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Fig. 4


Stability analysis of the nominal fit of the HD 219828 planetary system (Table 5). For fixed initial conditions, the phase space of the system is explored by varying the semi-major axis ab and eccentricity eb of the inner planet. The step size is 10-2 in eccentricity, and 5 × 10-3 (top) or 2 × 10-4 AU (bottom) in semi-major axis. For each initial condition, the system is integrated over 103 yr and a stability criterion is derived with the frequency analysis of the mean longitude (Laskar 1990, 1993). As in Correia et al. (2005, 2009, 2010), the chaotic diffusion is measured by the variation in the frequencies. The red zone corresponds to highly unstable orbits, while the dark blue region can be assumed to be stable on a billion-year timescale.

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