Resonant structure, formation and stability of the planetary system HD 155358

Resonant structure, formation and stability of the planetary system HD155358

Authors:

Silburt et al

Abstract:

Two Jovian-sized planets are orbiting the star HD155358 near exact mean motion resonance (MMR) commensurability. In this work we re-analyze the radial velocity (RV) data previously collected by Robertson et al. (2012). Using a Bayesian framework we construct two models - one that includes and one that excludes gravitational planet-planet interactions (PPI). We find that the orbital parameters from our PPI and noPPI models differ by up to 2σ, with our noPPI model being statistically consistent with previous results. In addition, our new PPI model strongly favours the planets being in MMR while our noPPI model strongly disfavours MMR. We conduct a stability analysis by drawing samples from our PPI model's posterior distribution and simulating them for 109 years, finding that our best-fit values land firmly in a stable region of parameter space.

We explore a series of formation models that migrate the planets into their observed MMR. We then use these models to directly fit to the observed RV data, where each model is uniquely parameterized by only three constants describing its migration history. Using a Bayesian framework we find that a number of migration models fit the RV data surprisingly well, with some migration parameters being ruled out.

Our analysis shows that planet-planet interactions are important to take into account when modelling observations of multi-planetary systems. The additional information that one can gain from interacting models can help constrain planet migration parameters.

HD 155358's Interacting Gas Giants

The orbital configuration of the two interacting Jupiters in HD 155358 system
Authors:

Ma et al

Abstract:
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.

On the orbital evolution of a pair of giant planets in mean motion resonance

On the orbital evolution of a pair of giant planets in mean motion resonance

Authors:

André et al

Abstract:

Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1 resonance occurring most frequently. Disc-planet interaction provides a mechanism for their origin. However, the time scale on which this could operate in particular cases is unclear. We perform 2D and 3D numerical simulations of pairs of giant planets in a protoplanetary disc as they form and maintain a mean motion commensurability. We consider systems with current parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and disc models of varying mass, decreasing mass corresponding to increasing age. For the lowest mass discs, systems with planets in the Jovian mass range migrate inwards maintaining a 2:1 commensurability. Systems with the inner planet currently at around 1 au from the central star could have originated at a few au and migrated inwards on a time scale comparable to protoplanetary disc lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1 resonance as observed. For a given mass accretion rate, results are insensitive to the disc model for the range of viscosity prescriptions adopted, there being good agreement between 2D and 3D simulations. However, in a higher mass disc a pair of Jovian mass planets passes through 2:1 resonance before attaining a temporary phase lasting a few thousand orbits in an unstable 5:3 resonance prior to undergoing a scattering. Thus finding systems in this commensurability is unlikely.