Stability of Co-Orbital Motion in Exoplanetary Systems

The stability of co-orbital motions is investigated in such exoplanetary systems, where the only known giant planet either moves fully in the habitable zone, or leaves it for some part of its orbit. If the regions around the triangular Lagrangian points are stable, they are possible places for smaller Trojan-like planets. We have determined the nonlinear stability regions around the Lagrangian point L₄ of nine exoplanetary systems in the model of the elliptic restricted three-body problem by using the method of the relative Lyapunov indicators. According to our results, all systems could possess small Trojan-like planets. Several features of the stability regions are also discussed. Finally, the size of the stability region around L₄ in the elliptic restricted three-body problem is determined as a function of the mass parameter and eccentricity.     

Links Between Dust Disks and Exoplanets

Since 1984, roughly 100 main sequence stars within 50 parsecs of the Sun have been identified as possibly possessing replenished, circumstellar dust disks. Optical to submillimeter imaging has resolved disk-like structure around 7 main sequence stars. We review these results, and discuss how they elucidate the existence and properties of exoplanetary systems.     

Orbital Migration Of Giant Planets: Using Numerical Integration To Investigate Consequences For Other Bodies

A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational interaction with a residual planetesimal disk together with several means of halting inward migration have been identified. These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration. The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient algorithms. This revised version was published online in July 2006 with corrections to the Cover Date.     

A study on dynamic processes at late stages in the formation of planetary systems in gas and dust disks

The discovered exoplanetary systems have highly diverse dynamic properties, which differ from those of the Solar System. A single model including planet migration effects and their gravitational interaction is used to investigate the features of dynamic processes that lead to the formation of giant-planet systems with different orbital characteristics. It is shown for a system of four giant planets similar to the Solar System how Type I migration could lead to all the planets being captured into resonant configurations. The resonant motion can continue for a long period of time after the transition to Type II migration and after the dissipation of the gas-and-dust disk. The three-planet system of GJ 876 is used to investigate the migration of the planets inward the orbit of the most massive planet and their capture into low-order resonant configurations under the conditions of Type II migration. A system similar to the exoplanetary system of HD 102272 is used to study the capture into high-order resonances followed by an increase in the orbit’s eccentricity.     

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.     

Multiple planetary systems: Properties of the current sample

We carry out analyses on stellar and planetary properties of multiple exoplanetary systems in the currently available sample. With regards to the stars, we study their temperature, distance from the Sun, and metallicity distributions, finding that the stars that harbour multiple exoplanets tend to have subsolar metallicities, in contrast to metal-rich Hot Jupiter hosts; while non-Hot Jupiter single planet hosts form an intermediate group between these two, with approximately solar metallicities. With regards to the planetary systems, we select those with four or more planets and analyse their configurations in terms of stability (via Hill radii), compactness, and size variations. We find that most planetary pairs are stable, and that the compactness correlates to the size variation: More compact systems have more similarly sized planets and vice versa. We also investigate the spectral energy distributions of the stars hosting multiple exoplanetary systems, seeking infra-red excesses that could indicate the presence of debris disks. These disks would be leftovers from the planetary formation process, and could be considered as analogues of the Solar System’s Asteroid or Kuiper belts. We identify potential candidates for disks that are good targets for far infra-red follow-up observations to confirm their existence.     

Numerical Instruments for the Analysis of Secular Dynamics of Exoplanetary Systems

A review is given of modern numerical methods for the analysis of resonant and chaotic dynamics: calculation of the Lyapunov characteristic exponents, the MEGNO method, and the maximum eccentricity method. These methods are used to construct stability diagrams for the planetary systems γ Cep, HD 196885, and HD 41004. The diagrams are analyzed to determine the most probable values taken by the orbital parameters of the exoplanets and obtain estimates for the Lyapunov time of their orbital dynamics. The stability diagrams constructed using the different methods are compared to analyze their effectiveness in the study of secular dynamics of exoplanetary systems.     

Tidal evolution of hierarchical and inclined systems

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20°). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to various situations in the HD 11964, HD 80606, and HD 98800 systems.     

Dynamics of the 3/1 planetary mean-motion resonance: an application to the HD60532 b-c planetary system

In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance. The case where the outer planet is more massive than its inner companion is considered. We show that the resonant dynamics can be described using two fundamental parameters, the total angular momentum and the spacing parameter. The topology of the Hamiltonian function describing the resonant behaviour is investigated on a large domain of the phase space without time-expensive numerical integrations of the equations of motion, and without any restriction on the magnitude of the planetary eccentricities. The families of the Apsidal Corotation Resonances (ACR) parameterized by the planetary mass ratio are obtained and their stability is analyzed. The main dynamical features in the domains around the ACR are also investigated in detail by means of spectral analysis techniques, which allow us to detect the regions of different regimes of motion of resonant systems. The construction of dynamical maps for various values of the total angular momentum shows the evolution of domains of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems.     

Periastron precession measurements in transiting extrasolar planetary systems at the level of general relativity

Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of transits T _D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits,   P _obs  . The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in   P _obs  (transit timing variations, TTV) or in T _D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a approximately 4 yr period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.     

On the global stability of single‐planet systems

In this paper, we estimate the global stability properties of single‐planet systems by using a catalogue of stability maps. The data of the catalogue were used to generate probability values on the mass parameter–eccentricity plane for the occurrence of stable orbits. We showed that the probability data can be well approximated by a second order surface. Using the resulted formula the likelihood of finding Earth‐like planets in single‐planet systems can be easily estimated. As an example, we derived estimations for four known exoplanetary systems. Our formula can be useful in selecting target stars for future space missions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Planetans—oceanic planets

The development of principles, systems, and instruments enable the detection of exoplanets with 6–8 Earth masses or less. The launches of specialized satellites, such as CoRoT (2006) and Kepler (2009), into orbits around the Earth have enabled the discovery of new exoplanetary systems. These missions are searching for relatively low-mass planets by observing their transits over the disks of their parent stars. At the same time, supporting studies of exoplanets using ground-based facilities (that measure Keplerian components of radial velocities) are in progress. The properties of at least two objects discovered by different methods, Kepler-22 and GJ 1214b, suggested that there was another class of celestial bodies among the known types of extrasolar planets: planetans, or oceanic planets. The structure of Kepler-22 and GJ 1214b suggest that they can be these oceanic planets. In this paper, we consider to what extent this statement is valid. The consideration of exoplanet Gl 581g as an oceanic planet is more feasible. Some specific features of the physical nature of these unusual planets are presented.     

The Relative Lyapunov Indicator: An Efficient Method of Chaos Detection

A recently introduced chaos detection method, the relative Lyapunov indicator (RLI) is investigated in the cases of symplectic mappings and of a continuous Hamiltonian system. It is shown that the RLI is an efficient and easy-to-calculate numerical tool in determining the true nature of individual orbits, and in separating ordered and regular regions of the phase space of dynamical systems. An application of the RLI for stability investigations of some recently discovered exoplanetary systems is also presented.     

Chemical modeling of exoplanet atmospheres

The past twenty years have revealed the diversity of planets that exist in the Universe. It turned out that most of exoplanets are different from the planets of our Solar System and thus, everything about them needs to be explored. Thanks to current observational technologies, we are able to determine some information about the atmospheric composition the thermal structure and the dynamics of these exoplanets, but many questions remain still unanswered. To improve our knowledge about exoplanetary systems, more accurate observations are needed and that is why the Exoplanet Characterisation Observatory (EChO) is an essential space mission. Thanks to its large spectral coverage and high spectral resolution, EChO will provide exoplanetary spectra with an unprecedented accuracy, allowing to improve our understanding of exoplanets. In this work, we review what has been done to date concerning the chemical modeling of exoplanet atmospheres and what are the main characteristics of warm exoplanet atmospheres, which are one of the main targets of EChO. Finally we will present the ongoing developments that are necessary for the chemical modeling of exoplanet atmospheres.     

Automated identification of transiting exoplanet candidates in NASA Transiting Exoplanets Survey Satellite (TESS) data with machine learning methods

A novel artificial intelligence (AI) technique that uses machine learning (ML) methodologies combines several algorithms, which were developed by ThetaRay, Inc., is applied to NASA’s Transiting Exoplanets Survey Satellite (TESS) dataset to identify exoplanetary candidates. The AI/ML ThetaRay system is trained initially with Kepler exoplanetary data and validated with confirmed exoplanets before its application to TESS data. Existing and new features of the data, based on various observational parameters, are constructed and used in the AI/ML analysis by employing semi-supervised and unsupervised machine learning techniques. By the application of ThetaRay system to 10,803 light curves of threshold crossing events (TCEs) produced by the TESS mission, obtained from the Mikulski Archive for Space Telescopes, the algorithm yields about 50 targets for further analysis, and we uncover three new exoplanetary candidates by further manual vetting. This study demonstrates for the first time the successful application of the particular combined multiple AI/ML-based methodologies to a large astrophysical dataset for rapid automated classification of TCEs.     

The contribution of the ARIEL space mission to the study of planetary formation

The study of extrasolar planets and of the Solar System provides complementary pieces of the mosaic represented by the process of planetary formation. Exoplanets are essential to fully grasp the huge diversity of outcomes that planetary formation and the subsequent evolution of the planetary systems can produce. The orbital and basic physical data we currently possess for the bulk of the exoplanetary population, however, do not provide enough information to break the intrinsic degeneracy of their histories, as different evolutionary tracks can result in the same final configurations. The lessons learned from the Solar System indicate us that the solution to this problem lies in the information contained in the composition of planets. The goal of the Atmospheric Remote-Sensing Infrared Exoplanet Large-survey (ARIEL), one of the three candidates as ESA M4 space mission, is to observe a large and diversified population of transiting planets around a range of host star types to collect information on their atmospheric composition. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres, which should show minimal condensation and sequestration of high-Z materials and thus reveal their bulk composition across all main cosmochemical elements. In this work we will review the most outstanding open questions concerning the way planets form and the mechanisms that contribute to create habitable environments that the compositional information gathered by ARIEL will allow to tackle.     

Detecting exoplanets with FAST?

We briefly review the various proposed scenarios that may lead to nonthermal radio emissions from exoplanetary systems(planetary magnetospheres, magnetosphere-ionosphere and magnetospheresatellite coupling, and star-planet interactions), and the physical information that can be drawn from their detection. The latter scenario is especially favorable to the production of radio emission above 70 MHz. We summarize the results of past and recent radio searches, and then discuss FAST characteristics and observation strategy, including synergies. We emphasize the importance of polarization measurements and a high duty-cycle for the very weak targets that radio-exoplanets prove to be.     

Stability of planetary systems with respect to masses

The stability in the sense of Lagrange of the Sun–Jupiter–Saturn system and 47 UMa system with respect to masses on a time scale of 10⁶ years was studied using the method of averaging and numerical methods. When the masses of Jupiter and Saturn increase by 20 times (approximately, more accurate value depends on a time-scale of stable motion), these planets can have close approaches. Close approaches appear when analyzing osculating elements; they are absent in the mean elements. A similar situation takes place in the case of 47 UMa and other exoplanetary systems. The study of Lagrange stability with respect to masses allows us to obtain upper limits for masses of extrasolar planets.     

On the Dynamical Foundations of the Lidov–Kozai Theory

The Lidov–Kozai theory developed by each of the authors independently in 1961–1962 is based on qualitative methods of studying the evolution of orbits for the satellite version of the restricted three-body problem (Hill’s problem). At present, this theory is in demand in various fields of science: in the field of planetary research within the Solar system, the field of exoplanetary systems, and the field of high-energy physics in interstellar and intergalactic space. This has prompted me to popularize the ideas that underlie the Lidov–Kozai theory based on the experience of using this theory as an efficient tool for solving various problems related to the study of the secular evolution of the orbits of artificial planetary satellites under the influence of external gravitational perturbations with allowance made for the perturbations due to the polar planetary oblateness.