Bayesian Analysis of Hot Jupiter Radius Anomalies: Evidence for Ohmic Dissipation?

The cause of hot Jupiter radius inflation, where giant planets with $T_{\rm eq}$ $>1000$ K are significantly larger than expected, is an open question and the subject of many proposed explanations. Rather than examine these models individually, this work seeks to characterize the anomalous heating as a function of incident flux, $\epsilon(F)$, needed to inflate the population of planets to their observed sizes. We then compare that result to theoretical predictions for various models. We examine the population of about 300 giant planets with well-determined masses and radii and apply thermal evolution and Bayesian statistical models to infer the anomalous power as a function of incident flux that best reproduces the observed radii. First, we observe that the inflation of planets below about $M=0.5 \;\rm{M}_\rm{J}$ appears very different than their higher mass counterparts, perhaps as the result of mass loss or an inefficient heating mechanism. As such, we exclude planets below this threshold. Next, we show with strong significance that $\epsilon(F)$ increases with $T_{\rm{eq}}$ towards a maximum of $\sim 2.5\%$ at $T_{\rm{eq}} \approx 1500$ K, and then decreases as temperatures increase further, falling to $\sim0.2\%$ at $T_\rm{eff}= 2500$ K. This high-flux decrease in inflation efficiency was predicted by the Ohmic dissipation model of giant planet inflation but not other models. We also explicitly check the thermal tides model and find that it predicts far more variance in radii than is observed. Thus, our results provide evidence for the Ohmic dissipation model and a functional form for $\epsilon(F)$ that any future theories of hot Jupiter radii can be tested against.