Effects of Secular Interactions in Extrasolar Planetary Systems

This paper studies the effects of dynamical interactions among the planets in observed extrasolar planetary systems, including hypothetical additional bodies, with a focus on secular perturbations. These interactions cause the eccentricities of the planets to explore a distribution of values over time scales that are long compared to observational time baselines, but short compared to the age of the systems. The same formalism determines the eccentricity forcing of hypothetical test bodies (terrestrial planets) in these systems and we find which systems allow for potentially habitable planets. Such planets would be driven to nonzero orbital eccentricity and we derive the distribution of stellar flux experienced by the planets over the course of their orbits. The general relativistic corrections to secular interaction theory are included in the analysis and such effects are important in systems with close planets ($\sim$4 day orbits). Some extrasolar planetary systems (e.g., Upsilon Andromedae) can be used as a test of general relativity, whereas in other systems, general relativity can be used to constrain the system parameters (e.g., $\sin i \gta 0.93$ for HD160691). For the case of hot Jupiters, we discuss how the absence of observed eccentricity implies the absence of companion planets.