Orbital Configurations and Dynamical Stability of Multiplanet Systems around Sun‐like Stars HD 202206, 14 Herculis, HD 37124, and HD 108874

We perform a dynamical analysis of the recently published radial velocity(RV) measurements of a few solar type stars which host multiple Jupiter-likeplanets. In particular, we re-analyze the data for HD 202206, 14 Her, HD 37124and HD 108874. We derive dynamically stable configurations which reproduce theobserved RV signals using our method called GAMP (an acronym of the GeneticAlgorithm with MEGNO Penalty). The GAMP relies on the N-body dynamics and makesuse of genetic algorithms merged with a stability criterion. For this purpose,we use the maximal Lyapunov exponent computed with the dynamical fast indicatorMEGNO. Through a dynamical analysis of the phase-space in a neighborhood of theobtained best-fit solutions, we derive meaningful limits on the parameters ofthe planets. We demonstrate that GAMP is especially well suited for theanalysis of the RV data which only partially cover the longest orbital periodand/or correspond to multi-planet configurations involved in low-order meanmotion resonances (MMRs). In particular, our analysis reveals a presence of asecond Jupiter-like planet in the 14 Her system (14 Her c) involved in a 3:1 or6:1 MMR with the known companion b. We also show that the dynamics of the HD202206 system may be qualitatively different when coplanar andmutually-inclined orbits of the companions are considered. We demonstrate thatthe two outer planets in the HD 37124 system may reside in a close neighborhoodof the 5:2 MMR. Finally, we found a clear indication that the HD 108874 systemmay be very close to, or locked in an exact 4:1 MMR.