Formation and evolution of the two 4/3 resonant giants planets in HD 200964

Abstract

Context. It has been suggested that HD 200964 is the first exoplanetary system with two Jovian planets evolving in the 4/3 mean-motion resonance (MMR). Previous scenarios to simulate the formation of two giant planets in the stable 4/3 resonance configuration have failed. Moreover, the orbital parameters available in the literature point out an unstable configuration of the planetary pair. Aims. The purpose of this paper is i) to determine the orbits of the planets from the radial velocity measurements and update the value of the stellar mass (1.57 M•); ii) to analyse the stability of the planetary evolution in the vicinity and inside the 4/3 MMR; and iii) to elaborate a possible scenario for the formation of systems in the 4/3 MMR. Methods. We use a previous model to simulate the formation of the stable planetary pair trapped inside the 4/3 resonance. Our scenario includes an interaction between the type I and type II of migration, planetary growth and stellar evolution from the main sequence to the sub-giant branch. The redetermination of the orbits is done using a biased Monte Carlo procedure, while the planetary dynamics is studied using numerical tools, such as dynamical maps and dynamical power spectra. Results. The results of the formation simulations are able to very closely reproduce the 4/3 resonant dynamics of the best-fit configuration obtained in this paper. Moreover, the confidence interval of the fit matches well with the very narrow stable region of the 4/3 MMR. Conclusions. The formation process of the HD 200964 system is very sensitive to the planetary masses and protoplanetary disk parameters. Only a thin, flat disk allows the embryo-sized planets to reach the 4/3 resonant configuration. The stable evolution of the resonant planets is also sensitive to the mass of the central star, because of overlapping high-order resonances inside the 4/3 resonance. Regardless of the very narrow domain of stable motion, the confidence interval of our fit closely matches the stability area.