Stability and chaos in the upsilon andromedae planetary system

The detection of three planets orbiting the star upsilon Andromedae marks t he first discovery of a multiple-planet extrasolar system associated with a main-sequence star (Butler et al. 1999). The unusual arrangement of upsilo n Andromedae's planetary companions immediately raises the question of long -term dynamical stability within the system. Focusing on the two outer plan ets, we have performed a number of extended numerical integrations that ind icate that the system experiences extremely chaotic evolution for all regio ns of parameter space allowed by the observations. Of the three nominal set s of system parameters (reported by Butler et al. 1999), our integrations s how that two of the configurations can be dynamically unstable on timescale s shorter than the present age of the star. The third reported configuratio n (representing the nominal Lick parameters) appears to be quite stable. We conclude that there are significant regions of observationally allowed par ameter space in which the outer two planets can remain on noncrossing orbit s 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 henc e the objects responsible for the observed velocity signatures are almost c ertainly planets (rather than brown dwarfs or small stars). The system tend s to favor configurations in which the two outer planets exhibit a signific ant relative inclination (i approximate to 15 degrees-20 degrees) between t heir two orbital planes. Dynamical studies of this type thus provide useful constraints on the observationally indeterminate properties of the system.