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, andweuse theseobservationsto obtain improvedestimatesfor the planetaryradius,Rpl ¼ (1:08 � 0:05)RJ,andthe planetary mass, Mpl ¼ (0:729 � 0:036)MJ. We also confirm that the inclination estimate of the planetary orbit as i ¼ 88N2. 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 ¼ 11:8 K0 V parent star. We derive estimates for the TrES-1 stellar parameters of R� =R� ¼ 0:83 � 0:03 (by combining independent estimates from stellar models, high-resolution spectra,andtransitlightcurvefitting)M� =M� ¼ 0:87 � 0:05(viafittingtoevolutionarytracks),TeA ¼ 5214 � 23 K, ½Me=H� ¼ 0:001 � 0:04, rotational velocity V sin (i) ¼ 1:08 � 0:3 km s � 1, log g ¼ 4:52 � 0:05 dex, logL� =L� ¼ � 0:32,d ¼ 157 � 6 pc, and anageof � ¼ 4 � 2 Gyr.Theseestimates of thephysical properties of thesystem allow us to compute evolutionary models for the planet that result in a predicted radius of Rpl ¼ 1:05RJ for a model that contains an incompressible 20 Mcore and a radius Rpl ¼ 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 ¼ (1:32 � 0:05)RJ, based on a new radius estimate of R� ¼ 1:12 Rfor the parent star. Our theoretical predictions for the radius of HD 209458b are Rpl ¼ 1:05RJ and1.09RJ formodelswithandwithoutcores.HD209458bisthereforetheonlytransitingplanetwhose radius does not agree well with our theoretical models. We argue that tidal heating stemming from dynamical inter- action with a second planet is currently the most viable explanation for its inflated size. Subject headinggs: planetary systems — planets and satellites: general — stars: individual (HD 209458, TrES-1)

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