Russian Journal of Earth Sciences
Vol. 5, No. 6, December 2003
Gravitational differentiation of liquid cores of planets and natural
satellites
S. V. Starchenko
Abstract
Initial equations are obtained, similarity criteria are estimated and a project
of simulation experiment is proposed for the gravitational differentiation of
liquid cores of planets and natural satellites. It is assumed that, first, the
liquid core in an adiabatic state without thermal convection and, second, the
inner solid core grows during the crystallization of a heavy component from the
liquid core in such a way that the buoyancy force acting on a lighter component
is directed strictly along the radius. It is also assumed that the radial
distribution of density in the liquid core does not change during the time
interval considered. These three natural assumptions enable an analytical
description of basic hydrostatic effects controlling slow growth of the solid
core, gravitational stratification of the liquid core, and sources of related
compositional convection. The similarity criteria of such convection are mostly
the same as for thermal convection. Additional criteria are the concentration
contrast (~1/10 in the Earth), the compressibility of the liquid core (~10%),
and the thickness of a concentration boundary layer (~10
-7 ) that, controlling
the freezing-out of the liquid at the inner sphere, can give rise to asymmetry
of the solid core. The excitation threshold of the compositional convection is
much higher than a similar threshold for thermal convection, and the
compositional convection itself can arise only at an intermediate stage of the
gravitational differentiation of the core. Observed magnetic fields are largely
due to compositional convection in the Earth's core and, probably, in deep
interiors of Mercury. At the contemporary evolutionary stage of Venus'
interiors, the intensity of compositional convection is most likely insufficient
for the magnetic field excitation and it is undoubtedly too weak in the Mars'
interiors.