Study of dynamical processes at the final stages of planetary system formation: Resonance motion of giant planets

According to current observational data, planets of many exoplanetary systems have resonant motion. The formation of resonance configurations is studied within a unified model of planetary migration. Planets in the observed systems 24 Sex, HD 37124, HD 73526, HD 82943, HD 128311, HD 160691, Kepler 9, NN Ser, which are moving in the 2: 1 resonance, could have been captured into this resonance due to both the Type I and II migration with a wide range of parameters. The migration conditions are defined for the formation of HD 45364 and HD 200964 that are in the 3: 2 and 4: 3 first-order resonances, correspondingly. The results obtained for HD 200964 show that planets can be captured in the first-order resonances, when the outer-to-inner orbital period ratios for the planets are less than 3: 2, only if Type I migration rates are large, and the mass of at least one planet is substantially less than the modern masses of the observed giant planets. The formation of the HD 102272, HD 108874, HD 181433 and HD 202206 systems with planets in high-order resonances is considered. The capture into these resonances can be realized with very slow Type II migration. Possible bounds for migration parameters are considered. In particular, it has been found that the capture of HD 108874 into the 4: 1 resonance is possible only if the angle between the plane of planetary orbits and the plane of sky is appreciably less than 90°, i.e., the planetary masses are a few times larger than the minimum values. The capture of HD 202206 into the 5: 1 resonance is possible at low migration rates; however, another mechanism is required to explain the high observed eccentricity of the inner planet (for example, strong gravitational interaction between the planets). Resonant configurations can be disrupted due to the interaction between planets and remaining fragments of the planetesimal disk as, for example, may occur in the three-planet system 47 UMa. The specific orbital features observed for this system are explained.