Slow Cooling and Fast Reinflation for Hot Jupiters

The unexpectedly large radii of hot Jupiters are a longstanding mystery whose solution will provide important insights into their interior physics. Many potential solutions have been suggested, which make diverse predictions about the details of inflation. In particular, although any valid model must allow for maintaining large planetary radii, only some allow for radii to increase with time. This reinflation process would potentially occur when the incident flux on the planet is increased. In this work, we examine the observed population of hot Jupiters to see if they grow as their parent stars brighten along the main sequence. We consider the relation between radius and other observables, including mass, incident flux, age, and fractional age (age over main-sequence lifetime), and show that main-sequence brightening is often sufficient to produce detectable reinflation. We further argue that these provide strong evidence for the relatively rapid reinflation of giant planets, and discuss the implications for proposed heating mechanisms. In our population analysis we also find evidence for a "delayed cooling effect," wherein planets cool and contract far more slowly than expected. While not capable of explaining the observed radii alone, it may represent an important component of the effect. Finally, we identify a weak negative relationship between stellar metallicity and planet radius that is presumably the result of enhanced planetary bulk metallicity around metal-rich stars and has important implications for planet formation theory.