Mean motion resonances with nearby moons: an unlikely origin for the gaps observed in the ring around the exoplanet J1407b

With the use of numerical models, we investigate whether Mean Motion Resonances (MMR) with nearby moons to the J1407b ring system were the cause of the observed 0.0267AU wide gap located at 0.4AU. Only one location of a moon at 0.63AU (corresponding to a 2:1 MMR) was found to form a gap at 0.4AU over short time periods of less than 100yr. However, the proximity of a low mass moon (0.08 Earth masses) caused significant scattering of the outer ring edge at 0.6AU, along with the formation of an additional gap at the 3:2 MMR (0.485 AU), which is not consistent with observations. Further models with moons located at MMR 3:1, 4:1, 7:3 and 5:3 failed to form gaps at 0.4AU for time periods less than 100yr. Instead, gaps were formed in the ring at 3:2 and 2:1 MMR which resulted in gaps at radial locations between 0.44-0.56AU. Additionally, gaps also take longer than one orbital period of J1407b about the primary to form. Given that J1407b is on a highly eccentric orbit and is thought to strongly perturb the ring at apocentre it appears unlikely that gaps form due to MMR with nearby moons as opposed to embedded moons. Including an appropriate total mass of the ring equal to Earth a dampening effect was witnessed on the gap formation process, causing an increase in the time required to open a gap due to MMR. Therefore, we conclude the observed gap at 0.4 AU is unlikely to be caused by MMR with nearby moons.