SIMBAD references

We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 planetary system, using the best-fit orbital solutions by Lovis and coworkers. In the simulations, we show that a triplet Neptunian system is stable for at least 2 Gyr and that the stability would not be greatly influenced even if we varied the planetary masses. In addition, we employ Laplace-Lagrange secular theory to investigate the long-term behavior 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 of the eccentricities are in good agreement with those from direct numerical integrations. We first reveal that the secular periods of the eccentricity, e₁and e₂, are identical. Moreover, we extensively explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet in 0.07 AU≤a≤1.20 AU, to examine the potential asteroid architecture. We underline that there are stable zones lasting for at least 10⁵ yr for low-mass terrestrial planets located between 0.3 and 0.5 AU and between 0.8 and 1.2 AU. We also find that the secular resonances can excite the eccentricities of the terrestrial bodies and that the accumulation or depletion of the asteroid belt is also shaped by orbital resonances of the outer planets; for example, the asteroidal gaps at the 2:1 and 3:2 mean motion resonances with planet c. In a dynamical sense, the proper candidate regions for the existence of potential terrestrial planets or habitable zones are 0.35 AU<a<0.50 AU and 0.80 AU<a<1.00 AU for relatively low eccentricities, implying the possible asteroidal structure in the system.