Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Records of migration in the exoplanet configurations

When compared to our Solar System, many exoplanet systems exhibit quite unusual planet configurations; some of these are hot Jupiters, which orbit their central stars with periods of a few days, others are resonant systems composed of two or more planets with commensurable orbital periods. It has been suggested that these configurations can be the result of a migration processes originated by tidal interactions of the planets with disks and central stars. The process known as planet migration occurs due to dissipative forces which affect the planetary semi-major axes and cause the planets to move towards to, or away from, the central star. In this talk, we present possible signatures of planet migration in the distribution of the hot Jupiters and resonant exoplanet pairs. For this task, we develop a semi-analytical model to describe the evolution of the migrating planetary pair, based on the fundamental concepts of conservative and dissipative dynamics of the three-body problem. Our approach is based on an analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces needs to be invoked. We show that, under assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the stationary solutions of the conservative problem (Birkhoff, Dynamical systems, 1966). The ultimate convergence and the evolution of the system along one of these modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the roper frequencies of the system. We show that it is possible to reassemble the starting configurations and migration history of the systems on the basis of their final states, and consequently to constrain the parameters of the physical processes involved.

Stability and dynamics of terrestrial planets in binary star systems: application on Alpha Centauri

Binary stars are frequent in the universe, with about 50% of the known main sequence stars being located at a multiple star system (Abt, 1979). Even though, they are universally thought as second rate sites for the location of exo-planets and the habitable zone, due to the difficulties of detection and high perturbation that could prevent planet formation and long term stability. In this work we show that planets in binary star systems can have regular orbits and remain on the habitable zone. We introduce a stability criterium based on the solution of the restricted three body problem and apply it to describe the short period planar and three-dimentional stability zones of S-type orbits around each star of the Alpha Centauri system. We develop as well a semi-analytical secular model to study the long term dynamics of fictional planets in the habitable zone of those stars and we verify that planets on the habitable zone would be in regular orbits with any eccentricity and with inclination to the binary orbital plane up until 35 degrees. We show as well that the short period oscillations on the semi-major axis is 100 times greater than the Earth's, but at all the time the planet would still be found inside the Habitable zone.

Effects of excess body mass on strength and fatigability of quadriceps in postmenopausal women

Objective: Obesity is a major public health problem leading to, among other things, reduced functional capacity. Moreover, obesity-related declines in functional capacity may be compounded by the detrimental consequences of menopause. The aim of this study was to understand the potential effects of excess body mass on measures of functional capacity in postmenopausal women. Methods: Forty-five postmenopausal women aged 50 to 60 years were divided into two groups according to body mass index (BMI): obese (BMI, >= 30 kg/m(2); n = 19) and nonobese (BMI, 18.5-29.9 kg/m(2); n = 26). To determine clinical characteristics, body composition, bone mineral density, and maximal exercise testing was performed, and a 3-day dietary record was estimated. To assess quadriceps function, isokinetic exercise testing at 60 degrees per second (quadriceps strength) and at 300 degrees per second (quadriceps fatigue) was performed. Results: The absolute value of the peak torque was not significantly different between the groups; however, when the data were normalized by body mass and lean mass, significantly lower values were observed for obese women compared with those in the nonobese group (128% +/- 25% vs 155% +/- 24% and 224% +/- 38% vs 257% +/- 47%, P < 0.05). The fatigue index did not show any significant difference for either group; however, when the data were normalized by the body mass and lean mass, significantly lower values were observed for obese women (69% +/- 16% vs 93% +/- 18% and 120% +/- 25% vs. 135% +/- 23%, P < 0.01). Conclusions: Our results show that despite reduced muscle force, the combination of obesity and postmenopause may be associated with greater resistance to muscle fatigue.

Relationship between body size and flying-related structures in Neotropical social wasps (Polistinae, Vespidae, Hymenoptera)

Body size influences wing shape and associated muscles in flying animals which is a conspicuous phenomenon in insects, given their wide range in body size. Despite the significance of this, to date, no detailed study has been conducted across a group of species with similar biology allowing a look at specific relationship between body size and flying structures. Neotropical social vespids are a model group to study this problem as they are strong predators that rely heavily on flight while exhibiting a wide range in body size. In this paper we describe the variation in both wing shape, as wing planform, and mesosoma muscle size along the body size gradient of the Neotropical social wasps and discuss the potential factors affecting these changes. Analyses of 56 species were conducted using geometric morphometrics for the wings and lineal morphometrics for the body; independent contrast method regressions were used to correct for the phylogenetic effect. Smaller vespid species exhibit rounded wings, veins that are more concentrated in the proximal region, larger stigmata and the mesosoma is proportionally larger than in larger species. Meanwhile, larger species have more elongated wings, more distally extended venation, smaller stigmata and a proportionally smaller mesosoma. The differences in wing shape and other traits could be related to differences in flight demands caused by smaller and larger body sizes. Species around the extremes of body size distribution may invest more in flight muscle mass than species of intermediate sizes.