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Fig. 7


Stability analysis of the WASP-148 planetary system, assuming coplanar orbits. For fixed initial conditions, the phase space of the system is explored by varying the semimajor axis ac and eccentricity ec of the outer planet WASP-148c. The step size is 10−2 in eccentricity and 10−3 in semimajor axis. For each initial conditions, the system is integrated over 50 kyr, and a stability criterion is derived with the frequency analysis of the mean longitude. The chaotic diffusion is measured by the variation in the frequencies. The color scale corresponds to values between − 9 (black) and − 3 (red) for the decimal logarithm of the stability index D used in Correia et al. (2010). The red zone corresponds to highly unstable orbits, while the dark blue region can be assumed to be stable on a billion-year timescale. The reduced-χ2 level curves of the Newtonian fit are also plotted.

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