Orbital dynamics of the planetary system HD 196885

The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 10⁴ years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < i _p < 90° and 30° < Ω_p < 90°, or 90° < i _p < 180° and 180° < Ω_p < 300°.     

Chaotic Dynamics of Satellite Systems

We consider the problem of calculating the Lyapunov time (the characteristic time of predictable dynamics) of chaotic motion in the vicinity of separatrices of orbital resonances in satellite systems. The primary objects of study are the chaotic regimes that have occurred in the history of the orbital dynamics of the second and fifth Uranian satellites (Umbriel and Miranda) and the first and third Saturnian satellites (Mimas and Tethys). We study the dynamics in the vicinity of separatrices of the resonance multiplets corresponding to the 3 : 1 commensurability of mean motions of Miranda and Umbriel and the multiplets corresponding to the 2 : 1 commensurability of mean motions of Mimas and Tethys. These chaotic regimes have most probably contributed much to the long-term orbital evolution of the two satellite systems. The equations of motion have been numerically integrated to estimate the Lyapunov time in models corresponding to various epochs of the system evolution. Analytical estimates of the Lyapunov time have been obtained by a method (Shevchenko, 2002) based on the separatrix map theory. The analytical estimates have been compared to estimates obtained by direct numerical integration.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 4, 2005, pp. 364–374.Original Russian Text Copyright © 2005 by Mel’nikov, Shevchenko.     

On the chaotic orbital dynamics of the planet in the system 16 Cyg

The chaotic orbital dynamics of the planet in the wide visual binary star system 16 Cyg is considered. The only planet in this system has a significant orbital eccentricity, e = 0.69. Previously, Holman et al. suggested the possibility of chaos in the orbital dynamics of the planet due to the proximity of 16 Cyg to the separatrix of the Lidov–Kozai resonance. We have calculated the Lyapunov characteristic exponents on the set of possible orbital parameters for the planet. In all cases, the dynamics of 16 Cyg is regular with a Lyapunov time of more than 30 000 yr. The dynamics is considered in detail for several possible models of the planetary orbit; the dependences of Lyapunov exponents on the time of their calculation and the time dependences of osculating orbital elements have been constructed. Phase space sections for the system dynamics near the Lidov–Kozai resonance have been constructed for all models. A chaotic behavior in the orbital motion of the planet in 16 Cyg is shown to be unlikely, because 16 Cyg in phase space is far from the separatrix of the Lidov–Kozai resonance at admissible orbital parameters, with the chaotic layer near the separatrix being very narrow.     

Application of a probabilistic neural network in radial‐velocity curve analysis of the spectroscopic binary stars HD 152218, HD 143511, HD 27149, and ER Vul

We use an Artificial Neural Network (ANN) to derive the orbital parameters of spectroscopic binary stars. Using measured radial velocity data of four double‐lined spectroscopic binary systems HD 152218, HD 143511, HD 27149, and ER Vul, we find corresponding orbital and spectroscopic elements. Our numerical results are in good agreement with those obtained by others using more traditional methods (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The dynamical stability of a Kuiper Belt-like region

The dynamics of the Kuiper Belt region between 33 and 63 au is investigated just taking into account the gravitational influence of Neptune. Indeed the aim is to analyse the information which can be drawn from the actual exoplanetary systems, where typically physical and orbital data of just one or two planets are available. Under this perspective we start our investigation using the simplest three-body model (with Sun and Neptune as primaries), adding at a later stage the eccentricity of Neptune and the inclinations of the orbital planes to evaluate their effects on the Kuiper Belt dynamics. Afterwards we remove the assumption that the orbit of Neptune is Keplerian by adding the effect of Uranus through the Lagrange–Laplace solution or through a suitable resonant normal form. Finally, different values of the mass ratios of the primary to the host star are considered in order to perform a preliminary analysis of the behaviour of exoplanetary systems. In all cases, the stability is investigated by means of classical tools borrowed from dynamical system theory, like Poincaré mappings and Lyapunov exponents.     

Contribution to the study of binaries with spectral types F,G, K,and M – XI. Orbital elements of three red‐giant spectroscopic binaries: HR 1304, HR 1908, and HD 126947

The orbital elements of three red‐giant single‐lined spectroscopic binaries, HR 1304, HR 1908 and HD 126947, are presented. They are obtained from observations made with two photoelectric spectrometers of CORAVEL type, the first located at the Observatoire de Haute‐Provence and the second at the Cambridge Observatories. HR 1304 and HR 1908 are known to be chromospherically active stars and to have high spatial velocities; HD 126947 is an intrinsic variable newly detected by Hipparcos. The three systems have long orbital periods: 1.9, 3.2 and 7.7 yr for HR 1304, HR 1908 and HD 126947, respectively. From the orbital elements that we determined and other data available in the literature, we deduce some information about the unseen companions and their separations with respect to the primaries. Finally we discuss the rotation–revolution synchronism and conclude that one star, HR 1908, may have reached the state of pseudo‐synchronism, despite of its long orbital period. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Velocity Curve Analysis of Spectroscopic Binary Stars AI Phe, GM Dra, HD 93917 and V502 Oph by Nonlinear Regression

We introduce a new method to derive the orbital parameters of spectroscopic bi-nary stars by nonlinear least squares of (o-c). Using the measured radial velocity data of the four double lined spectroscopic binary systems, AI Phe, GM Dra, HD 93917 and V502 Oph, we derived both the orbital and combined spectroscopic elements of these systems. Our numerical results are in good agreement with the those obtained using the method of Lehmann-Filhe's.     

Velocity curve analysis of the spectroscopic binary stars RZ Cas,CC Cas,HS Her,HD 93917, V921 Her and Y Cygni by the artificial neural networks

We use an Artificial Neural Network (ANN) to derive the orbital parameters ofspectroscopic binary stars. Using measured radial velocity data of six double‐lined spectroscopic binary systems RZ Cas, CC Cas, HS Her, HD 93917, V921 Her and Y Cygni, we find corresponding orbital and spectroscopic elements. Our numerical results are in good agreement with those obtained by others using more traditional methods (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Velocity curve analysis of the spectroscopic binary stars PV Pup,HD 141929, EE Cet and V921 Her by nonlinear regression

We use the method introduced by Karami & Mohebi (2007), and Karami & Teimoorinia (2007) which enable us to derive the orbital parameters of the spectroscopic binary stars by the nonlinear least squares of observed vs. curve fitting (o-c). Using the measured experimental data for radial velocities of the four double-lined spectroscopic binary systems PV Pup, HD 141929, EE Cet and V921 Her, we find both the orbital and the combined spectroscopic elements of these systems. Our numerical results are in good agreement with those obtained using the method of Lehmann-Filhés.     

Resonances in Multiple Planetary Systems

Since the first extrasolar planet was discovered about 10 years ago, a major point of dynamical investigations was the determination of stable regions in extrasolar planetary systems where additional planets may exist. Using numerical methods, we investigate the dynamical stability in known multiple planetary systems (HD74156, HD38529, HD168443, HD169830) with special interest on the region between the two known planets and on the mean motion resonances inside this region. As a dynamical model we take the restricted 4-body problem containing the host star, the two planets and massless test-planets. For our numerical integrations, we used the Lie-integrator and additionally the Fast Lyapunov Indicators as a tool for detecting chaotic motion. We also investigated the inner resonances with the outer planet and the outer resonances with the inner planet with test-planets located inside the resonances.     

Study of dynamical processes at the final stages of planetary system formation: Resonance motion of giant planets

According to current observational data, planets of many exoplanetary systems have resonant motion. The formation of resonance configurations is studied within a unified model of planetary migration. Planets in the observed systems 24 Sex, HD 37124, HD 73526, HD 82943, HD 128311, HD 160691, Kepler 9, NN Ser, which are moving in the 2: 1 resonance, could have been captured into this resonance due to both the Type I and II migration with a wide range of parameters. The migration conditions are defined for the formation of HD 45364 and HD 200964 that are in the 3: 2 and 4: 3 first-order resonances, correspondingly. The results obtained for HD 200964 show that planets can be captured in the first-order resonances, when the outer-to-inner orbital period ratios for the planets are less than 3: 2, only if Type I migration rates are large, and the mass of at least one planet is substantially less than the modern masses of the observed giant planets. The formation of the HD 102272, HD 108874, HD 181433 and HD 202206 systems with planets in high-order resonances is considered. The capture into these resonances can be realized with very slow Type II migration. Possible bounds for migration parameters are considered. In particular, it has been found that the capture of HD 108874 into the 4: 1 resonance is possible only if the angle between the plane of planetary orbits and the plane of sky is appreciably less than 90°, i.e., the planetary masses are a few times larger than the minimum values. The capture of HD 202206 into the 5: 1 resonance is possible at low migration rates; however, another mechanism is required to explain the high observed eccentricity of the inner planet (for example, strong gravitational interaction between the planets). Resonant configurations can be disrupted due to the interaction between planets and remaining fragments of the planetesimal disk as, for example, may occur in the three-planet system 47 UMa. The specific orbital features observed for this system are explained.     

On the stability of circumbinary planetary systems

The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.     

Contribution to the study of F‐G‐K‐M binaries: XII. Orbital elements of seven new spectroscopic binaries

The orbital elements of seven single‐lined spectroscopic binaries, HD 31855, HD 59643, HD 60092, HD 133189, HD 162262, HD 203522, BD +43° 1331 are presented. They are obtained from observations made with two photoelectric spectrometers of CORAVEL type, the first located at the Observatoire de Haute‐Provence and the second at the Cambridge Observatories. From those orbital elements and other data available in the literature, we deduce some information about the unseen companions and their separations with respect to the primaries. We then discuss the rotation‐revolution synchronism and conclude that some of those stars have probably reached the state of (pseudo‐)synchronism. Finally we give a synopsis of the results obtained in this series of papers. Our radial velocity monitoring of more than three decades has allowed us to derive accurate orbital elements of 35 spectroscopic binaries, with a cool primary star of type F‐G‐K‐M. The corresponding range of periods varies from a few days to more than 10 years. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Are the W Ursae Majoris-type systems EK Comae Berenices and UX Eridani surrounded by circumstellar matter?

The variations of the orbital periods of two nearly neglected W UMa-type eclipsing binaries, EK Comae Berenices and UX Eridani, are presented through a detailed analysis of the O–C diagrams. It is found that the orbital period of EK Com is decreasing and the period of UX Eridani is increasing, and several sudden jumps have occurred in the orbital periods of both binaries. We analyze the mechanism(s), which might underlie the changes of the orbital periods of both systems, and obtain some new results. The long-term decrease of the orbital period of EK Comae Berenices might be caused by the decrease of the orbital angular momentum due to a magnetic stellar wind (MSW) or by mass transfer from the more massive to the less massive component. The secular increase in the orbital period of UX Eridani might be caused by mass transfer from the less massive to the more massive star. The possible mechanisms, which underlie the sudden changes in the orbital periods of the close binary systems are as the followings: (1) the variations of the structure due to the variation of the magnetic field; (2) the rapid mass exchange between the close binaries and their circumstellar matter. Finally, the evolutionary status of the systems EK Comae Berenices and UX Eridani is discussed.     

Polarization measurement and study of thirty RS CVn stars

We made polarization measurement on 30 RS CVn systems using the Berger polarimeter of McDonald Observatory in July-December 1984, of which 26 systems were measured for the first time. The results are given here. They show that for most RS CVn systems, the optical linear polarization is weak, generally below 0.45%, averaging about 0.20%. Some systems, like AR Lac, HR 5110, HD 8357, HK Lac, HR 7275 and HR 7428 have polarization above 0.03%, which showed time variations by factors between 10 and 30. For HD 8357 and ER Vul, there is a clear connection between the polarization and the orbital phase.     

First photometric analysis of the two EW binaries ZTF J214226.88+435827.1 and KAO-EGYPT J214216.38+440015.1

The EW-type eclipsing binaries are strongly interacting systems known to have often both component stars filling their crucial Roche lobes and having a common envelope. We present new BVRI light curves of the eclipsing binaries ZTF J214226.88+435,827.1 (ZTF21+43) and KAO-EGYPT J214216.38+440,015.1 (KAO21+44) based on CCD observations acquired with the 1.88-m Kottamia Astronomical Observatory (KAO) at Newtonian and Cassegrain telescope focus. The modeling results show that these two systems are to be W UMa contact binaries belonging to EW subtypes. All the light curves show the inverse O'Connell effect. We computed new ephemeris for each system using our times of minima and that available in the literature. Using our new times of minima and epochs for both systems from all available observations, the orbital period changes of these structures are studied for our systems. Using the PHOEBE package, a preliminary determination of the two systems' photometric orbital and physical parameters has been present. The positions of the systems were also depicted on the Hertzsprung-Russell (H-R), M-L, and T_eff-L diagrams to test their evolutionary status.     

High-eccentricity planets from the Anglo-Australian Planet Search

We report Doppler measurements of the stars HD 187085 and HD 20782 which indicate two high eccentricity low-mass companions to the stars. We find HD 187085 has a Jupiter-mass companion with a ∼1000-d orbit. Our formal 'best-fitting' solution suggests an eccentricity of 0.47, however, it does not sample the periastron passage of the companion and we find that orbital solutions with eccentricities between 0.1 and 0.8 give only slightly poorer fits (based on rms and  χ²_ν  ) and are thus plausible. Observations made during periastron passage in 2007 June should allow for the reliable determination of the orbital eccentricity for the companion to HD 187085. Our data set for HD 20782 does sample periastron and so the orbit for its companion can be more reliably determined. We find the companion to HD 20782 has   M sin   i = 1.77 ± 0.22  M _Jup  , an orbital period of 595.86 ± 0.03 d and an orbit with an eccentricity of 0.92 ± 0.03. The detection of such high-eccentricity (and relatively low-velocity amplitude) exoplanets appears to be facilitated by the long-term precision of the Anglo-Australian Planet Search. Looking at exoplanet detections as a whole, we find that those with higher eccentricity seem to have relatively higher velocity amplitudes indicating higher mass planets and/or an observational bias against the detection of high-eccentricity systems.     

The stabilising mechanism of the HD 82943 planetary system

We carry out simulations to investigate the dynamics of the HD 82943 planetary system with two resonant Jupiter-like planets, and to reveal possible stabilizing mechanism for the system. By following different coplanar configurations in the neighborhood of the best-fit orbits, we find that all the stable cases are involved in the 2:1 mean motion resonance and that the alignment of the periastra of the two planets also plays important part in the secular orbital evolution, indicating that these two kinds of mechanisms could be responsible for the dynamics of the system under study.     

Study of resonances for the restricted 3‐body problem

Our aim is to identify and classify mean‐motion resonances (MMRs) for the coplanar circular restricted three‐body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an indicator for the location of the resonances, the Fast Fourier Transform (FFT) used for determining what kind of resonances are present, and the inspection of the orbital elements to classify the periodicity. We show that the 2:1 resonance occurs the most frequently. Among other resonances, the 3:1 resonance is the second most common, and furthermore both 3:2 and 5:3 resonances occur more often than the 4:1 resonance. Moreover, the resonances in the coplanar CR3BP are classified based on the behaviour of the orbits. We show that orbital stability is ensured for high values of resonance (i.e., high ratios) where only a single resonance is present. The resonances attained are consistent with the previously established resonances for the solar system, i.e., specifically, in regards to the asteroid belt. Previous work employed digital filtering and Lyapunov characteristic exponents to determine stochasticity of the eccentricity, which is found to be consistent with our usage of Lyapunov exponents as an alternate approach based on varying the mass ratio instead of the eccentricity. Our results are expected to be of principal interest to future studies, including augmentations to observed or proposed resonances, of extra‐solar planets in binary stellar systems (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)