Thermal Evolution of Non-synchronous Lava Worlds

Planetary rotation periodically changes the incoming stellar flux that keeps the star-facing side of lava worlds in a molten state. Previous studies have focused on the evolution of a permanent magma ocean on the dayside of synchronously rotating planets. Here, we investigate the day-night cycle effect on the thermal evolution of a hemispheric magma ocean on an airless, rotating planet. Our model accounts for heating effect of stellar radiation during the day, radiative cooling and heat flow due to mantle convection. We put constraints on planet size, incident stellar radiation and orbital resonances to understand when lava worlds are a permanent or transient state for those planets. We find that within 100 Myrs exoplanets with an instellation of <10⁶ W m^-2 (i.e., ~ 10³ times the solar flux at Earth's orbit) are subject to complete magma ocean crystallization. The magma ocean either turns into a solid crust for a limited time or remains solid once crystallized. For smaller planetary radii, the amount of flux necessary to eventually remelt the crust is larger compared to that for larger planets. In contrast, an instellation >10⁶ W m^-2 is sufficient to retain the magma ocean permanently. We create synthetic lightcurves for asynchronously rotating planets to understand what secondary eclipses would look like for various spin-orbit configurations. The outcome of the model can inform current and future JWST observations of lava worlds candidates, providing a better understanding of the magma ocean stage lifetime.