HD 209458: Physical Parameters of the Parent Star and the Transiting Planet

The Sun-like star HD 209458 harbors a close-in giant planet that transits across the star's disk, and thus allows an unprecedented access to the basic parameters of the planet, given a certain knowledge of the basic parameters of the star, namely, its mass and radius. We present theoretical stellar evolution model calculations for HD 209458 and discuss the uncertainties involved in deriving the stellar mass and radius. We derive the mass, M=1.06M_solar, radius, R=1.18R_solar, and age, t=5.2 Gyr of the star with uncertainties of 10% or more. The dominant sources of uncertainty remain the helium abundance estimate and the treatment of convection, even after an optimistic estimate for the effective temperature of the star. However, we find that in deriving the radius of the planet, R_p, the relevant stellar model input is the M/R relation, which runs orthogonal to a degeneracy in the transit light-curve solution and greatly improves the estimate of R_p. Theoretically, the M/R relation has a lower uncertainty than the M and R separately. We estimate the planet radius and mass to be R_p=1.42^+0.10_-0.13R_J and M_p=0.69+/-0.02M_J.