The orbital configuration of the two interacting Jupiters in HD 155358 system
Ma et al
Recent observation reveals two interacting Jupiters possibly trapped in a 2:1 mean motion resonance (MMR) around the star HD 155358. For the 2:1 MMR, Beaugé et al. found that as long as the orbital decay was sufficiently slow, the trapped planets should also be in apsidal co-rotation. So it is very interesting to explore whether HD 155358 did undergo such an evolution and presents an apsidal co-rotation. Based on the existing results of spectroscopic orbital determination, the global dynamics of the system shows that the two planets are in an apsidal co-rotation if the eccentricity of the outer planet (ec) takes values very close to the lower limit of its 1σ confidence interval. This makes us conjecture that the globally minimizing solution could be missed in the previous orbital determination. Using an efficient global optimization method, we do find a better solution, reducing χ2 from 1.4 to 1.2. This new solution is significantly different from the previous one, and in particular, with smaller ec. However, the increased possibility for the system to be trapped in a 2:1 MMR with apsidal co-rotation is still not high. A set of simulations of the adiabatic convergent migration process are then performed. The results consistently indicate that the 2:1 MMR forms before apsidal co-rotation. Finally, the long-term stability of the formed system and of its resonant structure are extensively explored, and the resulting statistics are given. A conclusion is that the 2:1 MMR with apsidal co-rotation is a very stable structure.