Heating and Cooling in Small Undifferentiated Planetary Interiors

Abstract:

During the early stages of planetary formation in the solar system, the interior temperature of a growing planetesimal can rise until it exceeds the melt temperature, leading to planetary differentiation, for instance into a rocky mantle and iron-rich core. This growth and differentiation process likely occurs within the first 10 million years of solar system history. At this early stage, decay of short-lived isotopes provide a significant energy source. Cooling to space is accomplished by radiative heat loss, but little is known about the interior heating and cooling history prior to differentiation. Most previously published models for the thermal history of small bodies assume that heat is transferred by conduction from the interior. In the interiors of sufficiently large planetary bodies, solid-state convection will be the primary mechanism of heat transfer from the interior. Convection more efficiently removes heat from the interior; in this presentation we therefore examine whether solid-state convection in an undifferentiated body can influence the timeline for heating, cooling, and attaining the melt temperature. The onset of convection in a self-gravitating sphere of radius r, heated from within at a rate H, and cooled from the outside, was discussed by Chandrasekhar in 1961 and further developed, for a different application, by Hsui et al. (1972), who note that convection occurs when the Rayleigh number for a self-gravitating sphere exceeds 5783 for a sphere with a fixed surface boundary. Depending on the assumed viscosity as the melt temperature is approached, solid-state convection may occur for objects of less than 1000 km radius. Heating and cooling are transient phenomena governed by competing timescales including radioactive decay and convection. Thermal histories for different scenarios are developed using a finite element model.