NEAR 3:2 AND 2:1 MEAN MOTION RESONANCE FORMATION IN THE SYSTEMS OBSERVED BYKEPLER

Abstract

The Kepler mission has released ∼ 4229 transiting planet candidates. There are approximately 222 candidate systems with three planets. Among them, the period ratios of planet pairs near 1.5 and 2.0 reveal that two peaks exist for which the proportions of the candidate systems are ∼ 7.0% and 18.0%, respectively. In this work, we study the formation of mean motion resonance (MMR) systems, particularly for the planetary configurations near 3:2 and 2:1 MMRs, and we concentrate on the interplay between the resonant configuration and the combination of stellar accretion rate, stellar magnetic field, speed of migration and additional planets. We perform more than 1000 runs by assuming a system with a solar-like star and three surrounding planets. From the statistical results, we find that under the formation scenario, the proportions near 1.5 and 2.0 can reach 14.5% and 26.0%, respectively. In addition,Ṁ = 0.1 × 10 −8 M ⊙ yr −1 is propitious toward the formation of 3:2 resonance, whereasṀ = 2 × 10 −8 M ⊙ yr −1 contributes to the formation of 2:1 resonance. The speed-reduction factor of type I migration f 1 ≥ 0.3 facilitates 3:2 MMRs, whereas f 1 ≥ 0.1 facilitates 2:1 MMRs. If additional planets are present in orbits within the innermost or beyond the outermost planet in a three-planet system, 3:2:1 MMRs can be formed, but the original systems trapped in 4:2:1 MMRs are not affected by the supposed planets. In summary, we conclude that this formation scenario will provide a likely explanation for Kepler candidates involved in 2:1 and 3:2 MMRs.

Terrestrial planet formation under migration: systems near the 4:2:1 mean motion resonance

“…However, as a comparison, if they are initially in a compact configuration, the probability of the forming planets in 2:1 MMRs will significantly decrease. As shown in the work of Wang & Ji (2014), they found that if the planets pairs were initially in compact configuration at the separations of ∼ 15 Hill radius, the probability of 2:1 MMRs decreased to 10% in 50 runs and there was no simulation that three planets were evolved into 4:2:1 MMRs. Secondly, in our simulations we slow down the speed of type I migration for low-mass planets, and this could further explain why two planets are fairly easier to be trapped into 2:1 MMRs.…”

Dynamical instability and its implications for planetary system architecture

“…The observed period ratios between adjacent pairs (Figure 1) show that most of the period ratios are smaller than three, and there is a pile-up of period ratios around the 3:2 and 2:1 mean motion resonances (MMRs). The existence of planet pairs near first-order MMRs is often ascribed to disk migration (Snellgrove et al 2001;Lee & Peale 2002;Lee & Thommes 2009;Wang & Ji 2014). However, we might expect the overabundance to be larger if disk migration is common, though Pan & Schlichting (2017) suggested that resonance zhoujl@nju.edu.cn † jason.steffen@unlv.edu 1 https://exoplanetarchive.ipac.caltech.edu capture is more difficult for smaller planets in a disk.…”

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

“…Convergent migration in protoplanetary discs is an effective and popular MMR formation mechanism (Snellgrove et al 2001), and can also achieve three-body resonances (Peale & Lee 2002;Libert & Tsiganis 2011), although some MMRs are harder to lock into than others (Rein et al 2012; Tadeu dos Santos et al 2015). Forming the 3:2 MMR in particular through energy dissipation has been widely investigated (Papaloizou & Szuszkiewicz 2005;Hadjidemetriou & Voyatzis 2010;Emel'yanenko 2012;Ogihara & Kobayashi 2013;Wang & Ji 2014;Zhang et al 2014). Capture into MMRs through gravitational scattering alone -after the dissipation of the protoplanetary disc -occurs relatively rarely (Raymond et al 2008).…”