ar X iv : a st ro - p h / 06 11 00 8 v 1 3 1 O ct 2 00 6 The Secular Evolution and Dynamical Architecture of the Neptunian Triplet Planetary System

We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 planetary system with the best-fit orbital solutions by Lovis and coworkers (2006). In the simulations, we show that the triplet Neptunian system can be stable at least for 2 Gyr and the stability would not be greatly influenced even if we vary the planetary masses from Neptune-mass to Jupiter-mass. In addition, we employ the Laplace-Lagrange secular theory to investigate the long-term behaviors of the system, and the outcomes demonstrate that this theory can well describe and predict the secular orbital evolution for three Neptune-mass planets, where the secular periods and amplitudes in the eccentricities are in good agreement with those of the direct numerical integrations. We first reveal that the secular periods of the eccentricity e1 and e2 are identical about 8,300 yr, i.e., P1 = P2 ≃ 2π/|g1 − g2| (g1,2 are respectively, the eigenfrequencies of the system), while the secular variation of e3 for the outermost planet has a period of ∼ 18, 200 yr. Moreover, we extensively explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet residing in 0.07 AU ≤ a ≤ 1.20 AU, to examine the asteroid structure in this system. We underline that there are stable zones at least 10 yr for low-mass terrestrial planets locating between 0.3 and 0.5 AU, and 0.8 and 1.2 AU with final eccentricities of e < 0.20. Still, we also find that the secular resonance ν1 and ν2 arising from two inner planets can excite the eccentricities of the terrestrial bodies, and the accumulation or depletion of the asteroid belt are also shaped Purple Mountain Observatory , Chinese Academy of Sciences , Nanjing 210008,China National Astronomical Observatory, Chinese Academy of Sciences,Beijing 100012, China Department of Terrestrial Magnetism, Carnegie Institute of Washington, 5241 Broad Branch Road NW, Washington, DC 20015-1305 National Astronomical Observatory, Mitaka, Tokyo 181-8588,Japan Department of Astronomy, Nanjing University, Nanjing 210093, China