ar X iv : a st ro - p h / 03 10 75 0 v 1 2 7 O ct 2 00 3 Long term stability and dynamical environment of the PSR 1257 + 12 planetary system

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, 1 Gyr 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. The analysis of the orbital stability in the neighborhood of the nominal initial condition reveals that the PSR 1257+12 system is localized in a wide stable region of the phase space. 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 180 o. SAR has been recently found in many extrasolar systems discovered by the radial velocity surveys (Ji et al. 2003). The fact that it is present both in planetary systems around main-sequence stars and around a neutron star may suggest that it is a common dynamical feature of exosystems. We also 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 0.5 AU from the parent 1 – 2 – star. For moderately low eccentricities, beyond 1 AU, the motion of massless particles does not suffer from strong instabilities and this zone is basically stable, independent on the inclinations of the orbits of the test particles to the mean orbital plane of the system. It is a very encouraging result supporting the search for a putative dust disk or a Kuiper belt, especially with the SIRTF mission.