On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

B. Funk, A. S. Libert, Á Süli, E. Pilat-Lohinger

Research output: Contribution to journalArticle

2 Downloads (Pure)

Abstract

Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis-inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

Original languageEnglish
Article numberA98
JournalAstronomy and Astrophysics
Volume526
Issue number12
DOIs
Publication statusPublished - 1 Feb 2011

Fingerprint

planetary systems
planets
eccentricity
planet
gases
gas
circular orbits
inclination
eccentric orbits
orbits
stars
gravitational effects
test
three body problem
orbitals

Keywords

  • celestial mechanics
  • methods: analytical
  • methods: numerical
  • planets and satellites: dynamical evolution and stability
  • planets and satellites: individual: HD 154345

Cite this

@article{06bf095e0dd6441bb7d2fbef495a20d9,
title = "On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems",
abstract = "Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis-inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.",
keywords = "celestial mechanics, methods: analytical, methods: numerical, planets and satellites: dynamical evolution and stability, planets and satellites: individual: HD 154345",
author = "B. Funk and Libert, {A. S.} and {\'A} S{\"u}li and E. Pilat-Lohinger",
year = "2011",
month = "2",
day = "1",
doi = "10.1051/0004-6361/201015218",
language = "English",
volume = "526",
journal = "Astronomy and Astrophysics",
issn = "0250-6335",
publisher = "Springer India",
number = "12",

}

On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems. / Funk, B.; Libert, A. S.; Süli, Á; Pilat-Lohinger, E.

In: Astronomy and Astrophysics, Vol. 526, No. 12, A98, 01.02.2011.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems

AU - Funk, B.

AU - Libert, A. S.

AU - Süli, Á

AU - Pilat-Lohinger, E.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis-inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

AB - Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem. Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis-inclination plane. The gas giant's initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant. Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone.

KW - celestial mechanics

KW - methods: analytical

KW - methods: numerical

KW - planets and satellites: dynamical evolution and stability

KW - planets and satellites: individual: HD 154345

UR - http://www.scopus.com/inward/record.url?scp=78650923651&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201015218

DO - 10.1051/0004-6361/201015218

M3 - Article

VL - 526

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0250-6335

IS - 12

M1 - A98

ER -