Abstract

Heat lost by melt eruption at the surface is a minor component of Earth’s internal heat budget and normally discarded from thermal history models. However, the strong temperature dependence of global melt production implies that an earlier, hotter Earth produced more melt, increasing internal heat loss via eruptive cooling. To address this we develop simple models for mantle melt production and eruptive cooling, and derive melt heat loss scaling laws. Including a melt heat sink in thermal history models results in more efficient mantle cooling, exacerbating the thermal catastrophe of the mantle, which can be overcome by adjustments to the present-day energy balance. In application to stagnant lid planets, cooling by melt eruption can compensate for slow conductive cooling but is dependent on the fraction of extrusive to intrusive melt. In the same vein, a generalized volatile cycling box-model illustrates how volatile reservoir size depends on melt eruption rates.