Factors affecting the radii of close-in transiting exoplanets

Context. The radius of an exoplanet may be affected by various factors, including irradiation received from the host star, the mass of the planet and its heavy element content. A significant number of transiting exoplanets have now been discovered for which the mass, radius, semi-major axis, host star metallicity and stellar effective temperature are known. Aims. We use multivariate regression models to determine the power-law dependence of planetary radius on planetary equilibrium temperature T-eq, planetary mass M-p, stellar metallicity [Fe/H], orbital semi-major axis a, and tidal heating rate H-tidal, for 119 transiting planets in three distinct mass regimes. Methods. We fit models initially to all 119 planets, resulting in fairly high scatter between fitted and observed radii, and subsequently to three subsets of these planets: Saturn-mass planets, Jupiter-mass planets, and high-mass planets. Results. We find models for each subset that fit the observed planetary radii well and show the importance of the various environmental parameters on each subset. Conclusions. We determine that heating leads to larger planet radii, as expected, increasing mass leads to increased or decreased radii of low-mass (<0.5 R-J) and high-mass (>2.0 R-J) planets, respectively (with no mass effect on Jupiter-mass planets), and increased host-star metallicity leads to smaller planetary radii, indicating a relationship between host-star metallicity and planet heavy element content. For Saturn-mass planets, a good fit to the radii may be obtained from log(R-p/R-J) = -0.077 + 0.450 log(M-p/M-J) - 0.314 [Fe/H] + 0.671 log(a/AU) + 0.398 log(T-eq/K). The radii of Jupiter-mass planets may be fit by log(R-p/R-J) = -2.217 + 0.856 log(T-eq/K) + 0.291 log(a/AU). High-mass planets' radii are best fit by log(R-p/R-J) = -1.067 + 0.380 log(T-eq/K) -0.093 log(M-p/M-J) -0.057 [Fe/H] + 0.019 log(H-tidal/1x10(20)). These equations produce a very good fit to the observed radii, with a mean absolute difference between fitted and observed radius of 0.11 R-J, compared to the mean reported uncertainty in observed radius of 0.07 R-J. A clear distinction is seen between the core-dominated Saturn-mass (0.1-0.5 M-J) planets, whose radii are determined almost exclusively by their mass and heavy element content, and the gaseous envelope-dominated Jupiter-mass (0.5-2.0 M-J) planets, whose radii increase strongly with irradiating flux, partially offset by a power-law dependence on orbital separation.