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

Abstract

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 0.0267 wide gap located at 0.4 . Only one location of a moon at 0.63 (corresponding to a 2:1 MMR) was found to form a gap at 0.4 over short time periods of < 100 . However, the proximity of a low mass moon (0.08 ⊕ ) caused significant scattering of the outer ring edge at 0.6 , along with the formation of an additional gap at the 3:2 MMR (0.485 ), which is not consistent with observations. Further models with moons located at MMR's 3:1, 4:1, 7:3 and 5:3 failed to form gaps at 0.4 for time periods < 100 . Instead, gaps were formed in the ring at 3:2 and 2:1 MMR's which resulted in gaps at radial locations between 0.44 − 0.56 . 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's 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's. Therefore, we conclude the observed gap at 0.4 is unlikely to be caused by MMR's with nearby moons.

A Self-Gravitating Exoring Around J1407b and Implications for In-Situ Exomoon Formation

“…We use the same ring model as used by Sutton (2019), which placed 10,000 particles around the exoplanet J1407b. Ring particles are distributed in the radial direction between 0.2AU < r < 0.6AU to produce a surface density profile Σ ∝ 1/r, which is a commonly used profile in models of astrophysical disks.…”

“…Three possible mechanisms can form a gap in a planetary ring: The first is due to Mean Motion Resonances (MMR) by moons external to the ring and is analogous to how Mimas causes the Cassini Division in Saturn's rings (Goldreich and Tremaine 1978;Noyelles et al, 2016). However, models of moons placed at various MMR's around J1407b's ring showed this was not possible without causing significant disruption to the outer region of the ring edge (Sutton 2019). Secondly, moons embedded within the ring can carve out a gap proportional to their Hill radius.…”

ALMA and NACO observations towards the young exoring transit system J1407 (V1400 Cen)

“…Circular orbits are strongly ruled out with these studies and the diameter of the ring system model, along with the detailed small-scale structure deduced from nightly flux variations, makes it very challenging to explain the apparent stability and coherence of the rings (Zanazzi & Lai 2017;Rieder & Kenworthy 2016). Another challenge is whether the ring gaps are caused by mean-motion resonances (MMRs) or by direct clearing, and the elliptical orbit at periastron disfavours the MMR hypothesis (Sutton 2019). With the central massive object undetected, we turn to detecting the thermal radiation from the rings themselves.…”

The Structure and Stability of Extended, Inclined Circumplanetary Disk or Ring Systems

“…The J1407b system has since been the subject of a number of subsequent studies, which have refined the simple ring model to accurately fit the reduced light curve (Van Werkhoven et al 2014;Kenworthy & Mamajek 2015), placed constraints on the mass and period of the companion (Kenworthy et al 2014;Mentel et al 2018), constrained the radial extent of the disk (Rieder & Kenworthy 2016), and explored whether the rapid flux variations in J1407's light curve can be attributed gaps opened by mean motion resonances with nearby moons (Sutton 2019). The best fitting ring model presented in Mamajek et al (2012) is flat, inclined with respect to the companion's orbital plane by 24.2 • , and very extended, with an outer radius of r out ∼ 0.6 au.…”