Modeling magma oceans in mantle convection simulations

Magma oceans play a fundamental role in the thermal evolution of rocky planets and moons. Most of these objects are thought to experience a magma ocean phase at least at their very early ages. Right after the formation of a planet or moon, its temperatures are expected to be very high mainly due to radiogenic heating from fast-decaying isotopes, and the release of energy due to the gravitational contraction of the object. Therefore, it is very likely that most, if not all, of these bodies, have or have hosted magma oceans. In addition, it is also possible to find, long after their formation, very hot planets or moons that contain large magma oceans in their interior. Perhaps the most famous example is Io, the innermost of the Galilean moons orbiting Jupiter. Due to strong tidal interactions with Jupiter and its moons, Io suffers from extreme tidal heating, strong enough to melt large regions of its interior.

On the other hand, mantle convection simulations are crucial to understanding the long-term thermal evolution of rocky planets and moons. These simulations are tailored to solid convection in the mantle, thus when considerable fractions of melt are present or are generated in the interior of the planet, the contrasting properties of the solidus and liquidus phases become too large for the simulations to handle. Properties such as the viscosity and the thermal conductivity are several orders of magnitude different between solidus and liquidus. As consequence, the time steps of the simulation become too short, and the simulation ends up 'frozen' in time. Besides, these large differences pose numerical restrictions that make the codes unstable and prone to crash. Due to these limitations, simulating the interior thermal evolution of hot rocky planets and moons with mantle convection codes turns out to be extremely challenging.

In this work, we apply our magma oceans modeling to Io, since it is an appropriate test case in the Solar System with evidence of hosting large amounts of magma in its interior (e.g., Khurana et al. 2011). We use the CHIC convective code (Noack et al. 2015) to model Io's interior thermal evolution. We then apply and expand an approach, originally developed by Golabek et al. 2011, in which the effective local properties are altered wherever melt is present or produced. Our modeling can be applied to any rocky planet with hot interiors, as could be the case of the innermost Trappist-1 planets, or many of the rocky exoplanets known.