A Comparison of Observationally Determined Radii with Theoretical Radius Predictions for Short‐Period Transiting Extrasolar Planets

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Abstract
Two extrasolar planets, HD 209458b and TrES-1, are currently known to transit bright parent stars for which physical properties can be accurately determined. The two transiting planets have very similar masses and periods and hence invite detailed comparisons between their observed and theoretically predicted properties. In this paper, we carry out these comparisons. We first report photometric and spectroscopic follow-up observations of TrES-1, and we use these observations to obtain improved estimates for the planetary radius, Rpl = (1.08 ± 0.05)RJ, and the planetary mass, Mpl = (0.729 ± 0.036)MJ. We also confirm that the inclination estimate of the planetary orbit as i = 882. These values agree with those obtained by Alonso et al. in their discovery paper, but the uncertainty in the planet radius has been improved as a result of both high-cadence photometry of two full transits and from independent radius determinations for the V = 11.8 K0 V parent star. We derive estimates for the TrES-1 stellar parameters of R*/R☉ = 0.83 ± 0.03 (by combining independent estimates from stellar models, high-resolution spectra, and transit light curve fitting) M*/M☉ = 0.87 ± 0.05 (via fitting to evolutionary tracks), Teff = 5214 ± 23 K, [Me/H] = 0.001 ± 0.04, rotational velocity V sin(i) = 1.08 ± 0.3 km s-1, log g = 4.52 ± 0.05 dex, log L*/L☉ = -0.32, d = 157 ± 6 pc, and an age of τ = 4 ± 2 Gyr. These estimates of the physical properties of the system allow us to compute evolutionary models for the planet that result in a predicted radius of Rpl = 1.05RJ for a model that contains an incompressible 20 M⊕ core and a radius Rpl = 1.09RJ for a model without a core. We use our grids of planetary evolution models to show that, with standard assumptions, our code also obtains good agreement with the observed radii of the other recently discovered transiting planets, including OGLE-TR-56b, OGLE-TR-111b, OGLE-TR-113b, and OGLE-TR-132b. We report an updated radius for HD 209458b of Rpl = (1.32 ± 0.05)RJ, based on a new radius estimate of R* = 1.12 R☉ for the parent star. Our theoretical predictions for the radius of HD 209458b are Rpl = 1.05RJ and 1.09RJ for models with and without cores. HD 209458b is therefore the only transiting planet whose radius does not agree well with our theoretical models. We argue that tidal heating stemming from dynamical interaction with a second planet is currently the most viable explanation for its inflated size.