Characterizing multi-planet systems with classical secular theory

Christa van Laerhoven, Richard J. Greenberg

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al. in Astophys J 675:790-801, 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.

Original languageEnglish (US)
Pages (from-to)215-234
Number of pages20
JournalCelestial Mechanics and Dynamical Astronomy
Volume113
Issue number2
DOIs
StatePublished - Jun 2012

Fingerprint

Eccentricity
Planets
planets
eccentricity
planet
Damped
Damping
damping
Physical process
orbital elements
Grouping
Partitioning
Alignment
Orbit
Scattering
Orbits
partitioning
alignment
scattering
Motion

Keywords

  • 55 Cancri planets
  • Dissipative forces
  • Long-term stability
  • Mutual perturbations
  • Planetary systems
  • Planets
  • Secular theory
  • Tides

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Characterizing multi-planet systems with classical secular theory. / van Laerhoven, Christa; Greenberg, Richard J.

In: Celestial Mechanics and Dynamical Astronomy, Vol. 113, No. 2, 06.2012, p. 215-234.

Research output: Contribution to journalArticle

@article{72a4cbddec7541689e625da24bfa6880,
title = "Characterizing multi-planet systems with classical secular theory",
abstract = "Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al. in Astophys J 675:790-801, 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.",
keywords = "55 Cancri planets, Dissipative forces, Long-term stability, Mutual perturbations, Planetary systems, Planets, Secular theory, Tides",
author = "{van Laerhoven}, Christa and Greenberg, {Richard J.}",
year = "2012",
month = "6",
doi = "10.1007/s10569-012-9410-6",
language = "English (US)",
volume = "113",
pages = "215--234",
journal = "Celestial Mechanics and Dynamical Astronomy",
issn = "0923-2958",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Characterizing multi-planet systems with classical secular theory

AU - van Laerhoven, Christa

AU - Greenberg, Richard J.

PY - 2012/6

Y1 - 2012/6

N2 - Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al. in Astophys J 675:790-801, 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.

AB - Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help identify tidal effects, early planet-planet scattering, and dynamical coupling among the planets, for systems in which mean-motion resonances do not play a role. Although tidal damping can result in aligned major axes after all but one eigenmode have damped away, such alignment may simply be fortuitous. An example of this is 55 Cancri (orbital solution of Fischer et al. in Astophys J 675:790-801, 2008) where multiple eigenmodes remain undamped. Various solutions for 55 Cancri are compared, showing differing dynamical groupings, with implications for the coupling of eccentricities and for the partitioning of damping among the planets. Solutions for orbits that include expectations of past tidal evolution with observational data, must take into account which eigenmodes should be damped, rather than expecting particular eccentricities to be near zero. Classical secular theory is only accurate for low eccentricity values, but comparison with other results suggests that it can yield useful qualitative descriptions of behavior even for moderately large eccentricity values, and may have advantages for revealing underlying physical processes and, as large numbers of new systems are discovered, for triage to identify where more comprehensive dynamical studies should have priority.

KW - 55 Cancri planets

KW - Dissipative forces

KW - Long-term stability

KW - Mutual perturbations

KW - Planetary systems

KW - Planets

KW - Secular theory

KW - Tides

UR - http://www.scopus.com/inward/record.url?scp=84863113605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863113605&partnerID=8YFLogxK

U2 - 10.1007/s10569-012-9410-6

DO - 10.1007/s10569-012-9410-6

M3 - Article

AN - SCOPUS:84863113605

VL - 113

SP - 215

EP - 234

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 2

ER -