2025MNRAS.536.2957N

Atmospheric energy transport is central to the cooling of primordial magma oceans. Theoretical studies of atmospheres on lava planets have assumed that convection is the only process involved in setting the atmospheric temperature structure. This significantly influences the ability for a magma ocean to cool. It has been suggested that convective stability in these atmospheres could preclude permanent magma oceans. We develop a new 1D radiative-convective model in order to investigate when the atmospheres overlying magma oceans are convectively stable. Using a coupled interior-atmosphere framework, we simulate the early evolution of two terrestrial-mass exoplanets: TRAPPIST-1 c and HD 63433 d. Our simulations suggest that the atmosphere of HD 63433 d exhibits deep isothermal layers which are convectively stable. However, it is able to maintain a permanent magma ocean and an atmosphere depleted in $\mathrm{H_{2}O}$. It is possible to maintain permanent magma oceans underneath atmospheres without convection. Absorption features of $\mathrm{CO_{2}}$ and $\mathrm{SO_{2}}$ within synthetic emission spectra are associated with mantle redox state, meaning that future observations of HD 63433 d may provide constraints on the geochemical properties of a magma ocean analogous with the early Earth. Simulations of TRAPPIST-1 c indicate that it is expected to have solidified within $100 \,\mathrm{M}\rm {yr}$, outgassing a thick atmosphere in the process. Cool isothermal stratospheres generated by low-molecular-weight atmospheres can mimic the emission of an atmosphere-less body. Future work should consider how atmospheric escape and chemistry modulates the lifetime of magma oceans, and the role of tidal heating in sustaining atmospheric convection.