DOCSLIB.ORG

Stability of Planets in Binary Star Systems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Stability of Planets in Binary Star Systems StabilityStability ofof PlanetsPlanets inin BinaryBinary StarStar SystemsSystems Ákos Bazsó in collaboration with: E. Pilat-Lohinger, D. Bancelin, B. Funk ADG Group Outline Exoplanets in multiple star systems Secular perturbation theory Application: tight binary systems Summary + Outlook About NFN sub-project SP8 “Binary Star Systems and Habitability” Stand-alone project “Exoplanets: Architecture, Evolution and Habitability” Basic dynamical types S-type motion (“satellite”) around one star P-type motion (“planetary”) around both stars Image: R. Schwarz Exoplanets in multiple star systems Observations: (Schwarz 2014, Binary Catalogue) ● 55 binary star systems with 81 planets ● 43 S-type + 12 P-type systems ● 10 multiple star systems with 10 planets Example: γ Cep (Hatzes et al. 2003) ● RV measurements since 1981 ● Indication for a “planet” (Campbell et al. 1988) ● Binary period ~57 yrs, planet period ~2.5 yrs Multiplicity of stars ~45% of solar like stars (F6 – K3) with d < 25 pc in multiple star systems (Raghavan et al. 2010) Known exoplanet host stars: single double triple+ source 77% 20% 3% Raghavan et al. (2006) 83% 15% 2% Mugrauer & Neuhäuser (2009) 88% 10% 2% Roell et al. (2012) Exoplanet catalogues The Extrasolar Planets Encyclopaedia http://exoplanet.eu Exoplanet Orbit Database http://exoplanets.org Open Exoplanet Catalogue http://www.openexoplanetcatalogue.com The Planetary Habitability Laboratory http://phl.upr.edu/home NASA Exoplanet Archive http://exoplanetarchive.ipac.caltech.edu Binary Catalogue of Exoplanets http://www.univie.ac.at/adg/schwarz/multiple.html Habitable Zone Gallery http://www.hzgallery.org Binary Catalogue Binary Catalogue of Exoplanets http://www.univie.ac.at/adg/schwarz/multiple.html Dynamical stability Stability limit for S-type planets Rabl & Dvorak (1988), Holman & Wiegert (1999), Pilat-Lohinger & Dvorak (2002) Parameters (a , e , μ) bin bin Outer limit at roughly max. ¼ of stellar separation (for μ = 0.5) Implications for planet formation → truncation of protoplanetary disk Secular perturbation theory in a nutshell Secular perturbation theory “secular” = long time-scales: T sec ≫T rev min. 3 interacting massive bodies (m , m , m ) 0 1 2 gravitational perturbations lead to ... ● mean motion resonances (MMR) ● secular resonances (SR) resonance = integer ratio of 2 frequencies f 1/f 2=p/q∈ℚ Single star – single planet two-body problem = indefinitely stable Basic parameters ● Semi-major axis a ● Eccentricity e 0 < e < 1 ● Solar system planets: e ≤ 0.2 pericenter apocenter Binary star system precession of pericenter (and line of nodes) with time Laplace-Lagrange linear theory Developed for solar system (low mass-ratio) Limits = low eccentricity / inclination Objects = host star + 2 perturbers + massless test planet Simple analytical formula (Murray & Dermott 1999) h(t)=e sin(g t+ϕ)+ A (g , g ,e )sin(g t+ϕ ) free ∑ j j j j j g = free (proper) secular frequency of test planet g = fundamental Eigenfrequencies of system j Free/forced eccentricity Example 1: frequencies for planets Example 2: asteroid main-belt Image: Tsiganis (2008) Application Binary star systems with separation a < 100 AU Typical setting: ● host star (“primary”) ● companion star (“secondary”) ● giant planet (Jupiter like) around primary ● stability of additional (terrestrial) planets ? Explanation for numerical results Semi-analytical method ● Determine secular frequency of giant planet ● Find intersection with analytical curve of free frequency Aim of study Investigated systems Star 1 Star 2 Planet name Mass Spectral Mass Distance Ecc. Mass Distance Ecc. M Type M AU M AU sun sun jup GJ 3021 0.90 G6V 0.15 (?) 68 0.20 (?) 3.37 0.49 0.51 Gliese 86 0.83 K0V 0.49 19 0.40 4.01 0.11 0.05 94 Cet 1.34 F8V 0.20 (?) ≥ 100 (?) 0.20 (?) 1.68 1.42 0.30 HD 41004 0.70 K2V 0.15 (?) 23 0.20 (?) 2.54 1.64 0.20 (?) τ Boo 1.30 F6IV 0.40 (?) 45 0.20 (?) 5.90 0.046 0.02 HD 177830 1.47 K0IV 0.23 97 0.20 (?) 1.49 1.22 ≈ 0.00 HD 196885 1.33 F8V 0.45 21 0.42 2.98 2.60 0.48 γ Cep 1.40 K1III 0.41 19 0.41 1.85 2.05 0.05 (?) = estimated values; minimum masses M sin(i) Selected systems Star 1 Star 2 Planet name Mass Spectral Mass Distance Ecc. Mass Distance Ecc. M Type M AU M AU sun sun jup GJ 3021 0.90 G6V 0.15 68 0.20 3.37 0.49 0.51 Gliese 86 0.83 K0V 0.49 19 0.40 4.01 0.11 0.05 94 Cet 1.34 F8V 0.20 ≥ 100 0.20 1.68 1.42 0.30 HD 41004 0.70 K2V 0.15 23 0.20 2.54 1.64 0.20 τ Boo 1.30 F6IV 0.40 45 0.20 5.90 0.046 0.02 HD 177830 1.47 K0IV 0.23 97 0.20 1.49 1.22 ≈ 0.00 HD 196885 1.33 F8V 0.45 21 0.42 2.98 2.60 0.48 γ Cep 1.40 K1III 0.41 19 0.41 1.85 2.05 0.05 Numerical results for HD 41004 Image: E. Pilat-Lohinger Why not the other systems ? HD 1237 HD 41004 Dependence on secondary star 1 increasing a 2 Dependence on secondary star 2 increasing m 2 HD 196885 Outlook Ongoing work Determine width of perturbation – dependence on parameters (mass, distance, eccentricity, …) Goals: ● Catalogue for observers ● Binary star systems allowing “unperturbed” habitable zone (small eccentricity) That'sThat's allall folksfolks ...... References Campbell, Walker & Yang (1988), ApJ 331, 902 Hatzes, Cochran, Endl et al. (2003), ApJ 599, 1383 Holman & Wiegert (1999), AJ 117, 621 Mugrauer & Neuhäuser (2009), A&A 494, 373 Murray & Dermott (1999), Solar System Dynamics, Cambridge Univ. Press Pilat-Lohinger & Dvorak (2002), CMDA 82, 143 Rabl & Dvorak (1988), A&A 191, 385 Raghavan, Henry, Mason et al. (2006), ApJ 646, 523 Raghavan, McAlister, Henry et al. (2010), ApJS 190, 1 Roell, Neuhäuser, Seifahrt & Mugrauer (2012), A&A 542, 92 Tsiganis (2008), Lecture Notes in Physics 729, 111, Springer .
Load more

Recommended publications
  • Neutron Stars
    Chandra X-Ray Observatory X-Ray Astronomy Field Guide Neutron Stars Ordinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons. The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% Chandra Image of Vela Pulsar open space! (NASA/PSU/G.Pavlov et al. What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons! Such extreme forces occur in nature when the central part of a massive star collapses to form a neutron star. The atoms are crushed completely, and the electrons are jammed inside the protons to form a star composed almost entirely of neutrons.
    [Show full text]
  • Lurking in the Shadows: Wide-Separation Gas Giants As Tracers of Planet Formation
    Lurking in the Shadows: Wide-Separation Gas Giants as Tracers of Planet Formation Thesis by Marta Levesque Bryan In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 Defended May 1, 2018 ii © 2018 Marta Levesque Bryan ORCID: [0000-0002-6076-5967] All rights reserved iii ACKNOWLEDGEMENTS First and foremost I would like to thank Heather Knutson, who I had the great privilege of working with as my thesis advisor. Her encouragement, guidance, and perspective helped me navigate many a challenging problem, and my conversations with her were a consistent source of positivity and learning throughout my time at Caltech. I leave graduate school a better scientist and person for having her as a role model. Heather fostered a wonderfully positive and supportive environment for her students, giving us the space to explore and grow - I could not have asked for a better advisor or research experience. I would also like to thank Konstantin Batygin for enthusiastic and illuminating discussions that always left me more excited to explore the result at hand. Thank you as well to Dimitri Mawet for providing both expertise and contagious optimism for some of my latest direct imaging endeavors. Thank you to the rest of my thesis committee, namely Geoff Blake, Evan Kirby, and Chuck Steidel for their support, helpful conversations, and insightful questions. I am grateful to have had the opportunity to collaborate with Brendan Bowler. His talk at Caltech my second year of graduate school introduced me to an unexpected population of massive wide-separation planetary-mass companions, and lead to a long-running collaboration from which several of my thesis projects were born.
    [Show full text]
  • 1 CHAPTER 18 SPECTROSCOPIC BINARY STARS 18.1 Introduction
    1 CHAPTER 18 SPECTROSCOPIC BINARY STARS 18.1 Introduction There are many binary stars whose angular separation is so small that we cannot distinguish the two components even with a large telescope – but we can detect the fact that there are two stars from their spectra. In favourable circumstances, two distinct spectra can be seen. It might be that the spectral types of the two components are very different – perhaps a hot A-type star and a cool K-type star, and it is easy to recognize that there must be two stars there. But it is not necessary that the two spectral types should be different; a system consisting of two stars of identical spectral type can still be recognized as a binary pair. As the two components orbit around each other (or, rather, around their mutual centre of mass) the radial components of their velocities with respect to the observer periodically change. This results in a periodic change in the measured wavelengths of the spectra of the two components. By measuring the change in wavelengths of the two sets of spectrum lines over a period of time, we can construct a radial velocity curve (i.e. a graph of radial velocity versus time) and from this it is possible to deduce some of the orbital characteristics. Often one component may be significantly brighter than the other, with the consequence that we can see only one spectrum, but the periodic Doppler shift of that one spectrum tells us that we are observing one component of a spectroscopic binary system.
    [Show full text]
  • Naming the Extrasolar Planets
    Naming the extrasolar planets W. Lyra Max Planck Institute for Astronomy, K¨onigstuhl 17, 69177, Heidelberg, Germany [email protected] Abstract and OGLE-TR-182 b, which does not help educators convey the message that these planets are quite similar to Jupiter. Extrasolar planets are not named and are referred to only In stark contrast, the sentence“planet Apollo is a gas giant by their assigned scientific designation. The reason given like Jupiter” is heavily - yet invisibly - coated with Coper- by the IAU to not name the planets is that it is consid- nicanism. ered impractical as planets are expected to be common. I One reason given by the IAU for not considering naming advance some reasons as to why this logic is flawed, and sug- the extrasolar planets is that it is a task deemed impractical. gest names for the 403 extrasolar planet candidates known One source is quoted as having said “if planets are found to as of Oct 2009. The names follow a scheme of association occur very frequently in the Universe, a system of individual with the constellation that the host star pertains to, and names for planets might well rapidly be found equally im- therefore are mostly drawn from Roman-Greek mythology. practicable as it is for stars, as planet discoveries progress.” Other mythologies may also be used given that a suitable 1. This leads to a second argument. It is indeed impractical association is established. to name all stars. But some stars are named nonetheless. In fact, all other classes of astronomical bodies are named.
    [Show full text]
  • Can There Be Additional Rocky Planets in the Habitable Zone of Tight Binary
    Mon. Not. R. Astron. Soc. 000, 1–10 () Printed 24 September 2018 (MN LATEX style file v2.2) Can there be additional rocky planets in the Habitable Zone of tight binary stars with a known gas giant? B. Funk1⋆, E. Pilat-Lohinger1 and S. Eggl2 1Institute for Astronomy, University of Vienna, Vienna, Austria 2IMCCE, Observatoire de Paris, Paris, France ABSTRACT Locating planets in Habitable Zones (HZs) around other stars is a growing field in contem- porary astronomy. Since a large percentage of all G-M stars in the solar neighborhood are expected to be part of binary or multiple stellar systems, investigations of whether habitable planets are likely to be discovered in such environments are of prime interest to the scientific community. As current exoplanet statistics predicts that the chances are higher to find new worlds in systems that are already known to have planets, we examine four known extrasolar planetary systems in tight binaries in order to determine their capacity to host additional hab- itable terrestrial planets. Those systems are Gliese 86, γ Cephei, HD 41004 and HD 196885. In the case of γ Cephei, our results suggest that only the M dwarf companion could host ad- ditional potentially habitable worlds. Neither could we identify stable, potentially habitable regions around HD 196885A. HD 196885 B can be considered a slightly more promising tar- get in the search forEarth-twins.Gliese 86 A turned out to be a very good candidate, assuming that the system’s history has not been excessively violent. For HD 41004 we have identified admissible stable orbits for habitable planets, but those strongly depend on the parameters of the system.
    [Show full text]
  • Arxiv:2105.11583V2 [Astro-Ph.EP] 2 Jul 2021 Keck-HIRES, APF-Levy, and Lick-Hamilton Spectrographs
    Draft version July 6, 2021 Typeset using LATEX twocolumn style in AASTeX63 The California Legacy Survey I. A Catalog of 178 Planets from Precision Radial Velocity Monitoring of 719 Nearby Stars over Three Decades Lee J. Rosenthal,1 Benjamin J. Fulton,1, 2 Lea A. Hirsch,3 Howard T. Isaacson,4 Andrew W. Howard,1 Cayla M. Dedrick,5, 6 Ilya A. Sherstyuk,1 Sarah C. Blunt,1, 7 Erik A. Petigura,8 Heather A. Knutson,9 Aida Behmard,9, 7 Ashley Chontos,10, 7 Justin R. Crepp,11 Ian J. M. Crossfield,12 Paul A. Dalba,13, 14 Debra A. Fischer,15 Gregory W. Henry,16 Stephen R. Kane,13 Molly Kosiarek,17, 7 Geoffrey W. Marcy,1, 7 Ryan A. Rubenzahl,1, 7 Lauren M. Weiss,10 and Jason T. Wright18, 19, 20 1Cahill Center for Astronomy & Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA 2IPAC-NASA Exoplanet Science Institute, Pasadena, CA 91125, USA 3Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305, USA 4Department of Astronomy, University of California Berkeley, Berkeley, CA 94720, USA 5Cahill Center for Astronomy & Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA 6Department of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA 7NSF Graduate Research Fellow 8Department of Physics & Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA 9Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA 10Institute for Astronomy, University of Hawai`i,
    [Show full text]
  • Chapter 16 the Sun and Stars
    Chapter 16 The Sun and Stars Stargazing is an awe-inspiring way to enjoy the night sky, but humans can learn only so much about stars from our position on Earth. The Hubble Space Telescope is a school-bus-size telescope that orbits Earth every 97 minutes at an altitude of 353 miles and a speed of about 17,500 miles per hour. The Hubble Space Telescope (HST) transmits images and data from space to computers on Earth. In fact, HST sends enough data back to Earth each week to fill 3,600 feet of books on a shelf. Scientists store the data on special disks. In January 2006, HST captured images of the Orion Nebula, a huge area where stars are being formed. HST’s detailed images revealed over 3,000 stars that were never seen before. Information from the Hubble will help scientists understand more about how stars form. In this chapter, you will learn all about the star of our solar system, the sun, and about the characteristics of other stars. 1. Why do stars shine? 2. What kinds of stars are there? 3. How are stars formed, and do any other stars have planets? 16.1 The Sun and the Stars What are stars? Where did they come from? How long do they last? During most of the star - an enormous hot ball of gas day, we see only one star, the sun, which is 150 million kilometers away. On a clear held together by gravity which night, about 6,000 stars can be seen without a telescope.
    [Show full text]
  • Binary Star Modeling: a Computational Approach
    TCNJ JOURNAL OF STUDENT SCHOLARSHIP VOLUME XIV APRIL 2012 BINARY STAR MODELING: A COMPUTATIONAL APPROACH Author: Daniel Silano Faculty Sponsor: R. J. Pfeiffer, Department of Physics ABSTRACT This paper illustrates the equations and computational logic involved in writing BinaryFactory, a program I developed in Spring 2011 in collaboration with Dr. R. J. Pfeiffer, professor of physics at The College of New Jersey. This paper outlines computational methods required to design a computer model which can show an animation and generate an accurate light curve of an eclipsing binary star system. The final result is a light curve fit to any star system using BinaryFactory. An example is given for the eclipsing binary star system TU Muscae. Good agreement with observational data was obtained using parameters obtained from literature published by others. INTRODUCTION This project started as a proposal for a simple animation of two stars orbiting one another in C++. I found that although there was software that generated simple animations of binary star orbits and generated light curves, the commercial software was prohibitively expensive or not very user friendly. As I progressed from solving the orbits to generating the Roche surface to generating a light curve, I learned much about computational physics. There were many trials along the way; this paper aims to explain to the reader how a computational model of binary stars is made, as well as how to avoid pitfalls I encountered while writing BinaryFactory. Binary Factory was written in C++ using the free C++ libraries, OpenGL, GLUT, and GLUI. A basis for writing a model similar to BinaryFactory in any language will be presented, with a light curve fit for the eclipsing binary star system TU Muscae in the final secion.
    [Show full text]
  • Ghost Imaging of Space Objects
    Ghost Imaging of Space Objects Dmitry V. Strekalov, Baris I. Erkmen, Igor Kulikov, and Nan Yu Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109-8099 USA NIAC Final Report September 2014 Contents I. The proposed research 1 A. Origins and motivation of this research 1 B. Proposed approach in a nutshell 3 C. Proposed approach in the context of modern astronomy 7 D. Perceived benefits and perspectives 12 II. Phase I goals and accomplishments 18 A. Introducing the theoretical model 19 B. A Gaussian absorber 28 C. Unbalanced arms configuration 32 D. Phase I summary 34 III. Phase II goals and accomplishments 37 A. Advanced theoretical analysis 38 B. On observability of a shadow gradient 47 C. Signal-to-noise ratio 49 D. From detection to imaging 59 E. Experimental demonstration 72 F. On observation of phase objects 86 IV. Dissemination and outreach 90 V. Conclusion 92 References 95 1 I. THE PROPOSED RESEARCH The NIAC Ghost Imaging of Space Objects research program has been carried out at the Jet Propulsion Laboratory, Caltech. The program consisted of Phase I (October 2011 to September 2012) and Phase II (October 2012 to September 2014). The research team consisted of Drs. Dmitry Strekalov (PI), Baris Erkmen, Igor Kulikov and Nan Yu. The team members acknowledge stimulating discussions with Drs. Leonidas Moustakas, Andrew Shapiro-Scharlotta, Victor Vilnrotter, Michael Werner and Paul Goldsmith of JPL; Maria Chekhova and Timur Iskhakov of Max Plank Institute for Physics of Light, Erlangen; Paul Nu˜nez of Coll`ege de France & Observatoire de la Cˆote d’Azur; and technical support from Victor White and Pierre Echternach of JPL.
    [Show full text]
  • The ELODIE Survey for Northern Extra-Solar Planets IV. HD196885, A
    Astronomy & Astrophysics manuscript no. hd196885 c ESO 2018 December 2, 2018 The ELODIE survey for northern extra-solar planets IV. HD 196885, a close binary star with a 3.7-year planet A.C.M. Correia1,2, S. Udry2, M. Mayor2, A. Eggenberger3,2, D. Naef4, J.-L. Beuzit3, C. Perrier3, D. Queloz2, J.-P. Sivan5, F. Pepe5, N.C. Santos6,2, and D. S´egransan5 1 Departamento de F´ısica da Universidade de Aveiro, Campus Universit´ario de Santiago, 3810-193 Aveiro, Portugal 2 Observatoire de Gen`eve, 51 Ch. des Maillettes, 1290 Sauverny, Switzerland 3 Laboratoire d’Astrophysique de Grenoble, Universit´eJoseph Fourier, BP 53, 38041 Grenoble Cedex 9, France 4 European Southern Observatory, Casilla 19001, Santiago 19, Chile 5 Laboratoire d’Astrophysique de Marseille, Traverse du Siphon BP 8, 13376 Marseille Cedex 12, France 6 Centro de Astrof´ısica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal Received 01 October, 2006; accepted ?? ABSTRACT Aims. We aim significantly increase the number of detected extra-solar planets in a magnitude-limited sample to improve our knowl- edge of their orbital elements distributions and thus obtain better constraints for planet-formation models. Methods. Radial-velocity data were taken at Haute-Provence Observatory (OHP, France) with the ELODIE echelle spectrograph. Results. We report the presence of a planet orbiting HD 196885 A, with an orbital period of 1349 days. This star was previously sug- gested to host a 386-day planet, but we cannot confirm its existence. We also detect the presence of a stellar companion, HD 196885 B, and give some constraints on its orbit.
    [Show full text]
  • Mètodes De Detecció I Anàlisi D'exoplanetes
    MÈTODES DE DETECCIÓ I ANÀLISI D’EXOPLANETES Rubén Soussé Villa 2n de Batxillerat Tutora: Dolors Romero IES XXV Olimpíada 13/1/2011 Mètodes de detecció i anàlisi d’exoplanetes . Índex - Introducció ............................................................................................. 5 [ Marc Teòric ] 1. L’Univers ............................................................................................... 6 1.1 Les estrelles .................................................................................. 6 1.1.1 Vida de les estrelles .............................................................. 7 1.1.2 Classes espectrals .................................................................9 1.1.3 Magnitud ........................................................................... 9 1.2 Sistemes planetaris: El Sistema Solar .............................................. 10 1.2.1 Formació ......................................................................... 11 1.2.2 Planetes .......................................................................... 13 2. Planetes extrasolars ............................................................................ 19 2.1 Denominació .............................................................................. 19 2.2 Història dels exoplanetes .............................................................. 20 2.3 Mètodes per detectar-los i saber-ne les característiques ..................... 26 2.3.1 Oscil·lació Doppler ........................................................... 27 2.3.2 Trànsits
    [Show full text]
  • AMD-Stability and the Classification of Planetary Systems
    A&A 605, A72 (2017) DOI: 10.1051/0004-6361/201630022 Astronomy c ESO 2017 Astrophysics& AMD-stability and the classification of planetary systems? J. Laskar and A. C. Petit ASD/IMCCE, CNRS-UMR 8028, Observatoire de Paris, PSL, UPMC, 77 Avenue Denfert-Rochereau, 75014 Paris, France e-mail: [email protected] Received 7 November 2016 / Accepted 23 January 2017 ABSTRACT We present here in full detail the evolution of the angular momentum deficit (AMD) during collisions as it was described in Laskar (2000, Phys. Rev. Lett., 84, 3240). Since then, the AMD has been revealed to be a key parameter for the understanding of the outcome of planetary formation models. We define here the AMD-stability criterion that can be easily verified on a newly discovered planetary system. We show how AMD-stability can be used to establish a classification of the multiplanet systems in order to exhibit the planetary systems that are long-term stable because they are AMD-stable, and those that are AMD-unstable which then require some additional dynamical studies to conclude on their stability. The AMD-stability classification is applied to the 131 multiplanet systems from The Extrasolar Planet Encyclopaedia database for which the orbital elements are sufficiently well known. Key words. chaos – celestial mechanics – planets and satellites: dynamical evolution and stability – planets and satellites: formation – planets and satellites: general 1. Introduction motion resonances (MMR, Wisdom 1980; Deck et al. 2013; Ramos et al. 2015) could justify the Hill-type criteria, but the The increasing number of planetary systems has made it nec- results on the overlap of the MMR island are valid only for close essary to search for a possible classification of these planetary orbits and for short-term stability.
    [Show full text]