Eugenio J. Rivera

A Pair of Resonant Planets Orbiting GJ 876

Precise Doppler measurements during 6 yr from the Lick and Keck observatories reveal two planets orbiting GJ 876 (M4V). The orbital Ðt yields companion masses of M sin i \ 0.56 and 1.89 orbital M J , periods of P \ 30.1 and 61.0 days, semimajor axes of a \ 0.13 and 0.21 AU, and eccentricities of e \ 0.28 and 0.10, respectively. The orbital periods are nearly in the ratio of 2:1, unprecedented among major planets but common among moons and asteroids. Moreover, the axes of the elliptical orbits appear to be nearly aligned. The inner companion was not recognized previously owing to the 2:1 ratio of periods, which allowed its signature to masquerade as added orbital eccentricity of the outer planet. Dynamical simulations show that the system is stable within a subset of the observed orbital parameters. The stability may be provided by a mean-motion resonance and the apparent alignment of the major axes. These planets pose unsolved questions about their formation and dynamical evolution, which brought them within 0.08 AU of each other and locked them in resonance. Subject headings : planetary systems E stars : individual (GJ 876)

Stability Analysis of the Planetary System Orbiting Upsilon Andromedae

We present numerical orbital integrations designed to test the stability of the three planets detected in orbit around υ Andromedae and possible smaller bodies orbiting in the system which have not yet been discovered. We find that some configurations are stable for at least 109 yr, whereas in other configurations planets can be ejected into interstellar space or crash into the star in less than 105 yr. The typical path to instability involves the outer planet exciting the eccentricity of the middle planets orbit to such high values that it ventures close to the inner planet. In some stable systems, a secular resonance between the outer two planets prevents close approaches between them by aligning their longitudes of periastron. In relatively stable systems, test particles can survive for long times between the inner and middle planets as well as several AU exterior to the outer planet, but we could find no stable orbits between the middle and outer planets.

Dynamical Models of the Resonant Pair of Planets Orbiting the Star GJ 876

We present two planet fits to the radial velocity measurements of the M dwarf star GJ 876 that account for the mutual perturbations between the planets, as well as their interactions with the star. We also give the results of long-term integrations testing the stability of some of our best-fit systems. Our Newtonian models fit the data much better than do Keplerian models, reducing the χ from 1.88 to as low as 1.34 for an unstable high-inclination system and 1.43 for a stable low-inclination system. Several different local minima with comparable χ are found in parameter space; thus, our results are not able to provide tight constraints on the inclinations of the orbits to the line of sight and actual planetary masses. Most sets of planetary parameters that we have derived represent systems that are stable for at least 108 yr. Test particles orbiting between the two planets within our best-fit planar system are lost in less than 300 yr.