Long term stability and dynamical environment of the PSR 1257+12 planetary system

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  • 27 October 2003
Abstract
We study the long-term dynamics of the PSR 1257+12 planetary system. Using the recently determined accurate initial condition by Konacki & Wolszczan (2003) who derived the orbital inclinations and the absolute masses of the planets, we investigate the system stability by long-term, 1Gyr direct integrations. No secular changes of the semi-major axes, eccentricities and inclinations appear during such an interval. This stable behavior is confirmed with the fast indicator MEGNO. Another feature confirming the long term stability is a negligible exchange of the Angular Momentum Deficit between the innermost planet A and the pair of the outer planets B and C. An important factor for maintaining the stability is also the presence of the secular apsidal resonance (SAR) between the planets B and C with the center of libration about 180deg. We perform a preliminary study of the short-term dynamics of massless particles in the system. It uncovers a relatively extended stable zone between the planets A and B. Beyond the planet C, the stable zone starts already at distances 0.5AU from the parent star. For moderately low eccentricities, beyond 1AU, the motion of massless particles is basically stable, independent on the inclinations of the orbits. It is a very encouraging result supporting the search for a putative dust disk or a Kuiper belt, especially with the SIRTF mission.

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