Abstract:
In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.

Abstract:
We perform numerical simulations to explore the dynamical evolution of the HD 82943 planetary system. By simulating diverse planetary configurations, we find two mechanisms of stabilizing the system: the 2:1 mean motion resonance between the two planets can act as the first mechanism for all stable orbits. The second mechanism is a dynamical antialignment of the apsidal lines of the orbiting planets, which implies that the difference of the periastron longitudes $\theta_{3}$ librates about $180^{\circ}$ in the simulations. We also use a semi-analytical model to explain the numerical results for the system under study.

Abstract:
We carry out numerical simulations to explore the dynamical evolution of the HD 82943 and HD 37124 planetary systems,which both have two Jupiter-like planets. By simulating various planetary configurations in the neighborhood of the fitting orbits, we find three mechanisms to maintain the stability of these systems: For HD 82943,we find that the 2:1 mean motion resonance can act as the first mechanism for all the stable orbits. The second mechanism is the alignment of the periastron of the two planets of HD 82943 system. In the paper,we show one case is simultaneously maintained by the two mechanisms. Additionally,we also use the corresponding analytical models successfully to explain the different numerical results for the system. The third mechanism is the Kozai resonance which takes place in the mutual highly orbits of HD 37124. In the simulations,we discover that the argument of periastron $\omega$ of the inner planet librates about $90^{\circ}$ or $270^{\circ}$ for the whole time span. The Kozai mechanism can explain the stable configuration of large eccentricity of the inner planet.

Abstract:
In this work we perform a global analysis of the radial velocity curve of the HD 12661 system. Orbital fits that are obtained by the genetic and gradient algorithms of minimization reveal the proximity of the system to the 6:1 mean motion resonance. The orbits are locked in the secular resonance with apsidal axes librating about 180 deg with the full amplitude $\simeq (90,180) deg$. Our solution incorporates the mutual interaction between the companions. The stability analysis with the MEGNO fast indicator shows that the system is located in an extended stable zone of quasi-periodic motions. These results are different from those obtained on the basis of the orbital fit published by Fischer et al. (2003)

Abstract:
The new 2-planetary system around HD169830 has been announced during the XIX-th IAP Colloquium "Extrasolar Planets: Today & Tomorrow" (Paris, June 30 - July 4, 2003) by the Geneva Extrasolar Planet Search team. We study the orbital dynamics of this system in the framework of the $N$-body problem. The analysis of its orbital stability is performed using the long-term integrations and the fast indicators, the Mean Exponential Growth factor of Nearby Orbits and the Frequency Map Analysis. The HD169830 appears to be located in a wide stable region of the phase space. The ratio of the mean motions of the planets HD169830b and c is between low-order mean motion resonances, 9:1 and 10:1. The long-term integration of the coplanar configurations, conducted over 1Gyr, reveals that the eccentricities of the companions vary with a large amplitude about 0.4-0.5 but there is no sign of instability. The orbital parameters of the planets resemble those of another 2-planetary system, around HD12661. Both of them can be classified as hierarchical planetary systems. We investigate whether these two exosystems are dynamically similar. Such similarities may be important for finding out if the formation and subsequent orbital evolution of exoplanetary systems obey common rules.

Abstract:
We present new radial velocities from Keck Observatory and both Newtonian and Keplerian solutions for the triple-planet system orbiting HD 37124. The orbital solution for this system has improved dramatically since the third planet was first reported in Vogt et al. 2005 with an ambiguous orbital period. We have resolved this ambiguity, and the outer two planets have an apparent period commensurability of 2:1. A dynamical analysis finds both resonant and non-resonant configurations consistent with the radial velocity data, and constrains the mutual inclinations of the planets to be less than about 30 degrees. We discuss HD 37124 in the context of the other 19 exoplanetary systems with apparent period commenserabilities, which we summarize in a table. We show that roughly one in three well-characterized multiplanet systems has a apparent low-order period commensuribility, which is more than would naively be expected if the periods of exoplanets in known multiplanet systems were drawn randomly from the observed distribution of planetary orbital periods.

Abstract:
In addition to the Sun, six other stars are known to harbor multiple planets and debris disks: HD 69830, HD 38529, HD 128311, HD 202206, HD 82943 and HR 8799. In this paper we set constraints on the location of the dust-producing planetesimals around the latter four systems. We use a radiative transfer model to analyze the spectral energy distributions of the dust disks (including two new Spitzer IRS spectra presented in this paper), and a dynamical model to assess the long-term stability of the planetesimals' orbits. As members of a small group of stars that show evidence of harboring a multiple planets and planetesimals, their study can help us learn about the diversity of planetary systems.

Abstract:
HD 82943 hosts a mysterious multi-planet system in the 2:1 mean-motion resonance that puzzles astronomers for more than a decade. We describe our new analysis of all radial velocity data currently available for this star, including both the most recent Keck data and the older but more numerous CORALIE measurements. Here we pay a major attention to the task of optimal scheduling of the future observation of this system. Applying several optimality criteria, we demonstrate that in the forthcoming observational season of HD 82943 (the winter 2014/2015) rather promising time ranges can be found. Observations of the near future may give rather remarkable improvement of the orbital fit, but only if we choose their time carefully.

Abstract:
We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combined with parameter grid search to investigate the orbital parameters and dynamical states of the qualitatively different types of fits, and we compare the results to those obtained with the differential evolution Markov chain Monte Carlo method. Our results support the coplanar 2:1 MMR configuration for the HD 82943 system, and show no evidence for either the 1:1 or 3-planet Laplace resonance fits. The inclination of the system with respect to the sky plane is well constrained at about 20(+4.9 -5.5) degree, and the system contains two planets with masses of about 4.78 MJ and 4.80 MJ (where MJ is the mass of Jupiter) and orbital periods of about 219 and 442 days for the inner and outer planet, respectively. The best fit is dynamically stable with both eccentricity-type resonant angles {\theta}1 and {\theta}2 librating around 0 degree.

Abstract:
The presence of possible blends in the spectral region of the Li resonance line at 6708 A in solar-type metal-rich stars is investigated using high resolution and high signal-to-noise spectroscopic observations. Our analysis does not confirm the identification of a weak absorption feature at 6708.025 A with the low excitation TiI line proposed by Reddy et al. (2002). Our spectrum synthesis suggests that the unidentified absorption is most probably produced by a high excitation SiI line originally proposed by Muller et al. (1975). Reanalysis of the Lithium-6/Lithium-7 isotopic ratio in HD82943 was performed by taking the SiI line into account and using new VLT/UVES spectra of HD82943 with a signal-to-noise ratio close to 1000. We confirm the presence of Lithium-6 in the star's atmosphere while the updated value for the isotopic ratio is f(Lithium-6) = 0.05+-0.02.