scholarly journals Orbital Stability of Planet-hosting Triple-star Systems according to Hill: Applications to Alpha Centauri and 16 Cygni

2021 ◽  
Vol 5 (12) ◽  
pp. 285
Author(s):  
Lindsey Boyle ◽  
Manfred Cuntz
Keyword(s):  
Orbital Stability ◽  
Hill Stability ◽  
Stellar Component ◽  
Triple Star

Abstract In this study we investigate aspects of orbital stability for the Alpha Centauri and 16 Cygni systems. They are planet-hosting triple star systems of highly hierarchic nature. For each system, orbital stability of the outlying stellar component and the observed exoplanet(s) are explored through assessing Hill stability. Orbital stability is identified for all components, including the observed system planets.

scholarly journals Long-term orbital stability of exosolar planetary systems with highly eccentric orbits

2015 ◽  
Vol 11 (A29A) ◽  
pp. 38-39
Author(s):  
Kyriaki I. Antoniadou ◽  
George Voyatzis
Keyword(s):  
Phase Space ◽  
Orbital Stability ◽  
Planetary Systems ◽  
Dynamical Analysis ◽  
Hill Stability ◽  
Mean Motion Resonances ◽  
Term Stability ◽  
Long Term Stability ◽  
Eccentric Orbits

AbstractNowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances can provide phase protection and orbits with long-term stability exist. We construct maps of dynamical stability based on the computation of chaotic indicators and we figure out regions in phase space, where the long-term stability is guaranteed. We focus on regions where at least one planet is highly eccentric and attempt to associate them with the existence of stable periodic orbits. The values of the orbital elements, which are derived from observational data, are often given with very large deviations. Generally, phase space regions of high eccentricities are narrow and thus, our dynamical analysis may restrict considerably the valid domain of the system's location.

scholarly journals Orbital Stability in the Elliptic Restricted Three Body Problem

1978 ◽  
Vol 41 ◽  
pp. 333-337
Author(s):  
C.A. Williams ◽  
J.G. Watts
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Orbital Stability ◽  
Restricted Three Body Problem ◽  
Invariant Relation ◽  
Three Body Problem ◽  
Hill Stability ◽  
Elliptic Restricted Problem ◽  
Three Body

AbstractBased on the concept of orbital stability introduced by G. W. Hill, a method is presented to facilitate the determination of the orbital stability of solutions to the planar elliptic restricted problem of three bodies. The invariant relation introduced by Szebehely and Giacaglia (1964) contains an integral which is expanded here about a Keplerian solution to the problem. If the expansion converges, it can be used to determine the conditions for Hill stability. With it one can also define stability in a periodic sense.

Tomographic Separation of Composite Spectra. V. The Triple Star System 55 Ursae Majoris

1997 ◽  
Vol 485 (1) ◽  
pp. 350-358 ◽  
Author(s):  
Ning Liu ◽  
Douglas R. Gies ◽  
Ying Xiong ◽  
Reed L. Riddle ◽  
William G. Bagnuolo, Jr. ◽  
...  
Keyword(s):  
Star System ◽  
Composite Spectra ◽  
Triple Star

scholarly journals The five axes of the Turtle: symmetry and asymmetry in NGC 6210

2021 ◽  
Author(s):  
William J Henney ◽  
J A López ◽  
Ma T García-Díaz ◽  
M G Richer
Keyword(s):  
Planetary Nebula ◽  
Morphological Study ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Line Of Sight ◽  
Velocity Mapping ◽  
High Ionization ◽  
Motion Measurements ◽  
Five Axes ◽  
Triple Star

Abstract We carry out a comprehensive kinematic and morphological study of the asymmetrical planetary nebula: NGC 6210, known as the Turtle. The nebula’s spectacularly chaotic appearance has led to proposals that it was shaped by mass transfer in a triple star system. We study the three-dimensional structure and kinematics of its shells, lobes, knots, and haloes by combining radial velocity mapping from multiple long-slit spectra with proper motion measurements from multi-epoch imaging. We find that the nebula has five distinct ejection axes. The first is the axis of the bipolar, wind-blown inner shell, while the second is the axis of the lop-sided, elliptical, fainter, but more massive intermediate shell. A further two axes are bipolar flows that form the point symmetric, high-ionization outer lobes, all with inclinations close to the plane of the sky. The final axis, which is inclined close to the line of sight, traces collimated outflows of low-ionization knots. We detect major changes in outflow directions during the planetary nebula phase, starting at or before the initial ionization of the nebula 3500 years ago. Most notably, the majority of redshifted low-ionization knots have kinematic ages greater than 2000 years, whereas the majority of blueshifted knots have ages younger than 2000 years. Such a sudden and permanent 180-degree flip in the ejection axis at a relatively late stage in the nebular evolution is a challenge to models of planetary nebula formation and shaping.

scholarly journals Two-component galaxy models with a central BH – II. The ellipsoidal case

2020 ◽  
Vol 500 (1) ◽  
pp. 1054-1070
Author(s):  
Luca Ciotti ◽  
Antonio Mancino ◽  
Silvia Pellegrini ◽  
Azadeh Ziaee Lorzad
Keyword(s):  
Dark Matter ◽  
Stellar Dynamics ◽  
Azimuthal Velocity ◽  
Dark Matter Halo ◽  
Gas Flows ◽  
Total Density ◽  
Density Distributions ◽  
Stellar Component ◽  
Two Component ◽  
Analytical Formulae

ABSTRACT Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

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