Alternative thermal histories of Earth-like planets: Influence of key parameters

The thermal evolution of any planet can be influenced by many factors: the initial temperature profile, the distribution of specific materials within the planet, the existence or lack of a gaseous atmosphere, the effects of early and “late” collision events. Insights concerning the influence of those factors can be obtained by examining solutions to the heat equation, applied to spherical bodies. General trends identified in this work include: 1) Moderate conductive materials contribute to efficiently flatten the temperature gradients, whereas insulating materials promote the preservation of steep temperature gradients. 2) It is not necessary to invoke convection to achieve a relatively flat temperature gradient; moderately conductive materials might achieve the same result without any advective motion involved. 3) Heat transport can take place both outwards and inwards, depending on the initial distribution of temperatures. 4) If the initial temperatures near the center of a planet are low, they will tend to remain low even if heat production takes place at its middle or upper parts. 5) Gradients of temperature near the surface of a planet may not reflect temperature variations at its middle or central parts. 6) Changes of phase exert a strong influence on the evolution of temperature profiles within a planet. 7) Highly insulating atmospheric layers can be important in determining the time of solidification of the upper layer of a magma ocean but not all atmospheres are equally efficient in that respect. As a result, models that give for granted the existence of deep mantle convection on Earth are justified only in the context of models of planet formation that require high initial temperatures; the standard model of a cold solar nebula is not consistent with such deep mantle convective movements.