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.

Hematologic Reference Values for Clinically Healthy Captive Golden Conures (Guaruba guarouba)

Golden conures or ararajubas (Guaruba guarouba) are endangered parrots endemic to the Brazilian Amazon forest. Body mass, blood cell counts, and total plasma protein were determined for 70 clinically healthy golden conures captive at zoologic parks and private breeder facilities in Brazil. Hematologic results (mean +/- SD) were: Erythrocytes 3.6 +/- 0.5 x 10(6) cells/mm(3), hemoglobin 12.8 +/- 1.4 g/dl, packed cell volume 46 +/- 3.8%, mean corpuscular volume 132 +/- 20 fl, mean corpuscular hemoglobin (MCH) 36 +/- 5.7 pg, mean corpuscular hemoglobin concentration (MCHC) 28 +/- 3.5%, thrombocytes 26.3 +/- 9.3 x 10(3) cells/mm(3), leukocytes 11.9 +/- 4.5 x 10(3) cells/mm(3), heterophils 6284 +/- 2715 cells/mm(3), lymphocytes 5473 +/- 2408 cells/mm(3), monocytes 113 +/- 162 cells/mm(3), eosinophils 10 +/- 42 cells/mm(3), basophils 27 +/- 64 cells/mm(3). Body mass was 254 +/- 24.9 g and total plasma protein (TPP) was 3.54 +/- 0.58 g/dl. No statistical differences were observed between genders within age groups. Differences between juveniles (J) and adults (A) were identified for TPP < A), MCH (J > A), and MCHC (J > A). These results provide reliable reference values for the clinical interpretation of hematologic results for the species. Hematology may be an important tool for population health investigations on free-ranging golden conure populations and will also be essential to survey the health of release candidates in future reintroduction programs.

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.

Dynamics of the 3:1 resonant planetary systems

Many of the discovered exoplanetary systems are involved inside mean-motion resonances. In this work we focus on the dynamics of the 3:1 mean-motion resonant planetary systems. Our main purpose is to understand the dynamics in the vicinity of the apsidal corotation resonance (ACR) which are stationary solutions of the resonant problem. We apply the semi-analytical method (Michtchenko et al., 2006) to construct the averaged three-body Hamiltonian of a planetary system near a 3:1 resonance. Then we obtain the families of ACR, composed of symmetric and asymmetric solutions. Using the symmetric stable solutions we observe the law of structures (Ferraz-Mello,1988), for different mass ratio of the planets. We also study the evolution of the frequencies of σ1, resonant angle, and Δω, the secular angle. The resonant domains outside the immediate vicinity of ACR are studied using dynamical maps techniques. We compared the results obtained to planetary systems near a 3:1 MMR, namely 55 Cnc b-c, HD 60532 b-c and Kepler 20 b-c.