Dynamics and Formation of the Near-resonant K2-24 System: Insights from Transit-timing Variations and Radial Velocities

While planets between the size of Uranus and Saturn are absent within the solar system, the star K2-24 hosts two such planets, K2-24b and c, with radii equal to 5.4 R⊕ and 7.5 R⊕, respectively. The two planets have orbital periods of 20.9 days and 42.4 days, residing only 1% outside the nominal 2:1 mean-motion resonance. In this work, we present results from a coordinated observing campaign to measure planet masses and eccentricities that combines radial velocity measurements from Keck/HIRES and transit-timing measurements from K2 and Spitzer. K2-24b and c have low, but nonzero, eccentricities of e_1 ~ e_2 ~ 0.08. The low observed eccentricities provide clues to the formation and dynamical evolution of K2-24b and K2-24c, suggesting that they could be the result of stochastic gravitational interactions with a turbulent protoplanetary disk, among other mechanisms. K2-24b and c are 19.0^(+2.2)_(-2.1) M⊕ and 15.4^(+1.9)_(-1.8) M⊕, respectively; K2-24c is 20% less massive than K2-24b, despite being 40% larger. Their large sizes and low masses imply large envelope fractions, which we estimate at 26^(+3)_(-3)% and 52^(+5)_(-3)%. In particular, K2-24c's large envelope presents an intriguing challenge to the standard model of core-nucleated accretion that predicts the onset of runaway accretion when ∫_(env) ≈ 50%.