Exploring the effects of a time- and space-dependent eruption efficiency on planetary evolution.

It has been shown that melting and crust production strongly influences the convection regime of terrestrial planets, potentially even more than the vigor of convection. A planet producing and erupting a lot of crust can hardly remain in the stagnant lid regime and produces resurfacings or even reaches some mobile-lid regime. On the other hand, a planet that intrudes its melt in the lithosphere tends to have a larger conductive heat flux and cools efficiently without much lid mobility. Thus, the question of the amount of melts being erupted or intruded might dominate the cooling of terrestrial planets. So far, an "eruption efficiency", which gives the ratio of melt that erupts over the remaining melt fraction, has been imposed in numerical simulations. The eruption efficiency in the convection code StagYY has thus far been treated as a constant in time and space. Here, we explore the effects of a time- and space-dependent eruption efficiency on planetary evolution in the planetary convection code StagYY. An equation was devised that describes how eruptive a system is, based on the main characteristics of lithospheric melt transport: the amount of melt and the local stress state. In a range of systematic simulations, we explore the consequences of this parameter. 

In a first set of simulations this parameter is explored while keeping the eruption efficiency constant. Results show that the most important parameters are the amount of melt, where the stress has smaller local effects. Additionally, changing the yield stress, viscosity or constant eruption efficiency has a large effect on what the eruptivity should be based on this equation. Parameters that govern the global mantle temperature are less important for the eruptivity. 

A second set of simulations was performed with the eruption efficiency behaving in a fully self-consistent manner. These models tend to behave like intrusive systems, except during resurfacing episodes when the models become very extrusive. Models that show mobile behaviour at almost all times in the planetary evolution will have an almost constant spatially averaged eruption efficiency. In these models the eruption efficiency does vary locally however.