Zsuzsanna Tóth, Imre Nagy
Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four certain planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is supported by the latest analysis of the radial velocity (RV) measurements. Vogt et al. (AN 333, 561-575, 2012) announced a 4- and a 5-planet model fitted to the RV curve with forced circular orbits. To characterize stability, we used the maximum eccentricity the planets reached over the time of the integrations and the Lyapunov Characteristic Indicator to identify chaotic motion. The integration of the 4-planet model shows that it is stable even for i = 5{\deg}, i. e. high planetary masses, on a longer timescale. The innermost low-mass planet e, which quickly became unstable in earlier eccentric models, remained stable, although the stable region around its initial semi-major axis and eccentricity is rather small. In the 4-planet model, we looked for stable regions for a fifth planetary body. We found extensive stable regions between the two super-Earth sized planets c and d, and beyond planet d. The Titius-Bode law and its revised version, Ragnarsson's formula applied to the Gliese 581 planetary system both predict distances of additional planets in these stable regions. The planet Gliese 581 g would have a dynamically stable orbit, even for a wider range of orbital parameters. Since circular orbits in the models seem to be a too strong restriction and the true orbits might be elliptic, we investigated the stability of the planets as a function of their eccentricity, and derived dynamical constraints for the ellipticity of the orbits.
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http://arxiv.org/abs/1302.1322
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