Birth and decline of magma oceans. Part 2: wobbling thermal history of early accreted planetesimals

Abstract

A theoretical model that describes the evolution of a suspension in which crystals can sediment to form a dense cumulate or may produce a light flotation crust has been derived in a companion paper. We use this model to study the thermal history of early accreted planetary bodies accreted during the very early stages of the formation of the solar system. We study the conditions required to form and preserve flotation crusts and basal cumulates, and the implications for the thermal evolution of planetesimals. We calculate the temperature evolution in an early accreted planetesimals internally heated by the decay of $\rm{^{26}Al}$ and $\rm{^{60}Fe}$. For planetesimal with radius $R>30\, \rm{km}$, partial melting reaches 40%, planetesimals undergo a rheological transition and form a magma ocean, i.e.: a suspension from which crystals can segregate and form a floating crust and/or a dense cumulate. Because of the formation of an insulation floating crust, this magma ocean episode is characterized by a relatively long time life, a slow cooling rate, and a weak surface heat flux. The model further predicts a cyclic evolution where episodes of crustal thickening alternate with episodes of melting-induced crustal thinning. These cycles produce in turn an oscillating thermal history and prevent runaway thermal heating of the planetesimals. At the end of the magma ocean episode, when the fraction of crystals becomes larger than 60\%, a transition occurs to solid-state convection in the planetesimal's mantle. This stage is characterized by high viscous shear stress that tends to erode previously formed crystal deposits. However, the time scale of this erosion process is larger that the lifetime of the planetesimal. Hence solid-state evolution can be described by a well mixed mantle embedded by a metastable crust and a preserved cumulate at its base.