Secular Evolution of HD 12661: A System Caught at an Unlikely Time

TL;DR

This study investigates the long-term orbital evolution of the HD 12661 planetary system, revealing large eccentricity oscillations and suggesting possible past perturbations or additional unseen planets affecting its current state.

Contribution

The paper combines radial velocity data with MCMC sampling and n-body simulations to explore the secular evolution of HD 12661, highlighting the system's dynamic behavior and potential influences from other planets.

Findings

Outer planet's eccentricity oscillates widely over time.

Weak mean motion resonances do not dominate the evolution.

System may be observed in a rare orbital state or influenced by unseen planets.

Abstract

The eccentricity evolution of multiple planet systems can provide valuable constraints on planet formation models. Unfortunately, the inevitable uncertainties in the current orbital elements can lead to significant ambiguities in the nature of the secular evolution. Integrating any single set of orbital elements inadequately describes the full range of secular evolutions consistent with current observations. Thus, we combine radial velocity observations of HD 12661 with Markov Chain Monte Carlo sampling to generate ensembles of initial conditions for direct n-body integrations. We find that any mean motion resonances are quite weak and do not significantly impact the secular evolution, and that current observations indicate circulation or large amplitude libration of the periapses. The eccentricity of the outer planet undergoes large oscillations for nearly all of the allowed two-planet orbital solutions. This type of secular evolution would arise if planet c had been impulsively perturbed, perhaps due to strong scattering of an additional planet that was subsequently accreted onto the star. Finally, we note that the secular evolution implied by the current orbital configuration implies that planet c spends ~96% of the time following an orbit more eccentric than that presently observed. Either this system is being observed during a relatively rare state, or additional planets are affecting the observed radial velocities and/or the system's secular eccentricity evolution.