm; for a planet with the mass of Jupiter, it is15 cm ≤ s < 30 cm. The accretion stops when the pebble size is less than 2 cm and the gas drag dominates the motion. © 2013 ESO.

Irregular satellites of Jupiter: capture configurations of binary-asteroids

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.

TERRESTRIAL PLANET FORMATION IN A PROTOPLANETARY DISK WITH A LOCAL MASS DEPLETION: A SUCCESSFUL SCENARIO FOR THE FORMATION OF MARS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of Jupiter's mass growth on satellite capture

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter's mass. We considered the particle's initial conditions to be prograde, at pericenter, in the region 100R(4) <= a <= 400R(4) and 0 <= e <= 0.5. The results give Jupiter's mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85R(Hill) (Hills' radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45R(Hill) from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.

Distant stable direct orbits around the Moon

In the present work we explore regions of distant direct stable orbits around the Moon. First, the location and size of apparently stable regions are searched for numerically, adopting the approach of temporary capture time presented in Vieira Neto & Winter (2001). The study is made in the framework of the planar, circular, restricted three-body problem, Earth-Moon-particle. Regions of the initial condition space whose trajectories are apparently stable are determined. The criterion adopted was that the trajectories do not escape from the Moon during an integration period of 10(4) days. Using Poincare surface of sections the reason for the existence of the two stable regions found is studied. The stability of such regions proved to be due to two families of simple periodic orbits, h1 and h2, and the associated quasi-periodic orbits that oscillate around them. The robustness of the stability of the larger region, h2, is tested with the inclusion of the solar perturbation. The size of the region decreases, but it is still significant in size and can be useful in spacecraft missions.

A compound model for the origin of Earth's water

One of the most important subjects of debate in the formation of the solar system is the origin of Earth's water. Comets have long been considered as the most likely source of the delivery of water to Earth. However, elemental and isotopic arguments suggest a very small contribution from these objects. Other sources have also been proposed, among which local adsorption of water vapor onto dust grains in the primordial nebula and delivery through planetesimals and planetary embryos have become more prominent. However, no sole source of water provides a satisfactory explanation for Earth's water as a whole. In view of that, using numerical simulations, we have developed a compound model incorporating both the principal endogenous and exogenous theories, and investigating their implications for terrestrial planet formation and water delivery. Comets are also considered in the final analysis, as it is likely that at least some of Earth's water has cometary origin. We analyze our results comparing two different water distribution models, and complement our study using the D/H ratio, finding possible relative contributions from each source and focusing on planets formed in the habitable zone. We find that the compound model plays an important role by showing greater advantage in the amount and time of water delivery in Earth-like planets. © 2013. The American Astronomical Society. All rights reserved.

Effects of the planetary migration on some primordial satellites of the outer planets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Close-in planets around giant stars: lack of hot-Jupiters and prevalence of multiplanetary systems

Extrasolar planets abound in almost any possible configuration. However, until five years ago, there was a lack of planets orbiting closer than 0.5 au to giant or subgiant stars. Since then, recent detections have started to populated this regime by confirming 13 planetary systems. We discuss the properties of these systems in terms of their formation and evolution off the main sequence. Interestingly, we find that 70.0 ± 6.6% of the planets in this regime are inner components of multiplanetary systems. This value is 4.2σ higher than for main-sequence hosts, which we find to be 42.4 ± 0.1%. The properties of the known planets seem to indicate that the closest-in planets (a< 0.06 au) to main-sequence stars are massive (i.e., hot Jupiters) and isolated and that they are subsequently engulfed by their host as it evolves to the red giant branch, leaving only the predominant population of multiplanetary systems in orbits 0.06 formation and evolution of hot Jupiters.

Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

High-contrast imaging search for planets and brown dwarfs around the most massive stars in the solar neighborhood

There has been a long-standing discussion in the literature as to whether core accretion or disk instability is the dominant mode of planet formation. Over the last decade, several lines of evidence have been presented showing that core accretion is most likely the dominant mechanism for the close-in population of planets probed by radial velocity and transits. However, this does not by itself prove that core accretion is the dominant mode for the total planet population, since disk instability might conceivably produce and retain large numbers of planets in the far-out regions of the disk. If this is a relevant scenario, then the outer massive disks of B-stars should be among the best places for massive planets and brown dwarfs to form and reside. In this study, we present high-contrast imaging of 18 nearby massive stars of which 15 are in the B2-A0 spectral-type range and provide excellent sensitivity to wide companions. By comparing our sensitivities to model predictions of disk instability based on physical criteria for fragmentation and cooling, and using Monte Carlo simulations for orbital distributions, we find that ~85% of such companions should have been detected in our images on average. Given this high degree of completeness, stringent statistical limits can be set from the null-detection result, even with the limited sample size. We find that

Magnetospheric Structure and Atmospheric Joule Heating of Habitable Planets Orbiting M-dwarf Stars

We study the magnetospheric structure and the ionospheric Joule Heating of planets orbiting M-dwarf stars in the habitable zone using a set of magnetohydrodynamic models. The stellar wind solution is used to drive a model for the planetary magnetosphere, which is coupled with a model for the planetary ionosphere. Our simulations reveal that the space environment around close-in habitable planets is extreme, and the stellar wind plasma conditions change from sub- to super-Alfvénic along the planetary orbit. As a result, the magnetospheric structure changes dramatically with a bow shock forming in the super-Alfvénic sectors, while no bow shock forms in the sub-Alfvénic sectors. The planets reside most of the time in the sub-Alfvénic sectors with poor atmospheric protection. A significant amount of Joule Heating is provided at the top of the atmosphere as a result of the intense stellar wind. For the steady-state solution, the heating is about 0.1%-3% of the total incoming stellar irradiation, and it is enhanced by 50% for the time-dependent case. The significant Joule Heating obtained here should be considered in models for the atmospheres of habitable planets in terms of the thickness of the atmosphere, the top-side temperature and density, the boundary conditions for the atmospheric pressure, and particle radiation and transport. Here we assume constant ionospheric Pedersen conductance similar to that of the Earth. The conductance could be greater due to the intense EUV radiation leading to smaller heating rates. We plan to quantify the ionospheric conductance in future study.