Reliability of orbital fits for resonant extrasolar planetary systems: the case of HD82943

We perform a statistical study of the process of orbital determination of the HD82943 extrasolar planetary system, using the current observational data set of N = 165 radial velocity (RV) measurements. Our aim is to analyse the dispersion of possible orbital fits leading to residuals compatible with the best solution, and to discuss the sensitivity of the results with respect to both the data set and the error distribution around the best fit. Although some orbital parameters (e.g. semimajor axis) appear well constrained, we show that the best fits for the HD82943 system are not robust, and at present it is not possible to estimate reliable solutions for these bodies. Finally, we discuss the possibility of a third planet, with a mass of 0.35M(Jup) and an orbital period of 900 d. Stability analysis and simulations of planetary migration indicate that such a hypothetical three-planet system could be locked in a double 2/1 mean-motion resonance, similar to the so-called Laplace resonance of the three inner Galilean satellites of Jupiter.

High precision astrometry mission for the detection and characterization of nearby habitable planetary systems with the Nearby Earth Astrometric Telescope (NEAT)

A complete census of planetary systems around a volume-limited sample of solar-type stars (FGK dwarfs) in the Solar neighborhood (d a parts per thousand currency signaEuro parts per thousand 15 pc) with uniform sensitivity down to Earth-mass planets within their Habitable Zones out to several AUs would be a major milestone in extrasolar planets astrophysics. This fundamental goal can be achieved with a mission concept such as NEAT-the Nearby Earth Astrometric Telescope. NEAT is designed to carry out space-borne extremely-high-precision astrometric measurements at the 0.05 mu as (1 sigma) accuracy level, sufficient to detect dynamical effects due to orbiting planets of mass even lower than Earth's around the nearest stars. Such a survey mission would provide the actual planetary masses and the full orbital geometry for all the components of the detected planetary systems down to the Earth-mass limit. The NEAT performance limits can be achieved by carrying out differential astrometry between the targets and a set of suitable reference stars in the field. The NEAT instrument design consists of an off-axis parabola single-mirror telescope (D = 1 m), a detector with a large field of view located 40 m away from the telescope and made of 8 small movable CCDs located around a fixed central CCD, and an interferometric calibration system monitoring dynamical Young's fringes originating from metrology fibers located at the primary mirror. The mission profile is driven by the fact that the two main modules of the payload, the telescope and the focal plane, must be located 40 m away leading to the choice of a formation flying option as the reference mission, and of a deployable boom option as an alternative choice. The proposed mission architecture relies on the use of two satellites, of about 700 kg each, operating at L2 for 5 years, flying in formation and offering a capability of more than 20,000 reconfigurations. The two satellites will be launched in a stacked configuration using a Soyuz ST launch vehicle. The NEAT primary science program will encompass an astrometric survey of our 200 closest F-, G- and K-type stellar neighbors, with an average of 50 visits each distributed over the nominal mission duration. The main survey operation will use approximately 70% of the mission lifetime. The remaining 30% of NEAT observing time might be allocated, for example, to improve the characterization of the architecture of selected planetary systems around nearby targets of specific interest (low-mass stars, young stars, etc.) discovered by Gaia, ground-based high-precision radial-velocity surveys, and other programs. With its exquisite, surgical astrometric precision, NEAT holds the promise to provide the first thorough census for Earth-mass planets around stars in the immediate vicinity of our Sun.

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.

History of the planetary systems from Thales to Kepler,

Mode of access: Internet.

Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

A SuperWASP search for additional transiting planets in 24 known systems

We present results from a search for additional transiting planets in 24 systems already known to contain a transiting planet. We model the transits due to the known planet in each system and subtract these models from light curves obtained with the SuperWASP (Wide Angle Search for Planets) survey instruments. These residual light curves are then searched for evidence of additional periodic transit events. Although we do not find any evidence for additional planets in any of the planetary systems studied, we are able to characterize our ability to find such planets by means of Monte Carlo simulations. Artificially generated transit signals corresponding to planets with a range of sizes and orbital periods were injected into the SuperWASP photometry and the resulting light curves searched for planets. As a result, the detection efficiency as a function of both the radius and orbital period of any second planet is calculated. We determine that there is a good (>50 per cent) chance of detecting additional, Saturn-sized planets in P ~ 10 d orbits around planet-hosting stars that have several seasons of SuperWASP photometry. Additionally, we confirm previous evidence of the rotational stellar variability of WASP-10, and refine the period of rotation. We find that the period of the rotation is 11.91 +/- 0.05 d, and the false alarm probability for this period is extremely low (~10-13).

The Kepler-10 Planetary System Revisited by HARPS-N: A Hot Rocky World and a Solid Neptune-Mass Planet

Kepler-10b was the first rocky planet detected by the Kepler satellite and confirmed with radial velocity follow-up observations from Keck-HIRES. The mass of the planet was measured with a precision of around 30%, which was
insufficient to constrain models of its internal structure and composition in detail. In addition to Kepler-10b, a second planet transiting the same star with a period of 45 days was statistically validated, but the radial velocities were only
good enough to set an upper limit of 20 M⊕ for the mass of Kepler-10c. To improve the precision on the mass for planet b, the HARPS-N Collaboration decided to observe Kepler-10 intensively with the HARPS-N spectrograph
on the Telescopio Nazionale Galileo on La Palma. In total, 148 high-quality radial-velocity measurements were obtained over two observing seasons. These new data allow us to improve the precision of the mass determination for Kepler-10b to 15%. With a mass of 3.33 ± 0.49 M⊕ and an updated radius of 1.47+0.03 −0.02 R⊕, Kepler-10b has a density of 5.8 ± 0.8 g cm−3, very close to the value predicted by models with the same internal structure and composition as the Earth. We were also able to determine a mass for the 45-day period planet Kepler-10c, with an even better precision of 11%. With a mass of 17.2 ± 1.9 M⊕ and radius of 2.35+0.09 −0.04 R⊕, Kepler-10c has a density of 7.1 ± 1.0 g cm−3. Kepler-10c appears to be the first strong evidence of a class of more massive solid planets with longer orbital periods