Removal of Hot Saturns in Mass–Radius Plane by Runaway Mass Loss

The hot Saturn population exhibits a boundary in mass–radius space, such that no planets are observed at a density less than ∼0.1 g cm ^−3 . Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role X-ray and extreme UV irradiation (XUV)-driven mass loss plays in sculpting the density boundary by constructing interior structure models that include radius inflation, photoevaporative mass loss, and a simple prescription of Roche lobe overflow. We demonstrate that planets puffier than ∼0.1 g cm ^−3 experience a runaway mass loss caused by adiabatic radius expansion as the gas layer is stripped away, providing a good explanation of the observed edge in mass–radius space. The process is also visible in the radius–period and mass–period spaces, though smaller, high-bulk-metallicity planets can still survive at short periods, preserving a partial record of the population distribution at formation.