Improving stellar and planetary parameters of transiting planet systems: The case of TrES-2

We report on a spectroscopic determination of the atmospheric parameters and chemical abundance of the parent star of the recently discovered transiting planet TrES-2. A detailed LTE analysis of a set of Fe I and Fe II lines from our Keck spectra yields T_eff = 5850 ±50 K, log g = 4.4 ±0.1, and [Fe/H] = -0.15 ±0.10. Several independent checks (e.g., additional spectroscopy, line-depth ratios) confirm the reliability of our spectroscopic T_eff estimate. The mass and radius of the star, needed to determine the properties of the planet, are traditionally inferred by comparison with stellar evolution models using T_eff and some measure of the stellar luminosity, such as the spectroscopic surface gravity. We apply here a new method in which we use instead of log g the normalized separation a/R_* (related to the stellar density), directly measurabele from the light curves of transiting planets with much greater precision. With the a/R_* value from the light-curve analysis of Holman and coworkers and our T_eff estimate, we obtain M_* = 0.980 ± 0.062 M⊙ and R_* = 1.000+0036/-0.033 R⊙, and an evolutionary age of 5.1+23/-2.3 Gyr, in good agreement with other constraints (Ca II H and K line cores, lithium abundance, and rotation). The new stellar parameters yield improved values for the planetary mass and radius of M_p = 1.198 ±0.053 M₃ and R_p = 1.220+0.045/-0.042 R_j, confirming that TrES-2 is the most massive among the currently known nearby (dp≳300pc) transiting hot Jupiters. The surface gravity of the planet, log g_p = 3.299 ±0.016, can be derived independently of the knowledge of the stellar parameters (i.e., directly from observations), and with a very high precision rivaling that of the best known double-lined eclipsing binaries.