K2-19b and c are in a 3:2 Commensurability but out of Resonance: A Challenge to Planet Assembly by Convergent Migration

Abstract

K2-19b and c were among the first planets discovered by NASA's K2 mission and together stand in stark contrast with the physical and orbital properties of the solar system planets. The planets are between the size of Uranus and Saturn at 7.0 ± 0.2 R ⊕ and 4.1 ± 0.2 R ⊕ , respectively, and reside a mere 0.1% outside the nominal 3:2 mean-motion resonance. They represent a different outcome of the planet formation process than the solar system, as well as the vast majority of known exoplanets. We measured the physical and orbital properties of these planets using photometry from K2 , Spitzer , and groundbased telescopes, along with radial velocities from Keck/HIRES. Through a joint photodynamical model, we found that the planets have moderate eccentricities of e ≈ 0.20 and well-aligned apsides ∆ ≈ 0 deg. The planets occupy a strictly non-resonant configuration: the resonant angles circulate rather than librate. This defies the predictions of standard formation pathways that invoke convergent or divergent migration, both of which predict ∆ ≈ 180 deg and eccentricities of a few percent or less. We measured masses of M p,b = 32.4 ± 1.7 M ⊕ and M p,c = 10.8 ± 0.6 M ⊕ . Our measurements, with 5% fractional uncertainties, are among the most precise of any sub-Jovian exoplanet. Mass and size reflect a planet's core/envelope structure. Despite having a relatively massive core of M core ≈ 15 M ⊕ , K2-19b is envelope-rich, with an envelope mass fraction of roughly 50%. This planet poses a challenge to standard models core-nucleated accretion, which predict that cores 10 M ⊕ will quickly accrete gas and trigger runaway accretion when the envelope mass exceeds that of the core.

Tidal Inflation Reconciles Low-density Sub-Saturns with Core Accretion

“…The mean and 1σ range of f env,0 inferred when neglecting tides are shown with the gray line and bar. The tides-free envelope fraction estimates are f env,0 =44.2%±2.8% for K2-19 b and f env,0 =14.2%±2.0% for K2-19 c, which are both consistent with the estimates from Petigura et al (2020). The agreement is reassuring, given that these estimates were obtained with two distinct core-envelope models.…”

“…Many sub-Saturns have such large radii and low masses that standard core-envelope structural models have suggested that they must have massive atmospheric envelopes comprising ∼50% of their total mass (e.g., Petigura et al 2018aPetigura et al , 2020Addison et al 2020). This posed a problem for the theory of core accretion, which dictates that planets undergo runaway gas accretion when their envelope mass reaches their core mass.…”

“…We begin with a case study of the K2-19 system, since the recent analysis of this system by Petigura et al (2020) was the motivation for this work, and the planetary masses and radii have been constrained at the ∼5% level. The system contains three known transiting planets: two sub-Saturns K2-19 b and c, with orbital periods of 7.9 days and 11.9 days, respectively, as well as K2-19 d, a close-in Earth-size planet at 2.5 days.…”

“…Using interpolation to the Lopez & Fortney (2014) coreenvelope planet model grid (which does not include tidal heating), Petigura et al (2020) estimated that planets b and c have large envelope mass fractions, f env,b =44%±3% and f env,c =14%±1%. As discussed in the introduction, planet b's near-50% inferred envelope fraction presents a particular challenge to core accretion theory.…”

A Tidal Origin for a Three-body Resonance in Kepler-221

“…In exceptional cases, important additional insight into the orbital machinery of a given system can be gleaned from combined transit timing analysis and radial velocity measurements (Petigura et al 2018(Petigura et al , 2020. Direct characterization aside, however, a thornier question concerns how orbital layouts of extrasolar planets arise in the first place.…”