Mass and Eccentricity Constraints in the WASP-47 Planetary System from a Simultaneous Analysis of Radial Velocities & Transit Timing Variations

Abstract: Measuring precise planet masses, densities, and orbital dynamics in individual planetary systems is an important pathway toward understanding planet formation. The WASP-47 system has an unusual architecture that motivates a complex formation theory. The system includes a hot Jupiter ("b") neighbored by interior ("e") and exterior ("d") sub-Neptunes, and a long-period eccentric giant planet ("c"). We simultaneously modeled transit times from the Kepler K2 Mission and 118 radial velocities to determine precise masses, densities, and Keplerian orbital elements of the WASP-47 planets. Combining RVs and TTVs provides a better estimate of the mass of planet d (13.6\pm2.0~M_\odot) than obtained with only RVs ($12.75\pm2.70~M_\odot$) or TTVs ($16.1\pm3.8~M_\odot$). Planets e and d have high densities for their size, consistent with a history of photo-evaporation and/or formation in a volatile-poor environment. Through our RV and TTV analysis, we find that the planetary orbits have eccentricities similar to the solar system planets. The WASP-47 system has three similarities to our own solar system: (1) the planetary orbits are nearly circular and coplanar, (2) the planets are not trapped in mean motion resonances, and (3) the planets have diverse compositions. None of the current single-process exoplanet formation theories adequately reproduce these three characteristics of the WASP-47 system (or our solar system). We propose that WASP-47, like the solar system, formed in two stages: first, the giant planets formed in a gas-rich disk and migrated to their present locations, and second, the high-density sub-Neptunes formed in situ in a gas-poor environment.