Characterizing Multi-planet Systems with Classical Secular Theory

TL;DR

Classical secular theory helps analyze multi-planet systems by examining eigenmodes to understand their history and dynamics, especially when mean-motion resonances are absent, providing qualitative insights even at moderate eccentricities.

Contribution

This paper demonstrates the utility of classical secular theory in characterizing multi-planet systems and comparing different orbital solutions, highlighting its advantages over other methods for qualitative analysis.

Findings

Eigenmodes reveal tidal effects and dynamical history.

Secular theory remains useful at moderate eccentricities.

Comparison of solutions for 55 Cancri shows different dynamical groupings.

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., 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.