Secular Behavior In Multi-planet Systems: 61 Virginis, 55 Cancri, Etc.

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Secular analytical theory can offer insight into the evolution of a multi-planet system as well as the interactions among its planets. Major axes locked in alignment (dominance of a single eigenfrequency) may indicate substantial tidal damping; Near-separatrix behavior would suggest an early mutual scattering event. For the 61 Virginis system, secular theory reproduces the general behavior from numerical integrations even though the eccentricities are quite large. The major axes of the two outer planets librate about a mutual alignment. However, rather than indicating tidal evolution, this alignment is the most likely behavior given the system's basic architecture, i.e. masses and semi-major axes. In general, an alignment of major axes of only a subset of planets does not necessarily imply that tides or any other eccentricity-damping process has been significant in the evolution of such a system. For the published orbits (Fischer et al. 2008) of the five-planet 55 Cancri system: The innermost planet ("e") has a surprisingly large eccentricity, dominated by a single frequency, which is precisely the one that tides should damp out first; The alignment of three major axes involves three different eigenfrequencies, so it has nothing to do with damping, and is improbable; The outer two planets undergo near-separatrix libration, which would suggest the outermost one underwent a scattering event. Recent alias corrections for 55 Cancri (Dawson and Fabryky 2010) allow a good fit with a circular orbit for the inner planet. Secular theory shows the orbit remains nearly circular even under the influence of the other planets. Moreover, the single eigenfrequency of the system that is controlled by tides has completely damped away in all the planets. 55 Cancri e has apparently undergone complete tidal damping, consistent with its proximity to the star. Secular theory is a valuable tool as data improve and new discoveries continue.

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