Possible scenarios for eccentricity evolution in the extrasolar planetary system HD 181433

We analyse the dynamics of the multiple planet system HD 181433. This consists of two gas giant planets (bodies c and d) with msini = 0.65 MJup and 0.53 MJup orbiting with periods 975 and 2468 days, respectively. The two planets appear to be in a 5:2 mean motion resonance, as this is required for the system to be dynamically stable. A third planet with mass mb sini = 0.023 MJup orbits close to the star with orbital period 9.37 days. Each planet orbit is significantly eccentric, with current values estimated to be eb = 0.39, ec = 0.27 and ed = 0.47. In this paper we assess different scenarios that may explain the origin of these eccentric orbits, with particular focus on the innermost body, noting that the large eccentricity of planet b cannot be explained through secular interaction with the outer pair. We consider a scenario in which the system previously contained an additional giant planet that was ejected during a period of dynamical instability among the planets. N-body simulations are presented that demonstrate that during scattering and ejection among the outer planets a close encounter between a giant and the inner body can raise eb to its observed value. Such an outcome occurs with a frequency of a few percent. We also demonstrate, however, that obtaining the required value of eb and having the two surviving outer planets land in 5:2 resonance is a rare outcome, leading us to consider alternative scenarios involving secular resonances. We consider the possibility that an undetected planet in the system increases the secular forcing of planet b by the exterior giant planets, but we find that the resulting eccentricity is not large enough to agree with the observed one. We also consider a scenario in which the spin-down of the central star causes the system to pass through secular resonance. In its simplest form this latter scenario fails to produce the system observed today, with the mode of failure depending sensitively on the rate of stellar spin-down. For spin-down rates above a critical value, planet b passes through the resonance too quickly, and the forced eccentricity only reaches maximum values eb ≃ 0.25. Spin-down rates below the critical value lead to longterm capture of planet b in secular resonance, driving the eccentricity toward unity. If additional short-period low mass planets are present in the system, however, we find that mutual scattering can release planet b from the secular resonance, leading to a system with orbital parameters similar to those observed today.