Thermal evolution of sub-Neptunes: the role of the rocky core

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 core, which is surrounded by a modest hydrogen-helium envelope. We study the longterm consequences of the core cooling on the planet
mass-radius relation. We consider the role of various core energy sources resulting from core formation, iron differentiation, rock solidification, core contraction, and radioactive decay. We follow the core
formation phase, which sets the initial conditions, the
magma ocean phase, characterized by rapid heat transport, and the solid-state phase, where cooling is inefficient. We find that for typical sub-Neptune planets (2 − 10 M⊕) with envelope mass of 0.5% − 10%,
the magma ocean phase lasts several gigayears, much
longer than for terrestrial planets. The magma ocean
phase effectively erases any signs of the initial core
thermodynamic state. After solidification, the reduced
heat flux from the rocky core causes a significant drop
in the rocky core surface temperature, but its effect on
the planet radius is limited. The overall long-term radius uncertainty by core effects is usually about 5%,
and not more than 15%. Therefore, the inferred envelope mass from mass-radius relation is mostly proportional to the envelope (H/He) mass fraction