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 $\sim$0.1 g cm$^{-3}$. Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role 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 $\sim$0.1 g cm$^{-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.