2024MNRAS.535.2404H

Rocky planets typically form with a transient magma ocean. Lava planets, however, maintain a permanent day-side magma ocean. The extent of this magma ocean depends on the planet's thermal history. We present numerical simulations of the thermal history of tidally locked lava planets over 10 billion years, starting from a completely molten mantle. The day-side surface temperature is fixed at 3000 K, while the night-side surface temperature cools by thermal radiation. We consider planets with radii of 1.0 and 1.5${\rm R}_{\oplus}$; super-Earths have shallower steady-state magma oceans due to their greater gravity. The night-side begins crystallizing within a few thousand years, fully solidifying in 800 Myr, in the absence of tidal heating or day-night heat transport. We find that a mushy night-side can persist if at least 20 per cent of absorbed stellar power is transferred from the day to night hemisphere through magma currents, which would be feasible at a viscosity of $10^{-3}$ Pa s. Maintaining a fully molten night-side by magma ocean circulation would require unrealistically low viscosities and therefore appears unlikely. Alternatively, the night-side may remain molten if the mush layer dissipates tidal energy at a rate of $8 \times 10^{-4}$ W kg^–1, which is plausible for orbital eccentricities greater than $7 \times 10^{-3}$. Night-side cooling, however, is a runaway process: increasing viscosity and mush solidification hinder both heat transport and tidal heating. Our results highlight the importance of measuring the night-side temperatures of lava planets, which would provide crucial insights into their thermal histories.