Stellar diameters and temperatures - VI. High angular resolution measurements of the transiting exoplanet host stars HD 189733 and HD 209458 and implications for models of cool dwarfs

We present direct radii measurements of the well-known transiting exoplanet host stars HD 189733 and HD 209458 using the CHARA Array interferometer. We find the limb-darkened angular diameters to be θ_LD = 0.3848 ± 0.0055 and 0.2254 ± 0.0072 mas for HD 189733 and HD 209458, respectively. HD 189733 and HD 209458 are currently the only two transiting exoplanet systems where detection of the respective planetary companion's orbital motion from high-resolution spectroscopy has revealed absolute masses for both star and planet. We use our new measurements together with the orbital information from radial velocity and photometric time series data, Hipparcos distances, and newly measured bolometric fluxes to determine the stellar effective temperatures (T_eff = 4875 ± 43, 6092 ± 103 K), stellar linear radii (R_* = 0.805 ± 0.016, 1.203 ± 0.061 R_⊙), mean stellar densities (ρ_* = 1.62 ± 0.11, 0.58 ± 0.14 ρ_⊙), planetary radii (R_p = 1.216 ± 0.024, 1.451 ± 0.074 R_Jup), and mean planetary densities (ρ_p = 0.605 ± 0.029, 0.196 ± 0.033 ρ_Jup) for HD 189733b and HD 209458b, respectively. The stellar parameters for HD 209458, an F9 dwarf, are consistent with indirect estimates derived from spectroscopic and evolutionary modelling. However, we find that models are unable to reproduce the observational results for the K2 dwarf, HD 189733. We show that, for stellar evolutionary models to match the observed stellar properties of HD 189733, adjustments lowering the solar-calibrated mixing-length parameter to α_MLT =1.34 need to be employed.