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R. Greenberg, R. Barnes (Lunar and Planetary Lab, Univ. of Arizona)
Extra-solar planetary systems display a range of behavior that can be understood in terms of the secular theory of classical celestial mechanics, including cases with libration about alignment of the major axes. Remarkably, >20% of the known systems with multiple planets (\upsilon And, 47 Uma, and 55 Cnc) have trajectories in orbital element space that lie close to the separatrix between libration and circulation. (55 Cnc is complicated by a 3:1 mean-motion commensurability.) A review of the basics of secular theory provides insight into this behavior, correcting misconceptions about the definition of secular resonance that have propagated in the literature of extra-solar planetary systems: Resonance is not synonymous with libration, and is not a commensurability of eigenfrequencies. Contrary to earlier reports, what makes these systems special is not that they are librating (they may not be) or that they are in resonance (they are not), but that each is so close to its separatrix. We have evaluated the behavior of the near-separatrix systems with updated orbital elements and compared both analytical and numerical results. The systems are so close to the separatrix that first-order theory analytic secular theory cannot reliably distinguish between circulation and libration. Similarly, uncertainty in observational orbit determination is great enough that, even with numerical integration, the libration state is uncertain. These near-separatrix systems are so common that they suggest that some physical process of planet formation or dynamical evolution may tend to set up systems near the separatrix. Explanations based on an impulsive increase in the eccentricity of one planet from near zero are promising, but some issues are unresolved. A successful explanation must explain why this remarkable dynamical condition is so common.
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Bulletin of the American Astronomical Society, 37 #3
© 2004. The American Astronomical Soceity.