The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects (original) (raw)

Chaos, Order, and Periodic Orbits in 3 : 1 Resonant Planetary Dynamics

The Astrophysical Journal, 2008

This study addresses the long-term evolution of possible two-planet extrasolar systems that are initially trapped in 3:1 mean motion resonance. A planar general three-body problem model is used, and its resonant dynamics are examined by computing periodic orbits in a rotating frame, Poincaré maps, and maps of dynamical stability. We computed the families of symmetric resonant periodic orbits that obey bifurcations, giving rise to families of asymmetric periodic orbits. The linear stability of such orbits has also been computed, and their relation to the long-term stability of their nearby phase-space domain has been studied. The maps of dynamical stability reveal a complicated structure in the phase space, where chaos and order coexist and alternate as the initial eccentricities or the phases of the planets change. The regular orbits are classified into various types according to the librating or rotating evolution of the resonant angles. Apsidal symmetric librations are common in the domain of resonant motion, but asymmetric ones are associated exclusively with the existence of asymmetric periodic orbits. Such a stable asymmetric configuration seems to correspond to the companions b and c of the 55 Cnc extrasolar system, which are trapped in the 3:1 mean motion resonance according to the study of McArthur et al. However, a recent study by Fischer et al. shows the existence of a new planet (the companion f) in the system, and that the planets b and c are not in mean motion resonance.

Resonances in Multiple Planetary Systems

Celestial Mechanics and Dynamical Astronomy, 2004

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.

Stability of fictitious Trojan planets in extrasolar systems

Astronomische Nachrichten, 2007

Our work deals with the dynamical possibility that in extrasolar planetary systems a terrestrial planet may have stable orbits in a 1:1 mean motion resonance with a Jovian like planet. We studied the motion of fictitious Trojans around the Lagrangian points L4/L5 and checked the stability and/or chaoticity of their motion with the aid of the Lyapunov Indicators and the maximum eccentricity. The computations were carried out using the dynamical model of the elliptic restricted three-body problem that consists of a central star, a gas giant moving in the habitable zone, and a massless terrestrial planet. We found 3 new systems where the gas giant lies in the habitable zone, namely HD 99109, HD 101930, and HD 33564. Additionally we investigated all known extrasolar planetary systems where the giant planet lies partly or fully in the habitable zone. The results show that the orbits around the Lagrangian points L4/L5 of all investigated systems are stable for long times (10 7 revolutions).

A dynamical stability study of Kepler Circumbinary planetary systems with one planet

Monthly Notices of the Royal Astronomical Society, 2014

To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. . In addition to their intrinsic interest, the study of such systems is an opportunity to test our understanding of planetary system formation and evolution around binaries. The investigation is done by means of numerical simulations. We perform numerical integrations of the full equations of motion of each system with the aim of checking the stability of the planetary orbit. The investigation of the stability of the above systems consists of three numerical experiments. In the first one, we perform a long-term (1 Gyr) numerical integration of the nominal solution of the six Kepler systems under investigation. In the second experiment, we look for the critical semimajor axis of the six planetary orbits, and finally, in the third experiment, we construct two-dimensional stability maps on the eccentricity-pericentre distance plane. Additionally, using numerical integrations of the nominal solutions we checked if these solutions were close to the exact resonance.

Resonances and stability of extra-solar planetary systems

Proceedings of the International Astronomical Union, 2004

This paper reviews recent results on the dynamics of multiple-planet extra-solar systems, including main sequence stars and the pulsar PSR B1257+12 and, comparatively, our own Solar System. Taking into account the degree of gravitational interaction of the planets, the known planetary systems may be separated into four main groups: (Ia) Planets in Mean-motion resonance (Ib) Low-eccentricity near-resonant pairs; (II) Non-resonant planets with a significant secular dynamics; and (III) Weakly interacting planet pairs. Different analytical and numerical tools can help to understand the structure of the phase space, to identify stability mechanisms and to categorize different types of motions in the cases of more significant dynamical interaction. The origin of resonant configurations is discussed in the light of the hypothesis of planetary migration.

Conditions of Dynamical Stability for the HD 160691 Planetary System

The Astrophysical Journal, 2003

In our previous paper we showed that the currently determined orbital parameters placed four recently announced planetary systems HD 12661, HD 38529, HD 37124, and HD 160691 in very different situations from the point of view of dynamical stability. In the present paper, we deal with the last of these systems, whose orbital parameters of the outer planet are yet uncertain. We discover a stabilizing mechanism that could be the key to its existence. The paper is devoted to the study of this mechanism by a global dynamics analysis in the orbital -2parameter space related to the HD 160691 system. We obtained our results using a new technique called MEGNO and verified them with the Fast Lyapunov Indicator technique (FLI). In order to be dynamically stable, the HD 160691 planetary system has to satisfy the following conditions : (1) a 2:1 mean motion resonance, (2) combined with an apsidal secular resonance, (3) in a configuration P c (ap) − S − P b (ap) (which means that the planets c and b may be considered as initially located at their apoastron around the central star S), (4) and specific conditions on the respective sizes of the eccentricities. High eccentricity for the outer orbit (e c > 0.52) is the most probable necessary condition, while the eccentricity of the inner orbit e b becomes relatively unimportant when e c > 0.7. We also show that there is an upper limit for planetary masses (in the interval permitted by the undetermined line-of-sight inclination factor sin i l ) due to the dynamical stability mechanism.

Orbital stability of coplanar two-planet exosystems with high eccentricities

Monthly Notices of the Royal Astronomical Society, 2016

The long-term stability of the evolution of two-planet systems is considered by using the general three body problem (GTBP). Our study is focused on the stability of systems with adjacent orbits when at least one of them is highly eccentric. In these cases, in order for close encounters, which destabilize the planetary systems, to be avoided, phase protection mechanisms should be considered. Additionally, since the GTBP is a non-integrable system, chaos may also cause the destabilization of the system after a long time interval. By computing dynamical maps, based on Fast Lyapunov Indicator, we reveal regions in phase space with stable orbits even for very high eccentricities (e > 0.5). Such regions are present in mean motion resonances (MMRs). We can determine the position of the exact MMR through the computation of families of periodic orbits in a rotating frame. Elliptic periodic orbits are associated with the presence of apsidal corotation resonances (ACRs). When such solutions are stable, they are associated with neighbouring domains of initial conditions that provide long-term stability. We apply our methodology so that the evolution of planetary systems of highly eccentric orbits is assigned to the existence of such stable domains. Particularly, we study the orbital evolution of the extrasolar systems HD 82943, HD 3651, HD 7449, HD 89744 and HD 102272 and discuss the consistency between the orbital elements provided by the observations and the dynamical stability.

Study of stability of mean-motion resonances in multiexoplanetary systems

Journal of Physics: Conference Series, 2016

Many exoplanetary systems have been found to harbour more than one planet. Some of them have commensurability in orbital periods of the planets (resonant-planet pair). The aim of this work is to analyse the stability of resonant-planet pair configuration in two multiexoplanetary systems which have two planets in near mean-motion resonances, i.e. Kepler-9 and HD 10180 systems. This work considers numerical and comparative empiric-analytical studies. Numerical studies are performed using the integrator package SWIFT with an integration time of 10 Myr. Results from numerical integrations indicate that all orbital solution sets of the systems are stable. Further numerical explorations also demonstrate that the systems are stable for small perturbations in the orbital elements and mass variations. Analyses of stability based on comparative empiric-analytical are done by applying a known stability criterion to all systems. We find that all systems tend to be stable.

Analysis of the dynamics of the resonant planetary system HD 45364

The aim of this work is to analyse the orbital dynamics and stability of exoplanetary system in which two planets are in nearly 3:2 MMR. We have taken HD 45364 system for our study in which two planets are most likely in a 3:2 MMR. We have plotted two resonant angles and the relative apsidal longitudes and it is observed that they are librating around a constant value. From this observation our opinion is that there exist nearly 3:2 MMR between HD 45364b and HD 45364c. The perturbative solution is obtained for the time variation of the semi-major axes. The short and long term variations of semimajor axes are studied. For the validation of our analytical results we have compared our analytical solutions with the numerical solutions. The effect of planetary perturbations on eccentricity is studied with the help of secular resonance dynamics theory. The short and long term variations of eccentricities of HD 45364b and HD 45364c are shown graphically. Moreover, using the latest stabilit...

Global dynamics of planetary systems with the MEGNO criterion

Astronomy & Astrophysics, 2001

In this paper we apply a new technique alternative to the numerically computed Lyapunov Characteristic Number (LCN) for studying the dynamical behaviour of planetary systems in the framework of the gravitational N-body problem. The method invented by P. Cincotta and C. Simó is called the Mean Exponential Growth of Nearby Orbits (MEGNO). It provides an efficient way for investigation of the fine structure of the phase space and its regular and chaotic components in any conservative Hamiltonian system. In this work we use it to study the dynamical behaviour of the multidimensional planetary systems. We investigate the recently discovered υ And planetary system, which consists of a star of 1.3 M and three Jupiter-size planets. The two outermost planets have eccentric orbits. This system appears to be one of the best candidates for dynamical studies. The mutual gravitational interaction between the two outermost planets is strong. Moreover the system can survive on a stellar evolutionary time scale as it is claimed by some authors (e.g., Rivera & Lissauer 2000b). As the main methodological result of this work, we confirm important properties of the MEGNO criterion such as its fast convergence, and short motion times (of the order of 10 4 times the longest orbital period) required to distinguish between regular and chaotic behaviors. Using the MEGNO technique we found that the presence of the innermost planet may cause the whole system to become chaotic with the Lyapunov time scale of the order of 10 3-10 4 yr only. Chaos does not induce in this case visible irregular changes of the orbital elements, and therefore its presence can be overlooked by studying variations of the elements. We confirm explicitly the strong and sensitive dependence of the dynamical behaviour on the companion masses.