Short-Term Dynamical Interactions Among Extrasolar Planets

Abstract

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. We apply our fitting methods to the GJ876 radial velocity data (Marcy et al. 2001), and argue that the mass factors for the two planets are likely in the 1.25-2.0 range