Accurate Empirical Radii and Masses of Planets and Their Host Stars with Gaia Parallaxes

We present empirical measurements of the radii of 116 stars that host transiting planets. These radii are determined using only direct observables—the bolometric flux at Earth, the effective temperature, and the parallax provided by the Gaia first data release—and thus are virtually model independent, with extinction being the only free parameter. We also determine each star's mass using our newly determined radius and the stellar density, a virtually model independent quantity itself from previously published transit analyses. These stellar radii and masses are in turn used to redetermine the transiting-planet radii and masses, again using only direct observables. The median uncertainties on the stellar radii and masses are 8% and 30%, respectively, and the resulting uncertainties on the planet radii and masses are 9% and 22%, respectively. These accuracies are generally larger than previously published model-dependent precisions of 5% and 6% on the planet radii and masses, respectively, but the newly determined values are purely empirical. We additionally report radii for 242 stars hosting radial-velocity (non-transiting) planets, with a median achieved accuracy of ≈2%. Using our empirical stellar masses we verify that the majority of putative "retired A stars" in the sample are indeed more massive than ∼1.2 $M_{\odot }$. Most importantly, the bolometric fluxes and angular radii reported here for a total of 498 planet host stars—with median accuracies of 1.7% and 1.8%, respectively—serve as a fundamental data set to permit the re-determination of transiting-planet radii and masses with the Gaia second data release to ≈3% and ≈5% accuracy, better than currently published precisions, and determined in an entirely empirical fashion.