Cooling history of Earth's core with high thermal conductivity

Thermal evolution models of Earth's core constrain the power available to the geodynamo process that generates the geomagnetic field, the evolution of the solid inner core and the thermal history of the overlying mantle. Recent upward revision of the thermal conductivity of liquid iron mixtures by a factor of 2-3 has drastically reduced the estimated power available to generate the present-day geomagnetic field. Moreover, this high conductivity increases the amount of heat that is conducted out of the core down the adiabatic gradient, bringing it into line with the highest estimates of present-day core-mantle boundary heat flow. These issues raise problems with the standard scenario of core cooling in which the core has remained completely well-mixed and relatively cool for the past 3.5. Ga. This paper presents cooling histories for Earth's core spanning the last 3.5. Ga to constrain the thermodynamic conditions corresponding to marginal dynamo evolution, i.e. where the ohmic dissipation remains just positive over time. The radial variation of core properties is represented by polynomials, which gives good agreement with radial profiles derived from seismological and mineralogical data and allows the governing energy and entropy equations to be solved analytically. Time-dependent evolution of liquid and solid light element concentrations, the melting curve, and gravitational energy are calculated for an Fe-O-S-Si model of core chemistry. A suite of cooling histories are presented by varying the inner core boundary density jump, thermal conductivity and amount of radiogenic heat production in the core. All models where the core remains superadiabatic predict an inner core age of ≲600Myr, about two times younger than estimates based on old (lower) thermal conductivity estimates, and core temperatures that exceed present estimates of the lower mantle solidus prior to the last 0.5-1.5. Ga. Allowing the top of the core to become strongly subadiabatic in recent times pushes the onset of inner core nucleation back to ~1.5Gyr, but the ancient core temperature still implies a partially molten mantle prior to ~2Ga. Based on these results, the scenario of a long-lived basal magma ocean and subadiabatic present-day core seems hard to avoid.