The Upsilon Andromedae System: Models and Stability
  Radial velocity observations of the F8 V star Upsilon Andromedae taken at Lick and at Whipple Observatories have revealed evidence of three periodicities in the line-of-sight velocity of the star. These periodicities have been interpreted as evidence for at least three low mass companions (LMCs) revolving around Upsilon Andromedae. The mass and orbital parameters inferred for these companions raise questions about the dynamical stability of the system. We report here results from our independent analysis of the published radial velocity data as well as new unpublished data taken at Lick Observatory. Our results confirm the finding of three periods in the data. Our best fits to the data, on the assumption that these periods arise from the gravitational perturbations of companions in keplerian orbits, is also generally in agreement, but with some differences, from the earlier findings. We find that the available data do not constrain well the orbital eccentricity of the middle companion in a three-companion model of the data. We also find that in order for our best-fit model to the Lick data to be dynamically stable over the lifetime of the star (~2 billion years), the system must have a mean inclination to the plane of the sky greater than 13 degrees. The corresponding minimum inclination for the best fit to the Whipple data set is 19 degrees. These values imply that the maximum mass for the outer companion can be no greater than about 20 Jupiter masses. Our analysis of the stability of the putative systems also places constraints on the relative inclinations of the orbital planes of the companions. We comment on global versus local (i.e., method of steepest descent) means of finding best-fit orbits from radial velocity data sets. 
Tomasz F. Stepinski, Renu Malhotra and David C. Black