  Low-mass low-density planets discovered by Kepler in the super-Earth mass
regime typically have large radii for their inferred masses, implying the
presence of H$_2$-He atmospheres. These planets are vulnerable to atmospheric
mass loss due to heating by the parent star's XUV flux. Models coupling
atmospheric mass loss with thermal evolution predicted a bimodal distribution
of planetary radii, which has gained observational support. However, a key
component that has been ignored in previous studies is the dissolution of these
gases into the molten core of rock and iron that constitute most of their mass.
Such planets have high temperatures ($>$2000 K) and pressures ($\sim$kbars) at
the core-envelope boundary, ensuring a molten surface and a subsurface
reservoir of hydrogen that can be 5-10 times larger than the atmosphere. This
study bridges this gap by coupling the thermal evolution of the planet and the
mass loss of the atmosphere with the thermodynamic equilibrium between the
dissolved H$_2$ and the atmospheric H$_2$ (Henry's law). Dissolution in the
interior allows a planet to build a larger hydrogen repository during the
planet formation stage. We show that the dissolved hydrogen outgasses to buffer
atmospheric mass loss. The slow cooling of the planet also leads to outgassing
because solubility decreases with decreasing temperature. Dissolution of
hydrogen in the interior therefore increases the atmosphere retention ability
of super-Earths. The study highlights the importance of including the
temperature- and pressure-dependent solubility of gases in magma oceans and
coupling outgassing to planetary evolution models.
