Stability and chaos in the υ andromedae planetary system

The detection of three planets orbiting the star upsilon Andromedae marks the first discovery of a multiple-planet extrasolar system associated with a main-sequence star (Butler et al. 1999). The unusual arrangement of upsilon Andromedae's planetary companions immediately raises the question of long-term dynamical stability within the system. Focusing on the two outer planets, we have performed a number of extended numerical integrations that indicate that the system experiences extremely chaotic evolution for all regions of parameter space allowed by the observations. Of the three nominal sets of system parameters (reported by Butler et al. 1999), our integrations show that two of the configurations can be dynamically unstable on timescales shorter than the present age of the star. The third reported configuration (representing the nominal Lick parameters) appears to be quite stable. We conclude that there are significant regions of observationally allowed parameter space in which the outer two planets can remain on noncrossing orbits over the present 2-3 Gyr age of the system. Our results also suggest that the overall inclination for the system is likely to be quite low, and hence the objects responsible for the observed velocity signatures are almost certainly planets (rather than brown dwarfs or small stars). The system tends to favor configurations in which the two outer planets exhibit a significant relative inclination (i approximate to 15 degrees-20 degrees) between their two orbital planes. Dynamical studies of this type thus provide useful constraints on the observationally indeterminate properties of the system.