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. Usingthe recently determined accurate initial condition by Konacki & Wolszczan(2003) who derived the orbital inclinations and the absolute masses of theplanets B and C, we investigate the system stability by long-term, 1Gyr directintegrations. No secular changes of the semi-major axes eccentricities andinclinations appear during such an interval. This stable behavior is confirmedwith the fast indicator MEGNO. The analysis of the orbital stability in theneighborhood of the nominal initial condition reveals that the PSR 1257+12system is localized in a wide stable region of the phase space but close to afew weak 2 and 3-body mean motion resonances. The long term stability isadditionally confirmed by a negligible exchange of the Angular Momentum Deficitbetween the innermost planet A and the pair of the outer planets B and C. Animportant feature of the system that helps sustain the stability is the secularapsidal resonance (SAR) between the planets B and C with the center oflibration about 180deg. We find useful limits on the elements of the innermostplanet A which are otherwise unconstrained by the observations. We also performa preliminary study of the short-term dynamics of massless particles in thesystem.Comment: 9 pages, 13 low resolution figures suitable for astro-ph. Accepted to Astrophysical Journal (11 October 04