Abstract
TOI-216 is a pair of close-in planets with orbits deep in the 2:1 mean motion resonance. The inner Neptune-class planet (TOI-216b) is near 0.12 au (orbital period P (b) similar or equal to 17 days) and has a substantial orbital eccentricity (e (b) similar or equal to 0.16) and large libration amplitude (A ( psi ) similar or equal to 60 degrees) in the resonance.
The outer planet (TOI-216c) is a gas giant on a nearly circular orbit. We carry out N-body simulations of planet migration in a protoplanetary gas disk to explain the orbital configuration of TOI-216 planets.
We find that TOI-216b's migration must have been halted near its current orbital radius to allow for a convergent migration of the two planets into the resonance. For the inferred damping-to-migration timescale ratio tau ( e )/tau ( a ) similar or equal to 0.02, overstable librations in the resonance lead to a limit cycle with A ( psi ) similar or equal to 80 degrees and e (b) < 0.1.
The system could have remained in this configuration for the greater part of the protoplanetary disk lifetime. If the gas disk was removed from inside out, this would have reduced the libration amplitude to A ( psi ) similar or equal to 60 degrees and boosted e (b) via the resonant interaction with TOI-216c.
Our results suggest a relatively fast inner-disk removal (similar to 10(5) yr). Another means of explaining the large libration amplitude is stochastic stirring from a (turbulent) gas disk.
For that to work, overstable librations would need to be suppressed, tau ( e )/tau ( a ) similar or equal to 0.05, and very strong turbulent stirring (or some other source of large stochastic forcing) would need to overcome the damping effects of gas. Hydrodynamical simulations can be performed to test these models.