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 that host multiple Jupiter-like planets. In particular, we reanalyze the data for HD 202206, 14 Her, HD 37124, and HD 108874. We derive dynamically stable configurations that reproduce the observed RV signals, using GAMP (the genetic algorithm with MEGNO penalty). GAMP relies on 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 to the analysis of the RV data that only partially cover the longest orbital period and/or are related to multiplanet configurations involved in low-order mean motion resonances (MMRs). Our analysis reveals a presence of a second Jupiter-like planet in the 14 Her system (14 Her c) that is involved in a 3:1 or 6:1 MMR with the known companion 14 Her 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. Our results confirm that the HD 108874 system may be very close to a, or locked in an exact, 4:1 MMR.