Capture into mean motion resonance

Abstract: Orbital or mean motion resonance (MMR) occurs when the orbital period ratio between two planets is close to a ratio of small integers. MMR can protect planets from collisions and affects the overall final architecture of the system. Observations of exoplanets have shown that the survival rate of MMR-chains is low, and most systems are near and just wide of an exact MMR. The most common chains are the 2:1 and 3:2 first order mean motion resonances. Theoretical studies have shown that it is easy to capture planets into MMR when considering convergent migration, a natural consequence of planet-disk interactions that leads to MMR capture. However, there are discrepancies when it comes to the survival rate. The first step is to better understand capture into MMR. In this project, we aim to investigate which and how, orbital initial conditions and migration parameters affect capture into MMR. Having a better view of the full parameter space and its effects, one can better constrain theoretical models. Which together with the already known aspects of resonance instabilities could be enough to correctly reproduce observations in the future. In order to study each parameter, I conducted N-body integrations with Rebound on a planar three body system, with varied initial conditions of orbital, planetary and migration parameters. Firstly, in a controlled setting of constant damping timescales, then using a realistic prescription of planetary migration, Type I. During this project I have seen that when varying both planetary mass and damping timescale of the semi-major axis, there is a dependency on mass for capture into MMR. These results confirmed that smaller planetary mass usually results in MMR with smaller separation. Moreover, the damping timescale can alter this; longer damping timescale leads to capture into the first encountered MMR. Whereas planets with short damping timescale cross multiple MMRs before settling into a tighter spaced MMR or becoming unstable. For the Type I migration setting, I find that capture into MMR has no dependency in planetary mass for larger planetary mass and initial surface density. For the largest masses there is no capture into MMR. However, capture into MMR depends on the initial surface density; larger values correspond to faster migration rate and capture into MMR with smaller separation, and more systems in the chaotic zone of overlapping resonances. Furthermore, the numerical results agree with the previously derived analytical prescription, which determines if a capture is possible. The analytical criterion gives a slightly steeper dependency on planetary mass, than what numerical results here show for both constant and Type I migration.