Analysis of the Cessation of Convection in Mercury's Mantle

Abstract

The question of whether the present-day mantle of Mercury is undergoing convection remains unresolved. We address this issue by estimating the minimum value of the core-mantle boundary (CMB) temperature needed to support mantle convection and considering the time required to cool the mantle below this threshold. A simple mathematical analysis of the cooling of the core, based on the assumption of a quasi-steady-state thermal equilibrium of Mercury's mantle, shows that the CMB temperature falls to the critical temperature for cessation of convection roughly halfway through the planet's evolutionary history. To first order, the duration of subsolidus convection does not depend on the absolute value of the viscosity. It depends primarily on parameters that control the viscosity function, such as the stress exponent and the activation energy. Our results based on conventional assumptions suggest the absence of present-day mantle convection in Mercury, which is consistent with numerical models of Mercury's thermal history. However, because of large uncertainties in the controlling parameters, the possibility of still ongoing mantle convection on Mercury cannot be ruled out.