Heat Transfer and Planetary Evolution

Abstract

The object of this account is to show how much one can interprete and predict about the present state of material forming planet size objects, despite the fact we do not and could never have the kind of exact or prior knowledge of initial conditions and in situ material behaviour that would make a formal mathematical analysis of the dynamical problems of planetary evolution an efficient or meaningful exercise. The interest and usefulness of results obtained within these limitations stem from the highly non linear nature of planetary scale heat transfer problems when posed in any physically plausible form. The non linearity arising from a strongly temperature dependent rheology assumed for in situ planetary material is particularly valuable in deriving results insensitive to such uncertainties. Qualitatively, the thermal evolution of a planet is quite unlike that given by heat conduction calculation below a very superficial layer, and much unnecessary argument and confusion results from a persistent failure to recognise that fact. At depths that are no greater on average than a few tens of kilometres in the case of Earth, the temperature distribution is determined by a convective flow regime inaccessible to the laboratory experimenter and to the numerical methods regularly employed to study convective movement. A central and guiding quantitative result is the creation in homogeneous planet size objects having surface temperatures less than about half the absolute melting temperature of their material, of internal states with horizontally averaged viscosity values ~ 10²¹ poise. This happens in times short compared with the present Solar System age. The significance of this result for an understanding of such processes and features as isostasy, continental drift, a minimum in seismic S wave velocity in Earth’s upper mantle, a uniformity of mantle viscosity values, the survival of liquid planetary cores and the differentiation of terrestrial planet material is examined. After a discussion and definition of üthospheric’ material, it is concluded that endogenous tectonic activity only continues on Earth’s surface on account of water enhancing the deformability of its rocks.

Metal/silicate differentiation of terrestrial planet material is predicted to have been a global scale catastrophic process in the many objects it formed predating the existing planets, but intersilicate and volatile/silicate separations are necessarily protracted, quasi continuous processes arising from local shear instabilities in the convective flow of such a viscous material. In particular, these local magma producing instabilities require the involvement of ‘Iithospheric’ planetary material in convective movements and it is shown how this unsteadiness accounts for the distribution and salient features of planetary seismicity and vulcanicity at the present time.

The picture that emerges for the state of Earth’s silicate shell material after more than four billion years of average viscosity regulation and shear instability is one of chemical and isotopic heterogeneity on a wide range of length scales. The larger length scales of this range are introduced by the pattern of heterogeneity remixing rather than its generation. For example, at the largest scale, the predicted heterogeneity is radial and a feature indirectly arising from properties conferred on the shell material by major mineral phase transitions at depths ~ 700 km. These increase the adiabatic temperature gradient and have the effect of a barrier adequate in strength to prevent wholesale mixing of the material above and below for at least a large fraction of the Earth’s history in which radiogenic heat has been the dominant cause of large scale internal movements. That such a barrier actually marks a chemical and isotopic heterogeneity of the mantle is because only the convective movements above it are prone to the shear heating instabilities on which differentiation absolutely depends. Many millions of such instabilities in this shallower shell material would by now have created a three dimensional heterogeneity extending downward in length scale to ~ 1 km. However, only 10% of this shell material has yet experienced these highly localised shear heating instabilities and one would predict a continuing emission of primitive volatile phases and a widespread metasomatism even if the same convective movements had not recycled material from the hydrosphere. Such recycling is a further aspect of convective self regulation.

The mesoscale and lateral heterogeneity of near surface material more familiarly referred to as continental crust and its underlying mantle is another cumulative feature of the remixing process - in this case the result of separated ultrabasic and less refractory fractions of the upper shell material from many shear heating events being able to form superficial blocks, whose net buoyancy and coherency make them immune to entrainment and remixing by the radiogenically driven flow. This partial but permanent concentration of lower melting point silicate and volatile phases near the external surface has in turn caused a gradual increase of the horizontally averaged temperatures associated with the self regulating convective state at upper mantle depths. This thermal evolution has strengthened the barrier to convective mixing of the whole silicate shell presented by its major phase transitions but it could explain a persistent small scale incorporation of more primitive, i.e. less differentiated shell material from the phase transition region into the upper shell convective circulation.

‘Clear your mind of cant’ (Johnson)