Homogeneous studies of transiting extrasolar planets - II. Physical properties

I present an homogeneous determination of the physical properties of 14 transiting extrasolar planetary systems for which good photometric and spectroscopic data are available. The input quantities for each system are the results of the light-curve analyses presented in Paper I, and published measurements of the stellar velocity amplitude, effective temperature and metal abundance. The physical properties are determined by interpolating within tabulated predictions from stellar theory to find the optimal match to these input data. Statistical uncertainties are found using a perturbation algorithm, which gives a detailed error budget for every output quantity. Systematic uncertainties are assessed for each quantity by comparing the values found using several independent sets of stellar models. As a theory-free alternative, physical properties are also calculated using an empirical mass-radius relation constructed from high-precision studies of low-mass eclipsing binary stars. I find that the properties of the planets depend mostly on parameters measured from the light and radial velocity curves, and have a relatively minor sensitivity to theoretical predictions. In contrast, the orbital semimajor axes and stellar masses have a strong dependence on theoretical predictions, and their systematic uncertainties can be substantially larger than the statistical ones. Using the empirical mass-radius relation instead, the semimajor axes and stellar masses are smaller by up to 15 per cent. Thus, our understanding of extrasolar planets is currently limited by our lack of understanding of low-mass stars. Using the properties of all known transiting extrasolar planets, I find that correlations between their orbital periods, masses and surface gravities are significant at the 2 sigma-3 sigma level. However, the separation of the known planets into two classes according to their Safronov number is weaker than previously found, and may not be statistically significant. Three systems, HAT-P-2, WASP-14 and XO-3, form their own little group of outliers, with eccentric orbits, massive planets and stars with masses similar to 1.3 M-circle dot. The detailed error budgets calculated for each system show where further observations are needed. XO-1 and WASP-1 could do with new transit light curves. TrES-2 and WASP-2 would benefit from more precise stellar temperature and abundance measurements. Velocity measurements of the parent stars are vital for determining the planetary masses: TrES-1, XO-1, WASP-1, WASP-2 and the OGLEs need additional data. The homogeneous analysis presented here is a step towards large-scale statistical studies of transiting extrasolar planetary systems, in preparation for the expected deluge of new detections from CoRoT and Kepler.