Effect of core cooling on the radius of sub-Neptune planets

Sub-Neptune planets are very common in our Galaxy and show a large diversity in their mass-radius relation. In sub-Neptunes most of the planet mass is in the rocky part (hereafter, core), which is surrounded by a modest hydrogen-helium envelope. As a result, the total initial heat content of such a planet is dominated by that of the core. Nonetheless, most studies contend that the core cooling only has a minor effect on the radius evolution of the gaseous envelope because the cooling of the core is in sync with the envelope; that is most of the initial heat is released early on timescales of ~10-100 Myr. In this Letter we examined the importance of the core cooling rate for the thermal evolution of the envelope. Thus, we relaxed the early core cooling assumption and present a model in which the core is characterized by two parameters: The initial temperature and the cooling time. We find that core cooling can significantly enhance the radius of the planet when it operates on a timescale similar to the observed age, i.e. ~Gyr. Consequently, the interpretation of the mass-radius observations of sub-Neptunes depends on the assumed core thermal properties and the uncertainty therein. The degeneracy of composition and core thermal properties can be reduced by obtaining better estimates of the planet ages (in addition to their radii and masses) as envisioned by future observations.