Why are many hot Jupiters larger than models predict?

In plain words

Strongly heated giant planets are often puffier than any standard cooling model allows. Some extra heat must be deposited deep inside them.

Precise statement

Hot Jupiters receiving incident flux $F > \sim 2x10^{8}\,\mathrm{erg}/\mathrm{s}/\mathrm{cm}^{2}$ have radii up to $\sim 2\,\text{Jupiter radii}$, exceeding standard evolution models. Identify the mechanism that deposits heat in the interior: Ohmic dissipation, tidal heating, downward advection of heat by atmospheric circulation, or delayed contraction, by matching the radius anomaly versus $F$, planet mass and age.

What would settle it

Measurement of the radius anomaly versus incident flux and age, including planets whose host stars have brightened (re-inflation test), compared with each mechanism's prediction.

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