2011A&A...525A..65P

Empirical evidence suggests a tantalising but unproven link between various indicators of solar activity and the barycentric motion of the Sun. The latter is exemplified by transitions between regular and more disordered motion modulated by the motions of the giant planets, and rare periods of retrograde motion with negative orbital angular momentum. An examination of the barycentric motion of exoplanet host stars, and their stellar activity cycles, has the potential of proving or disproving the Sun's motion as an underlying factor in the complex patterns of short- and long-term solar variability indices, by establishing whether such correlations exist in other planetary systems. In either case, these studies may lead to further insight into the nature of the solar dynamo. Some 40 multiple exoplanet systems are now known, all with reasonably accurate orbital elements. The forms and dynamical functions of the barycentric motion of their host stars are examined. These results can be compared with long-term activity indicators of exoplanet host stars, as they become available, to examine whether the correlations claimed for the Sun also exist in other systems. Published orbital elements of multiple exoplanetary systems are used to examine their host star barycentric motions. For each system, we determine analytically the orbital angular momentum of the host star, and its rate of change. A variety of complex patterns of barycentric motions of exoplanet host stars is demonstrated, depending on the number, masses and orbits of the planets. Each of the behavioural types proposed to correlate with solar activity are also evident in exoplanet host stars: repetitive patterns influenced by massive multiple planets, epochs of rapid change in orbital angular momentum, and intervals of negative orbital angular momentum. The study provides the basis for independent investigations of the widely-studied but unproven suggestion that the Sun's motion is somehow linked to various indicators of solar activity. We show that, because of the nature of their barycentric motions, the host stars HD 168443 and HD 74156 offer particularly powerful tests of this hypothesis.