TY - JOUR
T1 - Characterizing multi-planet systems with classical secular theory
AU - van Laerhoven, Christa
AU - Greenberg, Richard
N1 - Funding Information:
Acknowledgements We thank D. Fabrycky, D. Hamilton, R. Barnes, R. Dawson, and B. Jackson for their insightful discussions on this topic. A. Morbidelli provided essential help with the manuscript. This work was partially funded by the National Science and Engineering Research Council of Canada through a Postgraduate Scholarship—Masters.
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
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U2 - 10.1007/s10569-012-9410-6
DO - 10.1007/s10569-012-9410-6
M3 - Article
AN - SCOPUS:84863113605
SN - 0923-2958
VL - 113
SP - 215
EP - 234
JO - CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
JF - CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
IS - 2
ER -