We present a systematic evaluation of the agreement between the observed radii of 90 well-characterized transiting extrasolar giant planets and their corresponding model radii .
Our model radii are drawn from previously published calculations of core-less giant planets that have attained their asymptotic radii , and which have been tabulated for a range of planet masses and equilibrium temperatures .
( We report a two-dimensional polynomial fitting function that accurately represents the models ) .
As expected , the model radii provide a statistically significant improvement over a null hypothesis that the sizes of giant planets are completely independent of mass and effective temperature .
As is well known , however , fiducial models provide an insufficient explanation ; the planetary radius anomalies , { \cal R } \equiv R _ { obs } - R _ { pred } , are strongly correlated with planetary equilibrium temperature .
We find that the radius anomalies have a best-fit dependence , { \cal R } \propto T _ { eff } ^ { \alpha } , with \alpha = 1.4 \pm 0.6 .
Incorporating this relation into the model radii leads to substantially less scatter in the radius correlation .
The extra temperature dependence represents an important constraint on theoretical models for Hot Jupiters .
Using simple scaling arguments , we find support for the hypothesis of Batygin and Stevenson ( 2010 ) that this correlation can be attributed to a planetary heating mechanism that is mediated by magnetohydrodynamic coupling between the planetary magnetic field and near-surface flow that is accompanied by ohmic dissipation at adiabatic depth .
Additionally , we find that the temperature dependence is likely too strong to admit kinetic heating as the primary source of anomalous energy generation within the majority of the observed transiting planets .