Evidence of Three Mechanisms Explaining the Radius Anomaly of Hot Jupiters

Abstract

The radii of hot Jupiters are still not fully understood and all of the proposed explanations are based on the idea that these close-in giant planets possess hot interiors. We approach the radius anomaly problem by adopting a statistical approach. We infer the internal luminosity for the sample of hot Jupiters, study its effect on the interior structure, and put constraints on which mechanism is the dominant one. We develop a flexible and robust hierarchical Bayesian model that couples the interior structure of exoplanets to their observed properties. We apply the model to 314 hot Jupiters and infer the internal luminosity distribution for each planet and study at the population level ({\it i}) the mass-luminosity-radius distribution and as a function of equilibrium temperature the distributions of the ({\it ii}) heating efficiency, ({\it iii}) internal temperature, and the ({\it iv}) pressure of the radiative-convective-boundary (RCB). We find that hot Jupiters tend to have high internal luminosity leading to hot interiors. This has important consequences on the cooling rate and we find that the RCB is located at low pressures. Assuming that the ultimate source of the extra heating is the irradiation from the host star, we illustrate that the heating efficiency follows a Gaussian distribution, in agreement with previous results. We discuss our findings in the context of the proposed heating mechanisms and illustrate that ohmic dissipation, advection of potential temperature, and thermal tides are in agreement with certain trends inferred from our analysis and thus all three models can explain aspects of the observations. We provide new insights on the interior structure of hot Jupiters and show that with our current knowledge it is still challenging to firmly identify the universal mechanism driving the inflated radii.