Sinking FE-Diapirs: A model for planetary core formation

Kurzfassung

The formation of a planetary core in terrestrial planets ist still not well understood. However, core formation is generally thought to have occured concurrently with or soon after planet formation and, therefore, determines the initial conditions for thermal evolution models to a significant extent. A possible scenario for the formation of a planetary core is the settling of iron melt diapirs in a solid matrix. Since the iron has a higher density than the underlying planetary mantle, it may sink in a Rayleigh-Taylor instability. Because the viscosity contrast is essentially infinite, the sinking melt diapirs will take the shape of a sphere. The size of the diapirs can be approximated using a wavelength analysis of the Rayleigh-Taylor instability. we have modelled the falling of an iron sphere through a silicate mantle with temperatures and stress dependent viscosity using a 2-D finite element software package (FEATFLOW) written by S. Turek. From these models the effect of the temperature and stress dependence of the silicate rock viscosity on the sinking rate can be estimated. Our models show that the implementation of a viscosity reducing rheology can easily reduce the drag force by several orders of magnitude. Equating the drag force with the body force woll allow to determine the terminal velocity of the diapir. In our models a viscosity contrast of 10_3 yields a terminal velocity which points to a core formation time of approximately 30 Ma for the Earth. The results are consistent with differentiation times of iron an sd silicate phases derived from isotope measurements in cosmochemistry.