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

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Abstract
The cause of hot-Jupiter radius inflation, where giant planets with > 1000 K are significantly larger than expected, is an open question and the subject of many proposed explanations. Many of these hypotheses postulate an additional anomalous power that heats planets’ convective interiors, leading to larger radii. Rather than examine these proposed models individually, we determine what anomalous powers are needed to explain the observed population’s radii, and consider which models are most consistent with this. We examine 281 giant planets with well-determined masses and radii and apply thermal evolution and Bayesian statistical models to infer the anomalous power as a fraction of (and varying with) incident flux ϵ(F) that best reproduces the observed radii. First, we observe that the inflation of planets below about M = 0.5 M 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 ϵ(F) increases with toward a maximum of ∼2.5% at T eq ≈ 1500 K, and then decreases as temperatures increase further, falling to ∼0.2% at T 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 show that the thermal tides model predicts far more variance in radii than is observed. Thus, our results provide evidence for the Ohmic dissipation model and a functional form for ϵ(F) that any future theories of hot-Jupiter radii can be tested against.

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