A one-dimensional core model for coupling to mantle convection simulations: Equations and results

Cooling of the core provides a substantial part of the mantle heat budget, while mantle convection determines the heat flux across the core-mantle boundary, hence the existence or not of a planetary dynamo. Thus, the thermal evolutions of core and mantle should be treated in a coupled manner. To accomplish this, the core has normally been coupled into mantle convection simulations assuming that it has an adiabatic temperature profile and can thus be characterized by single temperature (e.g. the CMB temperature) (e.g. Nakagawa & Tackley, 2014 GCubed), allowing a simple 0-dimensional parameterization such as a uniform "heat bath" or one including inner core growth (e.g. Buffett et al, 1996 JGR).

However, when the CMB heat flux F_CMB becomes lower than adiabatic, core convection no longer occurs (as evidenced by no magnetic field on Venus and Mars) and thus the core temperature profile is not adiabatic. F_CMB can even become negative in models with a layer of dense heat-producing-element (HPE)-enriched material above the CMB: assuming this heats the entire core uniformly is unrealistic as heating from above is a very inefficient way of heating a layer. Another end-member approximation is to decouple the core and mantle temperatures in the latter case (Cheng et al, 2025 JGR).

To treat cases where F_CMB is sub-adiabatic or negative, a 1-D conductive core model is presented. When the temperature profile is adiabatic to super-adiabatic, an eddy diffusivity acting on the super-adiabatic temperature parameterizes heat transport by turbulent convection and keeps the temperature profile very close to adiabatic (see Abe, 1997 PEPI). When the temperature profile is sub-adiabatic, normal thermal diffusion is the dominant heat transport process. Compressibility, crystallization of an inner core and the presence of light elements are included.

A MATLAB implementation is presented. Then, results from coupling this 1-D core model to 2-D thermo-chemical mantle evolution models using StagYY (Tackley, 2008 PEPI) are presented. When F_CMB is always super-adiabatic, similar results are obtained for 1-D and 0-D models, but:

(i) Results for a post-giant-impact core superadiabatic temperature profile with the outermost core extremely hot were presented by Tackley (2025 AGU Meeting; https://agu.confex.com/agu/agu25/meetingapp.cgi/Paper/1909859). A thin, convecting layer forms at the top of the core and rapidly thickens until the whole core becomes adiabatic again.

(ii) For an HPE-enriched dense layer above the core-mantle boundary the layer and CMB temperatures to rise quickly if the core is decoupled from the mantle, slowly for a 0-D coupled core model, and at an intermediate rate with this 1-D core model. The layer temperature has implications for the formation of plumes, as well as other thermal evolution characteristics.

In conclusion, the new 1-D core model facilitates more realistic core-mantle coupled evolution simulations in the case that CMB heat flux is lower than that conducted down the core adiabat or even into the core.