A Dynamical Analysis of the Kepler-80 System of Five Transiting Planets

Abstract

Kepler has discovered hundreds of systems with multiple transiting exoplanets which hold tremendous potential both individually and collectively for understanding the formation and evolution of planetary systems. Many of these systems consist of multiple small planets with periods less than ∼50 days known as Systems with Tightly-spaced Inner Planets, or STIPs. One especially intriguing STIP, Kepler-80 (KOI-500), contains five transiting planets: f, d, e, b, and c with periods of 1.0, 3.1, 4.6, 7.1, 9.5 days, respectively. We provide measurements of transit times and a transit timing variation (TTV) dynamical analysis. We find that TTVs cannot reliably detect eccentricities for this system, though mass estimates are not affected. Restricting the eccentricity to a reasonable range, we infer masses for the outer four planets (d, e, b, and c) to be 6.75 −0.86 Earth masses, respectively. The similar masses but different radii are consistent with terrestrial compositions for d and e and ∼2% H/He envelopes for b and c. We confirm that the outer four planets are in a rare dynamical configuration with four interconnected three-body resonances that are librating with few degree amplitudes. We present a formation model that can reproduce the observed configuration by starting with a multi-resonant chain and introducing dissipation. Overall, the information-rich Kepler-80 planets provide an important perspective into exoplanetary systems.

The K2-138 System: A Near-resonant Chain of Five Sub-Neptune Planets Discovered by Citizen Scientists

“…Like TRAPPIST-1, K2-138 may Another notable feature of the TRAPPIST-1 system is that the seven known planets form a complex chain of linked three-body Laplace resonances (Luger et al 2017). Similarly, Kepler-80 (KOI-500) is a five-planet system where the four outer planets form a tightly linked pair of three-body resonances (Lissauer et al 2011;MacDonald et al 2016); Kepler-223, described above, also contains a pair of three-body resonances. One other system, Kepler-60, appears to be in either a true three-body Laplace resonance or a chain of two-planet mean motion resonances (Goździewski et al 2016).…”

“…In simulating the Kepler-80 system, MacDonald et al (2016) find that their migration simulations can naturally describe the final system architecture, with dissipative forces pushing the interlocked planets out of two-body resonances and into three-body resonances; the K2-138 system may have undergone something similar. K2-138 joins a relatively modest population of known systems with four or more planets in or close to a resonant chain, and a very small population of systems with interlocking chains of three-body resonances, making it an ideal target to study for TTVs.…”

The Compositional Diversity of Low-Mass Exoplanets

“…In such cases, the ratio of the planetary masses may well be better constrained than the individual masses, since this depends only on the ratio of periods and TTV amplitudes. Furthermore, even where the TTV phases tightly constrain the difference in eccentricity vectors between neighboring planets, individual eccentricities are often poorly constrained, such that adding the same eccentricity vector to an interacting pair of planets has little effect on the TTVs (Jontof-Hutter et al 2015, 2016bMacDonald et al 2016). In such cases, individual eccentricities are limited only by our prior expectation that, in compact multiplanet systems, they ought to be small.…”

Breaking Resonant Chains: Destabilization of Resonant Planets Due to Long-term Mass Evolution

“…In particular, the information about orbital resonances provides useful constraints (Ogihara et al 2018). Although several planetary systems are in chains of resonances (Mills et al 2016;MacDonald et al 2016;Gillon et al 2017), most multiple-planet systems are not (Fabrycky et al 2014;Winn & Fabrycky 2015). The number of planets in resonant chains are between four and seven, which is larger than the average number of Kepler planets (3.0 ± 0.3, Zhu et al 2018).…”

“…We can also discuss the origin of the observed systems in resonant chains. Most of the observed planets in resonant chains are located at 0.1 au (Mills et al 2016;MacDonald et al 2016;Jontof-Hutter et al 2016;Gillon et al 2017). These planets received strong stellar radiation, which causes planetary mass loss.…”