Apsidal Behavior of Planetary Systems

The apsidal behavior of a planetary system is a description of how the shape of an orbit changes with time. Over long timescales (> 10,000 years), most planetary systems cycle through a range of orbits in which their eccentricities and relative orientations oscillate within a fixed interval. Although this behavior sounds complicated, there are (relatively) simple equations that model these oscillations.

The orientations of the orbits can oscillate such that the points of closest approach to the star librate about each other (think of child on a swing, or the pendulum of a clock), or they may circulate (think of the pendulum swinging all the way around). Those are the two simple types of motion that the orientations may exhibit. The curious thing about many planetary systems is that they lie close to the boundary between these two types of oscillations.

A system that evolves such that it is near this boundary is said to be "near-separatrix" (the separatrix separates the two types of motion). Click here to see a movie of near-separatrix motion. After it was discovered that near-separatrix motion was present in &upsilon Andromedae, Richard Greenberg and I studied its geometry and found that, assuming a uniform distribution of orbital properties, we would expect only a few percent of systems to exhibit such behavior (Barnes & Greenberg 2006a). When we wrote that first paper, we thought about 10% of multiple planet systems were close to the separatrix, which seemed large, but not crazy.

In the summer of 2006 a revised catalog of extrasolar planet systems was released and we found that the fraction of systems near separatrix was actually closer to 50% (Barnes & Greenberg 2006c; see also my Extrasolar Planet Interactions page). This fraction seems very large, and suggests some sort of systematic effect is favoring the creation of such systems.

What sort of mechanism could create such near-separatrix behavior? When the motion was first identified, it was suggested that an original member of the &upsilon And system could have been responsible. In the proposed scenario, this extra planet was on an unstable orbit. It gravitationally interacted with another member of the system and was thrown from the system. This sudden change (the ejection would take a few years, where as the long-term oscillations require tens of thousands), could produce near-separatrix motion. It turns out that this mechanism is not very robust, and only predicts a few percent chance of near-separatrix motion (Barnes & Greenberg 2007a). So the origin of this surprisingly large fraction of systems near a separatrix is unknown, but we hypothesize it could be from the ejection of a smaller "protoplanet". We obviously plan on exploring this idea in the future.


Last Update: 1 Aug 2007