Orbital configurations and dynamical stability of multi-planet systems around Sun-like stars HD 202206, 14 Her, HD 37124 and HD 108874

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Abstract
We perform a dynamical analysis of the recently published radial velocity (RV) measurements of a few solar type stars which host multiple Jupiter-like planets. In particular, we re-analyze the data for HD 202206, 14 Her, HD 37124 and HD 108874. We derive dynamically stable configurations which reproduce the observed RV signals using our method called GAMP (an acronym of the Genetic Algorithm with MEGNO Penalty). The GAMP relies on the N-body dynamics and makes use of genetic algorithms merged with a stability criterion. For this purpose, we use the maximal Lyapunov exponent computed with the dynamical fast indicator MEGNO. Through a dynamical analysis of the phase-space in a neighborhood of the obtained best-fit solutions, we derive meaningful limits on the parameters of the planets. We demonstrate that GAMP is especially well suited for the analysis of the RV data which only partially cover the longest orbital period and/or correspond to multi-planet configurations involved in low-order mean motion resonances (MMRs). In particular, our analysis reveals a presence of a second Jupiter-like planet in the 14 Her system (14 Her c) involved in a 3:1 or 6:1 MMR with the known companion b. We also show that the dynamics of the HD 202206 system may be qualitatively different when coplanar and mutually-inclined orbits of the companions are considered. We demonstrate that the two outer planets in the HD 37124 system may reside in a close neighborhood of the 5:2 MMR. Finally, we found a clear indication that the HD 108874 system may be very close to, or locked in an exact 4:1 MMR.

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